**Meet the editor**

Dr. Raúl Igmar Gregor Recalde was born in Asunción, Paraguay, in 1979. He received his bachelor's degree in electronic engineering from the Catholic University of Asunción, Paraguay, in 2005. He received his M.Sc. and Ph.D. degrees in electronics, signal processing, and communications from the Higher Technical School of Engineering (ETSI), University of Seville, Spain, in 2008

and 2010, respectively. Since March 2010, Dr. Gregor has been Head of the Laboratory of Power and Control Systems (LSPyC) of the Engineering Faculty of the National University of Asuncion (FIUNA), Paraguay. Dr. Gregor has authored or coauthored about 40 technical papers in the field of power electronics and control systems, six of which have been published in high-impact journals. He obtained the Best Paper Award from the *IEEE Transactions on Industrial Electronics*, Industrial Electronics Society, in 2010, and the Best Paper Award from the *IET Electric Power Applications*, in 2012. His research interests include multiphase drives, advanced control of power converter topologies, quality of electrical power, renewable energy, modeling, simulation, optimization and control of power systems, smart metering and smart grids, and predictive control.

## Contents

### **Preface XI**



## Preface

Chapter 7 **Development of Fuzzy Applications for High Performance**

Chapter 8 **A Robust Induction Motor Control using Sliding Mode Rotor**

Chapter 9 **An Optimized Hybrid Fuzzy-Fuzzy Controller for PWM-driven**

Chapter 11 **Open-End Winding Induction Motor Drive Based on Indirect**

Chapter 12 **Open-Phase Fault Operation on Multiphase Induction**

Nordin Saad, Muawia A. Magzoub, Rosdiazli Ibrahim and

Rafael Rodríguez-Ponce, Fortino Mendoza-Mondragón, Moisés Martínez-Hernández and Marcelino Gutiérrez-Villalobos

Javier Riedemann, Rubén Peña and Ramón Blasco-Giménez

Hugo Guzman, Ignacio Gonzalez, Federico Barrero and Mario

Raúl Gregor, Jorge Rodas, Derlis Gregor and Federico Barrero

Chapter 13 **Reduced-order Observer Analysis in MBPC Techniques Applied to the Six-phase Induction Motor Drives 357**

Oscar Barambones, Patxi Alkorta, Jose M. Gonzalez de Duran and

**Induction Motor Drive 181**

**Variable Speed Drives 231**

Chapter 10 **DTC-FPGA Drive for Induction Motors 263**

**Matrix Converter 291**

**Section 4 Multiphase Induction Motors 325**

**Motor Drives 327**

Durán

Jose A. Cortajarena

**VI** Contents

Muhammad Irfan

Ali Saghafinia and Atefeh Amindoust

**Flux and Load Torque Observers 209**

AC motors play a major role in modern industrial applications. Squirrel-cage induction mo‐ tors (SCIMs) are probably the most frequently used when compared to other AC motors because of their low cost, ruggedness, and low maintenance. The material presented in this book is organized into four sections, covering the applications and structural properties of induction motors (IMs), fault detection and diagnostics, control strategies, and the more re‐ cently developed topology based on the multiphase (more than three phases) induction mo‐ tors. This material should be of specific interest to engineers and researchers who are engaged in the modeling, design, and implementation of control algorithms applied to in‐ duction motors and, more generally, to readers broadly interested in nonlinear control, health condition monitoring, and fault diagnosis.

Section I gives an introduction of squirrel-cage induction generators (SCIGs) and doubly fed induction generators (DFIGs) with regard to modelling and control. Furthermore, a power control system applied to the induction generator is explained. This section concludes with anthIM sttural properties of IMs, emphasizing a methodology to determine experimentally the parasitic capacitances in (VSI)-fed IM drives based on the (PWM) techique.

Section II focuses on the health condition monitoring of induction motors and fault diagno‐ sis of squirrel-cage induction motors with broken rotor bars and end rings. Condition moni‐ toring of electric machines has received a strong impulse from the industry to ensure consistent and reliable operation of the modern industrial systems.

Section III reviews the fundamentals of the modeling, simulation, and control of IMs. It fo‐ cuses mainly on the direct torque control (DTC), hybrid fuzzy–fuzzy controller (HFFC), adaptive fuzzy sliding-mode controller (AFSMC) for an indirect field-oriented control (IFOC), and robust control. In general, some of the requirements of the motor control system developed and evaluated in this section are accuracy, dynamic performance, and robust‐ ness.

Multiphase induction motors have become one of the main research topics in the field of IM during the past decade for various applications, especially in those where high reliability and fault tolerance are needed. Different topologies of multiphase IMs have been recently developed mainly for high-power applications, where an increase in the number of phases enables reduction in the power per phase, which leads to a reduction in the power per inver‐ ter leg. Section IV explains the fundamentals of the modeling and control of two different topologies of multiphase motors. On the one hand, regarding the five-phase IM, some simu‐ lation and experimental results are presented to show the behavior of the entire system in healthy and faulty conditions. On the other hand, with regard to the asymmetrical six-phase IM, the implementation of the model-based predictive control (MBPC) techniques as well as a comparative study of reduced-order observers used to estimate the rotor currents in an MBPC current control are presented.

Finally, I wish to express my gratitude to the authors of the chapters as well as to the Engi‐ neering Faculty of the National University of Asuncion (FIUNA).

**Raúl Igmar Gregor Recalde**

Engineering Faculty of the National University of Asuncion Asuncion, Paraguay **Applications and Structural Properties**

a comparative study of reduced-order observers used to estimate the rotor currents in an

Finally, I wish to express my gratitude to the authors of the chapters as well as to the Engi‐

**Raúl Igmar Gregor Recalde**

Asuncion, Paraguay

Engineering Faculty of the National University of Asuncion

neering Faculty of the National University of Asuncion (FIUNA).

MBPC current control are presented.

VIII Preface

## **Induction Generator in Wind Power Systems**

### Yu Zou

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60958

### **Abstract**

Wind power is the fastest growing renewable energy and is promising as the number one source of clean energy in the near future. Among various generators used to convert wind energy, the induction generator has attracted more attention due to its lower cost, lower requirement of maintenance, variable speed, higher energy capture efficiency, and improved power quality [1-2]. Generally, there are two types of induction generators widely used in wind power systems – Squirrel-Cage Induction Generator (SCIG) and Doubly-Fed Induction Generator (DFIG). The straightforward power conversion technique using SCIG is widely accepted in fixed-speed applica‐ tions with less emphasis on the high efficiency and control of power flow. However, such direct connection with grid would allow the speed to vary in a very narrow range and thus limit the wind turbine utilization and power output. Another major problem with SCIG wind system is the source of reactive power; that is, an external reactive power compensator is required to hold distribution line voltage and prevent whole system from overload. On the other hand, the DFIG with variable-speed ability has higher energy capture efficiency and improved power quality, and thus dominates the large-scale power conversion applications. With the advent of power electronics techniques, a back-to-back converter, which consists of two bidirectional converters and a dc-link, acts as an optimal operation tracking interface between DFIG and loads [3-5]. Field orientation control (FOC) is applied to both rotor- and stator-side converters to achieve desirable control on voltage and power [6,7].

In this chapter, a brief introduction of wind power system is presented first, which is followed by introduction of SCIG and DFIG from aspects of modeling and control. The basic FOC algorithm is derived based on DFIG model in *dq* reference frame. At last, the power generation efficiency is considered through different Maximum Power Point Tracking (MPPT) methods that have attracted a lot of attention in the variable-

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

speed operation systems. A comparative analysis involving advantage and disad‐ vantage of the methods is conducted.

**Keywords:** wind power systems, SCIG, DFIG, back-to-back converter, FOC, MPPT

### **1. Introduction**

The core component of a modern induction generator wind power system is the turbine nacelle, which generally accommodates the mechanisms, generator, power electronics, and control cabinet. The mechanisms, including yaw systems, shaft, and gear box, etc., facilitate necessary mechanical support to various dynamic behavior of the turbine. The generator is dedicated to the conversion between mechanical energy, which is captured by turbine rotor, and electrical energy. The generated electrical energy then needs to be regulated and condi‐ tioned to be connected to the power grid for use. In this section, the wind power system layout and classification are introduced first, which is followed by the outlining of the feasible power electronic converter interface between generators and loads. Lastly, the control scheme is briefly addressed and discussed in detail in section 2.

### **1.1. Overview of wind power systems**

Figure 1 shows the general layout of a wind turbine nacelle. The generator is either driven (in generation mode) or propelling (in motoring mode) the turbine blades through a shaft. The gearbox can be used to facilitate the speed difference between turbine and generator. The blade stall and pitch mechanisms are also involved to limit the power as well as the turbine plane yawing and tilting. By these means, the blade effective aerofoil cross section and thus the interface with wind pressure can be controlled. The performance coefficients responding to different yaw angle and pitch angle show significant variations [1-3]. In addition, as the most dynamically efficient choice, three blades connected through a hub with flanges is the commonly used topology in the front of the nacelle. The flanges are designed to enable the pitch angle adjustment. In most of the variable-speed wind systems, the high-efficiency operation always relies on the wind speed information. As a result, the anemometer can be used as one of the solutions. The basic function of the tower is to reach a higher position in order to obtain more airstream and wind speed. The tower can be constructed in either soft or stiff ways. A stiff tower has a natural frequency which lies above the blade passing frequency. Soft towers are lighter and cheaper but have to withstand more movement, and thus suffer from higher stress levels [2].

There are a number of classifications that group the wind power systems into different categories. According to the loads, grid integrated system and islanded system are employed to feed power grid and isolated load, respectively. According to the generators used, popular options are SCIG wind system, DFIG wind system, and Permanent Magnet Synchronous Generator (PMSG) wind system. Other alternative generator systems are also mentioned in

**Figure 1.** Wind power system nacelle [8]

speed operation systems. A comparative analysis involving advantage and disad‐

**Keywords:** wind power systems, SCIG, DFIG, back-to-back converter, FOC, MPPT

The core component of a modern induction generator wind power system is the turbine nacelle, which generally accommodates the mechanisms, generator, power electronics, and control cabinet. The mechanisms, including yaw systems, shaft, and gear box, etc., facilitate necessary mechanical support to various dynamic behavior of the turbine. The generator is dedicated to the conversion between mechanical energy, which is captured by turbine rotor, and electrical energy. The generated electrical energy then needs to be regulated and condi‐ tioned to be connected to the power grid for use. In this section, the wind power system layout and classification are introduced first, which is followed by the outlining of the feasible power electronic converter interface between generators and loads. Lastly, the control scheme is

Figure 1 shows the general layout of a wind turbine nacelle. The generator is either driven (in generation mode) or propelling (in motoring mode) the turbine blades through a shaft. The gearbox can be used to facilitate the speed difference between turbine and generator. The blade stall and pitch mechanisms are also involved to limit the power as well as the turbine plane yawing and tilting. By these means, the blade effective aerofoil cross section and thus the interface with wind pressure can be controlled. The performance coefficients responding to different yaw angle and pitch angle show significant variations [1-3]. In addition, as the most dynamically efficient choice, three blades connected through a hub with flanges is the commonly used topology in the front of the nacelle. The flanges are designed to enable the pitch angle adjustment. In most of the variable-speed wind systems, the high-efficiency operation always relies on the wind speed information. As a result, the anemometer can be used as one of the solutions. The basic function of the tower is to reach a higher position in order to obtain more airstream and wind speed. The tower can be constructed in either soft or stiff ways. A stiff tower has a natural frequency which lies above the blade passing frequency. Soft towers are lighter and cheaper but have to withstand more movement, and thus suffer

There are a number of classifications that group the wind power systems into different categories. According to the loads, grid integrated system and islanded system are employed to feed power grid and isolated load, respectively. According to the generators used, popular options are SCIG wind system, DFIG wind system, and Permanent Magnet Synchronous Generator (PMSG) wind system. Other alternative generator systems are also mentioned in

vantage of the methods is conducted.

4 Induction Motors - Applications, Control and Fault Diagnostics

briefly addressed and discussed in detail in section 2.

**1.1. Overview of wind power systems**

from higher stress levels [2].

**1. Introduction**

the literature, such as brushless DFIGs (BDFIG) system [5,6], direct-drive synchronous generator (DDSG) system [7,9], switched reluctance generator (SRG) system [10], multiplestage geared SCIG system [10], and radial/axial/transversal-flux PM generator systems [7,12-14]. These solutions generally require relatively complex operation principle and equipment assembly. According to the presence of the gear box, there are multistage gear box wind system, single-stage gear box wind system, and direct drive wind system (without gear box) in where the Synchronous Generator (SG) qualifies the system to have a simpler and more reliable drive train. However, the lower generator speed, and thus larger torque, requires more poles, larger diameter, and volume, and hence higher cost.

The most promising classifications in induction generator wind systems are fixed-speed, limited-variable-speed, and variable-speed wind systems, according to the operations of induction generator speed. Comparisons between these wind power systems have been intensively conducted, based on different speed variation levels [12,15-19]. A summary of their advantages and disadvantages is presented in Table 1. The fixed-speed concept has been successfully applied in SCIG wind systems. The drive train applies multiple-stage gearbox and a SCIG is directly connected to the grid via a transformer. To support the grid, external reactive power compensation and soft starter are necessary [5,6]. The limited variable-speed system is an improved version of the SCIG type but it uses a wound rotor induction generator instead, which allows the stator to be connected to the grid, and the rotor to have a variable resistance controlled by a power converter. Through the control of rotor resistance, the slip of the generator is varied. The variable-speed system is a concept commonly used in large power rating applications (>1.5 MW). Different combinations among DFIG, SCIG, partial or full converters would lead to variable-speed operation systems. The control system maintains the optimal generator speed, thus the optimal output power, through controlling the generator currents and voltages. Due to the high efficiency and capability of Faults Ride Through (FRT), this type of wind power system dominates the high-capacity power market nowadays.


**Table 1.** Comparison among different wind power systems

### **1.2. Power electronics interface topologies in wind power systems**

Power electronics is the key element enabling the regulation and conditioning of the power, voltage, and frequency with high efficiency and flexibility. In addition, more involvement of distributed power systems nowadays emphasizes the crucial role of power electronics interface among energy generation, storage, and transmission.

Due to the developments in semiconductor switches and microprocessors, many power electronics techniques have been developed during the past decades [20,21]. Besides the diode converters, line-commutated thyristor converters and self-commutated IGBT/MOSFET converters are found applicable to wind power systems. The line-commutated converters are generally used in high-power applications but they are incapable of controlling the reactive power. The self-commutated converters are able to transfer and control power bidirectionally because of the capability of controllable switch turning-off. Nowadays, wind power systems, especially the variable-speed wind power system, primarily rely on the converters that implement full power control. Different converter topologies and combinations have been successfully employed in this field, as shown in Figure 2.

generator is varied. The variable-speed system is a concept commonly used in large power rating applications (>1.5 MW). Different combinations among DFIG, SCIG, partial or full converters would lead to variable-speed operation systems. The control system maintains the optimal generator speed, thus the optimal output power, through controlling the generator currents and voltages. Due to the high efficiency and capability of Faults Ride Through (FRT), this type of wind power system dominates the high-capacity power market nowadays.

> a. Not optimal operation, thus low efficiency b. Easy power fluctuation caused by wind speed

c. External reactive power compensation is

a. Speed variation range depends on the size of

b. The controlled rotor power must be dissipated

c. Still need reactive power compensation and

c. May need a multistage gearbox and slip ring in

d. May need expensive PM material and large

a. Relatively complicated control system b. Higher converters and control costs

and tower pressure

d. Weak capability of FRT

by heat in the resistor

DFIG system

cannot support the grid alone

diameter design in direct drive

the variable rotor resistance (<10%)

needed

**Advantages Disadvantages**

a. Simple construction and robust b. Low cost and maintenance

6 Induction Motors - Applications, Control and Fault Diagnostics

a. Limited speed variation is implemented b. The slip ring may be replaced by optical

a. Large range of speed variation

for maximum power extraction

is able to support the grid d. High FRT capability

**Table 1.** Comparison among different wind power systems

wind farms

b. Appropriate control enables optimal operation

c. No external power compensation is needed and

e. Suitable and commonly used for large-scale

**1.2. Power electronics interface topologies in wind power systems**

interface among energy generation, storage, and transmission.

Power electronics is the key element enabling the regulation and conditioning of the power, voltage, and frequency with high efficiency and flexibility. In addition, more involvement of distributed power systems nowadays emphasizes the crucial role of power electronics

Due to the developments in semiconductor switches and microprocessors, many power electronics techniques have been developed during the past decades [20,21]. Besides the diode converters, line-commutated thyristor converters and self-commutated IGBT/MOSFET converters are found applicable to wind power systems. The line-commutated converters are generally used in high-power applications but they are incapable of controlling the reactive

c. Easy control

coupling

Fixed-speed system

Limited-speed system

Variable-speed system

**Figure 2.** Commonly used power electronics converter topologies for wind power system ((a) diode and line-commu‐ tated converter, combined with reactive power compensation; (b) diode and PWM VSI converter; (c) diode and DC/DC chopper and PWM VSI converter; (d) back-to-back PWM VSI converter; (e) matrix converter)

Due to the employment of diode rectifier, the topology in Figure 2(a) is uncontrolled and a thyristor inverter is used to regulate the generator speed through dc-link voltage to obtain firing angle commands. Obviously, this scheme is simple for control and costs less than selfcommutated converter. More importantly, it is suitable for high power rating applications. However, the weakness is that extra reactive power compensation is required, which contains a voltage source converter (VSC). The grid voltage may be regulated to obtain reference current for the compensator and the control signal comes from the regulation of the compensator current [22,23]. To remove the compensator, a self-commutated converter could be used to take the place of thyristor inverter, as shown in Figure 2(b). Again, the regulation of dc-link voltage can provide current reference, which is controlled to generate control signals for the PWM inverter [24]. Two self-commutated converters connected through a dc-link, as shown in Figure 2(d), enable bidirectional power flow, which is the key to ensuring high efficiency in motoring operation of generator. The FOC is applied on both sides of converters based on *dq* reference frame [23,25]. The grid-side converter keeps a constant dc-link voltage, while the generator-side converter is responsible for both active and reactive power control [23]. In the generator-side converter control, the *d*-axis current could be set at zero to maximize the torque, while the *q*-axis current is derived from power regulation [26,27]. An alternative topology of Figure 2(d) is shown in Figure 2(c), where the generator-side self-commutated converter is replaced by a diode rectifier connected to an intermediate chopper [28]. This configuration is impossible for bidirectional power flow caused by the diode rectifier. But it can achieve a similar wide range of speed variation as two self-commutated converters. The grid-side converter controls the dc-link voltage for *d*-axis current reference and controls the reactive power for *q*-axis current reference. The active power regulation and thus the speed control are carried out to generate reference dc-link current. The duty cycle of chopper switch can be obtained using current regulation. The converter configurations discussed are actually multistage implementation of AC conversion. An intermediate DC stage is needed to assist conversion and associated control. In recent years, such procedure has been investigated by a single-stage converter, the matrix converter, which performs the energy transformation without help from a bulky storage stage. The controllable switches are arranged in such a way that any input phase may be connected to any output phase at any time. The matrix converter may be applied to the DFIG system, like the topology in Figure 2(e) [29,30]. According to the stator flux FOC, the reactive and active power can be regulated by *d*- and *q*-axis current, respectively [30]. An alternative control strategy is by regulating the rotor winding voltage to control the power factor (PF) and applying the double space vector PWM technique [29]. It is worth noting that the SCIG system has high starting currents. One effective way to limit the starting current is by using the soft-starter that applies thyristors to limit the RMS starter current below rated current. The starter is shorted after the full load is reached. The torque peak can be decreased as well, which reduces the gearbox pressure [9,10].

The high-efficiency energy conversion and full control of power exclusively rely on the power electronic converter and the control scheme applied on. Consequently, the broadly accepted total wind power system topologies subject to above power electronics are reviewed as follows. Since the high-efficiency variable speed systems are the primary focus, Figure 3 summarizes the feasible variable-speed system topologies, for induction generator systems as well as synchronous generator systems for systematized purpose. Due to the low demand on the converter power rating of approximately 30% of the total power rating, the DFIG with partial converter, shown in Figure 3(a), is a widespread topology for wind power systems. Also, due to the presence of a rotor-side converter, the rotor power is fed back to the grid without dissipation in the resistor. Instead of a partial converter, PMSG or SCIG can be connected to a full rating converter, as shown Figure 3(b). This topology has better grid FRT ability because the generator-side is totally independent of the grid-side. However, the converter rating and loss are high. Figure 3(c) shows the direct drive system, which is aimed at removing the gearbox and associated loss [16]. The generator rotor is connected to the turbine shaft directly and runs at the same very slow speed. Therefore, a high torque and a large machine radius are required to transfer the same amount of power. Fewer components enable less loss and thus more reliable performance in this type of system. To compromise between machine size and spinning speed, the single-stage gearbox, shown in Figure 3(d), is applied [15]. Figure 3(e) shows the electrically excited synchronous generator (EESG) system, which has a rotor-side converter to provide DC excitation while the stator is connected to a full converter like the case in Figure 3(c). Although there is an increase in cost due to the extra winding for excitation and it also requires more maintenance, the EESG could minimize the loss through controlling the flux via rotor converter [7,11,12].

**Figure 3.** Commonly used wind power system topologies ((a) DFIG with partial/matrix converter; (b) PMSG/SCIG with full converter; (c) direct drive; (d) PMSG with full converter and less stage gearbox; (e) EESG direct drive)

### **1.3. Generator control schemes in wind power systems**

generator-side converter is responsible for both active and reactive power control [23]. In the generator-side converter control, the *d*-axis current could be set at zero to maximize the torque, while the *q*-axis current is derived from power regulation [26,27]. An alternative topology of Figure 2(d) is shown in Figure 2(c), where the generator-side self-commutated converter is replaced by a diode rectifier connected to an intermediate chopper [28]. This configuration is impossible for bidirectional power flow caused by the diode rectifier. But it can achieve a similar wide range of speed variation as two self-commutated converters. The grid-side converter controls the dc-link voltage for *d*-axis current reference and controls the reactive power for *q*-axis current reference. The active power regulation and thus the speed control are carried out to generate reference dc-link current. The duty cycle of chopper switch can be obtained using current regulation. The converter configurations discussed are actually multistage implementation of AC conversion. An intermediate DC stage is needed to assist conversion and associated control. In recent years, such procedure has been investigated by a single-stage converter, the matrix converter, which performs the energy transformation without help from a bulky storage stage. The controllable switches are arranged in such a way that any input phase may be connected to any output phase at any time. The matrix converter may be applied to the DFIG system, like the topology in Figure 2(e) [29,30]. According to the stator flux FOC, the reactive and active power can be regulated by *d*- and *q*-axis current, respectively [30]. An alternative control strategy is by regulating the rotor winding voltage to control the power factor (PF) and applying the double space vector PWM technique [29]. It is worth noting that the SCIG system has high starting currents. One effective way to limit the starting current is by using the soft-starter that applies thyristors to limit the RMS starter current below rated current. The starter is shorted after the full load is reached. The torque

8 Induction Motors - Applications, Control and Fault Diagnostics

peak can be decreased as well, which reduces the gearbox pressure [9,10].

The high-efficiency energy conversion and full control of power exclusively rely on the power electronic converter and the control scheme applied on. Consequently, the broadly accepted total wind power system topologies subject to above power electronics are reviewed as follows. Since the high-efficiency variable speed systems are the primary focus, Figure 3 summarizes the feasible variable-speed system topologies, for induction generator systems as well as synchronous generator systems for systematized purpose. Due to the low demand on the converter power rating of approximately 30% of the total power rating, the DFIG with partial converter, shown in Figure 3(a), is a widespread topology for wind power systems. Also, due to the presence of a rotor-side converter, the rotor power is fed back to the grid without dissipation in the resistor. Instead of a partial converter, PMSG or SCIG can be connected to a full rating converter, as shown Figure 3(b). This topology has better grid FRT ability because the generator-side is totally independent of the grid-side. However, the converter rating and loss are high. Figure 3(c) shows the direct drive system, which is aimed at removing the gearbox and associated loss [16]. The generator rotor is connected to the turbine shaft directly and runs at the same very slow speed. Therefore, a high torque and a large machine radius are required to transfer the same amount of power. Fewer components enable less loss and thus more reliable performance in this type of system. To compromise between machine size and spinning speed, the single-stage gearbox, shown in Figure 3(d), is applied [15]. Figure 3(e) shows the electrically excited synchronous generator (EESG) system, which has a rotor-side

SCIG and DFIG are used almost exclusively in the energy conversion stage of the induction generator wind power system. The most commonly used system topologies are SCIG directly connected into the power grid and DFIG fed by back-to-back converter (Figure 3(a) and Figure 3(d)). The first topology implies a constant frequency and voltage of the SCIG that establishes a fixed-speed operation. In such system, the SCIG relies on the grid (or capacitor bank) to provide reactive power which is necessary to build electromagnetic excitation for rotary field. The generating mode of SCIG is triggered by driven torque which acts opposite to the generator speed within the super-synchronous speed operation region. Due to the absence of the power electronics interface, such system can only serve the grid support applications, wherein just limited control (pitch angle control) can be applied.

The DFIG system, on the other hand, enables the flexible and efficient operations with FOC applied on the rotor-winding-side power electronics interface. The FOC is an instantaneous control that effectively manipulates the position-dependent variables, such as torque and power, in induction generator wind power systems. By aligning a particular space variable with *d*-axis, stator currents could be decoupled into flux component and torque component in *dq* rotating frame. The currents can be thus controlled separately like in DC motor drive. To implement the control in hardware, PWM technique is generally employed based on Space Vector Modulation (SVM). The SVM is based on space reference voltage vector and associated switching logics. Any space vector can be comprised of vector sum of two adjacent voltage vectors, and the duty cycles of three-phase voltages are calculated based on the dwelling time of two voltage vectors. This is the method widely used in standard industry applications.

The following section examines the detailed modeling and control strategies of both systems.

### **2. Model and control of induction generator in wind power systems**

### **2.1. Model of wind power and wind turbine**

As a typical kinetic energy, wind energy is extracted through wind turbine blades and then transferred by the gearbox and rotor hub to mechanical energy in shaft. The shaft drives the generator to convert the mechanical energy to electrical energy. According to Newton's law, the kinetic energy for the wind with particular wind speed *V*w is described as:

$$E\_k = \frac{1}{2} m V\_w^{\;\;\;\;2} \tag{1}$$

where *m* represents the mass of the wind, and its power can be written as:

$$P\_w = \frac{\partial E\_k}{\partial t} = \frac{1}{2} \frac{\partial m}{\partial t} V\_w^{\ 2} = \frac{1}{2} (\rho A V\_w) V\_w^{\ 2} = \frac{1}{2} \rho A V\_w^{\ 3} \tag{2}$$

where *ρ* and *A* are the air density and turbine rotor swipe area, respectively. The extracted mechanical power can thus be expressed as:

$$P\_m = \mathbb{C}\_p\left(\mathbb{A}, \,\, \beta\right) \\ P\_w = \mathbb{C}\_p\left(\mathbb{A}, \,\, \beta\right) \frac{1}{2} \rho A V\_w \,^3 \tag{3}$$

where *P*<sup>m</sup> is the mechanical output power in watt, which depends on performance coefficient *C*p(*λ*, *β*), *C*<sup>p</sup> depends on tip speed ratio *λ* and blade pitch angle *β*, and determines how much of the wind kinetic energy can be captured by the wind turbine system. A nonlinear model describes *C*p(*λ*, *β*) as [3]:

$$\mathbf{C}\_{p}\begin{pmatrix} \mathcal{A}, \ \beta \end{pmatrix} = \mathbf{c}\_{1}\left(\mathbf{c}\_{2} - \mathbf{c}\_{3}\beta - \mathbf{c}\_{4}\beta^{2} - \mathbf{c}\_{5}\right)e^{-\mathbf{c}\_{6}}\tag{4}$$

where, c1=0.5, c2=116/λ<sup>i</sup> , c3=0.4, c4=0, c5=5, c6=21/λ<sup>i</sup> and

with *d*-axis, stator currents could be decoupled into flux component and torque component in *dq* rotating frame. The currents can be thus controlled separately like in DC motor drive. To implement the control in hardware, PWM technique is generally employed based on Space Vector Modulation (SVM). The SVM is based on space reference voltage vector and associated switching logics. Any space vector can be comprised of vector sum of two adjacent voltage vectors, and the duty cycles of three-phase voltages are calculated based on the dwelling time of two voltage vectors. This is the method widely used in standard industry applications.

The following section examines the detailed modeling and control strategies of both systems.

As a typical kinetic energy, wind energy is extracted through wind turbine blades and then transferred by the gearbox and rotor hub to mechanical energy in shaft. The shaft drives the generator to convert the mechanical energy to electrical energy. According to Newton's law,

1 <sup>2</sup>

( ) 11 1 2 23 22 2

*w w w w w <sup>E</sup> <sup>m</sup> <sup>P</sup> V AV V AV*

( ) ( ) <sup>1</sup> 3 , , 2 *m p wp <sup>w</sup> P C P C AV* = =

lb

r

where *ρ* and *A* are the air density and turbine rotor swipe area, respectively. The extracted

 lb

where *P*<sup>m</sup> is the mechanical output power in watt, which depends on performance coefficient *C*p(*λ*, *β*), *C*<sup>p</sup> depends on tip speed ratio *λ* and blade pitch angle *β*, and determines how much of the wind kinetic energy can be captured by the wind turbine system. A nonlinear model

> ( ) ( ) <sup>2</sup> <sup>6</sup> 12 3 4 5 , *<sup>c</sup> C cc c c ce <sup>p</sup>*

 b  b


<sup>2</sup> *k w E mV* <sup>=</sup> (1)

(3)

 r

¶ ¶ == = = ¶ ¶ (2)

 r

**2. Model and control of induction generator in wind power systems**

the kinetic energy for the wind with particular wind speed *V*w is described as:

where *m* represents the mass of the wind, and its power can be written as:

*k*

mechanical power can thus be expressed as:

describes *C*p(*λ*, *β*) as [3]:

*t t*

lb

**2.1. Model of wind power and wind turbine**

10 Induction Motors - Applications, Control and Fault Diagnostics

$$\mathcal{A}\_{\text{l}} = \frac{1}{\mathcal{A} + 0.08\beta} - \frac{0.035}{\beta^3 + 1} \tag{5}$$

With the dependence on the *λ* and *β*, maximum value of *C*<sup>p</sup> could be reached and maintained through controlling the pitch angle and generator speed at particular wind speed. A group of typical *C*p – *λ* curves for different *β* is shown in Figure 4 and there is always a maximum value for *C*p at one particular wind speed. Correspondingly, the output power is determined by different *C*p and also the generator speed at different wind speed, as shown in Figure 5, where there is always one maximum power value for each wind speed, which is the goal of the MPPT control.

**Figure 4.** *C*p versus *λ* curve for a wind turbine (*β* is the pitch angle) [23]

### **2.2. Model and control of SCIG**

As a fixed-speed wind power system, SCIG is directly connected to the grid through trans‐ former and thus operates at almost constant speed without controlling from power electronics interface. It was commonly used in Denmark during 1980s and 1990s and thus is also called "Danish Concept" system. The robust and simple configuration qualifies such system for many applications where the cost is a higher priority concern than efficiency. Figure 6 shows the schematics of entire SCIG wind system including the wind turbine, pitch control, and reactive

**Figure 5.** Power versus generator speed curve for wind turbine [31]

power compensator. The entire system includes three stages for delivering the energy from wind turbine to the power grid. The first one is wind farm stage which handles with lowvoltage *V*wt; the second is distribution stage which has medium-voltage *V*dis; the third is grid transmission stage which has high-voltage *V*grid. The three-phase transformers take care of the interface between two stages [10]. The nominal power is considered as active power reference to regulate the pitch angle, while the distribution line-to-line voltage and phase current are monitored to favor the reactive power compensation for distribution line. This fairly straight‐ forward technique was firstly used since it is simple, with rugged construction, has reliable operation and is low cost. However, the fixed-speed nature and potential voltage instability problem severely limit the operations of SCIG wind system [1,3].

It is clear from Figure 5 that at a particular wind speed, the output active power is also a fixed value in the case of fixed generator speed. Thus, the output power is exclusively wind speed dependent until the nominal power is reached. The wind speed at nominal power is called nominal wind speed. Beyond this wind speed, the pitch angle system will prevent the output power from exceeding the nominal value. The pitch angle is determined by an open-loop control of regulated output active power and, as shown in Figure 7. Due to the huge size of blade and thus the huge inertia, pitch angle has to change at a slow rate and within a reasonable range. It is also worth noting that without reactive power source, the SCIG system tends to a voltage droop in distribution line which will cause overload problem.

Simulation in [23] illustrates the operation of a 0.855MW SCIG system. From Figure 8, the initial generator speed is set at slip s = -0.01 p.u. with respect to synchronous speed and then response to the wind speed input disturbance. Since the power is lower than the nominal value (0.855

**Figure 6.** SCIG wind power system configuration

**Figure 7.** Pitch angle control

power compensator. The entire system includes three stages for delivering the energy from wind turbine to the power grid. The first one is wind farm stage which handles with lowvoltage *V*wt; the second is distribution stage which has medium-voltage *V*dis; the third is grid transmission stage which has high-voltage *V*grid. The three-phase transformers take care of the interface between two stages [10]. The nominal power is considered as active power reference to regulate the pitch angle, while the distribution line-to-line voltage and phase current are monitored to favor the reactive power compensation for distribution line. This fairly straight‐ forward technique was firstly used since it is simple, with rugged construction, has reliable operation and is low cost. However, the fixed-speed nature and potential voltage instability

It is clear from Figure 5 that at a particular wind speed, the output active power is also a fixed value in the case of fixed generator speed. Thus, the output power is exclusively wind speed dependent until the nominal power is reached. The wind speed at nominal power is called nominal wind speed. Beyond this wind speed, the pitch angle system will prevent the output power from exceeding the nominal value. The pitch angle is determined by an open-loop control of regulated output active power and, as shown in Figure 7. Due to the huge size of blade and thus the huge inertia, pitch angle has to change at a slow rate and within a reasonable range. It is also worth noting that without reactive power source, the SCIG system tends to a

Simulation in [23] illustrates the operation of a 0.855MW SCIG system. From Figure 8, the initial generator speed is set at slip s = -0.01 p.u. with respect to synchronous speed and then response to the wind speed input disturbance. Since the power is lower than the nominal value (0.855

problem severely limit the operations of SCIG wind system [1,3].

**Figure 5.** Power versus generator speed curve for wind turbine [31]

12 Induction Motors - Applications, Control and Fault Diagnostics

voltage droop in distribution line which will cause overload problem.

MW) before t = 10 s, pitch angle control is not online. Since that moment, the wind speed increases and so do the generator speed and power until the wind speed exceeds the nominal value (11 m/s) at where the pitch control is triggered to block the further increase of output power. In this way, the output power persists at nominal value thereafter.

It is noted that the generator speed can only vary in very small range around 1 p.u. and thus it is impossible to attain the optimal output power. Also, without independent control ability, SCIG system consumes reactive power of 0.41 Mvar at the steady state, which will lead to line voltage droop. To provide necessary reactive power, a Static Synchronous Compensator (STATCOM) is applied in distribution line. As in Figure 9, distribution line voltage can drop by approximately 0.055 p.u. in SCIG system without STATCOM, which will be a potential induction of overload in system. In contrast, SCIG system with STATCOM can hold distribu‐ tion voltage at 0.99 p.u., which is favorable to grid system stability. The compensated reactive power from STATCOM is shown in Figure 10 and is equal to 0.3 Mvar at the steady state. Although STACOM provides impressive help to a constant distribution line voltage, DFIG wind system presents more attractive attributes.

**Figure 8.** Pitch angle control for SCIG system [23]

**Figure 9.** Grid voltages comparison between SCIG w/o. STACOM, SCIG w. STACOM and DFIG [23]

**Figure 10.** Compensated reactive power from STATCOM [23]

### **2.3. Model and control of DFIG**

**Figure 8.** Pitch angle control for SCIG system [23]

14 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 9.** Grid voltages comparison between SCIG w/o. STACOM, SCIG w. STACOM and DFIG [23]

Traditionally, the dynamic slip control is employed to fulfill the variable-speed operation in induction generator wind system, in which the rotor windings are connected with variable resistor and control the slip by varied resistance [3,11]. This type of system attains limited variations of generator speed but external reactive power source is still necessary. In order to completely remove the reactive power compensation and control both active and reactive power independently, DFIG wind power system is one of most popular methods in wind energy applications [1,3,7]. The DFIG wind power system with associated back-to-back converter is a typical variable speed system as shown in Figure 11, which complies with the topologies in Figures 3(a) and 2(d). The generator stator windings are connected directly to grid (with fixed voltage and frequency of grid) while the rotor windings are fed by an AC/DC/ AC IGBT-based PWM converter (back-to-back converter with capacitor dc-link), at variable frequency through slip rings and brushes. Although such system needs the gearbox and slip rings to function, many advantages enable DFIG system to dominate most wind market nowadays. It facilitates variation of a wide speed range (±30% around synchronous speed), the lower rating requirement on power converters (30% of generator power), and thus lower cost. Also, it has high efficiency induced by bidirectional power flow, and the ability to perform reactive power compensation and smooth grid integration. In this configuration, the back-toback converter consists of two parts: the stator/grid-side converter and the rotor-side converter. Both are voltage source converters while a capacitor bank between two converters acts as a dc voltage interface.

In this section, the modeling of DFIG is introduced first and followed by the consequent FOC algorithm which is divided into two parts: stator-side converter control and rotor-side converter control. The SVM method and islanded operation control are also addressed.

**Figure 11.** DFIG wind power system configuration

### *2.3.1. dq model of DFIG*

The modeling is conducted under the *dq* reference frame. The equivalent circuits of DFIG in the *dq* reference frame are depicted in Figure 12(a, b) and the relationships between voltage V, current *I*, flux *Ψ*, and torque *T*<sup>e</sup> can be derived by writing KVL equations. For stator-side, the *d*- and *q*-axis voltage components are given as:

$$\begin{aligned} V\_{ds} &= R\_s I\_{ds} - a o\_s \Psi\_{qs} + \left( L\_{ls} + L\_m \right) \frac{dI\_{ds}}{dt} + L\_m \frac{dI\_{dr}}{dt} a \\ V\_{qs} &= R\_s I\_{qs} + a o\_s \Psi\_{ds} + \left( L\_{ls} + L\_m \right) \frac{dI\_{qs}}{dt} + L\_m \frac{dI\_{qr}}{dt} b \end{aligned} \tag{6}$$

And similarly, the *d*- and *q*-axis voltage components in rotor-side are given as:

#### Induction Generator in Wind Power Systems http://dx.doi.org/10.5772/60958 17

$$\begin{aligned} V\_{dr} &= \mathcal{R}\_r I\_{dr} - s o\_s \Psi\_{qr} + \left( L\_{lr} + L\_m \right) \frac{dI\_{dr}}{dt} + L\_m \frac{dI\_{ds}}{dt} a \\ V\_{qr} &= \mathcal{R}\_r I\_{qr} + s o\_s \Psi\_{dr} + \left( L\_{lr} + L\_m \right) \frac{dI\_{qr}}{dt} + L\_m \frac{dI\_{qs}}{dt} b \end{aligned} \tag{7}$$

Because the flux linkage along *d*- and *q*-axis follow:

back converter consists of two parts: the stator/grid-side converter and the rotor-side converter. Both are voltage source converters while a capacitor bank between two converters acts as a dc

In this section, the modeling of DFIG is introduced first and followed by the consequent FOC algorithm which is divided into two parts: stator-side converter control and rotor-side converter control. The SVM method and islanded operation control are also addressed.

The modeling is conducted under the *dq* reference frame. The equivalent circuits of DFIG in the *dq* reference frame are depicted in Figure 12(a, b) and the relationships between voltage V, current *I*, flux *Ψ*, and torque *T*<sup>e</sup> can be derived by writing KVL equations. For stator-side, the

( )

*ds s ds s qs ls m m*

= - Y+ + +

w

w

*dI dI V RI LL L a*

*V RI LL L b*

*qs s qs s ds ls m m*

= + Y+ + +

And similarly, the *d*- and *q*-axis voltage components in rotor-side are given as:

( )

*ds dr*

*dt dt dI dI*

*dt dt*

*qs qr*

(6)

voltage interface.

16 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 11.** DFIG wind power system configuration

*d*- and *q*-axis voltage components are given as:

*2.3.1. dq model of DFIG*

$$\begin{aligned} \Psi\_{\rm ds} &= L\_s I\_{\rm ds} + L\_m I\_{\rm dr} a \\ \Psi\_{\rm qs} &= L\_s I\_{\rm qs} + L\_m I\_{\rm qr} b \end{aligned} \tag{8}$$

$$\begin{aligned} \Psi\_{\,dr} &= L\_r I\_{\,dr} + L\_m I\_{\,ds} a \\ \Psi\_{\,qr} &= L\_r I\_{\,qr} + L\_m I\_{\,qs} \, b \end{aligned} \tag{9}$$

The reorganized DFIG stator voltages in *d*- and *q*-axis, respectively, are presented as:

$$\begin{aligned} V\_{ds} &= R\_s I\_{ds} - a o\_s \Psi\_{qs} + \frac{d\Psi\_{ds}}{dt} a \\ V\_{qs} &= R\_s I\_{qs} + a o\_s \Psi\_{ds} + \frac{d\Psi\_{qs}}{dt} b \end{aligned} \tag{10}$$

And the DFIG rotor voltages in *d*- and *q*-axis, respectively, are presented as:

$$\begin{aligned} V\_{dr} &= R\_r I\_{dr} - s o\_s \Psi\_{qr} + \frac{d\Psi\_{dr}}{dt} a \\ V\_{qr} &= R\_r I\_{qr} + s o\_s \Psi\_{dr} + \frac{d\Psi\_{qr}}{dt} b \end{aligned} \tag{11}$$

The generator electromagnetic torque is correspondingly given as:

$$T\_e = \frac{3}{2} n\_p \left(\Psi\_{ds} I\_{qs} - \Psi\_{qs} I\_{ds}\right) \tag{12}$$

where *L*s=*L*ls+*L*m; *L*r=*L*lr+*L*m; and sωs = ωs – ωr represents the difference between synchronous speed and generator speed; subscripts r, s, m, d, q denote the rotor, stator, magnitizing, *d*-axis and *q*-axis components, respectively; *T*e is electromagnetic torque; *L*m and *n*p are generator mutual inductance and the number of pole pairs, respectively.

**Figure 12.** Equivalent circuit of DFIG ((a) *d*-axis; (b) *q*-axis)

#### *2.3.2. Control of rotor-side converter*

The control of DFIG modeled above is applied on back-to-back converter and is therefore also divided into rotor-side control and stator-side control.

First, the rotor-side converter is studied. To *d*-axis, the rotor flux linkage *Ψ*qr in Equation (7a) is substituted by Equation (9b), resulting in:

$$\mathbf{V}\_{dr} = \mathbf{R}\_r \mathbf{I}\_{dr} - \text{soc}\_s \left( \mathbf{L}\_r \mathbf{I}\_{qr} + \mathbf{L}\_m \mathbf{I}\_{qs} \right) + \frac{d\left( \mathbf{L}\_r \mathbf{I}\_{dr} + \mathbf{L}\_m \mathbf{I}\_{ds} \right)}{dt} \tag{13}$$

By substituting the *I*ds by *Ψ*ds in Equation (8a), the Equation (13) can be expressed as:

$$V\_{dr} = R\_r I\_{dr} - s o\_s L\_r I\_{qr} - s o\_s L\_m I\_{qs} + L\_r \frac{dI\_{dr}}{dt} + \frac{L\_m}{L\_s} \frac{d\left(\Psi\_{ds} - L\_m I\_{dr}\right)}{dt} \tag{14}$$

Because it is directly connected to the grid, the stator voltage shares constant magnitude and frequency of grid voltage. One could make the *d*-axis align with stator voltage vector, and it is true that *V*s=*V*ds and *V*qs=0, thus *Ψ*s=*Ψ*qs and *Ψ*ds=0, which are stator voltage-oriented vector control scheme, as depicted in Figure 13. Therefore, Equation (14) can be organized as:

Induction Generator in Wind Power Systems http://dx.doi.org/10.5772/60958 19

$$\mathbf{V}\_{dr} = \left[\mathbf{R}\_r + \left(\mathbf{L}\_r - \frac{\mathbf{L}\_m}{\mathbf{L}\_s}\right)\frac{d}{dt}\right]\mathbf{I}\_{dr} - \mathrm{s}\mathbf{o}\_s\left[\mathbf{L}\_r\mathbf{I}\_{qr} + \mathbf{L}\_m\mathbf{I}\_{qs}\right] \tag{15}$$

Equation (15) implies that the *d*-axis rotor voltage consists of two voltage components *V*dr1 and *V*dr2 :

$$\begin{aligned} \left[V\_{dr}\right]^1 &= \left[R\_r + \left(L\_r - \frac{L\_m}{L\_s}\right)\frac{d}{dt}\right]I\_{dr}\,a\\ \left[V\_{dr}\right]^2 &= -\text{sao}\_s\left[L\_r I\_{qr} + L\_m I\_{qs}\right]\,b\end{aligned} \tag{16}$$

**Figure 13.** Stator voltage FOC reference frame

**Figure 12.** Equivalent circuit of DFIG ((a) *d*-axis; (b) *q*-axis)

18 Induction Motors - Applications, Control and Fault Diagnostics

is substituted by Equation (9b), resulting in:

divided into rotor-side control and stator-side control.

*dr r dr s r qr m qs*

*V RI s LI L I*

*dr r dr s r qr s m qs r*

 w

*V RI s LI s L I L*

w

w

The control of DFIG modeled above is applied on back-to-back converter and is therefore also

First, the rotor-side converter is studied. To *d*-axis, the rotor flux linkage *Ψ*qr in Equation (7a)

Because it is directly connected to the grid, the stator voltage shares constant magnitude and frequency of grid voltage. One could make the *d*-axis align with stator voltage vector, and it is true that *V*s=*V*ds and *V*qs=0, thus *Ψ*s=*Ψ*qs and *Ψ*ds=0, which are stator voltage-oriented vector control scheme, as depicted in Figure 13. Therefore, Equation (14) can be organized as:

By substituting the *I*ds by *Ψ*ds in Equation (8a), the Equation (13) can be expressed as:

( ) ( *r dr m ds* )

*d LI L I*

*s*

=- - + + (14)

*dt L dt*

*dt*

*dr m* ( ) *ds m dr*

Y -

*dI L d LI*

+ =- + + (13)

*2.3.2. Control of rotor-side converter*

The *V*dr1 is called current regulation part and depicted by Figure 14, where *σ* = *L*r - *L*<sup>m</sup> 2 /*L*s. Due to the linear relationship between *V*dr1 and *I*dr, the PI controller is employed. Besides, *V*dr2 is the cross-coupling part and requires feedforward compensation for a complete control. Eventu‐ ally, the rotor-side converter voltage in *d*-axis is derived as:

$$V\_{\rm drc} = \left. V\_{\rm dr} = \left. V\_{\rm dr}^{\ 1} + \left. V\_{\rm dr}^{\ 2} \right. \right. \tag{17}$$

where subscript rc denotes the rotor-side converter. After the conversion of *dq*-*abc*, the rotorside converter voltage *V*abc\_rc can be obtained, which is used to generate PWM control signals for rotor-side converter.

**Figure 14.** Current regulation part of *d*-axis rotor-side converter voltage

If only steady-state is considered, the derivative parts in Equation (10) are neglected and one can obtain stator flux as:

$$\begin{aligned} \Psi\_{ds} &= \frac{V\_{qs} - R\_s I\_{qs}}{\alpha\_s} \\ \Psi\_{qs} &= \left(V\_{ds} - R\_s I\_{ds}\right) / \left(-\alpha\_s\right) \mathbf{b} \\ \Psi\_s &= \sqrt{\Psi\_{ds}^2 + \Psi\_{qs}^2} \mathbf{c} \end{aligned} \tag{18}$$

According to Equations (8), (10), and (12), the rotor-side converter reference current is derived as:

$$I\_{dr\\_ref} = -\frac{2L\_sT\_e}{\Im n\_p L\_m \Psi\_s} \tag{19}$$

where

$$\begin{aligned} P\_{c\_{-}ref} &= P\_{opt} - P\_{loss} = T\_c \alpha\_r & a \\ P\_{loss} &= R\_s I\_s^2 + R\_r I\_r^2 + R\_c I\_{sc}^2 + Fo\_r^2 \, b \end{aligned} \tag{20}$$

where *I*sc, *R*c, and *F* are stator-side converter current, choke resistance, and friction factor, respectively. *P*opt, *P*e\_ref, and *P*loss are desired optimal output active power, reference active power, and system power loss, respectively. Combining Equations (8), (10), and (11), the active power is used as command inputs to determine current references *I*dr\_ref.

Similarly, the *q*-axis rotor-side converter voltage consists of current regulation and crosscoupling parts too:

$$\begin{aligned} \left| V\_{qr}^{-1} = \left[ R\_r + \left( L\_r - \frac{L\_m}{L\_s} \right) \frac{d}{dt} \right] I\_{qr} \right| \quad a\\ \left| V\_{qr} \right|^2 = \text{so} \partial\_s \left[ L\_r I\_{dr} + L\_m I\_{ds} + \frac{L\_m}{L\_s} \frac{d \Psi\_s}{dt} \right] b \end{aligned} \tag{21}$$

$$V\_{qv} = V\_{qr} = V\_{qr}^{\ 1} + |V\_{qr}|^2 \tag{22}$$

where the derivative of stator flux in Equation (21b) is considered as zero at steady-state. Also, the current regulation part is illustrated in Figure 15. If the stator-side converter's reactive power is controlled to be zero, the output reactive power is stator reactive output power. Then, one has:

$$\mathbf{Q}\_{s} = \mathbf{Q}\_{s} + \mathbf{Q}\_{\kappa \epsilon} = \mathbf{Q}\_{s} = \begin{pmatrix} -V\_{ds}I\_{qs} = -V\_{ds}\frac{1}{L\_{s}}\left(\Psi\_{s} - L\_{m}I\_{qr}\right) \end{pmatrix} \tag{23}$$

Thus, the regulation of reactive power can lead to *I*qr\_ref.

**Figure 15.** Current regulation part of *q*-axis rotor-side converter voltage

Involving the deviations of rotor voltage and reference currents in both *d*- and *q*-axis, Figure 16 exhibits the total control scheme for rotor-side converter, where the *P*opt is obtained from MPPT.

### *2.3.3. Control of stator-side converter*

1 2 *V VV V drc dr dr dr* == + (17)

where subscript rc denotes the rotor-side converter. After the conversion of *dq*-*abc*, the rotorside converter voltage *V*abc\_rc can be obtained, which is used to generate PWM control signals

If only steady-state is considered, the derivative parts in Equation (10) are neglected and one

/ ( ) b

According to Equations (8), (10), and (12), the rotor-side converter reference current is derived

2 3

2 2 22

where *I*sc, *R*c, and *F* are stator-side converter current, choke resistance, and friction factor, respectively. *P*opt, *P*e\_ref, and *P*loss are desired optimal output active power, reference active

w

w

*L T <sup>I</sup>*

*e ref opt loss e r loss s s r r c sc r*

=-= =++ +

*P PP T a P RI RI RI F b*

*s e*

*pm s*

*a*

(18)

(20)

*c*

*n L* = - <sup>Y</sup> (19)

w

( ) 2 2

w

*V RI*

Y= - -

*s ds qs*

*qs s qs*

*s qs ds s ds s*

Ψ Ψ

*V RI*

*ds*


Y= +

\_

\_

*dr ref*

for rotor-side converter.

20 Induction Motors - Applications, Control and Fault Diagnostics

can obtain stator flux as:

as:

where

**Figure 14.** Current regulation part of *d*-axis rotor-side converter voltage

The stator-side converter is controlled based on relationship between voltage, flux, and current of stator and choke, which is modeled by a cross-coupling model, as described in Figure 17. It

**Figure 16.** Total rotor-side converter control scheme

is seen that the grid (stator) voltage is equal to the sum of stator-side converter voltage and choke occupied voltage. By KVL:

$$\begin{split} V\_{ds} &= \mathcal{R}\_c I\_{dsc} - \alpha\_s \Psi\_{qsc} + \mathcal{L}\_c \frac{dI\_{dsc}}{dt} + V\_{dsc} a \\ V\_{qs} &= \mathcal{R}\_c I\_{qsc} + \alpha\_s \Psi\_{dsc} + \mathcal{L}\_c \frac{dI\_{qsc}}{dt} + V\_{qsc} b \end{split} \tag{24}$$

The flux linkage follows:

$$\begin{aligned} \Psi\_{\text{dsc}} &= L\_c I\_{\text{dsc}} \, a \\ \Psi\_{\text{qsc}} &= L\_c I\_{\text{qsc}} \, b \end{aligned} \tag{25}$$

Thus, the reorganized stator-side converter voltage in *d*- and *q*-axis, respectively, are presented as:

$$\begin{split} V\_{\rm desc} &= V\_{\rm ds} - \mathcal{R}\_c I\_{\rm desc} + o\_s L\_c I\_{\rm qsc} - L\_c \frac{dI\_{\rm dsc}}{dt} a \\ V\_{\rm qsc} &= V\_{\rm qs} - \mathcal{R}\_c I\_{\rm qsc} - o\_s L\_c I\_{\rm dsc} - L\_c \frac{dI\_{\rm qsc}}{dt} b \end{split} \tag{26}$$

where the subscripts sc and ch denote the variables of stator-side converter and choke, respectively. *L*c and *R*c are the inductance and resistance of the choke.

Based on the model in Equation (26a, b), the current regulation part of choke voltage in *d*- and *q*-axis are described as (27a, b) and Figure 18(a, b).

**Figure 17.** Equivalent circuit of stator-side converter choke [23]

is seen that the grid (stator) voltage is equal to the sum of stator-side converter voltage and

*ds c dsc s qsc c dsc*

= -Y+ +

w

w

*dI V RI L Va*

*qs c qsc s dsc c qsc*

*dsc c dsc qsc c qsc*

Y =

*dsc ds c dsc s c qsc c*

=- + -

*dI V V RI LI L a*

w

*V V RI LI L b*

w

where the subscripts sc and ch denote the variables of stator-side converter and choke,

Based on the model in Equation (26a, b), the current regulation part of choke voltage in *d*- and

*qsc qs c qsc s c dsc c*

respectively. *L*c and *R*c are the inductance and resistance of the choke.

*q*-axis are described as (27a, b) and Figure 18(a, b).

=- - -

*LI a LI b*

Thus, the reorganized stator-side converter voltage in *d*- and *q*-axis, respectively, are presented

*V RI L Vb*

= +Y+ +

*dsc*

*dt dI*

*dt*

*qsc*

Y = (25)

*dsc*

*dt dI*

*dt*

*qsc*

(24)

(26)

choke occupied voltage. By KVL:

**Figure 16.** Total rotor-side converter control scheme

22 Induction Motors - Applications, Control and Fault Diagnostics

The flux linkage follows:

as:

$$\begin{aligned} V\_{dch}^{-1} &= \left( R\_c + L\_c \frac{d}{dt} \right) I\_{dsc} \, a \\ V\_{qch}^{-1} &= \left( R\_c + L\_c \frac{d}{dt} \right) I\_{qsc} \, b \end{aligned} \tag{27}$$

**Figure 18.** Current regulation part of choke voltage ((a) *d*-axis; (b) *q*-axis)

The cross-coupling part of choke voltage *V*dch2 and *V*qch2 are expressed as (28a, b) and the total stator-side converter voltage is derived as (29a, b).

$$\begin{aligned} \left| \left. V \right|\_{\text{left}} \right|^2 &= -a \rho\_s \mathbf{L}\_c \mathbf{I}\_{qsc} \ a\\ \left| \left. V \right|\_{qch} \right|^2 &= a \rho\_s \mathbf{L}\_c \mathbf{I}\_{dsc} \ \ \mathbf{b} \end{aligned} \tag{28}$$

$$\begin{aligned} V\_{\rm dsc} &= V\_{\rm ds} - \left| V\_{\rm dch} \right|^{1} - \left| V\_{\rm dch} \right|^{2} a \\ V\_{qsc} &= V\_{qs} - \left| V\_{qch} \right|^{1} - \left| V\_{qch} \right|^{2} b \end{aligned} \tag{29}$$

The current reference *I*qsc\_ref is generally set at zero for zero reactive power output from statorside converter while *I*dsc\_ref is determined by the regulation of dc-link voltage *V*dc. The statorside converter voltage control is depicted in Figure 19.

**Figure 19.** Total stator-side converter control scheme [23]

With both rotor- and stator-side converter controls, the simulation results [23] in Figure 20 present a stable and controllable dynamic response to a gusty wind speed. Also, an FRT capability is verified by a voltage droop happening within a constant wind speed. Figure 21 shows twice oscillations at two dynamic moments and the control system effectively recovers the system-regulated outputs in short amount of time.

### *2.3.4. Space Vector Modulation (SVM)*

The purpose of both rotor- and stator-side converter controls is to obtain the reference voltages which are expected to be produced by the converter. The next step is obviously to generate the corresponding PWM gate signals for the converter. To a 2-level three-phase voltage source inverter, there are six switches of three legs in inverter controlling the phase voltage and thus the current of induction generator. By defining the "ON" and "OFF" states of upper switch by "1" and "0," respectively, for one leg, there exist up to eight different states for inverter outputs. They are summarized in Table 2 as well as the resulted phase voltage in *abc* and *αβ* frames. Eight inverter output voltages can be considered as eight voltage vectors [0, 0, 0] through [1, 1, 1] that are illustrated in Figure 22.

2

side converter voltage control is depicted in Figure 19.

24 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 19.** Total stator-side converter control scheme [23]

*2.3.4. Space Vector Modulation (SVM)*

1, 1] that are illustrated in Figure 22.

the system-regulated outputs in short amount of time.

2 *dch s c qsc qch s c dsc*

> 1 2 1 2

The current reference *I*qsc\_ref is generally set at zero for zero reactive power output from statorside converter while *I*dsc\_ref is determined by the regulation of dc-link voltage *V*dc. The stator-

With both rotor- and stator-side converter controls, the simulation results [23] in Figure 20 present a stable and controllable dynamic response to a gusty wind speed. Also, an FRT capability is verified by a voltage droop happening within a constant wind speed. Figure 21 shows twice oscillations at two dynamic moments and the control system effectively recovers

The purpose of both rotor- and stator-side converter controls is to obtain the reference voltages which are expected to be produced by the converter. The next step is obviously to generate the corresponding PWM gate signals for the converter. To a 2-level three-phase voltage source inverter, there are six switches of three legs in inverter controlling the phase voltage and thus the current of induction generator. By defining the "ON" and "OFF" states of upper switch by "1" and "0," respectively, for one leg, there exist up to eight different states for inverter outputs. They are summarized in Table 2 as well as the resulted phase voltage in *abc* and *αβ* frames. Eight inverter output voltages can be considered as eight voltage vectors [0, 0, 0] through [1,

<sup>=</sup> (28)

=- - (29)

*V LI a V LI b* w

= -

w

 *dsc ds dch dch qsc qs qch qch V V V Va V V V Vb* =- -

**Figure 20.** Gusty wind responses ((a) DC-link voltage *V*dc; (b) generator speed ωr; (c) active power *P*; (d) reactive power *Q*; (e) wind speed *V*w)

**Figure 21.** Dynamic responses to grid voltage droop ((a) DC-link voltage *V*dc; (b) generator speed ωr; (c) active power *P*; (d) reactive power *Q*; (e) grid voltage *V*grid)

**Figure 22.** Eight inverter voltage space vectors


**Table 2.** Space vector states (L1–L3 represent inverter leg1–leg3)

Once the reference space vector voltage in *αβ* frame is achieved by current regulation, the magnitude and angle of the voltage are used to implement the SVM. With constant PWM frequency, a space vector is always realized by a vector sum of two adjacent vectors in Table 2. Taking the space vector voltage (0 to 60 degree section) in Figure 23 as an example, it is equal to the vector sum of *V*1 and *V*2 with magnitudes of *d*x and *d*y, respectively, which are the duty cycles of two vectors [32]:

#### Induction Generator in Wind Power Systems http://dx.doi.org/10.5772/60958 27

$$\begin{aligned} d\_x &= \frac{\left| V\_{sp} \right|}{\sqrt{\frac{2}{3}} V\_{dc}} \frac{\sin \left( 60^\circ - \gamma \right)}{\sin 60^\circ} a \\ d\_y &= \frac{\left| V\_{sp} \right|}{\sqrt{\frac{2}{3}} V\_{dc}} \frac{\sin \gamma}{\sin 60^\circ} \quad b \\ d\_z &= 1 - d\_x - d\_y \quad c \end{aligned} \tag{30}$$

where *d*<sup>z</sup> denotes the duty cycle of zero vector. Generally, the zero vectors [0, 0, 0] or [1, 1, 1] contribute the remaining PWM period after *d*x and *d*y. The space vector voltages located in other sections can follow the same procedure to obtain the duty cycles of *d*x, *d*y, and *d*z. Then, the Minimum-Loss Space Vector PWM (MLSVPWM) technique is applied to determine the sequence of vectors [32]. The PWM signals are eventually obtained based on computed duty cycles and sequence of vectors. Figures 24 and 25 show the simulation and experimental threephase duty ratios for inverter phase A, B, and C, where no switching action happens if 0 or 1 duty cycle is the case. It is seen that there is always one phase being absent of switching at any moment, which minimizes the switching loss of the semiconductor switches. Also, the experimental results reveal the sinusoidal nature of the line voltage duty ratio that is expected for sinusoidal fundamental line voltage output of inverter. With this PWM SVM technique, the rotor- and stator-side converters are controlled by previously derived FOC.

**Figure 23.** Duty cycles of vectors for reference space vector voltage

**Figure 22.** Eight inverter voltage space vectors

26 Induction Motors - Applications, Control and Fault Diagnostics

**L1 L2 L3 Van Vbn Vcn V<sup>α</sup> V<sup>β</sup>** 1110 0 0 0 0 1002*V* dc/3 -*V* dc/3 -*V* dc/3 √(2/3)*V* dc 0

0 1 1 -2*V* dc/3 *V*dc/3 *V*dc/3 -√(2/3)*V* dc 0

0000 0 0 0 0

**Table 2.** Space vector states (L1–L3 represent inverter leg1–leg3)

cycles of two vectors [32]:

110 *V*dc/3 *V*dc/3 -2*V* dc/3 √(1/6)*V* dc √(1/2)*V* dc 010- *V* dc/3 2*V* dc/3 - *V* dc/3 -√(1/6)*V* dc √(1/2)*V* dc

001- *V* dc/3 - *V* dc/3 2*V* dc/3 -√(1/6)*V* dc -√(1/2)*V* dc 101 *V*dc/3 -2*V* dc/3 *V*dc/3 √(1/6)*V* dc -√(1/2)*V* dc

Once the reference space vector voltage in *αβ* frame is achieved by current regulation, the magnitude and angle of the voltage are used to implement the SVM. With constant PWM frequency, a space vector is always realized by a vector sum of two adjacent vectors in Table 2. Taking the space vector voltage (0 to 60 degree section) in Figure 23 as an example, it is equal to the vector sum of *V*1 and *V*2 with magnitudes of *d*x and *d*y, respectively, which are the duty

**Figure 24.** Three-phase duty cycles using MLSVPWM (simulation results [33])

**Figure 25.** Phase duty cycles and phase-to-phase duty cycle using MLSVPWM (experiment results [33])

### *2.3.5. Islanded operation*

Compared to the grid integration DFIG wind system, the isolated DFIG wind system operating at regulated voltage (magnitude and frequency) is also found applicable and valuable to some independent power subgrid or distributed power systems. One of the application examples – DFIG-Synchronous machine system configuration – is shown in Figure 26. Modified FOC for power generation in Figure 27 is used and the line voltage magnitude and frequency are stabilized by extra variable load and synchronous machine. The line frequency is held by compensating the resistive load, while the line voltage is held by feeding controlled field voltage of synchronous machine. The proposed controller scheme in [34] is employed for synchronous machine field voltage controller. As shown in Figure 28(a, b), the line frequency is regulated at 60Hz with limited error while the line voltage is regulated at 1 p.u. The constant frequency and magnitude in transmission line voltage is the basic requirement for a controllable power delivery. Based on the regulations of frequency and line voltage, the active power and reactive power are also under control‐ led respectively [25]. The dc-link voltage is kept at nominal value, while the generator speed is controlled at optimal 0.95 p.u., as shown in Figure 29.

**Figure 26.** Islanded DFIG-Synchronous machine wind power system

**Figure 24.** Three-phase duty cycles using MLSVPWM (simulation results [33])

28 Induction Motors - Applications, Control and Fault Diagnostics

*2.3.5. Islanded operation*

**Figure 25.** Phase duty cycles and phase-to-phase duty cycle using MLSVPWM (experiment results [33])

Compared to the grid integration DFIG wind system, the isolated DFIG wind system operating at regulated voltage (magnitude and frequency) is also found applicable and valuable to some independent power subgrid or distributed power systems. One of the application examples – DFIG-Synchronous machine system configuration – is shown in

**Figure 27.** DFIG-Synchronous machine system control scheme

**Figure 28.** Line voltage and frequency in islanded DFIG system ((a) line frequency; (b) line voltage)

**Figure 29.** Simulation results for islanded operation ((a) dc-link voltage *V*dc; (b) generator speed ωr; (c) active power *P*; (d) reactive power *Q*; (e) wind speed *V*w)

### **2.4. Grid synchronization**

The key to performing FOC is to follow the position angle of the *d*-axis component so that the output can be synchronized with *dq* frame, especially in the grid integration operation mode. In order to operate in this mode, the induction generator voltage must be synchronized with the grid voltage by applying the Phase Lock Loop (PLL) technique. The technique takes the grid signal as input and keeps track of the position angle of the grid voltage for FOC as well as reproducing the grid voltage frequency as output, in a real-time manner. To introduce the algorithm, assume an estimated grid voltage angle (accurate grid voltage angle of *θ*); the resulting grid voltages in *dq* frame are written as:

$$\begin{aligned} V\_d &= V\_a \cos \hat{\theta} + V\_\rho \sin \hat{\theta} \, a \\ V\_q &= -V\_a \sin \hat{\theta} + V\_\rho \cos \hat{\theta} \, b \end{aligned} \tag{31}$$

where

**Figure 28.** Line voltage and frequency in islanded DFIG system ((a) line frequency; (b) line voltage)

30 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 29.** Simulation results for islanded operation ((a) dc-link voltage *V*dc; (b) generator speed ωr; (c) active power *P*;

(d) reactive power *Q*; (e) wind speed *V*w)

$$\begin{aligned} V\_a &= V\_m \cos \theta \, a \\ V\_\beta &= V\_m \sin \theta \, b \end{aligned} \tag{32}$$

and *V*<sup>m</sup> denotes the magnitude of the voltage space vector. By substituting *V*α and *V*β in (31a, b) by (32a, b), the *V*d and *V*q can be organized as:

$$\begin{aligned} V\_d &= \, V\_m \cos \left(\theta - \hat{\theta}\right) a \\ V\_q &= \, V\_m \sin(\theta - \hat{\theta}) b \end{aligned} \tag{33}$$

It is seen that if is equal to *θ*, *V*d is equal to *V*m, and *V*q is equal to 0. Therefore, the accurate grid voltage angle *θ* can be obtained by regulating the grid voltage *V*<sup>q</sup> to zero. Assuming there is an error δ between and *θ* that δ = *θ - ,* due to the small value of δ, it is true that Vq ≅ Vmδ and the PLL system in s-domain can be described as Figure 30, where (s) denotes the estimated grid voltage angular frequency and Kc(s) is a PI controller. After removing the unknown accurate θ, the PLL scheme is essentially a regulation of Vq in Figure 31, where the measured Vq goes through a 1st-order low-pass filter whose cutoff frequency is ωc. In this way, the noise is effectively eliminated.

The introduced PLL algorithm is simulated and shown in Figure 32, as well as zoom-in image in Figure 33 [33], where 0 radian grid voltage position coincides with the zero-crossing of phase voltage Van and the frequency can be detected to be 60Hz after short transient (the initial grid frequency is assumed as 55Hz). These results indicate a successful "locking" of grid frequency and position angle, with which the FOC (Figures 16 and 19) are conducted on back-to-back converter in a real-time manner and can thus continuously "match" the generated voltage with the grid voltage.

**Figure 30.** PLL scheme for grid voltage angle estimation

**Figure 31.** PLL scheme with regulation of Vq

**Figure 32.** PLL results of grid voltage angle and frequency for grid integration operation ((a) phase A voltage Van; (b) grid voltage angular position; (c) grid voltage frequency)

**Figure 33.** Zoom-in image of Figure 32

**Figure 32.** PLL results of grid voltage angle and frequency for grid integration operation ((a) phase A voltage Van; (b)

grid voltage angular position; (c) grid voltage frequency)

**Figure 30.** PLL scheme for grid voltage angle estimation

32 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 31.** PLL scheme with regulation of Vq

### **3. Maximum Power Point Tracking (MPPT)**

Efficiency always plays an important role in induction generator wind systems. While the SCIG system loses precise control of power due to the fixed-speed operation, to achieve high efficiency in wind power conversion systems, the MPPT in variable-speed DFIG system has been intensively investigated. Basically, the studied techniques in MPPT include three strategies: (1) the methods relying on wind speed, (2) the methods relying on output power measurement and calculation, and (3) the methods relying on reference power curve.

### **3.1. Pitch angle control of induction generator wind systems**

An overall picture of induction generator wind system operation versus wind speed is depicted in Figure 34, where the output power must be "truncated" after reaching certain level. Pitch angle control, as investigated in section 2.2, is used not only in SCIG system but also in DFIG system for this purpose. It is seen that the capability of pitch angle control in response to the increase of wind speed, on limiting the power output, is primarily dependent on turbine blade physical structure. Therefore, the system needs to be shut down by brake system in the case of wind speed cutoff. Figure 34 also emphasizes the augmented power output of MPPT operation over fixed-speed operation and this inspires the investigation of advanced variablespeed wind systems, where the induction generator speed can always be controlled in a large range to capture desired output power by combining the previously discussed FOC with MPPT strategies.

**Figure 34.** Wind power system operations

### **3.2. MPPT methods for DFIG wind systems**

### *3.2.1. Wind speed based method*

Most DFIG wind power systems are dependent of wind speed measurement [2,4]. In these systems, anemometers are applied to measure the wind speed and thus the systems suffer from additional cost of sensors and complexity. In order to solve this problem, wind speed estimation methods have been reported [25, 35-36]. Relying on the complex algorithms, the accurate wind speed can be captured for controlling the optimal tip speed ratio so that the MPPT can be performed accordingly, as shown in Figure 35. However, the wind speed information and associated efforts on software/hardware are still necessary and significant. To eliminate the dependence on wind speed, some sensorless control strategies have been developed [31,37-38]. These methods are in test for small-scale stand-alone systems and the complicated estimation algorithms remain, which will result in weakening of accuracy and control speed in real operating environment where the wind speed changes rapidly.

### *3.2.2. Power variation rate based method*

Tracking the maximum power can also be accomplished through measuring the output power directly [39-42]. The idea of this method is through checking the variation rate of the output power with respect to that of generator speed (dP/dω), the power operation point location can

**Figure 35.** Estimated wind speed and real measured wind speed [35]

speed wind systems, where the induction generator speed can always be controlled in a large range to capture desired output power by combining the previously discussed FOC with

Most DFIG wind power systems are dependent of wind speed measurement [2,4]. In these systems, anemometers are applied to measure the wind speed and thus the systems suffer from additional cost of sensors and complexity. In order to solve this problem, wind speed estimation methods have been reported [25, 35-36]. Relying on the complex algorithms, the accurate wind speed can be captured for controlling the optimal tip speed ratio so that the MPPT can be performed accordingly, as shown in Figure 35. However, the wind speed information and associated efforts on software/hardware are still necessary and significant. To eliminate the dependence on wind speed, some sensorless control strategies have been developed [31,37-38]. These methods are in test for small-scale stand-alone systems and the complicated estimation algorithms remain, which will result in weakening of accuracy and

control speed in real operating environment where the wind speed changes rapidly.

Tracking the maximum power can also be accomplished through measuring the output power directly [39-42]. The idea of this method is through checking the variation rate of the output power with respect to that of generator speed (dP/dω), the power operation point location can

MPPT strategies.

**Figure 34.** Wind power system operations

*3.2.1. Wind speed based method*

*3.2.2. Power variation rate based method*

**3.2. MPPT methods for DFIG wind systems**

34 Induction Motors - Applications, Control and Fault Diagnostics

be determined and be accordingly controlled thereafter. Theoretically, the maximum power operating point can be reached when dP/dω = 0, as shown in Figure 36. A flowchart of the algorithm is shown in Figure 37, where the operation point (ωm (k), P(k)) is measured and compared with (ωm(k-1), P(k-1)) under wind speed Vw(i), where i is the index of wind speed; k is given as the test step index under particular wind speed Vw(i). Among all the tested points, only one point holds the truth that dP/dω = 0 and it is the optimal operation point (ωmopt(i), Popt(i)) that will be returned and saved. This procedure is required in a means of real-time for different wind speed (i=1,2,...,). According to the information from the optimal points, either the generator speed or the duty cycle of converter can be tuned.

**Figure 36.** MPPT based on output power varying rate [41]

### *3.2.3. Reference power curve based method*

Besides the above strategies, MPPT can be carried out by means of tracking the reference (optimal) power curve, which is the fitting curve going through all the maximum power points of all wind speeds [43-45]. A generalized reference power curve is given as:

**Figure 37.** Flow chart of power variation rate testing algorithm

$$P\_{\mathbf{e}} = b\_{\mathbf{k}} o\_{\mathbf{m}}^{\mathbf{k}} + b\_{\mathbf{k}-1} o\_{\mathbf{m}}^{\mathbf{k}-1} + \dots + b\_{1} o\_{\mathbf{m}} + b\_{0} \tag{34}$$

To determine the optimal degree of the polynomial, comparison is conducted for a 2.678 MW DFIG wind system [33]. Under a particular wind speed, four reference curves lead to four different operation points and the 3rd-order polynomial in Equation (35) leads to the most accurate reference curve along optimal operation points, as shown in Figure 38.

$$P\_{\rm e} = \left| b\_3 \rho\_{\rm m}^3 + b\_2 \rho\_{\rm m}^2 + b\_1 \rho\_{\rm m} + b\_0 \right. \tag{35}$$

**Figure 38.** Comparison of reference power curve fittings

k k 1 e k m k1 m 1m 0 *Pb b b b* ...

accurate reference curve along optimal operation points, as shown in Figure 38.

3 2 e 3m 2m 1m 0 *Pb b b b* =+++ www

 w


(35)


To determine the optimal degree of the polynomial, comparison is conducted for a 2.678 MW DFIG wind system [33]. Under a particular wind speed, four reference curves lead to four different operation points and the 3rd-order polynomial in Equation (35) leads to the most

ww

**Figure 37.** Flow chart of power variation rate testing algorithm

36 Induction Motors - Applications, Control and Fault Diagnostics

This method has been widely used due to its simple concept and absence of extra wind measurement costs. The optimal reference power curve is constructed according to the experimental tests and programmed in a microcontroller memory, to be used as a lookup table. The algorithm diagram is illustrated in Figure 39. Either the generator speed is measured to obtain power reference for power regulation, or the wind speed is measured to obtain generator speed reference for generator speed regulation. The former method produces more accurate output power, while the latter has faster control speed [25]. Some research works simply apply a cube function of generator speed as reference power or a square function of generator speed as reference torque. Despite these feasible solutions, the accurate maximum power and corresponding optimal generator speed are undervalued. Such approximation will obviously lead to harmed power generation efficiency. More importantly, analysis is necessary to verify the stability of the method in terms of vary‐ ing wind speed and output power.

An evolved solution was proposed in [47] to effectively minimize the drawback of the above method. The real-time tuning of reference power curve coefficients is conducted and followed by updating the reference power curve. First, instead of disturbing output power directly, the most significant coefficient is incrementally disturbed by constant. This change of reference power curve induces the variation of the output power, which is measured and compared with previous step power. When the difference in output power between two consecutive steps approaches a small enough value, the disturbed coefficient is returned to update the reference power curve. The resulting reference power curve is the accurate optimal reference power curve. Due to the existence of reference power curve, such tuning

**Figure 39.** MPPT based on reference power curve [46]

calculation does not need to be conducted continuously with high frequency. In addition, without disturbing output power directly, this method can conduct updating and perturba‐ tion faster. Moreover, any deviation of system model will not give rise to deviation of optimal power generation because of the real-time tuning. Thus, the method is robust. As depicted in Figure 40, power variation is checked to capture the optimal coefficient and the reference power curve is updated accordingly to lead the system running in MPPT mode. The whole procedure is described in the simulation results in Figures 41 and 42, where the perturbation of coefficient b3, the generator speed, and generated power halt after reach‐ ing the optimal values. No more perturbation and updating are needed, thus saving the calculation cost. Despite the oscillations at each b3 perturbation step, the dc-link voltage and the reactive power remain at desired values while the output power and generator speed are updated, step by step, toward the optimal values. The generator speed and output power are generally measured with much higher frequency than that of perturbation. It is also worth noting that the bandwidth of b3 updating must ensure that both generator speed and output power are able to reach their steady-states.

**Figure 40.** Novel MPPT algorithm proposed in [47]

calculation does not need to be conducted continuously with high frequency. In addition, without disturbing output power directly, this method can conduct updating and perturba‐ tion faster. Moreover, any deviation of system model will not give rise to deviation of optimal power generation because of the real-time tuning. Thus, the method is robust. As depicted in Figure 40, power variation is checked to capture the optimal coefficient and the reference power curve is updated accordingly to lead the system running in MPPT mode. The whole procedure is described in the simulation results in Figures 41 and 42, where the perturbation of coefficient b3, the generator speed, and generated power halt after reach‐ ing the optimal values. No more perturbation and updating are needed, thus saving the calculation cost. Despite the oscillations at each b3 perturbation step, the dc-link voltage and the reactive power remain at desired values while the output power and generator speed are updated, step by step, toward the optimal values. The generator speed and output power are generally measured with much higher frequency than that of perturbation. It is

**Figure 39.** MPPT based on reference power curve [46]

38 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 41.** DFIG system operation applying the novel MPPT (simulation results)

**Figure 42.** DFIG speed variation induced by the novel MPPT (experiment result)

### **4. Conclusion**

Wind power systems have been widely studied and applied for years. By virtue of many advantages, induction generators are found to be suitable in this area. This chapter introduced and studied two popular types of induction generators – SCIG and DFIG. An overview of the generators, power electronics, and control strategies was presented first, followed by detailed modeling of entire wind system. Most importantly, the control algorithms were illustrated, ranging from FOC, SVM, PLL, to MPPT. Especially, different MPPT strategies were investi‐ gated and compared.

## **Acknowledgements**

The contents of this chapter are the result of work at the Power Electronics Research Lab at the University of Akron, where my research was funded by Dr. Yilmaz Sozer; and work at the Renewable Energy Lab at Saginaw Valley State University, where my research was funded by the Faculty Research Grant.

I highly appreciate Dr. Yilmaz Sozer and Dr. Malik Elbuluk at the University of Akron for supervising my research work as well as guiding my progress in a peaceful and productive direction. I highly appreciate the support from Saginaw Valley State University that granted my start-up lab platform for long-term research commitment.

I am also very grateful to my wife, parents, and mother-in-law for their support. They established the foundation on which rests every success of my career.

## **Author details**

Yu Zou\*

**Figure 41.** DFIG system operation applying the novel MPPT (simulation results)

40 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 42.** DFIG speed variation induced by the novel MPPT (experiment result)

Address all correspondence to: yzou123@svsu.edu

Saginaw Valley State University, Michigan, USA

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ron; 2012, 44-90.

October 2002. 144-148.

nsselaer Polytechnic Institute; 1999, 54-73.

44 Induction Motors - Applications, Control and Fault Diagnostics


## **Active and Reactive Power Control of Wound Rotor Induction Generators by Using the Computer and Driver**

Fevzi Kentli

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61130

### **Abstract**

In this chapter, a power control system for a wound rotor induction generator has been explained. This power control system has realized a control method using a rotating reference frame fixed on the air-gap flux of the generator. Application of such a system allows control of the active and reactive power of generators independently and stably. So, a two-step process is presented here. The first step is to acquire the complex power expression (and thus the active and reactive power expressions) for an induction machine in space vector notation and in two-axes system. Then, a computer aided circuit is given to realize the power and current control by analyzing them. Also, the results of an experiment given in literature are shown to be able to compare the results.

**Keywords:** Doubly-fed wound rotor, Induction generator, Active and reactive pow‐ er control

### **1. Introduction**

Energy is defined as the capacity of a body to do mechanical work. Energy is preserved in earth in many different forms, such as solid (coal), liquid (petroleum), and gas (natural gas). Also, several resources are available such as solar, wind, wave, geothermal, and nuclear energy. On the other hand, energy cannot be found in nature in electrical form. However, electric energy has many advantages: easy to transmit at long distances and complying with customer's needs through adequate control.

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

More than 30% of energy is converted into electrical energy before usage by the help of electric generators that convert mechanical energy into electric energy [1]. There are two kinds of electric generators: synchronous generators and induction generators. Generally, synchronous generators are generally used in big power plants to produce electricity. On the other hand, induction generators are used in utilizing nonstable small energy resources such as uncon‐ trollable and automatically load-regulated small running water and wind turbines (plants) [2, 3]. Wind turbines have become much more popular due to the increasing demand for clean energy. Due to expensive production and maintenance costs, multiwatt turbines/wind farms are preferred. Configurations of generators and their controllers differ. Squirrel cage genera‐ tors, wound rotor generators, permanent magnet generators, DC generators, and variable reluctance generators are operated in these systems. But nowadays a kind of wound rotor, doubly-fed induction generator, has begun to be used more [4].

Both, the synchronous generator with rotating DC magnetic field and the induction generator, have similar fixed stator winding arrangement, which, when energized by a rotating magnetic field, produces a three-phase (or single phase) voltage output. However, the rotors of the two machines are quite different, with the rotor of an induction generator typically consisting of one of two types of arrangements: "squirrel cage" or a "wound rotor." Also, unlike the synchronous generator that has to be "synchronized" with the electrical grid before it can generate power, induction generator can be connected directly to the utility grid and driven directly by the turbines rotor blades at variable wind or running water speeds. Induction motor is an economical and reliable choice as generator in many wind and running water power turbines where its rotational speed, performance, and efficiency can be increased by coupling a mechanical gearbox.

Being cheap, reliable, and readily available in a wide power range from fractional horse power to multi-megawatt capacities leads squirrel cage induction motor type machines to be used in both domestic and commercial renewable energy/running water power applications. The features that make this motor desirable make also the induction generator desirable over other types of generators. Generally, induction generators are constructed based on the squirrel cage induction motor type.

However, the induction generator may provide the necessary power directly to the mains utility grid, but it also needs reactive power to its supply which is provided by the utility grid. Stand-alone (off-grid) operation of the induction generator is also possible but the disadvant‐ age here is that the generator requires additional capacitors connected to its windings for selfexcitation.

Three-phase induction machines are very well-suited for wind power and even hydroelectric (running water) generation. Induction machines, when functioning as generators, have a fixed stator and a rotational rotor, the same as that for the synchronous generator. However, excitation (creation of a magnetic field) of the rotor is performed differently and typical designs of the rotors are the squirrel-cage structure where conducting bars are embedded within the rotors' body and connected together at their ends by shorting rings and the wound (slip-ring) rotor structure that carries a normal 3-ph winding, connected in star or delta and terminated on three slip-rings, which are short- circuited when the machine is in normal operation.

Induction machines are also known as asynchronous machines, that is, they rotate below synchronous speed when used as a motor and above its synchronous speed by some prime mover when used as a generator. The prime mover may be a turbine, an engine, a windmill, or anything that is capable of supplying the torque and speed needed to drive the motor into the overspeed condition. So when rotated faster than its normal operating or no-load speed, induction generator produces AC electricity. In this position, the speed is hypersynchronous, the slip is negative (and usually small), the rotor e.m.f.s and currents have such direction as to demand active power output from the stator terminals. But magnetization is still dependent on the stator winding accepting reactive power for this purpose from the electrical source, so that the induction generator can only operate when connected to a live and synchronous AC system. If a lagging reactive power input is equated with a leading reactive power output, then the generator can be described as operating with a lending power factor. The torque acts in a direction opposite to that of the rotating field, requiring a mechanical drive at the shaft. Because an induction generator synchronizes directly with the main utility grid– that is, produces electricity at the same frequency and voltage – no rectifiers or inverters are required. A major advantage of the induction generator is frequency regulation. The output frequency and volts are regulated by the power system in the induction generators and are independent of speed variations. The self-regulation effect minimizes control system complexity. But the perform‐ ance characteristics as a generator will vary slightly from those as a motor. In general, the slip rpm and power factor will be lower and the efficiency will be higher. The differences may be so insignificant as to be undetectable by normal field measuring methods. On the other hand, alongside advantages mentioned above of the squirrel-cage and wound rotor induction generators whose rotor windings are short- circuited, there are some disadvantages [2, 3]. For example, the active and reactive power of generators cannot be controlled independently and stably. A computer and a cycloconverter in rotor circuit are needed to accomplish this task.

More than 30% of energy is converted into electrical energy before usage by the help of electric generators that convert mechanical energy into electric energy [1]. There are two kinds of electric generators: synchronous generators and induction generators. Generally, synchronous generators are generally used in big power plants to produce electricity. On the other hand, induction generators are used in utilizing nonstable small energy resources such as uncon‐ trollable and automatically load-regulated small running water and wind turbines (plants) [2, 3]. Wind turbines have become much more popular due to the increasing demand for clean energy. Due to expensive production and maintenance costs, multiwatt turbines/wind farms are preferred. Configurations of generators and their controllers differ. Squirrel cage genera‐ tors, wound rotor generators, permanent magnet generators, DC generators, and variable reluctance generators are operated in these systems. But nowadays a kind of wound rotor,

Both, the synchronous generator with rotating DC magnetic field and the induction generator, have similar fixed stator winding arrangement, which, when energized by a rotating magnetic field, produces a three-phase (or single phase) voltage output. However, the rotors of the two machines are quite different, with the rotor of an induction generator typically consisting of one of two types of arrangements: "squirrel cage" or a "wound rotor." Also, unlike the synchronous generator that has to be "synchronized" with the electrical grid before it can generate power, induction generator can be connected directly to the utility grid and driven directly by the turbines rotor blades at variable wind or running water speeds. Induction motor is an economical and reliable choice as generator in many wind and running water power turbines where its rotational speed, performance, and efficiency can be increased by coupling

Being cheap, reliable, and readily available in a wide power range from fractional horse power to multi-megawatt capacities leads squirrel cage induction motor type machines to be used in both domestic and commercial renewable energy/running water power applications. The features that make this motor desirable make also the induction generator desirable over other types of generators. Generally, induction generators are constructed based on the squirrel cage

However, the induction generator may provide the necessary power directly to the mains utility grid, but it also needs reactive power to its supply which is provided by the utility grid. Stand-alone (off-grid) operation of the induction generator is also possible but the disadvant‐ age here is that the generator requires additional capacitors connected to its windings for self-

Three-phase induction machines are very well-suited for wind power and even hydroelectric (running water) generation. Induction machines, when functioning as generators, have a fixed stator and a rotational rotor, the same as that for the synchronous generator. However, excitation (creation of a magnetic field) of the rotor is performed differently and typical designs of the rotors are the squirrel-cage structure where conducting bars are embedded within the rotors' body and connected together at their ends by shorting rings and the wound (slip-ring) rotor structure that carries a normal 3-ph winding, connected in star or delta and terminated on three slip-rings, which are short- circuited when the machine is in normal operation.

doubly-fed induction generator, has begun to be used more [4].

48 Induction Motors - Applications, Control and Fault Diagnostics

a mechanical gearbox.

induction motor type.

excitation.

In recent years, there has been an increased attention toward wind power generation. Con‐ ventionally, grid-connected cage rotor induction machines are used as wind generators at medium power level. When connected to the constant frequency network, the induction generator runs at near-synchronous speed drawing the magnetizing current from the mains, thereby resulting in constant-speed constant-frequency (CSCF) operation. However, the power capture due to fluctuating wind speed can be substantially improved if there is flexibility in varying the shaft speed. In such variable-speed constant-frequency (VSCF) application, rotor-side control of grid-connected wound rotor induction machine is an attractive solution [5]. A doubly-fed wound rotor induction generator can produce constant stator frequency even though rotor speed varies. This system can be controlled by a smallcapacity converter compared with the generator capacity, when the control range speed is narrow. Because of these features, this system is currently considered to be adaptable to power systems for hydroelectric and wind-mill-type power plants [6-8].

When adapted to the power system, it is important to examine the effects of this system on the power system. In the system under consideration, the stator is directly connected to the three-phase grid and the rotor of the doubly-fed induction machine is excited by threephase low-frequency AC currents, which are supplied via slip-rings by either a cycloconvert‐ er or a voltage–fed PWM rectifier-inverter. The AC excitation on the basis of a rotorposition feedback loop makes it possible to achieve stable variable-speed operation. Adjusting the rotor speed makes the induction machine either release the electric power to the utility grid or absorb it from the utility grid [9]. The concept of power control was applied to reactive power compensator applications some 20 years ago, but the applica‐ tion to electrical machine control is new [10].

To control induction generator, several methods are used: electrically [vector control [11], active and reactive power control [12], direct torque control [13], direct power control [14], variable structure or sliding mode control [15], passivity control [16]], and mechanical (pitch, stall, and active stall control [17], yaw control [18], flywheel storage [9]). More information can be found in [19].

In literature, two kinds of approach are proposed for independent control of active and reactive powers. One of them is stator flux oriented vector control with rotor position sensors. The other is position sensorless vector control method. The control with rotor position sensors is the conventional approach and the performance of the system depends on the accuracy of computation of the stator flux and the accuracy of the rotor position information derived from the position encoder. Alignment of the position sensor is, moreover, difficult in a doubly-fed wound rotor machine [5].

Position sensorless vector control methods have been proposed by several research groups in the recent past [20-23]. A dynamic torque angle controller is proposed. This method uses integration of the PWM rotor voltage to compute the rotor flux; hence, satisfactory perform‐ ance can not be achieved at or near synchronous speed. Most of the other methods proposed make use of the measured rotor current and use coordinate transformations for estimating the rotor position [21-23]. Varying degree of dependence on machine parameters is observed in all these strategies.

Alternative approaches to field-oriented control such as direct self control (DSC) and direct torque control (DTC) have been proposed for cage rotor induction machines. In these strat‐ egies, two hysteresis controllers, namely a torque controller and a flux controller, are used to determine the instantaneous switching state for the inverter. These methods of control are computationally very simple and do not require rotor position information. However, the application of such techniques to the control of wound rotor induction machine has not been considered so far. A recently developed algorithm for independent control of active and reactive powers with high dynamic response in case of a wound rotor induction machine is direct power control. In direct power control, the directly controlled quantities are the stator active and reactive powers. The proposed algorithm as direct power control also differs from DTC in that it does not use integration of PWM voltages. Hence, it can work stably even at zero rotor frequency. The method is inherently position sensorless and does not depend on machine parameters like stator/rotor resistance. It can be applied to VSCF applications like wind power generation as well as high-power drives [5].

Little literature has been published on control strategy and dynamic performance of doublyfed induction machines [22; 24-27]. Leonhard (1985) describes a control strategy for an adjustable-speed doubly-fed induction machine intended for independent control of the active and reactive power. The control strategy provides two kinds of current controllers: inner feedback loops of the rotor currents on the d-q coordinates and outer feedback loops of the stator currents on the M-T coordinates. However, it is not clarified theoretically why the control strategy requires the two kinds of current controllers.

This chapter describes the power control characteristics on the rotating reference frame fixed on the air-gap flux of a doubly-fed wound rotor induction generator and proposes a new approach to control with rotor position sensor. The proposed approach is the enhanced version of a previous study [28]. Thus, in this chapter, a new power control system that has been developed by using the computer and driver for a wound rotor induction generator takes place. This system is a new theoretical approach and this power control system has applied a control method using a rotating reference frame fixed on the air-gap flux of the generator. By using this control system, the active and reactive power of generator can be controlled independently and stably. Therefore, to achieve this purpose, firstly the complex power expression (and thus the active and reactive power expressions) for an induction machine in space vector notation and in two-axis system has been gotten. Then, power and current control, which are fundamental subjects, have been analyzed and as a result a computer- and driveraided circuit is given to achieve the power and current control.

### **2. Analysis of the control system**

er or a voltage–fed PWM rectifier-inverter. The AC excitation on the basis of a rotorposition feedback loop makes it possible to achieve stable variable-speed operation. Adjusting the rotor speed makes the induction machine either release the electric power to the utility grid or absorb it from the utility grid [9]. The concept of power control was applied to reactive power compensator applications some 20 years ago, but the applica‐

To control induction generator, several methods are used: electrically [vector control [11], active and reactive power control [12], direct torque control [13], direct power control [14], variable structure or sliding mode control [15], passivity control [16]], and mechanical (pitch, stall, and active stall control [17], yaw control [18], flywheel storage [9]). More information can

In literature, two kinds of approach are proposed for independent control of active and reactive powers. One of them is stator flux oriented vector control with rotor position sensors. The other is position sensorless vector control method. The control with rotor position sensors is the conventional approach and the performance of the system depends on the accuracy of computation of the stator flux and the accuracy of the rotor position information derived from the position encoder. Alignment of the position sensor is, moreover, difficult in a doubly-fed

Position sensorless vector control methods have been proposed by several research groups in the recent past [20-23]. A dynamic torque angle controller is proposed. This method uses integration of the PWM rotor voltage to compute the rotor flux; hence, satisfactory perform‐ ance can not be achieved at or near synchronous speed. Most of the other methods proposed make use of the measured rotor current and use coordinate transformations for estimating the rotor position [21-23]. Varying degree of dependence on machine parameters is observed in

Alternative approaches to field-oriented control such as direct self control (DSC) and direct torque control (DTC) have been proposed for cage rotor induction machines. In these strat‐ egies, two hysteresis controllers, namely a torque controller and a flux controller, are used to determine the instantaneous switching state for the inverter. These methods of control are computationally very simple and do not require rotor position information. However, the application of such techniques to the control of wound rotor induction machine has not been considered so far. A recently developed algorithm for independent control of active and reactive powers with high dynamic response in case of a wound rotor induction machine is direct power control. In direct power control, the directly controlled quantities are the stator active and reactive powers. The proposed algorithm as direct power control also differs from DTC in that it does not use integration of PWM voltages. Hence, it can work stably even at zero rotor frequency. The method is inherently position sensorless and does not depend on machine parameters like stator/rotor resistance. It can be applied to VSCF applications like

Little literature has been published on control strategy and dynamic performance of doublyfed induction machines [22; 24-27]. Leonhard (1985) describes a control strategy for an

wind power generation as well as high-power drives [5].

tion to electrical machine control is new [10].

50 Induction Motors - Applications, Control and Fault Diagnostics

be found in [19].

wound rotor machine [5].

all these strategies.

For the stable control of the active and reactive power, it is necessary to independently control them. As known, the active power control is the control of torque produced by the machine and the reactive power control is the control of flux. The stator active and reactive power of doubly-fed wound rotor induction generator is controlled by regulating the current and voltage of the rotor windings. Therefore, to achieve independent control, the current and voltage of the rotor windings must be divided into components related to stator active and reactive power. It is well-known that an induction machine can be modeled as a voltage behind a total leakage inductance. Therefore, after a three-phase to two-phase power variant trans‐ formation, the induction machine model becomes that of Fig. 1 [10].

Approximate vector diagram of an induction machine is shown in Fig. 2. In this section, the analysis of the doubly-fed wound rotor induction generator on the rotating frame fixed on the air-gap flux (M-T frame) is carried out.

The M-axis is fixed in the air-gap flux and the T-axis is fixed in the quadrature with the M-axis. The relations of stator α1-β1 axis, rotor α2-β2 axis, and M-T axis are shown in Fig. 3.

### **2.1. Complex power expression**

Assuming that the voltage vector is used as the reference for the determination of lagging and leading, we can write the complex stator power expression for a machine in space vector notation as:

**Figure 1.** Two-phase representation of a three-phase induction machine (→generating; ⇢ motoring)

**Figure 2.** Approximate vector diagram of an induction machine

$$S\_1 = I\_1 \mathcal{L} I\_1^"\tag{1}$$

which can be written in two-phase stationary frame variables as:

$$S\_1 = \left[ I\_{M1, T1} \right] \left[ \mathcal{U}\_{M1, T1} \right]^\* \tag{2}$$

where

Active and Reactive Power Control of Wound Rotor Induction Generators by Using the Computer and Driver http://dx.doi.org/10.5772/61130 53

**Figure 3.** Vector diagram of M-T frame

$$\left[\begin{bmatrix} I\_{M1,T1} \end{bmatrix} \right] = I\_{M1} + jI\_{T1}; \left[\begin{bmatrix} \mathcal{U}\_{M1,T1} \end{bmatrix} \right]^\* = \mathcal{U}I\_{M1} - j\mathcal{U}I\_{T1}$$

Expanding Equation (2) we get the expressions for the stator active and reactive power as defined in [29]:

$$S\_1 = \mathcal{U}\_{M1} I\_{M1} + \mathcal{U}\_{T1} I\_{T1} + j \left( \mathcal{U}\_{M1} I\_{T1} - \mathcal{U}\_{T1} I\_{M1} \right) \tag{3}$$

Therefore,

\*

1 1, 1 1, 1 *MT MT SI U* = é ùé ù

**Figure 1.** Two-phase representation of a three-phase induction machine (→generating; ⇢ motoring)

\*

which can be written in two-phase stationary frame variables as:

**Figure 2.** Approximate vector diagram of an induction machine

52 Induction Motors - Applications, Control and Fault Diagnostics

where

1 11 *S IU* = . (1)

ë ûë û (2)

$$P\_1 = \mathcal{U}I\_{M1}I\_{M1} + \mathcal{U}I\_{T1}I\_{T1} \tag{4}$$

$$\mathbb{Q}\_1 = \mathbb{U}\_{M1}\mathbf{I}\_{T1} - \mathbb{U}\_{T1}\mathbf{I}\_{M1} \tag{5}$$

where P1 is the stator active power, and Q1 is the stator reactive power, IM1 and IT1 are the M and T axis stator currents, and UM1 and UT1 are the M and T axis stator voltages.

#### **2.2. Power control**

In this section, the relationship between stator power and rotor current is analyzed. In Equations (4) and (5), the stator active and reactive power was expressed by the stator current based on the M-T frame. The relationships between the rotor and stator currents are:

$$I\_{T1} = I\_{q1} \text{Cost} \mathbf{y} - I\_{d1} \text{Simy} \tag{6}$$

$$I\_{T2} = I\_{q2} \text{Cost} \chi - I\_{d2} \text{Simy} \tag{7}$$

$$I\_{T1} + I\_{T2} = \left(I\_{q1} + I\_{q2}\right) \text{Cov}\chi - \left(I\_{d1} + I\_{d2}\right) \text{Sim}\chi\tag{8}$$

$$I\_{d1} = I\_{M1} \mathbb{C}os \gamma \text{; } I\_{d2} = I\_{M2} \mathbb{C}os \gamma \tag{9}$$

$$I\_{q1} = I\_{M1} \text{Sim}\gamma ; \; I\_{q2} = I\_{M1} \text{Sim}\gamma \tag{10}$$

$$I\_{T1} + I\_{T2} = 0 \\ \vdots \\ I\_{T1} = -I\_{T2} \tag{11}$$

By using Equations (9) and (10), the term of (IT1 + IT2) is expressed in terms of ψδ and LM:

$$I\_{T1} + I\_{T2} = \left(\frac{\mu\_{\delta}}{L\_{\text{M}}}\right) \text{Sin} \gamma \text{Cosy} - \left(\frac{\mu\_{\delta}}{L\_{\text{M}}}\right) \text{Cosy} \text{Sin} \gamma = 0 \tag{12}$$

$$\Psi\_{\mathcal{S}} = \mathcal{L}\_M \left( I\_{M1} + I\_{M2} \right) \tag{13}$$

where ψδ is the air-gap flux, IM2 and IT2 are the M and T axis rotor currents, and LM is the mutual inductance.

By using Equations (12) and (13), the stator active and reactive power is expressed in terms of ψδ and LM:

$$\begin{aligned} P\_1 &= \mathcal{U}\_{M1} \Big[ \Big( L\_{\mathcal{M}} \Big( I\_{M1} + I\_{M2} \Big) / L\_{\mathcal{M}} \Big) - I\_{M2} \Big] + \mathcal{U}\_{T1} \Big( -I\_{T2} \Big) \\ P\_1 &= \Big( \mathcal{V}\_{\mathcal{S}} \Big/ L\_{\mathcal{M}} \Big) \mathcal{U}\_{M1} - \mathcal{U}\_{M1} I\_{M2} - \mathcal{U}\_{T1} I\_{T2} \end{aligned} \tag{14}$$

$$\begin{aligned} \mathbf{Q}\_1 &= \mathbf{U}\_{M1} \left( -I\_{T2} \right) - \mathbf{U}\_{T1} \left[ \left( L\_M \left( I\_{M1} + I\_{M2} \right) / L\_M \right) - I\_{M2} \right] \\ \mathbf{Q}\_1 &= \mathbf{U}\_{T1} I\_{M2} - \left( \mathbf{\nu}\_{\mathcal{S}} / L\_M \right) \mathbf{U}\_{T1} - \mathbf{U}\_{M1} I\_{T2} \end{aligned} \tag{15}$$

In this system, the stator winding is directly connected to the power system. The conditions UM1 ≈ 0, UT1 ≈ constant, ψδ ≈ constant are derived from this feature [25]. By using these relationships and Equations (12), (13), (14), and (15), the stator active and reactive power is expressed in terms of rotor current. Equations (4) and (5) are rewritten as follows:

$$P\_1 \approx -\mathcal{U}\_{T1} I\_{T2} \tag{16}$$

$$\mathbb{Q}\_1 \approx \mathbb{U}\_{T1} \mathbf{I}\_{M2} - \left(\boldsymbol{\psi}\_{\boldsymbol{\delta}} \,/ \, \mathbf{L}\_{\mathcal{M}}\right) \mathbf{U}\_{T1} \tag{17}$$

Equation (16) shows that the stator active power (P1) is expressed by the terms proportional to the rotor current IT2. Equation (17) shows that the stator reactive power (Q1) is expressed by the terms proportional to the rotor current IM2 and constant value (ψδ/LM).UT1. From the above relationships, the rotor current is divided into the active power (P1) and the reactive power (Q1) components. That is, the independent control of the stator active and reactive power can be actualized by regulating rotor currents IM2 and IT2.

### **2.3. Current control**

*Tq d* 11 1 *I I Cos I Sin* = g

54 Induction Motors - Applications, Control and Fault Diagnostics

*Tq d* 22 2 *I I Cos I Sin* = g

*I I I I Cos I I Sin TT qq dd* 1 2 12 12 += + - + ( ) g

> 11 22 ; *dM dM I I Cos I I Cos* = = g

11 21 ; *qM qM I I Sin I I Sin* = = g

By using Equations (9) and (10), the term of (IT1 + IT2) is expressed in terms of ψδ and LM:

1 2 0 *T T M M I I Sin Cos Cos Sin L L*

*MM M* ( ) 1 2 *LI I*

where ψδ is the air-gap flux, IM2 and IT2 are the M and T axis rotor currents, and LM is the mutual

By using Equations (12) and (13), the stator active and reactive power is expressed in terms of

( ( ) ) ( )

/ *M MM M M M T T*

*M M MM TT*

1 1 1 2 2 12 1 1 1 2 12

*PU LI I L I U I P L U U I UI*

= + -+- é ù ë û

/

() ( ) ( ) ( ) 1 12 1 1 2 2 1 12 1 12

= -- + - é ù

*QU I U LI I L I Q UI L U U I* y d

/ *M T T MM M M M T M M T MT*

æö æö + = ç÷ ç÷ - = èø èø

g g  y

 d

 gg

y

d

y d

( )

y d

inductance.

ψδ and LM:

 g

> g

> > g

 g  g

12 1 2 0 ; *TT T T II I I* + = =- (11)

= + (13)

= -- (14)

=- - (15)

/

ë û

(6)

(7)

( ) (8)

(9)

(10)

(12)

In this section, the relation between the rotor currents and the rotor voltages is analyzed. The equations for wound rotor induction machine based on M-T frame are shown as follows:

$$\mathcal{U}\_{M1} = R\_{\text{I}} I\_{M1} + \frac{L\_{1\sigma} d\mathcal{I}\_{M1}}{dt} - \left(\alpha\_{\text{I}} + \alpha\_{\text{\beta}}\right) L\_{1\sigma} I\_{\text{T}1} + \frac{d\nu\_{M1\delta}}{dt} - \left(\alpha\_{\text{I}} + \alpha\_{\delta}\right) \nu\_{\text{T}1\delta} \tag{18}$$

$$\mathcal{U}\_{T1} = \mathcal{R}\_1 I\_{T1} + \frac{L\_{1\sigma} dI\_{T1}}{dt} + \left(\alpha\_1 + \alpha\_\delta\right) L\_{1\sigma} I\_{M1} + \frac{d\nu\_{T1\delta}}{dt} + \left(\alpha\_1 + \alpha\_\delta\right) \mathcal{V}\_{M1\delta} \tag{19}$$

$$\mathcal{U}\_{M2} = R\_2 I\_{M2} + \frac{L\_{2\sigma} dI\_{M1}}{dt} - \left(\alpha\_\\$ + \alpha\_\delta\right) L\_{2\sigma} I\_{T2} + \frac{d\nu\_{M2\delta}}{dt} - \left(\alpha\_\circ + \alpha\_\delta\right) \mathcal{V}\_{T2\delta} \tag{20}$$

$$\mathcal{U}\_{T2} = \mathcal{R}\_2 I\_{T2} + \frac{L\_{2\sigma} dI\_{T2}}{dt} + \left(\alpha\_\odot + \alpha\_\delta\right) L\_{2\sigma} I\_{M2} + \frac{d\nu\_{T2\delta}}{dt} + \left(\alpha\_\S + \alpha\_\delta\right) \nu\_{M2\delta} \tag{21}$$

where ψM1δ and ψT1δ are the M and T axis stator air-gap flux, R1 and R2 are the stator and rotor resistance, ω1 is the stator angular speed, ωδ is the angular speed of the air-gap flux, ψM2δ and ψT2δ are the M and T axis rotor air-gap flux, L1σ and L2σ are the stator and rotor leakage inductance, ωS is the slip angular speed.

These equations are transformed by using the relationships ψT1δ = ψT2δ, ψM1δ = ψM2δ, and ωS = ω1-ω2, and the following expressions are derived:

$$\mathcal{U}\_{M2} = R\_2 I\_{M2} + \frac{L\_{2\sigma} dI\_{M2}}{dt} - \left(\alpha\_\circ + \alpha\_\circ\right) L\_{2\sigma} I\_{T2} + \frac{d\nu\_{M1\delta}}{dt} - \left(\alpha\_\circ + \alpha\_\circ\right) \nu\_{T2\delta} \tag{22}$$

$$\mathcal{U}\_{T2} = \mathcal{R}\_2 I\_{T2} + \frac{L\_{2\sigma} dI\_{T2}}{dt} + \left(\alpha\_\circ + \alpha\_\circ\right) L\_{2\sigma} I\_{M2} + \frac{d\nu\_{T1\delta}}{dt} + \left(\alpha\_\circ + \alpha\_\circ\right) \nu\_{M2\delta} \tag{23}$$

$$\mathrm{d}\mathbf{U}\_{M2} = \mathbf{R}\_2 \mathbf{I}\_{M2} + \frac{\mathbf{L}\_{2\sigma} d\mathbf{I}\_{M2}}{dt} - \left(\alpha\_\mathrm{\mathcal{S}} + \alpha\_\mathrm{\mathcal{S}}\right) \mathbf{L}\_{2\sigma} \mathbf{I}\_{T2} + \mathbf{U}\_{M1\delta} + \alpha\_\mathrm{\mathcal{B}} \boldsymbol{\mu}\_{T2\delta} \tag{24}$$

$$\mathrm{d}I\_{T2} = \mathrm{R}\_2 I\_{T2} + \frac{\mathrm{L}\_{2\sigma} dI\_{T2}}{dt} + \left(o\_\mathrm{\mathcal{S}} + o\_\mathcal{\mathcal{S}}\right) \mathrm{L}\_{2\sigma} I\_{M2} + \mathrm{L} I\_{T1\mathcal{\delta}} - o\_2 \mathcal{\mathcal{Y}}\_{M2\mathcal{\delta}} \tag{25}$$

where ω2 is the rotor angular speed.

When the Equations (22), (23), (24), and (25) are transformed by the rotor current IM2 and IT2, Equations (26) and (27) are given:

$$I\_{M2} = \left(\mathcal{U}\_{M2} + \left(a\_{\mathcal{S}} + a\_{\mathcal{S}}\right)\mathcal{L}\_{2\sigma}I\_{T2} - \mathcal{U}\_{M1\delta}\right) / \left(\mathcal{R}\_2 + p\mathcal{L}\_{2\sigma}\right) \tag{26}$$

$$\mathcal{U}\_{T2} = \left(\mathcal{U}\_{T2} - \left(o\varrho\_{\mathcal{S}} + o\varrho\_{\mathcal{S}}\right)\mathcal{L}\_{2\sigma}\mathcal{U}\_{M2} - \mathcal{U}\_{T1\mathcal{S}} + o\varrho\_{2}\mathcal{W}\_{\mathcal{S}}\right) / \left(\mathcal{R}\_{2} + p\mathcal{L}\_{2\sigma}\right) \tag{27}$$

where p is the differential operator.

The stator winding is directly connected to the power system. Therefore, stator voltage becomes constant in the normal state, leading to the conditions UM1δ ≈ 0 and UT1δ ≈ constant. And L2σ is negligible because it is generally small [25].

Thus, Equations (26) and (27) become as follows:

$$I\_{M2} = \mathcal{U}\_{M2} \;/\; R\_2 \tag{28}$$

$$I\_{T2} = \left(\mathcal{U}\_{T2} - \mathcal{U}\_{T1\delta} + \alpha\_2 \mathcal{\boldsymbol{\nu}}\_{\delta}\right) / \mathcal{R}\_2 \tag{29}$$

Equations (28) and (29) show that rotor voltages along the M and T axes, respectively depend only on the rotor currents along the M and T axes. In other words, the relationships between the currents and voltages along the M and T axes are linear. Consequently, the rotor currents IM2 and IT2 can be controlled independently by regulating the rotor voltages UM2 and UT2.

### **2.4. Composition of the control system**

These equations are transformed by using the relationships ψT1δ = ψT2δ, ψM1δ = ψM2δ, and ωS =

( ) ( ) 2 2 <sup>1</sup> 2 22 2 2 2 *M M M M S T S T*

( ) ( ) 2 2 <sup>1</sup> 2 22 2 2 2 *T T T T S M S M*

 d

 d w wy

w wy

 d

 d w y

w y

s

2 22 / *M M I UR* = (28)

(29)

s

y

y

d

d

 d

 d  d

 d

(22)

(23)

(24)

(25)

*dt dt*

*dt dt*

*M M S TM T*

*T T S MT M*

*I U T T S MT* 2 2 ( ( ) *LI U* 22 1 2 2 2 ) /( ) *R pL*

2 2 12 2 ( ) / *T TT I UU R* =-+d

Equations (28) and (29) show that rotor voltages along the M and T axes, respectively depend only on the rotor currents along the M and T axes. In other words, the relationships between the currents and voltages along the M and T axes are linear. Consequently, the rotor currents IM2 and IT2 can be controlled independently by regulating the rotor voltages UM2 and UT2.

 d w y

 d

The stator winding is directly connected to the power system. Therefore, stator voltage becomes constant in the normal state, leading to the conditions UM1δ ≈ 0 and UT1δ ≈ constant.

When the Equations (22), (23), (24), and (25) are transformed by the rotor current IM2 and IT2,

 d*L I U R pL* 22 1 2 2 ) /( )

= ++ - + (26)

 d w y

= -+ - + + (27)

 = + ++ + w wds

 = + -+ + + w wds

d s

 = + ++ + ++ w w

( ) 2 2 2 22 2 2 1 22

( ) 2 2 2 22 2 2 1 22

*M*

*T*

*I U M M S TM* 2 2 ( ( ) w wds

> w wds

And L2σ is negligible because it is generally small [25].

Thus, Equations (26) and (27) become as follows:

*dt* s

*L dI U RI LI U*

*L dI U RI LI U dt* s

 = + -+ + -+ w w

d s

ω1-ω2, and the following expressions are derived:

56 Induction Motors - Applications, Control and Fault Diagnostics

*L dI <sup>d</sup> U RI L I*

*L dI <sup>d</sup> U RI L I*

s

s

where ω2 is the rotor angular speed.

Equations (26) and (27) are given:

where p is the differential operator.

Figure 4 illustrates the control system diagram. Considering the analysis of control system, it can be interpreted that M-T frame can be used to describe the composition of the active and the reactive power. Mentioned control system has six parts: (1) power control loop (regulation of the rotor current references from the deviation between detection and reference values for both active and reactive power); (2) current PI regulator for rotor currents IM2 and IT2 (same application with the first part for regulation of the voltage); (3) air-gap flux calculator (using the stator currents, voltages, and the signals of the position sensor); (4) P1 and Q1 detector (calculation of the stator active and reactive power); (5) detector of the rotor current (vector values of M-T axis, Equation (30)); (6) coordinate transformer (three-phase voltage references, Equation (31)) [25].

$$
\begin{bmatrix} I\_{M2} \\ I\_{I2} \end{bmatrix} = \begin{bmatrix} \cos(\lambda + \gamma) & \sin(\lambda + \gamma) \\ \sin(\lambda + \gamma) & \cos(\lambda + \gamma) \end{bmatrix} \begin{bmatrix} 1 & -1/2 & -1/2 \\ 0 & \sqrt{3}/2 & -\sqrt{3}/2 \end{bmatrix} \begin{bmatrix} I\_{s2} \\ I\_{b2} \\ I\_{c2} \end{bmatrix} \tag{30}
$$

$$
\begin{bmatrix} \mathcal{U}\_{a2} \\ \mathcal{U}\_{b2} \\ \mathcal{U}\_{c2} \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ -1/2 & \sqrt{3}/2 \\ -1/2 & -\sqrt{3}/2 \end{bmatrix} \begin{bmatrix} \cos(\lambda + \gamma) & -\sin(\lambda + \gamma) \\ \sin(\lambda + \gamma) & \cos(\lambda + \gamma) \end{bmatrix} \begin{bmatrix} \mathcal{U}\_{M2} \\ \mathcal{U}\_{T2} \end{bmatrix} \tag{31}
$$

**Figure 4.** Block diagram of the control system

### **2.5. Power reference generation**

Power Reference Generation (PRG) is one of the key modules of the algorithm. Strangely, it is the only module that depends on the parameter values. Due to direct connection to the torque, active power reference is the simplest way to find out the torque value desired to produce. On the other hand, there are some difficulties related with the active power reference.

Normally, the following equation is enough to calculate active power reference [10]:

$$P\_{ref} = T\_{ref} \alpha\_{m2} = T\_{ref} \left(2\pi m\_2\right) \tag{32}$$

where Tref is supplied from some outer loop such as a speed control loop, and n2 is the actual mechanical shaft speed at a particular instant of time.

Equation (32) is reliable under some limits so that calculated value of active power is not adequate to generate the torque Tref. Main reason is the losses (losses in the stator and rotor resistance and iron losses) where all input power can not be transmitted to output. Loss in rotor resistance is influenced by the slip of the machine. Schematic demonstration of the power flows under motoring and generating for an induction machine are shown in Fig. 5.

**Figure 5.** Schematic demonstration of the power flows in an induction machine under (a) motoring and (b) generating (Pi = input power (taken from supply in motor mode, given from shaft in generator mode), Pm = mechanical power, P<sup>δ</sup> = air-gap power (transferred from stator to rotor under motoring and from rotor to stator under generating), Pl = pow‐ er loss, Pfe = iron loss, Pcu = copper loss, Pa = additional losses produced by harmonics, Pf,w = friction and windage loss‐ es, Pel = effective electrical power taken from rotor circuit, Po = output power (shaft power in motor mode, electrical power in generation mode) (1 subscript means stator, 2 subscript means rotor) [28]

As seen in literature, whilst some researchers can assume that the stator resistance power and the iron losses can be ignored (under many practical situations), the power in the rotor resistance cannot be ignored, especially under heavy load conditions when the slip of the machine can be large [10].

As the diagram shows, under the motoring condition the input power separates into two parts: one part is for the losses (stator, iron, and harmonics) and the other part is related with the rotating field power (air-gap power).

Also, under generating the input shaft power separates into two parts: the losses (friction, windage) and mechanical power. All these parts should be balanced to reach the goal power value. To manage this aim, we should be able to calculate the slip and afterward we could calculate required power expressions as follows for the motoring/generating situation (if the friction and windage losses are neglected):

$$P\_{ref} = \frac{P\_{shaft}}{\left(1 - s\right)} = \frac{T\_{ref} \alpha\_{m2}}{\left(1 - s\right)}\tag{33}$$

where Pshaft is the desired shaft power, and Pref is the terminal reference power as defined previously.

The reactive power reference generation is linked with the slip. So, first we should deal with it. Figure 2 gives an approximate vector diagram of the voltages, currents, and fluxes of an induction machine. Reactive power can be calculated as the multiplication of the emf voltage E in one axis (e.g. qr) of the machine by the current in the other axis (e.g. dr):

$$\left| \mathbf{Q} \right| = I\_{nr} E \tag{34}$$

$$\left| \mathbf{Q} \right| = I\_{mr} \alpha\_1 \nu\_m \tag{35}$$

where ψm is the flux magnitude, Imr is the magnetising current, and ω<sup>1</sup> is the stator angular speed related with electrical frequency.

Rearranging (35) one can write:

$$\alpha\_{sref} = -\left(\frac{\left|Q\_{rf}\right|}{\left(I\_{mrrf}\nu\_{mrf}\right)}\right) - \alpha\_2\tag{36}$$

realizing:

= pow‐

active power reference is the simplest way to find out the torque value desired to produce. On

where Tref is supplied from some outer loop such as a speed control loop, and n2 is the actual

Equation (32) is reliable under some limits so that calculated value of active power is not adequate to generate the torque Tref. Main reason is the losses (losses in the stator and rotor resistance and iron losses) where all input power can not be transmitted to output. Loss in rotor resistance is influenced by the slip of the machine. Schematic demonstration of the power

**Figure 5.** Schematic demonstration of the power flows in an induction machine under (a) motoring and (b) generating

er loss, Pfe = iron loss, Pcu = copper loss, Pa = additional losses produced by harmonics, Pf,w = friction and windage loss‐ es, Pel = effective electrical power taken from rotor circuit, Po = output power (shaft power in motor mode, electrical

As seen in literature, whilst some researchers can assume that the stator resistance power and the iron losses can be ignored (under many practical situations), the power in the rotor

power in generation mode) (1 subscript means stator, 2 subscript means rotor) [28]

 = input power (taken from supply in motor mode, given from shaft in generator mode), Pm = mechanical power, P<sup>δ</sup> = air-gap power (transferred from stator to rotor under motoring and from rotor to stator under generating), Pl

 p

(32)

the other hand, there are some difficulties related with the active power reference.

Normally, the following equation is enough to calculate active power reference [10]:

2 2 ( ) 2 *ref ref m ref PT T n* = = w

flows under motoring and generating for an induction machine are shown in Fig. 5.

mechanical shaft speed at a particular instant of time.

58 Induction Motors - Applications, Control and Fault Diagnostics

(Pi

f2 = pp.n2

ω2 = pp.ωm2

ω1 = ω2 + ω<sup>s</sup>

ωs = slip angular speed related with slip frequency

ωs ref = the desired slip angular speed related with slip frequency

Imr ref = the desired magnetizing current

pp = the pole pairs

│Qref│ = the desired reactive power

The negative sign in Equation (36) results from the sign of Qref, the reference reactive power. Given Equation (36), we can now write the expression for the slip:

$$\mathbf{s} = \frac{\alpha \mathbf{o}\_s}{\left(\alpha \mathbf{o}\_2 + \alpha \mathbf{o}\_s\right)} = \mathbf{1} + \left(\alpha \mathbf{o}\_2 \mathbf{I}\_{mnrq} \mathbf{y} \mathbf{v}\_{mrq} \,/\, \mathbf{Q}\_{nq}\right) = \mathbf{1} + \left(\alpha \mathbf{o}\_2 \mathbf{L}\_n \mathbf{I}\_{mnrq}^2 \,/\, \mathbf{Q}\_{nq}\right) \tag{37}$$

This expression can be substituted into the active power slip compensation term 1/(1-s). The Imr ref and ψm ref terms in this expression are reference values. Clearly, Imr and ψm for an induction machine are related, that is, ψm = Lm.Imr. Hence, we have written the numerator of Equation (37) as Lm.Imr ref2. This requires acquiring the value of magnetizing inductance of the machine.

The reactive power expression can be written as:

$$\left| \bigotimes\_{ref} \right| = I\_{mr} \alpha \rho\_1 \nu\_m = I\_{mr} \nu\_m \left( \alpha \rho\_2 + o \rho\_s \right) \tag{38}$$

So, it can be concluded that the reactive power is dependent on the slip frequency. The slip frequency is well-related with the torque. In case a rapid change in torque is needed, slip frequency changes as a step and consequently the reactive power value changes. The torque T and ωs expressions of an induction machine can be written as (using the standard expression from Field Oriented Control):

$$T = \mathbf{1.5p}\_p \mathbf{L}\_m^2 \left| I\_{mr} \right| I\_p \text{ / } \mathbf{L}\_2 \tag{39}$$

$$
\alpha \alpha\_s = I\_p \nmid \left( \pi\_2 \left| I\_{mr} \right| \right) \tag{40}
$$

where τ2 = L2 /R2, L2 = the rotor inductance, and R2 = the rotor resistance. Therefore, τ2 is the rotor time constant.

Rearranging Equation (39), one can write:

Active and Reactive Power Control of Wound Rotor Induction Generators by Using the Computer and Driver http://dx.doi.org/10.5772/61130 61

$$I\_p = \left(TL\_2\right) / \left(1.5 p\_p L\_m^2 \left| I\_{mr} \right|\right) \tag{41}$$

Substituting Equation (41) into Equation (40) gives:

ω1 = ω2 + ω<sup>s</sup>

pp = the pole pairs

ωs = slip angular speed related with slip frequency

60 Induction Motors - Applications, Control and Fault Diagnostics

Imr ref = the desired magnetizing current

│Qref│ = the desired reactive power

2

w w

from Field Oriented Control):

rotor time constant.

Rearranging Equation (39), one can write:

w

*s*

The reactive power expression can be written as:

ωs ref = the desired slip angular speed related with slip frequency

Given Equation (36), we can now write the expression for the slip:

The negative sign in Equation (36) results from the sign of Qref, the reference reactive power.

( ) ( ) ( ) <sup>2</sup> 2 2

This expression can be substituted into the active power slip compensation term 1/(1-s). The Imr ref and ψm ref terms in this expression are reference values. Clearly, Imr and ψm for an induction machine are related, that is, ψm = Lm.Imr. Hence, we have written the numerator of Equation (37) as Lm.Imr ref2. This requires acquiring the value of magnetizing inductance of the machine.

> y w w

So, it can be concluded that the reactive power is dependent on the slip frequency. The slip frequency is well-related with the torque. In case a rapid change in torque is needed, slip frequency changes as a step and consequently the reactive power value changes. The torque T and ωs expressions of an induction machine can be written as (using the standard expression

2

( ) <sup>2</sup> / *s p mr*

 t

where τ2 = L2 /R2, L2 = the rotor inductance, and R2 = the rotor resistance. Therefore, τ2 is the

w

*mrref mref ref m mrref ref*

 w

<sup>+</sup> (37)

1 2 ( )*<sup>s</sup>* == + (38)

<sup>2</sup> 1.5 / *p m mr p T pL I I L* = (39)

= *I I* (40)

1 /1 / *<sup>s</sup>*

*s I Q LI Q*

wy

*QI I ref mr m mr m* wy

= =+ = +

$$
\rho \alpha\_s = \left( TL\_2 \right) / \left( 1.5 \, p\_p \, L\_m^2 \left| I\_{mr} \right|^2 \pi\_2 \right) \tag{42}
$$

The denominator in Equation (42) can be simplified by assuming that the leakage inductance of the machine is very small in relation to L2, and hence L2 ≈ Lm. Therefore, Equation (42) can be written as:

$$\rho o\_s \approx \frac{2T}{\left(3p\_p L\_m \left| I\_{mr} \right|^2 \tau\_2\right)} = \frac{2T}{\left(3p\_p \nu\_m \left| I\_{mr} \right| \tau\_2\right)}\tag{43}$$

We are now in a position to write an expression for the reference reactive power. Substituting Equation (43) into Equation (38) and simplifying, we get Equation (44):

$$\mathbf{Q}\_{n\circ f} = -\left[ \left( \left| I\_{n\circ} \right|\_{n\circ f} \alpha\_2 \mathbf{y}\_{n\circ n\circ f} \right) + \left( \frac{2T\_{n\circ f}}{3\mathcal{p}\_p \pi\_2} \right) \right] = -\left[ L\_m \left( \left| I\_{n\circ r} \right|\_{n\circ f} \right)^2 \alpha\_2 + \left( \frac{2T\_{n\circ f}}{3\mathcal{p}\_p \pi\_2} \right) \right] \tag{44}$$

### **3. Experimental studies**

An experimental setup using the control system shown in Fig. 4 was established by Yamamoto and Motoyoshi and the characteristics of the control system along the M-T frame have been experimentally examined. Experimental data are taken from their study [25]. The schematic diagram of the experimental system is shown in Fig. 6. Specifications of the generator used in experimental system are shown in Table 1. Equations (16) and (17) show that active and reactive power is proportional to the rotor currents IT2 and IM2.


**Table 1.** Specifications of the generator used in experimental system [25]

**Figure 6.** Experimental system [25]

### **3.1. Experimental results**

Figures 7 and 8 show the relationships between stator power and rotor current reference and Figs. 9 and 10 show the relationships between stator power and stator power reference.

Figure 10 shows the step response of the stator reactive power Q1 and the step response of the rotor current IM2 which is in proportion to the stator reactive power (Q1). Figure 8 shows the step response of the rotor current IT2 which is in proportion to the stator active power (P1). Figure 9 shows the step response of the stator active power P1. IM2 and IT2 respond to stepping of I\*M2 and I\*T2 in 20 ms without any effect on IT2 and IM2. P1 and Q1 respond to stepping of P\*1 and Q\*1 in 80 ms without any effect on Q1 and P1. The effects of this active and reactive power control method have been proved by these experimental results.

**Figure 7.** Step response of the M-axis current [25]

Active and Reactive Power Control of Wound Rotor Induction Generators by Using the Computer and Driver http://dx.doi.org/10.5772/61130 63

**Figure 8.** Step response of the T-axis current [25]

**3.1. Experimental results**

**Figure 6.** Experimental system [25]

62 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 7.** Step response of the M-axis current [25]

Figures 7 and 8 show the relationships between stator power and rotor current reference and Figs. 9 and 10 show the relationships between stator power and stator power reference.

Figure 10 shows the step response of the stator reactive power Q1 and the step response of the rotor current IM2 which is in proportion to the stator reactive power (Q1). Figure 8 shows the step response of the rotor current IT2 which is in proportion to the stator active power (P1). Figure 9 shows the step response of the stator active power P1. IM2 and IT2 respond to stepping of I\*M2 and I\*T2 in 20 ms without any effect on IT2 and IM2. P1 and Q1 respond to stepping of P\*1 and Q\*1 in 80 ms without any effect on Q1 and P1. The effects of this active and reactive

power control method have been proved by these experimental results.

**Figure 9.** Step response of the active power [25]

**Figure 10.** Step response of the reactive power [25]

### **3.2. Harmonic analysis**

For the power converter of this system, the cycloconverter which is suitable for a large capacity system is often used. Generally, when the large-scale converter is applied to the electric power network system, it is a very important item to analyze the harmonic currents of the power converter. As known, the harmonic currents of the power converter are transmitted to the electric power network system through the rotor and stator windings. In this chapter, the characteristics of the transmission of the harmonic currents caused by the cycloconverter are analyzed theoretically.

Before beginning analysis, let us remember the basic principles of cycloconverter and mathe‐ matical background (taken from [30]) for the understanding of the subject.

### *3.2.1. Principle of the cycloconverter*

[30]

As known, cycloconversion is concerned mostly with direct conversion of energy to a different frequency by synthesizing a low-frequency wave from appropriate sections of a higherfrequency source. As shown in Fig. 11a, a cycloconverter can be considered to be composed of two converters connected back-to-back. The load waveforms of Fig. 11b show that in the general case, the instantaneous power flows in the load fall into one of four periods. The two periods, when the product of load voltage and current is positive, require power flow into the load, dictating a situation where the converter groups rectify, the positive and negative groups conducting respectively during the appropriate positive and negative load-current periods. periods. The two periods, when the product of load voltage and current is positive, require power flow into the load, dictating a situation where the converter groups rectify, the positive and negative groups conducting respectively during the appropriate positive and negative load‐current periods.

Figure 11. General cycloconverter layout (a) Block diagram representation, (b) Ideal load waveforms **Figure 11.** General cycloconverter layout (a) Block diagram representation, (b) Ideal load waveforms [30]

group labeled P and the negative group for reverse current labeled N.

Figure 12. Single‐phase load fed from a three‐pulse cycloconverter [30]

The other two periods represent times when the product of load voltage and current is negative; hence, the power flow is out of the load, demanding that the converters operate in the inverting mode. As shown in Fig. 11a, the principle of the cycloconverter can be demonstrated by using the simplest possible single‐phase input to single‐phase output with a pure resistance as load. Each converter is a bi‐phase half‐wave connection, the positive The other two periods represent times when the product of load voltage and current is negative; hence, the power flow is out of the load, demanding that the converters operate in the inverting mode. As shown in Fig. 11a, the principle of the cycloconverter can be demon‐ strated by using the simplest possible single-phase input to single-phase output with a pure resistance as load. Each converter is a bi-phase half-wave connection, the positive group labeled P and the negative group for reverse current labeled N.

[Placeholder for fig. 1Please, do not alter]

The operation of the blocked group cycloconverter with various loads can be readily explained by reference to the three‐pulse connection shown in Fig. 12, with the associated waveforms for inductive load in Figs. 13 and 14. As known, the wound rotor induction motor is an inductive load. In this chapter, waveforms are drawn for inductive load.

Active and Reactive Power Control of Wound Rotor Induction Generators by Using the Computer and Driver http://dx.doi.org/10.5772/61130 65

**Figure 12.** Single-phase load fed from a three-pulse cycloconverter [30]

**3.2. Harmonic analysis**

64 Induction Motors - Applications, Control and Fault Diagnostics

analyzed theoretically.

*3.2.1. Principle of the cycloconverter*

negative load‐current periods.

[30]

For the power converter of this system, the cycloconverter which is suitable for a large capacity system is often used. Generally, when the large-scale converter is applied to the electric power network system, it is a very important item to analyze the harmonic currents of the power converter. As known, the harmonic currents of the power converter are transmitted to the electric power network system through the rotor and stator windings. In this chapter, the characteristics of the transmission of the harmonic currents caused by the cycloconverter are

Before beginning analysis, let us remember the basic principles of cycloconverter and mathe‐

As known, cycloconversion is concerned mostly with direct conversion of energy to a different frequency by synthesizing a low-frequency wave from appropriate sections of a higherfrequency source. As shown in Fig. 11a, a cycloconverter can be considered to be composed of two converters connected back-to-back. The load waveforms of Fig. 11b show that in the general case, the instantaneous power flows in the load fall into one of four periods. The two periods, when the product of load voltage and current is positive, require power flow into the load, dictating a situation where the converter groups rectify, the positive and negative groups conducting respectively during the appropriate positive and negative load-current periods.

periods. The two periods, when the product of load voltage and current is positive, require power flow into the load, dictating a situation where the converter groups rectify, the positive and negative groups conducting respectively during the appropriate positive and

matical background (taken from [30]) for the understanding of the subject.

(a) (b)

**Figure 11.** General cycloconverter layout (a) Block diagram representation, (b) Ideal load waveforms [30]

Figure 11. General cycloconverter layout (a) Block diagram representation, (b) Ideal load waveforms

The other two periods represent times when the product of load voltage and current is negative; hence, the power flow is out of the load, demanding that the converters operate in the inverting mode. As shown in Fig. 11a, the principle of the cycloconverter can be demon‐ strated by using the simplest possible single-phase input to single-phase output with a pure resistance as load. Each converter is a bi-phase half-wave connection, the positive group

demonstrated by using the simplest possible single‐phase input to single‐phase output with a pure resistance as load. Each converter is a bi‐phase half‐wave connection, the positive

[Placeholder for fig. 1Please, do not alter]

The operation of the blocked group cycloconverter with various loads can be readily explained by reference to the three‐pulse connection shown in Fig. 12, with the associated waveforms for inductive load in Figs. 13 and 14. As known, the wound rotor induction motor is an inductive load. In this chapter, waveforms are drawn for inductive load.

The other two periods represent times when the product of load voltage and current is negative; hence, the power flow is out of the load, demanding that the converters operate in

the inverting mode. As shown in Fig. 11a, the principle of the cycloconverter can be

group labeled P and the negative group for reverse current labeled N.

labeled P and the negative group for reverse current labeled N.

Figure 12. Single‐phase load fed from a three‐pulse cycloconverter [30]

The operation of the blocked group cycloconverter with various loads can be readily explained by reference to the three-pulse connection shown in Fig. 12, with the associated waveforms for inductive load in Figs. 13 and 14. As known, the wound rotor induction motor is an inductive load. In this chapter, waveforms are drawn for inductive load.

**Figure 13.** Waveforms with maximum voltage to an inductive load [30]

**Figure 14.** Waveforms when the load voltage is at half maximum (inductive load current continuous) [30]

bridge [30] The waveforms are as shown in Fig. 13 when the load is inductive, these being at a condition **Figure 15.** Cycloconverter connections with three-phase output. (a) Three-pulse bridge, (b) Six-pulse bridge [30]

Figure 15. Cycloconverter connections with three‐phase output. (a) Three‐pulse bridge, (b) Six‐pulse

of maximum voltage. The load current will lag the voltage and, as the load‐current direction determines which group is conducting, the group on‐periods are delayed relative to the desired output voltage. The group thyristors are fired at such angles to achieve an output as close as possible to a sinewave, but now the lagging load current takes each group The waveforms are as shown in Fig. 13 when the load is inductive, these being at a condition of maximum voltage. The load current will lag the voltage and, as the load-current direction determines which group is conducting, the group on-periods are delayed relative to the desired output voltage. The group thyristors are fired at such angles to achieve an output as close as possible to a sinewave, but now the lagging load current takes each group into the inverting mode. The group will cease conducting when the load current reverses. The loadvoltage waveform is shown as a smooth transfer between groups, but in practice, a short gap would be present to ensure cessation of current in, and the regaining of the blocking state in, the outgoing group, before the incoming group is fired. The waveforms drawn assume the current is continuous within each load half-cycle. The effects of overlap will in practice be present in the waveforms.

In practice, the load-current waveform in Fig. 13 is assumed to be sinusoidal, although it would contain a ripple somewhat smaller than that in the voltage waveform. A light load inductance would result in discontinuous current, giving short zero-voltage periods. Each thyristor will conduct the appropriate block of load current, having the branch currents shown. The current ia - ib would represent the transformer input line current if one assumed the supply to be via a delta primary transformer. The input-current waveform shows changes in shape from cycle to cycle but where the input and output frequencies are an exact multiple, the waveform will repeat over each period of output frequency.

**Figure 14.** Waveforms when the load voltage is at half maximum (inductive load current continuous) [30]

(a) (b)

bridge [30]

66 Induction Motors - Applications, Control and Fault Diagnostics

Figure 15. Cycloconverter connections with three‐phase output. (a) Three‐pulse bridge, (b) Six‐pulse

**Figure 15.** Cycloconverter connections with three-phase output. (a) Three-pulse bridge, (b) Six-pulse bridge [30]

The waveforms are as shown in Fig. 13 when the load is inductive, these being at a condition of maximum voltage. The load current will lag the voltage and, as the load‐current direction determines which group is conducting, the group on‐periods are delayed relative to the desired output voltage. The group thyristors are fired at such angles to achieve an output as close as possible to a sinewave, but now the lagging load current takes each group

The waveforms are as shown in Fig. 13 when the load is inductive, these being at a condition of maximum voltage. The load current will lag the voltage and, as the load-current direction determines which group is conducting, the group on-periods are delayed relative to the desired output voltage. The group thyristors are fired at such angles to achieve an output as close as possible to a sinewave, but now the lagging load current takes each group into the inverting mode. The group will cease conducting when the load current reverses. The loadvoltage waveform is shown as a smooth transfer between groups, but in practice, a short gap would be present to ensure cessation of current in, and the regaining of the blocking state in, the outgoing group, before the incoming group is fired. The waveforms drawn assume the

As shown in Fig. 14, a reduction in the output voltage can be obtained by firing angle delay. Here firing is delayed, even at the peak of the output voltage, so that control is possible over the magnitude of the output voltage. Comparison of Fig. 14 with Fig. 13 indicates a higher ripple content when the output voltage is reduced.

As shown in Fig. 15a, the three-pulse cycloconverter when feeding a three-phase load can be connected with a total of 18 thyristors. As shown in Fig. 15b, a six-pulse cycloconverter can be based on either six-phase half-wave blocks or the bridge connection when 36 thyristors are required.

**Figure 16.** Cycloconverter load-voltage waveform with a lagging power factor load (six-pulse connection) [30]

An example of the cycloconverter output waveforms for the higher-pulse connections is given in Fig. 16, with an output frequency of one-third of the input frequency. It is clear from these waveforms that the higher the pulse-number, the closer is the output waveform to the desired sinusoidal waveform. In general, the output frequency is in general limited to about one-half to one-third of the input frequency, the higher-pulse connections permitting a higher limit.

As in Fig. 15, when the three-pulse cycloconverter feeds a three-phase balanced load, the current loading on the supply is much more evenly balanced. The waveforms to illustrate this are given in Fig. 17 for a frequency ratio of 4/1 with a load of 0.707 power factor lagging. It has been assumed that the load current is sinusoidal, although in practice it must contain ripple. The total load current is not identical from one cycle to the next, obviously contains harmonics, and its fundamental component lags the supply voltage by a larger amount than the load power factor angle.

**Figure 17.** Development of total input current to three-pulse cycloconverter with three-phase lagging power factor load [30]

The thyristors of a cycloconverter are commutated naturally, and whether the load is resistive, inductive, or capacitive, the firing of the thyristors must be delayed to shape the output. The net result is that the AC supply input current will always lag its associated voltage.

### *3.2.2. Circulating current mode*

The previous section specified cycloconverter operation where either the positive or negative groups were conducting, but never together. As shown in Fig. 18, if a center-tapped reactor is connected between the positive group P and negative group N, then both groups can be permitted to conduct. The reactor will limit the circulating current, that is, the value of its inductance to the flow of load current from either group being one quarter of its value to the circulating current, because inductance is proportional to the square of the number of turns.

In Fig. 19, typical waveforms are shown for the three-pulse cycloconverter shown in Fig. 18. Each group conducts continuously, with rectifying and inverting modes as shown. The mean between the two groups will be fed to the load, some of the ripple being cancelled in the combination of the two groups. Both groups synthesize the same fundamental sinewave. The reactor voltage is the instantaneous difference between the two group voltages. The circulating current shown in Fig. 19 can only flow in one direction, the thyristors preventing reverse flow. Hence, the current will build up during the reactor voltage positive periods until in the steady state it is continuous, rising and falling as shown.

**Figure 18.** Three-pulse cycloconverter with intergroup reactor [30]

### *3.2.3. Mathematical analysis*

been assumed that the load current is sinusoidal, although in practice it must contain ripple. The total load current is not identical from one cycle to the next, obviously contains harmonics, and its fundamental component lags the supply voltage by a larger amount than the load

**Figure 17.** Development of total input current to three-pulse cycloconverter with three-phase lagging power factor

The thyristors of a cycloconverter are commutated naturally, and whether the load is resistive, inductive, or capacitive, the firing of the thyristors must be delayed to shape the output. The

The previous section specified cycloconverter operation where either the positive or negative groups were conducting, but never together. As shown in Fig. 18, if a center-tapped reactor is connected between the positive group P and negative group N, then both groups can be

net result is that the AC supply input current will always lag its associated voltage.

power factor angle.

68 Induction Motors - Applications, Control and Fault Diagnostics

load [30]

*3.2.2. Circulating current mode*

The above subjects have demonstrated that almost all the waveforms associated with power electronic equipment are non-sinusoidal, which contains harmonic components. The purpose of this subject is to analyze the harmonic content of the various waveforms and discuss their effects as regards both supply and load.

Any periodic waveform may be shown to be composed of the superposition of a direct component with a fundamental pure sinewave component, together with pure sinewaves known as harmonics at frequencies which are integral multiples of the fundamental. A nonsinusoidal wave is often referred to as a complex wave [30].

Mathematically, it is more convenient to express the independent variable as x and the dependent variable as y. Then, the series may be expressed as:

$$y = f\left(\mathbf{x}\right) = a\_0 + a\_1 \cos\left(\mathbf{x}\right) + a\_2 \cos\left(2\mathbf{x}\right) + \dots + a\_n \cos(n\mathbf{x}) + b\_1 \sin(\mathbf{x}) + b\_2 \sin(2\mathbf{x}) + \dots + b\_n \sin\left(n\mathbf{x}\right) \tag{45}$$

**Figure 19.** Waveform of a three-pulse cycloconverter with circulating current but without load [30]

Equation (45) is known as a Fourier series, and where f(x) can be expressed mathematically, a Fourier analysis yields that the coefficients are [31]:

$$a\_0 = \frac{1}{2\pi} \int\_{-\pi}^{\pi} f(\mathbf{x}) d\mathbf{x} \tag{46}$$

$$a\_n = \frac{1}{\pi} \int\_{-\pi}^{\pi} f(\mathbf{x}) \cos nx \mathbf{x} d\mathbf{x} \tag{47}$$

$$b\_n = \frac{1}{\pi} \int\_{-\pi}^{\pi} f(\mathbf{x}) \sin nx dx \tag{48}$$

Alternatively, the series may be expressed as:

$$y = f\left(\mathbf{x}\right) = \mathbf{R}\_0 + \mathbf{R}\_1 \sin\left(\mathbf{x} - \phi\_1\right) + \mathbf{R}\_2 \sin\left(2\mathbf{x} - \phi\_2\right) + \mathbf{R}\_3 \sin\left(3\mathbf{x} - \phi\_3\right) + \dots + \mathbf{R}\_n \sin\left(n\mathbf{x} - \phi\_n\right)\tag{49}$$

Equations (49) and (45) are equivalent, with:

Active and Reactive Power Control of Wound Rotor Induction Generators by Using the Computer and Driver http://dx.doi.org/10.5772/61130 71

$$a\_n \cos n\mathbf{x} + b\_n \sin n\mathbf{x} = R\_n \sin \left(n\mathbf{x} - \phi\_n\right) \tag{50}$$

From which the resultant and phase angle:

$$R\_u = \left(a\_u^2 + b\_u^2\right)^{1/2} \tag{51}$$

$$\phi\_n = \arctan \frac{a\_n}{b\_n} \tag{52}$$

Electrically, it expresses the independent variable as ωt instead of x and the dependent variable as volts or amperes instead of y. Then, the series may be expressed as:

$$\nabla \cdot \mathbf{v} = V\_0 + V\_1 \sin \left( \alpha t - \phi\_1 \right) + V\_2 \sin \left( 2 \alpha t - \phi\_2 \right) + V\_3 \sin \left( 3 \alpha t - \phi\_3 \right) + \dots + V\_n \sin \left( n \alpha t - \phi\_n \right) \tag{53}$$

where

Equation (45) is known as a Fourier series, and where f(x) can be expressed mathematically, a

<sup>=</sup> ò (46)

<sup>=</sup> ò (47)

<sup>=</sup> ò (48)

sin 2 sin 3 ... sin *n n* ( ) (49)

 f

<sup>0</sup> ( ) <sup>1</sup> <sup>2</sup> *a f x dx* p

**Figure 19.** Waveform of a three-pulse cycloconverter with circulating current but without load [30]

( ) <sup>1</sup> cos *<sup>n</sup> a f x nxdx* p

( ) <sup>1</sup> sin *<sup>n</sup> b f x nxdx* p

p p-

p p-

*y f x R R x R x R x R nx* = = + - + - + - ++ - ( ) 01 1 2 2 3 3 sin() ( ) ( ) fff

p p-

Fourier analysis yields that the coefficients are [31]:

70 Induction Motors - Applications, Control and Fault Diagnostics

Alternatively, the series may be expressed as:

Equations (49) and (45) are equivalent, with:

v is the instantaneous value of the voltage at any time t;

Vo is the direct (or mean) value of the voltage;

V1 is the maximum value of the fundamental component of the voltage;

V2 is the maximum value of the second harmonic component of the voltage;

V3 is the maximum value of the third harmonic component of the voltage;

Vn is the maximum value of the nth harmonic component of the voltage;

ϕ defines the relative angular reference; and

ω = 2πf, where f is the frequency of the fundamental component, 1/f

defining the time over which the complex wave repeats itself.

The constant term of Equation (46) is the mean value of the function, and is the value found in, for example, the calculation of the direct (mean) voltage output of a rectifier. In the analysis of a complex wave, certain statements and simplifications are possible by inspection of any given waveform. If the areas of the positive and negative half-cycles are equal, then a0 is zero. If f(x + π) = - f(x), then there are no even harmonics, that is, no second, fourth, etc. In plain terms, this means the negative half-cycle is a reflection of the positive half-cycle. If f(- x) = f(x), then an= 0; that is, there are no sine terms. If f(- x) = f(x), then bn= 0; that is, there are no cosine terms. Symmetry of the waveform can result in Equations (47) and (48) being taken as twice the value of the integral from 0 to π, or four times the value of the integral from 0 to π / 2, hence simplifying the analysis.

Where it is difficult to put a mathematical expression to f(x), or where an analysis of an experimental or practical waveform obtained from a piece of equipment is required, graphical analysis can be performed [30].

The conditions of analysis are as follows.


Using these conditions, the three-phase rotor current can be defined as follows:

$$I\_{a2} = \sum\_{m} \sum\_{n} \frac{A\_{\left(\delta n - 1\right)n} \operatorname{Sim}\left\{6m\theta\_{1} - \left(6n - 1\right)\theta\_{s}\right\} + A\_{\left(\delta n - 5\right)n} \operatorname{Sim}\left\{6m\theta\_{1} - \left(6n - 5\right)\theta\_{s}\right\}}{\left\{6m\theta\_{1} - \left(6n - 1\right)\theta\_{s}\right\} + B\_{\left(\delta n - 5\right)n} \operatorname{Sim}\left\{6m\theta\_{1} - \left(6n - 5\right)\theta\_{s}\right\}}\tag{54}$$

$$\begin{aligned} A\_{(\kappa n - 1)w} \operatorname{Sim} \left\{ \left. \left\{ \mathfrak{Im} \theta\_1 - \left( \mathfrak{Im} - 1 \right) \left( \theta\_s - \frac{2 \pi}{3} \right) \right\} \right| \\\ I\_{b2} = \sum\_m \sum\_n & + B\_{(\kappa n - 3)w} \operatorname{Sim} \left\{ \left. \mathfrak{Im} \theta\_1 - \left( \mathfrak{Im} - 5 \right) \left( \theta\_s - \frac{2 \pi}{3} \right) \right\} \right| \\\ I\_{b2} = \sum\_m \sum\_n & + B\_{(\kappa n - 1)w} \operatorname{Sim} \left\{ \left. \mathfrak{Im} \theta\_1 - \left( \mathfrak{Im} - 1 \right) \left( \theta\_s - \frac{2 \pi}{3} \right) \right\} \right| \\\ & + B\_{(\kappa n - 3)w} \operatorname{Sim} \left\{ \left. \mathfrak{Im} \theta\_1 - \left( \mathfrak{Im} - 5 \right) \left( \theta\_s - \frac{2 \pi}{3} \right) \right\} \right| \end{aligned} \tag{55}$$

$$\begin{aligned} A\_{(\delta n - 1)w} \operatorname{Sim} \left\{ \left. \left\{ \mathfrak{Im} \theta\_1 - \left( \delta n - 1 \right) \left( \theta\_s + \frac{2 \pi}{3} \right) \right\} \right| \\\ I\_{c2} = \sum\_{m} \sum\_{n} & + B\_{(\delta n - 3)w} \operatorname{Sim} \left\{ \left. \mathfrak{Im} \theta\_1 - \left( \delta n - 5 \right) \theta\_s + \frac{2 \pi}{3} \right\} \right\} \\\ I\_{c2} = \sum\_{m} \sum\_{n} & + B\_{(\delta n - 1)w} \operatorname{Sim} \left\{ \left. \mathfrak{Im} \theta\_1 - \left( \delta n - 1 \right) \left( \theta\_s + \frac{2 \pi}{3} \right) \right\} \right| \\\ & + B\_{(\delta n - 5)w} \operatorname{Sim} \left\{ \left. \mathfrak{Im} \theta\_1 - \left( \delta n - 5 \right) \theta\_s + \frac{2 \pi}{3} \right\} \right\} \end{aligned} \tag{56}$$

where m=1,2,....., n=1,2,......, θ<sup>l</sup> =ω<sup>l</sup> t: ω<sup>l</sup> is the stator angular speed, θs=ωst: ωs is the slip angular speed.

Where it is difficult to put a mathematical expression to f(x), or where an analysis of an experimental or practical waveform obtained from a piece of equipment is required, graphical

**1.** The frequency of the harmonic current for the three-pulse and six-pulse cycloconverter is 6mfl ± (2n + 1)fs, where m is any integer from 1 to infinity, n is any integer from 0 to infinity, fl is the frequency of the power source, and fs is the output frequency of the cycloconverter

( ) { ( ) } ( ) { ( ) }

*n m s s n m*

6 61 6 65


<sup>+</sup> -- + - - åå (54)

3

p

3

p

p

3

3

3

p

3

p

p

3

3

p

p

qq

qq

6 61 6 65

<sup>2</sup> 6 61

ì ü ï ï æ ö í ý -- - ç ÷ ï ï î þ è ø

 q

> q

åå (55)

 q

> q

 q

> q

åå (56)

 q

> q

<sup>2</sup> 6 65

ì ü ï ï æ ö

<sup>2</sup> 6 61

<sup>2</sup> 6 65

<sup>2</sup> 6 61

ì ü ï ï æ ö í ý -- + ç ÷ ï ï î þ è ø

<sup>2</sup> 6 65

ì ü ï ï æ ö

<sup>2</sup> 6 61

<sup>2</sup> 6 65

ì ü ï ï æ ö

ì ü ï ï æ ö

( ) { ( ) } ( ) { ( ) }

**3.** Zero-phase-sequence current (harmonic currents of multiple of 3) is neglected.

**2.** The analysis is carried out only on the harmonic components.

**4.** The stator is connected to the fundamental frequency voltage source.

Using these conditions, the three-phase rotor current can be defined as follows:

qq


qq


6 1 1









*A Sin m n*

6 5 1

*A Sin m n*

*B Sin m n*

*B Sin m n*

6 1 1

6 5 1

6 1 1

*A Sin m n*

6 5 1

*A Sin m n*

*B Sin m n*

*B Sin m n*

6 1 1

6 5 1

6 1 1 1 6 5

6 1 1 1 6 5

( ) ( )

*n m s*

q

*n m s*

q

*n m s*

<sup>+</sup> í ý -- - ç ÷ ï ï î þ è ø

<sup>+</sup> í ý -- - ç ÷ ï ï î þ è ø

q

*n m s*

q

( ) ( )

<sup>+</sup> í ý -- - ç ÷ ï ï î þ è ø <sup>=</sup> ì ü ï ï æ ö

( ) ( )

( ) ( )

( ) ( )

*n m s*

q

*n m s*

q

*n m s*

<sup>+</sup> í ý -- + ç ÷ ï ï î þ è ø

<sup>+</sup> í ý -- + ç ÷ ï ï î þ è ø

q

*n m s*

q

( ) ( )

<sup>+</sup> í ý -- + ç ÷ ï ï î þ è ø <sup>=</sup> ì ü ï ï æ ö

( ) ( )

( ) ( )

*m n n m s s n m*

*B Sin m n B Sin m n*

*A Sin m n A Sin m n*

analysis can be performed [30].

[32].

2

=

2

2

*m n*

*c*

*I*

*m n*

*b*

*I*

*a*

*I*

The conditions of analysis are as follows.

72 Induction Motors - Applications, Control and Fault Diagnostics

When Equations (54)–(56) are transformed to the d-q axis based on the stator voltage, (57) and (58) are derived:

$$A\_{\left(\delta n - 1\right)m} \operatorname{Sim}\left\{\left\{m\theta\_1 - \delta n\theta\_s\right\}\right\}$$

$$I\_{d2} = \sum\_m \sum\_n + A\_{\left(\delta n - 5\right)m} \operatorname{Sim}\left\{\left\{mn\theta\_1 - \left(\delta n - 1\right)\theta\_s\right\}\right\}$$

$$+ B\_{\left(\delta n - 1\right)m} \operatorname{Sim}\left\{\left\{mn\theta\_1 + \delta n\theta\_s\right\}\right\}$$

$$+ B\_{\left(\delta n - 3\right)m} \operatorname{Sim}\left\{\left\{mn\theta\_1 + \left(\delta n - 1\right)\theta\_s\right\}\right\}$$

$$\begin{aligned} A\_{\left(\mathfrak{s}n-1\right)w} \mathbb{C} \cos\left\{6m\theta\_1 - 6n\theta\_s\right\} \\\ I\_{q2} = \sum\_{m} & + A\_{\left(\mathfrak{s}n-5\right)w} \mathbb{C} \cos\left\{6m\theta\_1 - \left(6n-1\right)\theta\_s\right\} \\\ I\_{q\left\{4n-1\right\}w} & + B\_{\left(\mathfrak{s}n-1\right)w} \mathbb{C} \cos\left\{6m\theta\_1 + 6n\theta\_s\right\} \\\ & + B\_{\left(\mathfrak{s}n-5\right)w} \mathbb{C} \cos\left\{6m\theta\_1 + \left(6n-1\right)\theta\_s\right\} \end{aligned} \tag{58}$$

The characteristics of transmission from the rotor winding to the stator winding are analyzed by substituting into the fundamental equation of a wound rotor induction machine. The analysis uses the symmetrical coordinate method for simplification. In this case, positive phase sequence component value (F component value) and negative phase sequence component value (B component value) have a conjugate relationship. The F component value is used for the analysis in this paper, which gives the following fundamental equation of the wound rotor induction machine:

$$
\begin{bmatrix} V\_{F1} \\ V\_{F2} \end{bmatrix} = \begin{bmatrix} R\_1 + \left( p + jo\_1 \right) \left( L\_1 + L\_m \right) & \left( p + jo\_1 \right) L\_m \\ \left( p + jo\_0 \right) L\_m & R\_2 + \left( p + jo\_0 \right) \left( L\_2 + L\_m \right) \end{bmatrix} \begin{bmatrix} I\_{r1} \\ I\_{r2} \end{bmatrix} \tag{59}
$$

When Equation (59) is transformed relative to IF1, the following equation is obtained:

$$I\_{F1} = \frac{\left(p + jo\_1\right)L\_m}{R\_1 + \left(p + jo\_1\right)\left(L\_1 + L\_m\right)} I\_{F2} + V\_{F1} \tag{60}$$

In this analysis, stator voltage is the fundamental voltage source, then, VF1 = 0 is defined. When IF1 is expressed by Id2 and Iq2, using Equation (60) and IF2 = (1/√2)(Id2 + jIq2), the following expression is derived:

$$I\_{F1} = \frac{\left(p + jo\_1\right)L\_m}{R\_1 + \left(p + jo\_1\right)\left(L\_1 + L\_m\right)}\frac{1}{\sqrt{2}}\left(I\_{d2} + jI\_{q2}\right) \tag{61}$$

Equation (59) is substituted into Equations (57) and (58). Applying Laplace transformation, the stator current is calculated. A-phase stator current is derived as follows:

$$\mathbb{C}\_{\left(\delta n-1\right)m} \mathbb{C} \cos\left\{ \left( \left( \delta m + 1 \right) \theta\_1 - \delta n \theta\_s \right\} \right. $$

$$I\_{\omega 1} = \sum\_{m} \sum\_{n} \frac{+\mathbb{C}\_{\left(\delta n-3\right)m} \mathbb{C} \cos\left\{ \left( \left( \delta m - 1 \right) \theta\_1 - \left( \delta n - 1 \right) \theta\_s \right\} \right.}{+D\_{\left(\delta n-1\right)m} \mathbb{C} \cos\left\{ \left( \left( \delta m - 1 \right) \theta\_1 + \delta n \theta\_s \right) \right\}} \tag{62}$$

$$+D\_{\left(\delta n - 3\right)m} \mathbb{C} \cos\left\{ \left( \delta m + 1 \right) \theta\_1 + \left( \delta n - 1 \right) \theta\_s \right\}$$

where

$$\begin{split} \mathbf{C}\_{\left(\epsilon u - 1\right)m} &\approx A\_{\left(\epsilon u - 1\right)m} \left( \frac{L\_{m}}{\left(L\_{m} + L\_{1}\right)} \right) , D\_{\left(\epsilon u - 1\right)m} \approx B\_{\left(\epsilon u - 1\right)m} \left( \frac{L\_{m}}{\left(L\_{m} + L\_{1}\right)} \right) \\ \mathbf{C}\_{\left(\epsilon u - 5\right)m} &\approx A\_{\left(\epsilon u - 5\right)m} \left( \frac{L\_{m}}{\left(L\_{m} + L\_{1}\right)} \right) , D\_{\left(\epsilon u - 5\right)m} \approx B\_{\left(\epsilon u - 5\right)m} \left( \frac{L\_{m}}{\left(L\_{m} + L\_{1}\right)} \right) . \end{split}$$

The results of this analysis show that the harmonic currents fed to the rotors winding are transmitted to the stator windings by changing its frequency. The rotor harmonic currents at 6mω1±(6n - 5)ωs change to stator harmonic currents at (6m±1)ω1±6(n - 1)ωs. And the rotor harmonic currents at 6mω1±(6n - 1)ωs change to stator harmonic currents at (6m±1)ω1±6nωs. This is the effect of the rotating speed of the wound rotor induction generator. Moreover, the ratio between the amplitude of harmonic currents in the rotor and the stator is nearly 1:1.

Analysis results are verified by the experimental system shown in Fig. 6. Table 2 gives an example of experimental results. It is seen that experimental values well match with the theoretical ones. Thus, experiments confirmed that the analysis gives reliable results.


**Table 2.** Experimental results (ω1=50 Hz, ωs=50 Hz, m=1, N= 1400 r/min, I1=I2=25 A) [25]

It has been proved by experiment that this control system can control the active and reactive power independently and stably. In addition, it has been confirmed by analysis and experi‐ ment that the harmonic currents fed to the rotor windings of the generator are transmitted to the stator windings changing its frequency [25].

### **3.3. Proposed experimental setup**

( )

+

w

the stator current is calculated. A-phase stator current is derived as follows:





1

74 Induction Motors - Applications, Control and Fault Diagnostics

=

*a*

*I*

where

1 11

( )( ) ( ) <sup>1</sup> 1 2 2

*m*

Equation (59) is substituted into Equations (57) and (58). Applying Laplace transformation,

6 1 1

*C Cos m n*

+ -+

+ - --

*C Cos m n*

6 1 1

*D Cos m n*

+ + +-

() () ( ) () () ( )

,

61 61 61 61


*nm nm nm nm*

*L L CA DB*

*L L CA DB*

65 65 65 65


*nm nm nm nm*

() () ( ) () () ( )

The results of this analysis show that the harmonic currents fed to the rotors winding are transmitted to the stator windings by changing its frequency. The rotor harmonic currents at 6mω1±(6n - 5)ωs change to stator harmonic currents at (6m±1)ω1±6(n - 1)ωs. And the rotor harmonic currents at 6mω1±(6n - 1)ωs change to stator harmonic currents at (6m±1)ω1±6nωs. This is the effect of the rotating speed of the wound rotor induction generator. Moreover, the ratio between the amplitude of harmonic currents in the rotor and the stator is nearly 1:1.

Analysis results are verified by the experimental system shown in Fig. 6. Table 2 gives an example of experimental results. It is seen that experimental values well match with the

theoretical ones. Thus, experiments confirmed that the analysis gives reliable results.

**Frequency Experimental Value Frequency Experimental Value Theoretical Value**

296.7 Hz 3.18 A 250 Hz 2.99 A 3.12 A 303.3 Hz 1.65 A 350 Hz 1.53 A 1.61 A 293.3 Hz 0.43 A 340 Hz 0.46 A 0.42 A 316.7 Hz 0.40 A 260 Hz 0.36 A 0.39 A

**Table 2.** Experimental results (ω1=50 Hz, ωs=50 Hz, m=1, N= 1400 r/min, I1=I2=25 A) [25]

**Rotor Harmonic Current Stator Harmonic Current**

,

*D Cos m n*

6 5 1

6 5 1

*m n n m <sup>s</sup>*

( ) {( ) }

*n m s*

61 6

q

+ -

 q

> q

åå (62)

1 1

*m m*

*L L L L*

+ + èø èø

*m m*

*L L L L*

+ + èø èø

*m m*

*m m*

1 1

 q

> q

6 1 61

q

61 6

q

6 1 61

q

( ) {( )( ) }

*n m s*

( ) {( ) }

( ) {( )( ) }

*n m s*

æö æö » » ç÷ ç÷

æö æö » » ç÷ ç÷

*m F d q*

*pj L <sup>I</sup> I jI R pj L L* w

= + ++ +

1 2

(61)

By using the computer and driver/buffer, the experimental setups to control active and reactive power of the wound rotor induction generator independently and stably are shown in Figs. 20 and 21 [28]. The terminals in experimental setups shown in Figs. 20 and 21 are numbered considering that the three-pulse cycloconverter with a total of 18 thyristors shown in Fig. 15a will be used.

**Figure 20.** Schematic block diagram of the experimental setup for computer-aided power control of wound rotor in‐ duction generator

**Figure 21.** Another schematic block diagram of the experimental setup for computer-aided power control of wound rotor induction generator

### **4. Conclusion**

New configurations for power control system of the doubly-fed wound rotor induction generator have been proposed. These configurations are based on a control method using a rotating reference frame fixed on the air-gap flux of the generator. By using them, the active and reactive power of generator can be controlled independently and stably. To achieve this purpose, power and current control that are fundamental subjects have been analyzed and as a result, a computer-aided circuit is given to achieve the power and current control. Using computers enables application of new technologies for easier control. For example, any new metaheuristic techniques or classification/identification techniques could be applied by just changing the code in the computer.

### **Author details**

Fevzi Kentli\*

Address all correspondence to: fkentli@marmara.edu.tr

Marmara University- Faculty of Technology – Department of Mechatronics Engineering Kadıköy-Istanbul, Turkey

### **References**


[6] Nakra H L, Dube B. Slip power recovery induction generators for large vertical axis wind turbines. *IEEE Transact Energy Convers*. 1988;3(4):733-737. DOI: 10.1109/60.9346

**4. Conclusion**

**Author details**

Kadıköy-Istanbul, Turkey

Fevzi Kentli\*

**References**

552.

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cessed: March 2015]

10.1109/TIE.2010.2103910

2001;16(3):390-399. DOI: 10.1109/63.923772

changing the code in the computer.

76 Induction Motors - Applications, Control and Fault Diagnostics

Address all correspondence to: fkentli@marmara.edu.tr

New configurations for power control system of the doubly-fed wound rotor induction generator have been proposed. These configurations are based on a control method using a rotating reference frame fixed on the air-gap flux of the generator. By using them, the active and reactive power of generator can be controlled independently and stably. To achieve this purpose, power and current control that are fundamental subjects have been analyzed and as a result, a computer-aided circuit is given to achieve the power and current control. Using computers enables application of new technologies for easier control. For example, any new metaheuristic techniques or classification/identification techniques could be applied by just

Marmara University- Faculty of Technology – Department of Mechatronics Engineering

[1] Boldea I. *The Electric Generators Handbook*. Florida, USA: Taylor & Francis; 2006. p.

[2] Induction Generator [Internet]. [Updated: March 2015]. Available from: http:// www.alternative-energy-tutorials.com/wind-energy/induction-generator.html [Ac‐

[3] Nidec Motor Corporation. Induction Generator [Internet]. Available from: http:// www.usmotors.com/TechDocs/ProFacts/Induction-Generator.aspx [Accessed: March

[4] Liserre M, Cárdenas R, Molinas M, Rodríguez J. Overview of multi-MW wind tur‐ bines and wind parks. *IEEE Transact Indus Electron*. 2011;58(4):1081-1095. DOI:

[5] Datta R, Ranganathan V T. Direct power control of grid-connected wound rotor in‐ duction machine without rotor position sensors. *IEEE Transact Power Electron*.


[29] Akagi H, Kanazawa Y, Nabae A. Instantaneous reactive power compensators com‐ prising switching devices without energy storage components. *IEEE Transact Indust Applic*. 1984;20(3):625-630. DOI: 10.1109/TIA.1984.4504460

[18] Fadaeinedjad R, Moallem M, Moschopoulos G. Simulation of a wind turbine with doubly fed induction generator by fast and simulink. *IEEE Transact Energy Conver*.

[19] Zin A A B M, Pesaran H A M, Khairuddin A B, Jahanshaloo L, Shariati O. An over‐ view on doubly fed induction generators' controls and contributions to wind based electricity generation. *Renew Sustain Energy Rev*. 2013;27:692–708. DOI: doi:10.1016/

[20] Xu L, Cheng W. Torque and reactive power control of a doubly fed induction ma‐ chine by position sensorless scheme. *IEEE Transact Indust Applic*. 1995;31(3):636 - 642.

[21] Datta R, Ranganathan V T. Decoupled control of active and reactive power for a gridconnected doubly-fed wound rotor induction machine without rotor position sen‐ sors. In: IEEE Industry Applications Conference: Thirty-Fourth Ias Annual Meeting;

[22] Morel L, Godfroid H, Mirzaian A, Kauffmann J M. Double-fed induction machine: Converter optimisation and field oriented control without position sensor. *IEE Proc*

[23] Bogalecka E. Power control of a double fed induction generator without speed or po‐ sition sensor. In: Fifth European Conference on Power Electronics and Applications; 13-16 September 1993; Brighton, England. London, England: Institution of Electrical

[24] Leonhard W. *Control of Electrical Drives*. 1st edn. New York, USA: Springer-Verlag;

[25] Yamamoto M, Motoyoshi O. Active and reactive power control for doubly-fed wound rotor induction generator. *IEEE Transact Power Electron*. 1991;6(4):624-629.

[26] Brune C, Spee R, Wallace A K. Experimental evaluation of a variable-speed, doublyfed wind-power generation system. In: IEEE Industry Applications Conference: 28th IAS annual meeting; 2-8 October 1993; Ontario, Canada. New Jersey, USA: Institute

[27] Bhowmik S, Spee R, Enslin J H L. Performance optimization for doubly-fed wind power generation systems. In: Cramer, Don et al. (eds.). Industry Applications Con‐ ference, The 1998 IEEE Conference; 12-15 October 1998; Missouri, USA. New York, USA: The Institute of Electrical and Electronic Engineers, Inc; 1998. p. 2387-2394. [28] Kentli F. Computer aided power control for wound rotor induction generator. *Ozean*

2008;23(2):690-700. DOI: 10.1109/TEC.2007.914307

3-7 October 1999; Arizona, USA. IEEE; 1999. p. 2623-2630.

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78 Induction Motors - Applications, Control and Fault Diagnostics

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## **Analysis and Methodology for Determining the Parasitic Capacitances in VSI-fed IM Drives Based on PWM Technique**

## Rudolf Ribeiro Riehl, Fernando de Souza Campos, Alceu Ferreira Alves and Ernesto Ruppert Filho

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61544

### **Abstract**

Three-phase induction motors present stray capacitances. The aim of this chapter is to present a methodology to experimentally determine these capacitances and also evaluate the effects of electromagnetic interference on motors in common mode. The proposed procedures for this methodology consist of: a) identifying the motor equivalent electrical circuit parameters through characteristic tests performed in the laboratory; b) setting up configurations between the PWM inverter and the motor for voltage and current meas‐ urements: common mode and shaft voltages, leakage and shaft (bearing) currents by us‐ ing a dedicated measuring circuit; c) calculating the parasitic capacitance values between stator and frame, stator and rotor, rotor and frame and bearings of the motor using the capacitance characteristic equation; d) using the dedicated software Pspice to simulate the system composed by the three-phase induction motor fed by PWM inverter with the equivalent electrical circuit parameters; e) determining the characteristic waveforms in‐ volved in the common mode phenomenon.

**Keywords:** Induction motors, parasitic capacitances, PWM inverter

### **1. Introduction**

The use of inverter controlled by pulse width modulation (PWM Inverter), on drive and control of the three-phase induction motors is increasingly common, especially for the power range of up to 10 Hp.

The recent developments in power semiconductor devices (IGBT, MOSFET, and others) have allowed these drives to achieve switching frequencies up to 20 kHz. In these frequencies, the

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

rise time of PWM voltage becomes very small and responsible for the appearance of phenom‐ ena, defined as electromagnetic interference (EMI) in the induction motor [12, 18, 25]. Due to the presence of parasitic capacitances in the motor caused by the free or isolated spaces between metal parts, capacitive couplings occur, which become flow paths of the high-frequency electric current between the motor phases (differential mode coupling) and between phases and the ground (common mode coupling). The higher the switching frequency, the greater are the extensions and consequences of these phenomena.

The differential mode phenomena are responsible for excessive heating of the motor, harming the electrical insulation characteristics, performance, and, consequently, their useful life, and can burn out the motor. This occurs because the PWM inverter does not feed the induction motor with a sinusoidal voltage, but by applying modulated or switched pulses, producing high-frequency harmonics, and high-voltage gradients values (high dV/dt) to the stator windings [3].

The phenomena due to the common mode are responsible for the appearance of circulating currents between motor and ground moving through the frame, bearings, and motor pedestals. As the common mode voltage is different from zero, it raises a shaft voltage between the bearing parts and the ground, which is dependent on both this common mode voltage and the parasitic capacitances that can circulate electric currents capacitive for multiple paths by the motor [10]. One of these paths passes through the bearings, and in this case the motor currents are known as bearing currents, which, due to discharges occurring at the dielectric break, can cause damages at their bearings and if the shaft locks, the motor would be forced to stop and it will cause burning of the windings. Another phenomenon that occurs is electric shock or electric discharge machining (EDM), due to the flow of leakage current motor to the frame when it is not grounded or this ground is not suitable [1, 4, 7].

The conventional method to determine these parasitic capacitances is by measuring the impedance of the induction motor using LCR Bridge [1 to 10]. In this method, the induction motor is disassembled for specific parameters to be measured. For the determination of the parameters between the stator and the motor frame, the rotor is removed and measurements are conducted with each phase bridge between the LCR and the frame and among the three phases (short-circuited in this case) and the frame. After that, the rotor is put back and its axis is short-circuited to the frame. Parameter values between stator and rotor are measured. The LCR Bridge is connected at the common point of the three phases (neutral) and the stator frame.

The parameters of the motor bearings are dynamic and depend on operating conditions (speed) of the three-phase induction motor and also the dielectric characteristics of resistivity of the lubricant temperature and the geometric construction of the motor [1 to 10]. The rotor parameters can only be determined after all previous parameters have been obtained. The LCR Bridge is connected between the rotor shaft and the frame of the induction motor.

In the absence of an LCR Bridge and an appropriate laboratory for this type of test, another methodology [40, 41] is used to determine the parameters of the equivalent circuit of the induction motor in steady state (nominal frequency) [26, 27] and for high frequency [1, 10, 14, 41], through laboratory measurements using features configurations of links between the PWM inverter and the motor for measuring the following parameters of interest: common mode voltage (VCM) and shaft voltage (VSHAFT); leakage (ILEAKAGE) and bearing (IB) currents, by measurement circuit designed for this purpose; and calculation of the values of the parasitic capacitances between the stator and motor frame (CSF), stator and rotor (CSR), rotor and motor frame (CRF) and bearings (CB) using characteristic equations as will be shown in this chapter. The computer application PSPICE [36, 40] is used to simulate the three-phase induction motor powered by a PWM inverter system using the high-frequency equivalent circuit of the motor. The characteristic waveforms that represent the common mode phenomena will be obtained to allow comparisons for validation of procedures to determine the capacitance.

rise time of PWM voltage becomes very small and responsible for the appearance of phenom‐ ena, defined as electromagnetic interference (EMI) in the induction motor [12, 18, 25]. Due to the presence of parasitic capacitances in the motor caused by the free or isolated spaces between metal parts, capacitive couplings occur, which become flow paths of the high-frequency electric current between the motor phases (differential mode coupling) and between phases and the ground (common mode coupling). The higher the switching frequency, the greater are

The differential mode phenomena are responsible for excessive heating of the motor, harming the electrical insulation characteristics, performance, and, consequently, their useful life, and can burn out the motor. This occurs because the PWM inverter does not feed the induction motor with a sinusoidal voltage, but by applying modulated or switched pulses, producing high-frequency harmonics, and high-voltage gradients values (high dV/dt) to the stator

The phenomena due to the common mode are responsible for the appearance of circulating currents between motor and ground moving through the frame, bearings, and motor pedestals. As the common mode voltage is different from zero, it raises a shaft voltage between the bearing parts and the ground, which is dependent on both this common mode voltage and the parasitic capacitances that can circulate electric currents capacitive for multiple paths by the motor [10]. One of these paths passes through the bearings, and in this case the motor currents are known as bearing currents, which, due to discharges occurring at the dielectric break, can cause damages at their bearings and if the shaft locks, the motor would be forced to stop and it will cause burning of the windings. Another phenomenon that occurs is electric shock or electric discharge machining (EDM), due to the flow of leakage current motor to the frame

The conventional method to determine these parasitic capacitances is by measuring the impedance of the induction motor using LCR Bridge [1 to 10]. In this method, the induction motor is disassembled for specific parameters to be measured. For the determination of the parameters between the stator and the motor frame, the rotor is removed and measurements are conducted with each phase bridge between the LCR and the frame and among the three phases (short-circuited in this case) and the frame. After that, the rotor is put back and its axis is short-circuited to the frame. Parameter values between stator and rotor are measured. The LCR Bridge is connected at the common point of the three phases (neutral) and the stator frame.

The parameters of the motor bearings are dynamic and depend on operating conditions (speed) of the three-phase induction motor and also the dielectric characteristics of resistivity of the lubricant temperature and the geometric construction of the motor [1 to 10]. The rotor parameters can only be determined after all previous parameters have been obtained. The LCR

In the absence of an LCR Bridge and an appropriate laboratory for this type of test, another methodology [40, 41] is used to determine the parameters of the equivalent circuit of the induction motor in steady state (nominal frequency) [26, 27] and for high frequency [1, 10, 14, 41], through laboratory measurements using features configurations of links between the

Bridge is connected between the rotor shaft and the frame of the induction motor.

the extensions and consequences of these phenomena.

82 Induction Motors - Applications, Control and Fault Diagnostics

when it is not grounded or this ground is not suitable [1, 4, 7].

windings [3].

In this methodology [40, 41], the three-phase induction motor does not need to be disassembled and reassembled as in the case of measurement with LCR Bridge. Only the bearings are insulated, and the determination of parasitic capacitances is performed while the motor is running. The results of testing for measurement and determination of two 1 Hp induction motor parasitic capacitances and simulations, using the Pspice program, are presented.

### **2. Equivalent circuit of three-phase induction motor at high frequencies**

At high frequencies, the capacitive reactance among the various parts of the three-phase induction motor are shown in Figure 1, which illustrates the equivalent circuit of the threephase induction motor fed by PWM inverter [1, 6, 15]. The distributed parameters R, L, and C represent the high-frequency coupling between the windings of the stator and the rotor.

ZRF is the impedance between the rotor and the motor frame, also called air gap impedance Zg; ZER is the impedance between the windings of the stator and the rotor; ZSF is the impedance between the stator windings and the frame; Zg is the air gap impedance; and ZB represents the impedance between the rotor and the bearing. RW and LW represent the equivalent impedance of the driver through which circulates the bearing current and Rg is the lead resistance connected between the frame and ground. Using the defined impedances shown by equations (1) through (4), one can obtain the high-frequency simplified circuit of the induction motor presented in Figure 2 [15]:

$$\mathbf{Z}\_{\rm rf} = \mathbf{Z}\_{\rm g} = \mathbf{jXC}\_{\rm g} \tag{1}$$

$$\mathbf{Z}\_{\rm sr} = \mathbf{R}\_{\rm sr} + \mathbf{jX}\mathbf{L}\_{\rm sr} + \mathbf{jX}\mathbf{C}\_{\rm sr} \tag{2}$$

$$\mathbf{Z}\_{sf} = \mathbf{R}\_{sf} + \mathbf{jX}\mathbf{L}\_{sf} + \mathbf{jX}\mathbf{C}\_{sf} \tag{3}$$

$$\mathbf{Z}\_b = \{\mathbf{R}\_l \mid \mathbf{/jXC\_b}\} + \mathbf{R}\_b + \mathbf{R}\_w + \mathbf{jXL\_w} \tag{4}$$

coupling between the windings of the stator and the rotor.

2. Equivalent circuit of three-phase induction motor at high frequencies

At high frequencies, the capacitive reactance among the various parts of the three-phase induction motor are shown in Figure 1, which illustrates the equivalent circuit of the three-phase induction motor

**Figure 1.** High-frequency equivalent circuit of induction motor

sfsf sf sf ++= jXCjXLRZ (2.3) **Figure 2.** High-frequency simplified circuit for three-phase induction motor according to its impedances

purely capacitive characteristic [10], according to the example shown in Figure 3.

capacitances at the high frequencies, as shown in Figure 4.

VCM

Figure 1: High-frequency equivalent circuit of induction motor

Simplifications of the circuit shown in Figure 2 can be done using the following considerations [1, 3, 6, 9, 10]: a) ZRF is purely capacitive; b) at frequencies lower than 200 kHz, ZSR assumes a capacitive characteristic; and c) ZSR represents a circuit with RC behavior. At frequencies of 4– 20 kHz range, which are typical switching frequencies of a PWM inverter, parasitic impedances lb wbb <sup>w</sup> = )//( +++ jXLRRjXCRZ (2.4) Simplifications of the circuit shown in Figure 2 can be done using the following considerations [1, 3, 6, 9, 10]: a) ZRF is purely capacitive; b) at frequencies lower than 200 kHz, ZSR assumes a capacitive characteristic; and c) ZSR represents a circuit with RC behavior. At frequencies of 4–20 kHz range, which

are typical switching frequencies of a PWM inverter, parasitic impedances of the induction motor assume

Figure 3: Capacitive impedance characteristic of the three-phase induction motor [10]

Thus, it is possible to simplify the equivalent circuit presented in Figure 2 keeping only the parasitic

VSHAFT

C<sup>B</sup>

Figure 4: Simplified equivalent circuit of high-frequency induction motor

CRF

R<sup>1</sup>

CSF

CSR

Figure 2: High-frequency simplified circuit for three-phase induction motor according to its impedances

Figure 2: High-frequency simplified circuit for three-phase induction motor according to its impedances

R<sup>1</sup>

VCM

ZSR

6, 9, 10]: a) ZRF is purely capacitive; b) at frequencies lower than 200 kHz, ZSR assumes a capacitive characteristic; and c) ZSR represents a circuit with RC behavior. At frequencies of 4–20 kHz range, which are typical switching frequencies of a PWM inverter, parasitic impedances of the induction motor assume

Simplifications of the circuit shown in Figure 2 can be done using the following considerations [1, 3,

ZRF

VSHAFT

ZSF Z<sup>B</sup>

of the induction motor assume purely capacitive characteristic [10], according to the example shown in Figure 3.

**Figure 3.** Capacitive impedance characteristic of the three-phase induction motor [10] Figure 3: Capacitive impedance characteristic of the three-phase induction motor [10]

capacitances at the high frequencies, as shown in Figure 4.

Thus, it is possible to simplify the equivalent circuit presented in Figure 2 keeping only the parasitic capacitances at the high frequencies, as shown in Figure 4. Thus, it is possible to simplify the equivalent circuit presented in Figure 2 keeping only the parasitic

Figure 4: Simplified equivalent circuit of high-frequency induction motor **Figure 4.** Simplified equivalent circuit of high-frequency induction motor

Simplifications of the circuit shown in Figure 2 can be done using the following considerations [1, 3, 6, 9, 10]: a) ZRF is purely capacitive; b) at frequencies lower than 200 kHz, ZSR assumes a capacitive characteristic; and c) ZSR represents a circuit with RC behavior. At frequencies of 4– 20 kHz range, which are typical switching frequencies of a PWM inverter, parasitic impedances

6, 9, 10]: a) ZRF is purely capacitive; b) at frequencies lower than 200 kHz, ZSR assumes a capacitive characteristic; and c) ZSR represents a circuit with RC behavior. At frequencies of 4–20 kHz range, which are typical switching frequencies of a PWM inverter, parasitic impedances of the induction motor assume

purely capacitive characteristic [10], according to the example shown in Figure 3.

capacitances at the high frequencies, as shown in Figure 4.

VCM

Figure 2: High-frequency simplified circuit for three-phase induction motor according to its impedances

**Figure 2.** High-frequency simplified circuit for three-phase induction motor according to its impedances

rf <sup>g</sup> <sup>g</sup> == jXCZZ (2.1)

srsr sr sr ++= jXCjXLRZ (2.2)

sfsf sf sf ++= jXCjXLRZ (2.3)

lb wbb <sup>w</sup> = )//( +++ jXLRRjXCRZ (2.4)

ZRF

ZSF Z<sup>B</sup>

Simplifications of the circuit shown in Figure 2 can be done using the following considerations [1, 3,

Figure 3: Capacitive impedance characteristic of the three-phase induction motor [10]

Thus, it is possible to simplify the equivalent circuit presented in Figure 2 keeping only the parasitic

VSHAFT

C<sup>B</sup>

Figure 4: Simplified equivalent circuit of high-frequency induction motor

CRF

R<sup>1</sup>

CSF

CSR

Figure 1: High-frequency equivalent circuit of induction motor

Frame

Cg <sup>L</sup>SF <sup>L</sup>SF

the impedance between the windings of the stator and the rotor; ZSF is the impedance between the stator windings and the frame; Zg is the air gap impedance; and ZB represents the impedance between the rotor and the bearing. RW and LW represent the equivalent impedance of the driver through which circulates the bearing current and Rg is the lead resistance connected between the frame and ground. Using the defined impedances shown by equations (2.1) through (2.4), one can obtain the high-frequency simplified circuit of

ZRF is the impedance between the rotor and the motor frame, also called air gap impedance Zg; ZER is

R<sup>1</sup>

ZSR

Rg

2. Equivalent circuit of three-phase induction motor at high frequencies

RSR

RSR

RSR

coupling between the windings of the stator and the rotor.

84 Induction Motors - Applications, Control and Fault Diagnostics

RSF RSF RSF

CSF CSF CSF

**Figure 1.** High-frequency equivalent circuit of induction motor

VCM

LSF

the induction motor presented in Figure 2 [15]:

At high frequencies, the capacitive reactance among the various parts of the three-phase induction motor are shown in Figure 1, which illustrates the equivalent circuit of the three-phase induction motor fed by PWM inverter [1, 6, 15]. The distributed parameters R, L, and C represent the high-frequency

LSR

CSR

CSR

CSR

<sup>Z</sup> <sup>Z</sup>RF=Zg SF <sup>Z</sup><sup>B</sup>

R<sup>B</sup>

Rl

L

VSHAFT

C<sup>B</sup>

R

LSR

LSR

ZSR

In Figure 4, VCM is the common mode voltage, CSF is the capacitance between the stator winding per phase and the induction motor frame, CSR is the capacitance among the windings of the stator and the rotor, CRF is the capacitance between the rotor and motor frame, and CB is the capacitance of the bearing. Using this high-frequency equivalent circuit of the induction motor, the equations of both shaft voltage (VSHAFT) and leakage current (ILEAKAGE) are obtained:

$$
\upsilon\_{CM} = \frac{\upsilon\_a + \upsilon\_b + \upsilon\_c}{3} \tag{5}
$$

$$V\_{SHAT} = \; V\_{CM} \cdot \left(\frac{\mathbf{C}\_{SR}}{\mathbf{C}\_{SR} + \mathbf{C}\_{RF} + \mathbf{C}\_{B}}\right) \tag{6}$$

$$I\_{LEAKAGE} = \frac{V\_{CM}}{X\mathcal{C}\_{SF}} + \frac{V\_{SHAT}}{X\mathcal{C}\_{RF}} + \frac{V\_{SHAT}}{X\mathcal{C}\_{B}} \tag{7}$$

The capacitances CSF, CSR, CRF, and CB are defined according to the geometric characteristics of both the stator as the rotor of a three-phase induction motor and its bearings [1, 2, 11, 12, 13, 23]. In [1], these capacitances are set according to the following equations, depending on the geometrical dimensions of the induction motor shown in Figure 5.

$$\mathbf{C\_{SF}} = \frac{\mathbf{K\_{SF}} \cdot \mathbf{N\_S} \, \mathbf{c\_r} \, \mathbf{c\_0} \left(\mathcal{W}\_d + \mathcal{W}\_s\right) \mathbf{L\_S}}{d} \tag{8}$$

$$\mathbf{C}\_{SR} = \frac{K\_{SR} \mathcal{N}\_R \mathcal{E}\_0 \mathcal{W}\_r L\_r}{\mathcal{S}} \tag{9}$$

$$\mathbf{C}\_{\rm RF} = \frac{\mathbf{K}\_{\rm RF} \cdot \pi \,\mathcal{E}\_0 \cdot \mathbf{L}\_r}{\ln \left( \mathcal{R}\_s / \mathcal{R}\_r \right)} \tag{10}$$

$$\mathbf{C}\_{B} = \frac{\mathbf{N}\_{b}\mathbf{4}.\pi\varepsilon\_{0}.\varepsilon\_{r}}{\left(\mathbf{R}\_{b} + \mathbf{R}\_{c}\,/\,\mathbf{R}\_{b} - \mathbf{1}\right)}\tag{11}$$

In the above equations, KSF, KSR, and KRF factors are stacked packages of magnetic stator and rotor, NS and NR are the number of slots of the stator winding and the rotor, Ws and Wd are the width and depth of the groove stator, Wr is the width of the rotor slot, Ls and Lr are the lengths of the stator and rotor slots, Rr and Rs are the radii of the stator and rotor, d is the thickness of the insulating dielectric material of the stator channel, g is the gap length, Nb is the number of bearing balls, Rb and Rc are the ball lightning and the raceway, ε0 and εr are the permittivity of the medium (air and insulation). The parasitic capacitances become important when, besides the common mode voltage is different from zero, the frequency of the phase voltages becomes high, resulting in small capacitive reactance and the circuit in parallel with the remaining equivalent.

When the three-phase induction motor is fed by pure sinusoidal voltages, at the power grid frequency, the effect of these capacitances is minimal or nonexistent. If there is an unbalance in phase voltages, the common mode voltage becomes nonzero, establishing current flow through these capacitances (Figure 4) which will be significant, if the amplitudes of phase voltages are high. Thus, assuming that the motor is supplied by balanced phase voltages, the common-mode voltage (5) is zero. When the three-phase induction motor is fed through a PWM inverter, it establishes a "capacitive coupling" created by the modulated phase voltages of the inverter output. These voltages have trapezoidal characteristic value with high dV/dt of (VSHAFT) and leakage current (ILEAKAGE) are obtained:

In Figure 4, VCM is the common mode voltage, CSF is the capacitance between the stator winding per

3

SR RF B

RF

SHAFT

XC

SR

v v v

v <sup>a</sup> <sup>b</sup> <sup>c</sup>

 

SHAFT CM C C C

<sup>+</sup> <sup>+</sup> <sup>=</sup>

<sup>+</sup> <sup>+</sup> <sup>=</sup>

V

CM

<sup>C</sup> <sup>V</sup> <sup>V</sup> .

The capacitances CSF, CSR, CRF, and CB are defined according to the geometric characteristics of both

SF

SR

Figure 5: Dimensions – induction motor and bearing [1]

the stator as the rotor of a three-phase induction motor and its bearings [1, 2, 11, 12, 13, 23]. In [1], these

SF

LEAKAGE XC

CM

XC <sup>V</sup> <sup>I</sup> <sup>=</sup> <sup>+</sup> <sup>+</sup>

capacitances are set according to the following equations, depending on the geometrical dimensions of the

(2.5)

(2.6)

(2.7)

(2.8)

(2.11)

( )

d

. . . . <sup>0</sup> <sup>ε</sup> <sup>=</sup> (2.9)

... <sup>0</sup> <sup>π</sup> <sup>ε</sup> <sup>=</sup> (2.10)

<sup>K</sup> <sup>N</sup> <sup>W</sup> <sup>W</sup> <sup>L</sup> <sup>C</sup> SF <sup>S</sup> <sup>r</sup> <sup>d</sup> <sup>s</sup> <sup>S</sup>

g

( ) <sup>s</sup> <sup>r</sup>

( ) / 1

<sup>+</sup> <sup>−</sup> <sup>=</sup> b c b

<sup>B</sup> R R R <sup>N</sup> <sup>C</sup> <sup>π</sup> <sup>ε</sup> <sup>ε</sup>

...4. <sup>0</sup>

b r

RF r

<sup>K</sup> <sup>N</sup> <sup>W</sup> <sup>L</sup> <sup>C</sup> SR <sup>R</sup> <sup>r</sup> <sup>r</sup>

 

B

SHAFT

V

RF R R <sup>K</sup> <sup>L</sup> <sup>C</sup>

ln /

. ... . <sup>0</sup> <sup>+</sup> <sup>=</sup> <sup>ε</sup> <sup>ε</sup>

phase and the induction motor frame, CSR is the capacitance among the windings of the stator and the

rotor, CRF is the capacitance between the rotor and motor frame, and CB is the capacitance of the bearing.

Using this high-frequency equivalent circuit of the induction motor, the equations of both shaft voltage

assuming that the motor is supplied by balanced phase voltages, the common-mode voltage (2.5) is zero. When the three-phase induction motor is fed through a PWM inverter, it establishes a "capacitive **Figure 5.** Dimensions – induction motor and bearing [1]

as shown in Figure 6 (a, b) [12, 18, 22].

kHz.

*CM SHAFT SHAFT*

=+ + (7)

<sup>+</sup> <sup>=</sup> (8)

= (9)

= (10)

<sup>=</sup> + - (11)

*VV V <sup>I</sup>*

*SF RF B*

*XC XC XC*

The capacitances CSF, CSR, CRF, and CB are defined according to the geometric characteristics of both the stator as the rotor of a three-phase induction motor and its bearings [1, 2, 11, 12, 13, 23]. In [1], these capacitances are set according to the following equations, depending on the

*SF S r d s S* . ... . <sup>0</sup> ( )

*KN W WL*

e e

*K N WL <sup>C</sup> g* e

*K L <sup>C</sup>*

*d*

<sup>0</sup> . .. . *SR R r r*

( ) <sup>0</sup> .. . ln / *RF r*

*R R* p e

( ) <sup>0</sup> .4. . . / 1 *b r*

In the above equations, KSF, KSR, and KRF factors are stacked packages of magnetic stator and rotor, NS and NR are the number of slots of the stator winding and the rotor, Ws and Wd are the width and depth of the groove stator, Wr is the width of the rotor slot, Ls and Lr are the lengths of the stator and rotor slots, Rr and Rs are the radii of the stator and rotor, d is the thickness of the insulating dielectric material of the stator channel, g is the gap length, Nb is the number of bearing balls, Rb and Rc are the ball lightning and the raceway, ε0 and εr are the permittivity of the medium (air and insulation). The parasitic capacitances become important when, besides the common mode voltage is different from zero, the frequency of the phase voltages becomes high, resulting in small capacitive reactance and the circuit in parallel with

When the three-phase induction motor is fed by pure sinusoidal voltages, at the power grid frequency, the effect of these capacitances is minimal or nonexistent. If there is an unbalance in phase voltages, the common mode voltage becomes nonzero, establishing current flow through these capacitances (Figure 4) which will be significant, if the amplitudes of phase voltages are high. Thus, assuming that the motor is supplied by balanced phase voltages, the common-mode voltage (5) is zero. When the three-phase induction motor is fed through a PWM inverter, it establishes a "capacitive coupling" created by the modulated phase voltages of the inverter output. These voltages have trapezoidal characteristic value with high dV/dt of

*b cb*

*R RR* pe e

*s r*

*LEAKAGE*

86 Induction Motors - Applications, Control and Fault Diagnostics

geometrical dimensions of the induction motor shown in Figure 5.

*SR*

*RF*

*<sup>N</sup> <sup>C</sup>*

*B*

the remaining equivalent.

*SF*

*C*

the inverter while the semiconductor switches are turned on or off, as shown in Figure 6 (a, b) [12, 18, 22]. coupling" created by the modulated phase voltages of the inverter output. These voltages have trapezoidal characteristic value with high dV/dt of the inverter while the semiconductor switches are turned on or off, In the above equations, KSF, KSR, and KRF factors are stacked packages of magnetic stator and rotor,

Figure 6: a) Terminal voltage of the PWM inverter , b) dV/dt voltage

As the supply voltages are not sinusoidal, the common mode voltage (VCM) takes nonzero values.

a)

 Time 71.0ms 71.1ms 71.2ms 71.3ms 71.4ms 71.5ms 71.6ms 71.7ms 71.8ms 71.9ms 72.0ms

0 2.0

a) t(ms)

Thus, this voltage and also the switching frequency (fS) of the PWM inverter now have an important role on common mode capacitive currents. For example, Figures 7a and 7b present the waveforms of the output phase voltages of the inverter and the common-mode voltage for a switching frequency (fS) of 16

**Figure 6.** a) Terminal voltage of the PWM inverter, b) dV/dt voltage

V(T,0) -200V -100V 0V 100V 200V

V(S,0) -200V -100V 0V 100V 200V V(R,0) -200V -100V 0V 100V V 200V RN(V) 200

SEL>>

0 -200

0


0 -200 VTN(V) 200 kHz.

relationships:

As the supply voltages are not sinusoidal, the common mode voltage (VCM) takes nonzero values. Thus, this voltage and also the switching frequency (fS) of the PWM inverter now have an important role on common mode capacitive currents. For example, Figures 7a and 7b present the waveforms of the output phase voltages of the inverter and the common-mode voltage for a switching frequency (fS) of 16 kHz. As the supply voltages are not sinusoidal, the common mode voltage (VCM) takes nonzero values. Thus, this voltage and also the switching frequency (fS) of the PWM inverter now have an important role on common mode capacitive currents. For example, Figures 7a and 7b present the waveforms of the output phase voltages of the inverter and the common-mode voltage for a switching frequency (fS) of 16

**Figure 7.** a) Phase voltage, b) a common mode voltage (VCM) - fS = 16 kHz

of the motor for high frequency presented in Figure 8b [1 to 10].

The higher the switching frequency, the better is the characteristic of the waveform of the current applied to the induction motor. Besides that, the frequency raise often implies an increase in the switching times of the IGBTs increasingly smaller, providing both increased feature dV/dt, which is directly related to the values of the capacitive currents of common mode current, as the reduction of the capacitive reactance significantly increased the amplitudes thereof. The following equations show these The higher the switching frequency, the better is the characteristic of the waveform of the current applied to the induction motor. Besides that, the frequency raise often implies an increase in the switching times of the IGBTs increasingly smaller, providing both increased feature dV/dt, which is directly related to the values of the capacitive currents of common mode current, as the reduction of the capacitive reactance significantly increased the ampli‐ tudes thereof. The following equations show these relationships:

> *I* 2.

*dt*

Observing equations (2.12) and (2.13), it is possible to conclude that V and I are effective values of

voltage and common mode current. Thus, from the down-movement of the common-mode electrical currents (also called capacitive currents) as shown in Figure 8a [18], one can obtain the equivalent circuit

**Motor**

Figure 7: a) Phase voltage, b) a common mode voltage (VCM) - fS = 16 kHz

$$
\dot{u} = C. \frac{dv}{dt} \tag{12}
$$

**Load**

.*fS* .*C*.*V* (2.13)

relationships: dv <sup>i</sup> <sup>=</sup> <sup>C</sup>. (2.12) Analysis and Methodology for Determining the Parasitic Capacitances in VSI-fed IM Drives Based on PWM Technique http://dx.doi.org/10.5772/61544 89

dt

Figure 7: a) Phase voltage, b) a common mode voltage (VCM) - fS = 16 kHz

 Time 71.0ms 71.1ms 71.2ms 71.3ms 71.4ms 71.5ms 71.6ms 71.7ms 71.8ms 71.9ms 72.0ms

0 2.0

The higher the switching frequency, the better is the characteristic of the waveform of the current

applied to the induction motor. Besides that, the frequency raise often implies an increase in the switching times of the IGBTs increasingly smaller, providing both increased feature dV/dt, which is directly related to the values of the capacitive currents of common mode current, as the reduction of the capacitive reactance significantly increased the amplitudes thereof. The following equations show these

$$I = 2.\pi.f\_{\mathbb{S}}.\text{C.V.}\tag{13}$$

b) t(ms)

Observing equations (12) and (13), it is possible to conclude that V and I are effective values of voltage and common mode current. Thus, from the down-movement of the common-mode electrical currents (also called capacitive currents) as shown in Figure 8a [18], one can obtain the equivalent circuit of the motor for high frequency presented in Figure 8b [1 to 10]. Observing equations (2.12) and (2.13), it is possible to conclude that V and I are effective values of voltage and common mode current. Thus, from the down-movement of the common-mode electrical currents (also called capacitive currents) as shown in Figure 8a [18], one can obtain the equivalent circuit

of the motor for high frequency presented in Figure 8b [1 to 10].

(V(R,0)+V(S,0)+V(T,0))/3


200


0V

0

100V

V 200V CM(V) 200

As the supply voltages are not sinusoidal, the common mode voltage (VCM) takes nonzero values. Thus, this voltage and also the switching frequency (fS) of the PWM inverter now have an important role on common mode capacitive currents. For example, Figures 7a and 7b present the waveforms of the output phase voltages of the inverter and the common-mode

Thus, this voltage and also the switching frequency (fS) of the PWM inverter now have an important role on common mode capacitive currents. For example, Figures 7a and 7b present the waveforms of the output phase voltages of the inverter and the common-mode voltage for a switching frequency (fS) of 16

As the supply voltages are not sinusoidal, the common mode voltage (VCM) takes nonzero values.

a)

 Time 71.0ms 71.1ms 71.2ms 71.3ms 71.4ms 71.5ms 71.6ms 71.7ms 71.8ms 71.9ms 72.0ms

0 2.0

a) t(ms)

b) t(ms)

Figure 7: a) Phase voltage, b) a common mode voltage (VCM) - fS = 16 kHz

 Time 71.0ms 71.1ms 71.2ms 71.3ms 71.4ms 71.5ms 71.6ms 71.7ms 71.8ms 71.9ms 72.0ms

0 2.0

The higher the switching frequency, the better is the characteristic of the waveform of the current

*dt*

Observing equations (2.12) and (2.13), it is possible to conclude that V and I are effective values of

voltage and common mode current. Thus, from the down-movement of the common-mode electrical currents (also called capacitive currents) as shown in Figure 8a [18], one can obtain the equivalent circuit

**Motor**

*dv <sup>i</sup> <sup>C</sup>*. (2.12)

*dt* <sup>=</sup> (12)

**Load**

.*fS* .*C*.*V* (2.13)

applied to the induction motor. Besides that, the frequency raise often implies an increase in the switching times of the IGBTs increasingly smaller, providing both increased feature dV/dt, which is directly related to the values of the capacitive currents of common mode current, as the reduction of the capacitive reactance significantly increased the amplitudes thereof. The following equations show these

The higher the switching frequency, the better is the characteristic of the waveform of the current applied to the induction motor. Besides that, the frequency raise often implies an increase in the switching times of the IGBTs increasingly smaller, providing both increased feature dV/dt, which is directly related to the values of the capacitive currents of common mode current, as the reduction of the capacitive reactance significantly increased the ampli‐

> *I* 2.

. *dv i C*

of the motor for high frequency presented in Figure 8b [1 to 10].

voltage for a switching frequency (fS) of 16 kHz.

88 Induction Motors - Applications, Control and Fault Diagnostics

V(T,0) -200V -100V 0V 100V 200V

(V(R,0)+V(S,0)+V(T,0))/3

**Figure 7.** a) Phase voltage, b) a common mode voltage (VCM) - fS = 16 kHz

tudes thereof. The following equations show these relationships:

V(S,0) -200V -100V 0V 100V 200V V(R,0) -200V -100V 0V 100V

SEL>>


200


0V

0

100V

V 200V CM(V) 200

0 -200

0


0


V 200V RN(V) 200

kHz.

relationships:

Figure 8: a) Circulating currents in the motor, b) high-frequency equivalent circuit and circulating currents [10] **Figure 8.** a) Circulating currents in the motor, b) high-frequency equivalent circuit and circulating currents [10]

The electric currents are established as follows: [10] a) II is the current flowing through the common mode voltage point (VCM), which passes through the pump capacitance for the motor frame, ground or neutral and returns to the system to VCM point. It is the largest component of the leakage current (ILEAKAGE), compared to other capacitive currents because CSF capacitance is much larger than others. This current is primarily responsible for the electrical discharge of the motor frame to the "ground." If the motor is not grounded to the frame satisfactorily, an important electrical discharge at various parts of it and even at the load may occur and cause an "electric shock" if someone leans on the motor frame. b) III is the current flowing through the common mode voltage point (VCM), which passes through the CSR and capacitances CRF, motor frame, ground or neutral system and returns to the VCM point. c) III is the current flowing through the common mode voltage point (VCM), which passes through the CSR capacitance motor shaft bearing capacitance CB motor frame, ground or neutral system and returns to the VCM point. d) IV is the current flowing shaft voltage point (VSHAFT); CRF capacitance thus stores energy through the motor shaft, the switch SH, the motor frame, and returns to the CRF capacitance.

The switch SH in Figure 8b is, when closed, the breaking of the bearing insulation dielectric (grease film). When this occurs, and CSR is much smaller than CRF, a new mesh current flow given by IV is then established. The IV mesh is responsible for the electrical discharge in the motor bearings due to the charge stored in the capacitor CRF.

### **3. Experimental method for determination of parasitic capacitances rotor cage three-phase induction motor [40]**

This item presents a methodology [40] for the determination of the parasitic capacitances of the equivalent high-frequency rotor three-phase induction motor circuit cage and the effects of electromagnetic interference caused in the same common mode, when it is driven by a PWM inverter. This is a methodology that uses an electronic circuit to measure variables needed to calculate these parameters.

The procedures proposed for the development of this methodology are: a) determination of the equivalent circuit parameters of the three-phase induction motor in steady state and high frequency and [1, 10, 15, 31] through typical laboratory test; b) establish settings of links between the PWM inverter and the motor for measurements of quantities of interest: common mode (VCM) and shaft (VSHAFT) voltages, leakage (ILEAKAGE) and shaft (ISHAFT) currents, developed by measuring circuit for this purpose [13, 14]; c) calculate the values of the parasitic capaci‐ tances between stator and frame (CSF), stator and rotor (CSR), rotor and frame (CRF) and bearings (CB), using their characteristic equations [10, 15]; d) using PSPICE [36] to simulate the system (three-phase induction motor fed by PWM inverter) with the high-frequency equivalent circuit in the same [6, 16]; e) to obtain the waveforms characteristics of the EMI phenomena.

### **3.1. Methodology determination procedure**

The methodology determines the high-frequency equivalent circuit parameters of rotor cage three-phase induction motor, through direct measurement of quantities of interest and, using equation (14), calculate the values of the parasitic capacitances. The quantities of interest are common mode voltage (VCM), shaft voltage (VSHAFT), leakage current (ILEAKAGE), and shaft current (ISHAFT).

$$\text{C} = \frac{I\_{\text{C}}}{2.\pi f\_{\text{s}} f\_{\text{s}} V\_{\text{C}}} \tag{14}$$

In equation (14), IC and VC represent the current and the effective voltage across the capacitor, respectively, and fS the switching frequency of the PWM inverter. The schematic diagram of the methodology is shown in Figure 9.

In equation (3.1), IC and VC represent the current and the effective voltage across the capacitor, respectively, and fS the switching frequency of the PWM inverter. The schematic diagram of the Analysis and Methodology for Determining the Parasitic Capacitances in VSI-fed IM Drives Based on PWM Technique http://dx.doi.org/10.5772/61544 91

(VCM), shaft voltage (VSHAFT), leakage current (ILEAKAGE), and shaft current (ISHAFT).

C

The methodology determines the high-frequency equivalent circuit parameters of rotor cage threephase induction motor, through direct measurement of quantities of interest and, using equation (3.1), calculate the values of the parasitic capacitances. The quantities of interest are common mode voltage

s C

<sup>2</sup><sup>π</sup> <sup>=</sup> (3.1)

C V.f.. I

3.1. Methodology determination procedure

**Figure 9.** Schematic diagram of the methodology

energy through the motor shaft, the switch SH, the motor frame, and returns to the CRF

The switch SH in Figure 8b is, when closed, the breaking of the bearing insulation dielectric (grease film). When this occurs, and CSR is much smaller than CRF, a new mesh current flow given by IV is then established. The IV mesh is responsible for the electrical discharge in the

**3. Experimental method for determination of parasitic capacitances rotor**

This item presents a methodology [40] for the determination of the parasitic capacitances of the equivalent high-frequency rotor three-phase induction motor circuit cage and the effects of electromagnetic interference caused in the same common mode, when it is driven by a PWM inverter. This is a methodology that uses an electronic circuit to measure variables needed to

The procedures proposed for the development of this methodology are: a) determination of the equivalent circuit parameters of the three-phase induction motor in steady state and high frequency and [1, 10, 15, 31] through typical laboratory test; b) establish settings of links between the PWM inverter and the motor for measurements of quantities of interest: common mode (VCM) and shaft (VSHAFT) voltages, leakage (ILEAKAGE) and shaft (ISHAFT) currents, developed by measuring circuit for this purpose [13, 14]; c) calculate the values of the parasitic capaci‐ tances between stator and frame (CSF), stator and rotor (CSR), rotor and frame (CRF) and bearings (CB), using their characteristic equations [10, 15]; d) using PSPICE [36] to simulate the system (three-phase induction motor fed by PWM inverter) with the high-frequency equivalent circuit

in the same [6, 16]; e) to obtain the waveforms characteristics of the EMI phenomena.

The methodology determines the high-frequency equivalent circuit parameters of rotor cage three-phase induction motor, through direct measurement of quantities of interest and, using equation (14), calculate the values of the parasitic capacitances. The quantities of interest are common mode voltage (VCM), shaft voltage (VSHAFT), leakage current (ILEAKAGE), and shaft

> 2. . . *C s C*

In equation (14), IC and VC represent the current and the effective voltage across the capacitor, respectively, and fS the switching frequency of the PWM inverter. The schematic diagram of

*f V* <sup>=</sup> (14)

p

*C*

*I*

motor bearings due to the charge stored in the capacitor CRF.

**cage three-phase induction motor [40]**

90 Induction Motors - Applications, Control and Fault Diagnostics

**3.1. Methodology determination procedure**

the methodology is shown in Figure 9.

calculate these parameters.

current (ISHAFT).

capacitance.

The structure consists of the following equipment: three-phase power supply 220V/60Hz, 1 Hp three-phase PWM inverter, two three-phase 1Hp induction motors, measuring circuit of the quantities of interest, data acquisition board LabView, notebook PWM inverter management and signal processing through dedicated software LabView 8.5 and MOVITOOLS, base for sustaining fully insulated equipment to allow measurements, especially the currents (as close as possible to an actual situation), connecting cable with the neutral system interconnected to the PWM inverter ground terminals and the induction motor providing a circulating path to the induction motor current. The structure consists of the following equipment: three-phase power supply 220V/60Hz, 1 Hp three-phase PWM inverter, two three-phase 1Hp induction motors, measuring circuit of the quantities of interest, data acquisition board LabView, notebook PWM inverter manage‐ ment and signal processing through dedicated software LabView 8.5 and MOVITOOLS, base for sustaining fully insulated equipment to allow measurements, especially the currents (as close as possible to an actual situation), connecting cable with the neutral system intercon‐ nected to the PWM inverter ground terminals and the induction motor providing a circulating path to the induction motor current.

The magnitudes of the measuring circuit (VCM, VSHAFT, ILEAKAGE, and ISHAFT) are shown in Figure 10. The common mode voltage (VCM) is the common point of the measuring voltage (neutral) to the motor frame when it uses star connection (Y). When the same connection uses delta (∆), it should be equivalent The magnitudes of the measuring circuit (VCM, VSHAFT, ILEAKAGE, and ISHAFT) are shown in Figure 10. The common mode voltage (VCM) is the common point of the measuring voltage (neutral) to the motor frame when it uses star connection (Y). When the same connection uses delta (Δ), it should be equivalent to a star connection using high-value resistors (1MΩ) connected to each phase of the motor with a common point (neutral). In the adjustment of the common mode voltage measurement (VCM) to the acquisition board, a resistive divider (R1, R2, R3, and R4) is added so that the measured voltage does not exceed the maximum allowed by the acquisition board, that is, +/- 10V, as shown in Figure 10.

For measuring the shaft voltage (VSHAFT), which is the voltage measured between the shaft and the induction motor frame, a copper ring carbon brush system is added to the induction motor shaft.

For leakage current (ILEAKAGE) and shaft current (ISHAFT) measurements, a Rogowski coil current sensor, developed for this methodology, was used [40]. The leakage current is the current measured in the connection cable between the induction motor frame and the metal frame of

the PWM inverter connected to the neutral system. It is composed of the sum of the currents flowing through the stator-frame capacitances (CSF), rotor-frame (CRF), and bearings (CB). to the neutral system. It is composed of the sum of the currents flowing through the stator-frame capacitances (CSF), rotor-frame (CRF), and bearings (CB).

connection cable between the induction motor frame and the metal frame of the PWM inverter connected

For measuring the shaft voltage (VSHAFT), which is the voltage measured between the shaft and the

For leakage current (ILEAKAGE) and shaft current (ISHAFT) measurements, a Rogowski coil current

to a star connection using high-value resistors (1MΩ) connected to each phase of the motor with a common point (neutral). In the adjustment of the common mode voltage measurement (VCM) to the acquisition board, a resistive divider (R1, R2, R3, and R4) is added so that the measured voltage does not

exceed the maximum allowed by the acquisition board, that is, +/- 10V, as shown in Figure 10.

induction motor frame, a copper ring carbon brush system is added to the induction motor shaft.

The shaft current (ISHAFT) is the current measured in the conductor which is connected to the brush and corresponding contributions from currents flowing through the rotor-frame capacitances (CRF) and bearings (CB). The shaft current (ISHAFT) is the current measured in the conductor which is connected to the brush and corresponding contributions from currents flowing through the rotor-frame capacitances (CRF) and bearings (CB).

Figure 10: Measuring circuit of the quantities of interest **Figure 10.** Measuring circuit of the quantities of interest

### *3.1.1. Induction motor preparation*

For the application of the proposed method, the motor rotor three-phase induction cage should be prepared so that the capacitance can be determined [1, 10, 14]. Under normal conditions, the motor bearings are directly connected to both the shaft and the motor frame. It causes the capacitance existing between the rotor and the frame (CRF) to short-circuit.

So the following changes are made. (a) Motor bearings are insulated by a nylon cover (tecnil) high electrical resistance. Thus, there will be no current flow by bearings (IB) and the contri‐ So the following changes are made. (a) Motor bearings are insulated by a nylon cover (tecnil) high

For the application of the proposed method, the motor rotor three-phase induction cage should be prepared so that the capacitance can be determined [1, 10, 14]. Under normal conditions, the motor

electrical resistance. Thus, there will be no current flow by bearings (IB) and the contribution branch rotor

frame can be evaluated, as shown in Figure 11 [10]. (b) A conductor is connected between the external

So the following changes are made. (a) Motor bearings are insulated by a nylon cover (tecnil) high

For the application of the proposed method, the motor rotor three-phase induction cage should be

prepared so that the capacitance can be determined [1, 10, 14]. Under normal conditions, the motor

bearings are directly connected to both the shaft and the motor frame. It causes the capacitance existing

bution branch rotor frame can be evaluated, as shown in Figure 11 [10]. (b) A conductor is connected between the external surface of one of the bearings and closest to the motor frame by a switch point. When the switch is open, there is the condition set out in item (a). When the switch is closed, then one has the rolling movement for the current frame and the returning to the bearing [10]. (c) The motor shaft settles in a ring and brush assembly, for measuring the shaft voltage (VSHAFT). This system is also used to measure the shaft current (ISHAFT) [14]. Figure 12 shows the items (b) and (c). electrical resistance. Thus, there will be no current flow by bearings (IB) and the contribution branch rotor frame can be evaluated, as shown in Figure 11 [10]. (b) A conductor is connected between the external surface of one of the bearings and closest to the motor frame by a switch point. When the switch is open, there is the condition set out in item (a). When the switch is closed, then one has the rolling movement for the current frame and the returning to the bearing [10]. (c) The motor shaft settles in a ring and brush assembly, for measuring the shaft voltage (VSHAFT). This system is also used to measure the shaft current the current frame and the returning to the bearing [10]. (c) The motor shaft settles in a ring and brush assembly, for measuring the shaft voltage (VSHAFT). This system is also used to measure the shaft current (ISHAFT) [14]. Figure 12 shows the items (b) and (c). Insulated

Figure 11 a, b): Insulation of the motor shaft bearings

b

(ISHAFT) [14]. Figure 12 shows the items (b) and (c).

bearings with

Figure 11 a, b): Insulation of the motor shaft bearings **Figure 11.** a, b): Insulation of the motor shaft bearings a) b)

3.1.1. Induction motor preparation

between the rotor and the frame (CRF) to short-circuit.

3.1.1. Induction motor preparation

the PWM inverter connected to the neutral system. It is composed of the sum of the currents flowing through the stator-frame capacitances (CSF), rotor-frame (CRF), and bearings (CB).

sensor, developed for this methodology, was used [40]. The leakage current is the current measured in the connection cable between the induction motor frame and the metal frame of the PWM inverter connected to the neutral system. It is composed of the sum of the currents flowing through the stator-frame

For measuring the shaft voltage (VSHAFT), which is the voltage measured between the shaft and the

For leakage current (ILEAKAGE) and shaft current (ISHAFT) measurements, a Rogowski coil current

to a star connection using high-value resistors (1MΩ) connected to each phase of the motor with a common point (neutral). In the adjustment of the common mode voltage measurement (VCM) to the acquisition board, a resistive divider (R1, R2, R3, and R4) is added so that the measured voltage does not

exceed the maximum allowed by the acquisition board, that is, +/- 10V, as shown in Figure 10.

induction motor frame, a copper ring carbon brush system is added to the induction motor shaft.

The shaft current (ISHAFT) is the current measured in the conductor which is connected to the brush and corresponding contributions from currents flowing through the rotor-frame

and corresponding contributions from currents flowing through the rotor-frame capacitances (CRF) and

3Φ PWM INVERTER V/f GINV

R<sup>1</sup>

R<sup>2</sup>

The shaft current (ISHAFT) is the current measured in the conductor which is connected to the brush

IM 3Φ 220V/60 Hz

CRF C<sup>B</sup>

SH

ISHAFT

R = 1MΩ

R<sup>3</sup>

R<sup>4</sup>

Figure 10: Measuring circuit of the quantities of interest

For the application of the proposed method, the motor rotor three-phase induction cage should be prepared so that the capacitance can be determined [1, 10, 14]. Under normal conditions, the motor bearings are directly connected to both the shaft and the motor frame. It causes the

So the following changes are made. (a) Motor bearings are insulated by a nylon cover (tecnil) high electrical resistance. Thus, there will be no current flow by bearings (IB) and the contri‐

capacitance existing between the rotor and the frame (CRF) to short-circuit.

CSF

CSR

VC<sup>M</sup>VSHAFT

capacitances (CRF) and bearings (CB).

LABVIEW

ACQUISITION & MEASUREMENT BOARD

CHANNELS

**Figure 10.** Measuring circuit of the quantities of interest

*3.1.1. Induction motor preparation*

a0+ a0 a1+ a1 a2+ a2 a3+ a3- GND

bearings (CB).

capacitances (CSF), rotor-frame (CRF), and bearings (CB).

92 Induction Motors - Applications, Control and Fault Diagnostics

N <sup>R</sup> SS

T

ILEAKAGE

R S T

Figure 12: Switch (b) and ring-brush assembly (c) for measuring **Figure 12.** Switch (b) and ring-brush assembly (c) for measuring

### *3.1.2. Data acquisition board and measuring*

In order to acquire the quantities and accomplish the measurements, LabView [32, 33, 34] platform is used. Four channels for the different measurements are defined as follows: (a) a0 channel: leakage current (ILEAKAGE); (b) A1 channel: the common mode voltage (VCM), which is set to the voltage of -10V to + 10V limits; (c) a2 channel: shaft voltage (VSHAFT); and (d) a3 channel: shaft current (ISHAFT). 3.1.2. Data acquisition board and measuring In order to acquire the quantities and accomplish the measurements, LabView [32, 33, 34] platform

Using dedicated software LabView 8.5, [35] created a block diagram (plant) of the measuring system for the magnitudes of interest. Figure 13 shows the block diagram for leakage current (ILEAKAGE). The configuration for each quantity to be measured using channels with differential inputs is shown in Figure 14 to minimize the effects of common-mode voltages (noise). is used. Four channels for the different measurements are defined as follows: (a) a0 channel: leakage current (ILEAKAGE); (b) A1 channel: the common mode voltage (VCM), which is set to the voltage of -10V to + 10V limits; (c) a2 channel: shaft voltage (VSHAFT); and (d) a3 channel: shaft current (ISHAFT). Using dedicated software LabView 8.5, [35] created a block diagram (plant) of the measuring

Observations (Figure 13): system for the magnitudes of interest. Figure 13 shows the block diagram for leakage current

Block A - CORRENTE DE FUGA - Ifuga <=> LEAKAGE CURRENT - Ileakage (ILEAKAGE). The configuration for each quantity to be measured using channels with differential inputs

Block D - FILTRO RUÍDO <=> NOTCH FILTER is shown in Figure 14 to minimize the effects of common-mode voltages (noise). Observations (Figure 13):

Block E - FILTRO PASSA-BAIXA <=> LOW-PASS FILTER Block A - CORRENTE DE FUGA - Ifuga <=> LEAKAGE CURRENT - Ileakage

Block F - ESPECTRO - Ifuga <=> ESPECTRUM - Ileakage Block D - FILTRO RUÍDO <=> NOTCH FILTER

Block G - RMS Ifuga\_fs <=> RMS Ileakage\_fs Block E - FILTRO PASSA-BAIXA <=> LOW-PASS FILTER Block F - ESPECTRO - Ifuga <=> ESPECTRUM - Ileakage

SAÍDA DO FILTRO - Ifuga <=> OUTPUT FILTER – Ileakage Block G - RMS Ifuga\_fs <=> RMS Ileakage\_fs

SAÍDA DO FILTRO - Ifuga <=> OUTPUT FILTER - Ileakage

**Figure 13.** Block diagram for reading the leakage current (ILEAKAGE)

CHANNEL R VSIGNAL Using the DAQ block (A), the following items are defined for each channel: a) type of quantity (voltage or current), b) name of greatness and sample rate, c) type of sampling, d) connection diagram channel and other settings which depend on the desired type of measurement. Can be used up to 16 signals for reading.

LABVIEW

Figure 14: Differential input of the A/D channels

100kΩ

Figure 13: Block diagram for reading the leakage current (ILEAKAGE)

C

F

In order to acquire the quantities and accomplish the measurements, LabView [32, 33, 34] platform is used. Four channels for the different measurements are defined as follows: (a) a0 channel: leakage current (ILEAKAGE); (b) A1 channel: the common mode voltage (VCM), which is set to the voltage of -10V to +

Using dedicated software LabView 8.5, [35] created a block diagram (plant) of the measuring system for the magnitudes of interest. Figure 13 shows the block diagram for leakage current (ILEAKAGE). The configuration for each quantity to be measured using channels with differential inputs

10V limits; (c) a2 channel: shaft voltage (VSHAFT); and (d) a3 channel: shaft current (ISHAFT).

is shown in Figure 14 to minimize the effects of common-mode voltages (noise).

Block A - CORRENTE DE FUGA - Ifuga <=> LEAKAGE CURRENT - Ileakage

Figure 13: Block diagram for reading the leakage current (ILEAKAGE)

D

**Figure 14.** Differential input of the A/D channels

3.1.2. Data acquisition board and measuring

Observations (Figure 13):

A

Block D - FILTRO RUÍDO <=> NOTCH FILTER

Block G - RMS Ifuga\_fs <=> RMS Ileakage\_fs

Block E - FILTRO PASSA-BAIXA <=> LOW-PASS FILTER Block F - ESPECTRO - Ifuga <=> ESPECTRUM - Ileakage

SAÍDA DO FILTRO - Ifuga <=> OUTPUT FILTER - Ileakage

*3.1.2. Data acquisition board and measuring*

94 Induction Motors - Applications, Control and Fault Diagnostics

3.1.2. Data acquisition board and measuring

Block D - FILTRO RUÍDO <=> NOTCH FILTER

Block G - RMS Ifuga\_fs <=> RMS Ileakage\_fs

Block G - RMS Ifuga\_fs <=> RMS Ileakage\_fs

B

be used up to 16 signals for reading.

Block D - FILTRO RUÍDO <=> NOTCH FILTER

Block E - FILTRO PASSA-BAIXA <=> LOW-PASS FILTER

is shown in Figure 14 to minimize the effects of common-mode voltages (noise).

Block A - CORRENTE DE FUGA - Ifuga <=> LEAKAGE CURRENT - Ileakage

Block F - ESPECTRO - Ifuga <=> ESPECTRUM - Ileakage

Block E - FILTRO PASSA-BAIXA <=> LOW-PASS FILTER Block F - ESPECTRO - Ifuga <=> ESPECTRUM - Ileakage

SAÍDA DO FILTRO - Ifuga <=> OUTPUT FILTER – Ileakage

SAÍDA DO FILTRO - Ifuga <=> OUTPUT FILTER - Ileakage

shaft current (ISHAFT).

Observations (Figure 13):

Observations (Figure 13):

A

In order to acquire the quantities and accomplish the measurements, LabView [32, 33, 34] platform is used. Four channels for the different measurements are defined as follows: (a) a0 channel: leakage current (ILEAKAGE); (b) A1 channel: the common mode voltage (VCM), which is set to the voltage of -10V to + 10V limits; (c) a2 channel: shaft voltage (VSHAFT); and (d) a3 channel:

Using dedicated software LabView 8.5, [35] created a block diagram (plant) of the measuring system for the magnitudes of interest. Figure 13 shows the block diagram for leakage current (ILEAKAGE). The configuration for each quantity to be measured using channels with differential inputs is shown in Figure 14 to minimize the effects of common-mode voltages (noise).

In order to acquire the quantities and accomplish the measurements, LabView [32, 33, 34] platform is used. Four channels for the different measurements are defined as follows: (a) a0 channel: leakage current (ILEAKAGE); (b) A1 channel: the common mode voltage (VCM), which is set to the voltage of -10V to +

Using dedicated software LabView 8.5, [35] created a block diagram (plant) of the measuring

Figure 13: Block diagram for reading the leakage current (ILEAKAGE)

Using the DAQ block (A), the following items are defined for each channel: a) type of quantity (voltage or current), b) name of greatness and sample rate, c) type of sampling, d) connection diagram channel and other settings which depend on the desired type of measurement. Can

E

D

R 100kΩ

VSIGNAL

**Figure 13.** Block diagram for reading the leakage current (ILEAKAGE)

C

F

G

LABVIEW CHANNEL

Figure 14: Differential input of the A/D channels

Block A - CORRENTE DE FUGA - Ifuga <=> LEAKAGE CURRENT - Ileakage

system for the magnitudes of interest. Figure 13 shows the block diagram for leakage current (ILEAKAGE). The configuration for each quantity to be measured using channels with differential inputs

10V limits; (c) a2 channel: shaft voltage (VSHAFT); and (d) a3 channel: shaft current (ISHAFT).

Signals Using Split (B) block quantities of simultaneous readings can be made. In this case, there are 4 outputs. The current ILEAKAGE a function of time is shown on the oscilloscope ILEAKAGE (t).

The Amplitude and Level Measurements block (C) allows for the signs readings DC values (DC) and effective (RMS). The value is shown on the display "RMS ILEAKAGE."

The blocks Noise Filter (D) and Pass Filter Range MFB (E) treat the signal so that it can be measured on the switching frequency of the PWM inverter. The filtered signal is displayed on the oscilloscope FILTER OUT – ILEAKAGE.

Noise Filter (NOTCH) has the function of not allowing passage of signals of a frequency band or a specific frequency. The Band Pass Filter MFB allows only the frequency band specified signal to pass. This filtering block allows you to define: a) type of filter: low-pass, high-pass, band-pass, band-reject; b) frequency band; c) the type of response: finite impulse response (FIR) or infinite impulse response (IIR); d) topology: Butterworth, Chebyshev, Inverse Chebyshev, Elliptic, and Bessel.

Spectral Measurement block (F) shows the oscilloscope through the spectrum ILEAKAGE already filtered at the desired frequency. And the block (G) similar to block (C) provides effective current at switching frequency fS, available in display RMS\_ILEAKAGE\_fS. This entire procedure aims to ensure that measurements are made in order to respect the equation for calculating the capacitance (14).

### *3.1.3. PWM inverter*

The PWM inverter used in this study is a new generation of static power converters that feature improvements in its modular structure, providing better functions in the lower-frequency range and greater overload capacity. Introducing control functions integrated with the possibility of use of communication accessories, this enables applications to AC inverter drive systems requiring high efficiency in a power range 0.55–160 kW.

The Inverter MOVIDRIVE MDX60B/61B [29] has the following main characteristics: a) The MOVIDRIVE MDX61B model allows application for asynchronous motors (induction motor) with or without encoder feedback, synchronous and asynchronous servomotors. b) Control modes: VFC (Voltage Flux Control): to control induction motors. Using encoder feedback, it operates with vector control activated. If there is no feedback loop, it operates with V/f control (scalar) and CFC (Current Flux Control); for controlling synchronous and asynchronous servomotors it always operates with encoder feedback. The inverter model used in this work is the Movidrive MDX61B 0037-2A3-4-0 with the following characteristics: Power 5 Hp (3.7 kw); phase power supply: 220 V/50–60 Hz; rated output current: 15.2 A and PWM switching frequency: 4, 8, 12, and 16 kHz. Using MOVITOOLS [31] dedicated program, both the switch‐ ing frequency fS of the inverter induction motor as well as the rotational speed can be changed, allowing a more complete analysis of the behavior of the parasitic capacitances to be realized.

### **3.2. Tests laboratory procedure**

A procedure was adopted within the Electrical Machines Laboratory for the measurement tests so that determining the high-frequency capacitance of the induction motors could be carried out in conditions where there is the least possible interference in the results thereof. These procedures are described as follows: a) Ensure the total isolation of the set: threephase induction motor being tested and PWM inverter from the base where they are supported in order that there is no current flow to the system from the motor frame and the inverter. b) Verification of the connections between the motor frame and the inverter with the NEUTRAL of three-phase power supply, allowing you to create a single move‐ ment path of the motor leakage current and hence its correct measurement. c) The entire measurement system (LABVIEW acquisition board) and the computer (notebook) used in the execution of dedicated programs and measured data storage must be the same reference system NEUTRAL. This ensures reliable measurements. d) Correct positioning and enough brush pressure in the ring, the induction motor shaft, ensuring good contact and, there‐ fore, reliable measurements of shaft voltage and current (VSHAFT and ISHAFT). e) Check all connections of the acquisition system/measurement and inverter with the computer. f) carrying out the tests in air-conditioned environment, to ensure the same conditions for the other tests, and g) if possible, work with a fully isolated power system, not only using an isolating transformer, but also ensuring electrical insulation. This way, voltage and current of the supply system will always be the same in any situation and time, providing measurements and better results. Following these procedures, tests of induction motors to determine the parasitic capacitances can be started.

### **3.3. Parasitic capacitances determination of the rotor cage three-phase induction motor**

The high-frequency equivalent circuit is shown again in Figure 15.

When determining the capacitance the following procedure should be followed: a) Switch SH open: Motor bearings are isolated. So there is no current flowing through the bearings and the CB capacitance does not contribute to the value of BVR (Bearing Voltage Ratio). b) Switch SH closed: a circulating current starts to flow through the bearings, and the CB capacitance becomes to influence the value of BVR.

Measurements are performed in the following quantities of interest: common mode voltage (VCM), shaft voltage (VSHAFT), leakage current (ILEAKAGE) shaft current with SH off (ISHAFT-OFF),

motor Analysis and Methodology for Determining the Parasitic Capacitances in VSI-fed IM Drives Based on PWM Technique http://dx.doi.org/10.5772/61544 97

3.3. Parasitic capacitances determination of the rotor cage three-phase induction

tests of induction motors to determine the parasitic capacitances can be started.

The high-frequency equivalent circuit is shown again in Figure 15.

switching frequency fS of the inverter induction motor as well as the rotational speed can be changed,

A procedure was adopted within the Electrical Machines Laboratory for the measurement tests so that determining the high-frequency capacitance of the induction motors could be carried out in conditions where there is the least possible interference in the results thereof. These procedures are described as follows: a) Ensure the total isolation of the set: three-phase induction motor being tested and PWM inverter from the base where they are supported in order that there is no current flow to the system from the motor frame and the inverter. b) Verification of the connections between the motor frame and the inverter with the NEUTRAL of three-phase power supply, allowing you to create a single movement path of the motor leakage current and hence its correct measurement. c) The entire measurement system (LABVIEW acquisition board) and the computer (notebook) used in the execution of dedicated programs and measured data storage must be the same reference system NEUTRAL. This ensures reliable measurements. d) Correct positioning and enough brush pressure in the ring, the induction motor shaft, ensuring good contact and, therefore, reliable measurements of shaft voltage and current (VSHAFT and ISHAFT). e) Check all connections of the acquisition system/measurement and inverter with the computer. f) carrying out the tests in air-conditioned environment, to ensure the same conditions for the other tests, and g) if possible, work with a fully isolated power system, not only using an isolating transformer, but also ensuring electrical insulation. This way, voltage and current of the supply system will always be the same in any situation and time, providing measurements and better results. Following these procedures,

allowing a more complete analysis of the behavior of the parasitic capacitances to be realized.

3.2. Tests laboratory procedure

**Figure 15.** Simplified equivalent circuit of high-frequency induction motor

operates with vector control activated. If there is no feedback loop, it operates with V/f control (scalar) and CFC (Current Flux Control); for controlling synchronous and asynchronous servomotors it always operates with encoder feedback. The inverter model used in this work is the Movidrive MDX61B 0037-2A3-4-0 with the following characteristics: Power 5 Hp (3.7 kw); phase power supply: 220 V/50–60 Hz; rated output current: 15.2 A and PWM switching frequency: 4, 8, 12, and 16 kHz. Using MOVITOOLS [31] dedicated program, both the switch‐ ing frequency fS of the inverter induction motor as well as the rotational speed can be changed, allowing a more complete analysis of the behavior of the parasitic capacitances to be realized.

A procedure was adopted within the Electrical Machines Laboratory for the measurement tests so that determining the high-frequency capacitance of the induction motors could be carried out in conditions where there is the least possible interference in the results thereof. These procedures are described as follows: a) Ensure the total isolation of the set: threephase induction motor being tested and PWM inverter from the base where they are supported in order that there is no current flow to the system from the motor frame and the inverter. b) Verification of the connections between the motor frame and the inverter with the NEUTRAL of three-phase power supply, allowing you to create a single move‐ ment path of the motor leakage current and hence its correct measurement. c) The entire measurement system (LABVIEW acquisition board) and the computer (notebook) used in the execution of dedicated programs and measured data storage must be the same reference system NEUTRAL. This ensures reliable measurements. d) Correct positioning and enough brush pressure in the ring, the induction motor shaft, ensuring good contact and, there‐ fore, reliable measurements of shaft voltage and current (VSHAFT and ISHAFT). e) Check all connections of the acquisition system/measurement and inverter with the computer. f) carrying out the tests in air-conditioned environment, to ensure the same conditions for the other tests, and g) if possible, work with a fully isolated power system, not only using an isolating transformer, but also ensuring electrical insulation. This way, voltage and current of the supply system will always be the same in any situation and time, providing measurements and better results. Following these procedures, tests of induction motors to

**3.3. Parasitic capacitances determination of the rotor cage three-phase induction motor**

When determining the capacitance the following procedure should be followed: a) Switch SH open: Motor bearings are isolated. So there is no current flowing through the bearings and the CB capacitance does not contribute to the value of BVR (Bearing Voltage Ratio). b) Switch SH closed: a circulating current starts to flow through the bearings, and the CB capacitance becomes

Measurements are performed in the following quantities of interest: common mode voltage (VCM), shaft voltage (VSHAFT), leakage current (ILEAKAGE) shaft current with SH off (ISHAFT-OFF),

**3.2. Tests laboratory procedure**

96 Induction Motors - Applications, Control and Fault Diagnostics

determine the parasitic capacitances can be started.

to influence the value of BVR.

The high-frequency equivalent circuit is shown again in Figure 15.

shaft current with SH on (ISHAFT-ON). The following values are determined from the following streams:

Figure 15: Simplified equivalent circuit of high-frequency induction motor

$$I\_{\mathcal{C}\_{\rm SF}} = I\_{\rm LEAKAGE} - I\_{\rm SHAT-OFF} \tag{15}$$

$$I\_{\mathcal{C}\_{\rm SR}} = I\_{\mathcal{C}\_{\rm RF}} = I\_{SHAT-OFF} \tag{16}$$

$$I\_{C\_{\mathfrak{g}}} = I\_{SHAT-OFF} - I\_{SHAT-ON} \tag{17}$$

The parasitic capacitances of the induction motor: CSF, CRF, CSR, and CB are determined through the rewritten equations below:

$$\mathcal{C}\_{\rm SF} = \frac{I\_{\mathcal{C}\_{\rm SF}}}{2.\pi f\_s V\_{\mathcal{C}\mathcal{M}}} \tag{18}$$

$$\mathbf{C}\_{\rm RF} = \frac{I\_{\rm C\_{\rm RF}}}{2.\pi.f\_s.V\_{\rm SHAFT}} \tag{19}$$

$$C\_{SR} = \frac{I\_{C\_{\rm sn}}}{2\,\pi f\_s \left(V\_{CM} - V\_{SHAT}\right)}\tag{20}$$

$$\mathbf{C}\_{B} = \frac{I\_{\mathbf{C}\_{B}}}{I\_{\mathbf{C}\_{\text{RC}}}} \cdot \mathbf{C}\_{\text{RC}} \tag{21}$$

### **4. Measurements and simulations**

The method described in the previous section was applied in three-phase induction motors (two 1 Hp motors). One of the 1 Hp motors no longer presents its original features because the stator windings were fully replaced without regard to the original design features. This procedure allowed to check if there were changes (or not) in the values of the capacitances for the other 1 Hp motor, which presents original project features, since the objective is to ratify that the parasitic capacitances depending only on geometric-constructive features of the motor. Since the determination of the capacitances depends on the quantities of interest at high frequency, the tests may be performed with or without load on the shaft of the induction motors.

### **4.1. Test of three-phase induction motors**

rated speed: 1710 rpm, f) number of poles: 4.

#### *4.1.1. Determination of low-frequency parameters* 4.1.1. Determination of low-frequency parameters

Initially, tests for determining the low-frequency equivalent circuit (nominal) parameters of the motors were performed [27, 37]. The parameters were determined from characteristic tests using the two wattmeter method: test empty and locked rotor test with characteristic equations [26, 27]. The equivalent circuit parameters of the two induction motors 1 Hp shown in Table 1 were determined. These parameters are used in the simulation using PSPICE for analysis and comparison with the results obtained in the laboratory (Figure 16). Initially, tests for determining the low-frequency equivalent circuit (nominal) parameters of the motors were performed [27, 37]. The parameters were determined from characteristic tests using the two wattmeter method: test empty and locked rotor test with characteristic equations [26, 27]. The equivalent circuit parameters of the two induction motors 1 Hp shown in Table 1 were determined. These parameters are used in the simulation using PSPICE for analysis and comparison with the results obtained in the

The two three-phase induction motors used in this test are as follows: a) manufacturer: WEG, b) rated power: 1 Hp, c) nominal voltage: 220V (Δ) / 380V (Y) d) current nominal: 3,8A (Δ) and 2,4a (Y), e) rated speed: 1710 rpm, f) number of poles: 4. laboratory (Figure 16). The two three-phase induction motors used in this test are as follows: a) manufacturer: WEG, b) rated power: 1 Hp, c) nominal voltage: 220V (∆) / 380V (Y) d) current nominal: 3,8A (∆) and 2,4a (Y), e)


**Table 1.** The low-frequency equivalent circuit parameters determined from laboratory 1 (IM1hp2) 8.70 6.53 18.22 366.40

Figure 16: Equivalent circuit of low-frequency induction motor

Using the application program MOVITOOLS [31], the PWM inverter is parameterized in terms of induction motor characteristics to be tested (plate data) as well as the drive and operating characteristics. PWM switching frequency and fundamental frequency of the induction motor can be changed in real time. The application program LabView [35] was set to adjust the frequencies of noise filters and band

After all measurements and calculations, the parasitic capacitance curves were constructed: a) capacitance as a function of motor drive frequency (Hz) to a fixed switching frequency, b) capacitance as a function of the switching frequency to drive 60 Hz motor, c) mean value of capacitance as a function of the switching frequency. The waveforms of the quantities of interest were also obtained by measuring with a

**Figure 16.** Equivalent circuit of low-frequency induction motor

4.1.2. High-frequency parameters determination

digital oscilloscope.

pass of the quantities of interest to the switching frequency of the PWM inverter.

### *4.1.2. High-frequency parameters determination*

Using the application program MOVITOOLS [31], the PWM inverter is parameterized in terms of induction motor characteristics to be tested (plate data) as well as the drive and operating characteristics. PWM switching frequency and fundamental frequency of the induction motor can be changed in real time.

The application program LabView [35] was set to adjust the frequencies of noise filters and band pass of the quantities of interest to the switching frequency of the PWM inverter.

After all measurements and calculations, the parasitic capacitance curves were constructed: a) capacitance as a function of motor drive frequency (Hz) to a fixed switching frequency, b) capacitance as a function of the switching frequency to drive 60 Hz motor, c) mean value of capacitance as a function of the switching frequency. The waveforms of the quantities of interest were also obtained by measuring with a digital oscilloscope.

### **4.2. Test of three-phase induction motors of 1 Hp**

### *4.2.1. Motor IM1hp1*

**4. Measurements and simulations**

98 Induction Motors - Applications, Control and Fault Diagnostics

**4.1. Test of three-phase induction motors**

*4.1.1. Determination of low-frequency parameters*

4.1.1. Determination of low-frequency parameters

motors.

laboratory (Figure 16).

digital oscilloscope.

The method described in the previous section was applied in three-phase induction motors (two 1 Hp motors). One of the 1 Hp motors no longer presents its original features because the stator windings were fully replaced without regard to the original design features. This procedure allowed to check if there were changes (or not) in the values of the capacitances for the other 1 Hp motor, which presents original project features, since the objective is to ratify that the parasitic capacitances depending only on geometric-constructive features of the motor. Since the determination of the capacitances depends on the quantities of interest at high frequency, the tests may be performed with or without load on the shaft of the induction

Initially, tests for determining the low-frequency equivalent circuit (nominal) parameters of the motors were performed [27, 37]. The parameters were determined from characteristic tests using the two wattmeter method: test empty and locked rotor test with characteristic equations [26, 27]. The equivalent circuit parameters of the two induction motors 1 Hp shown in Table 1 were determined. These parameters are used in the simulation using PSPICE for analysis

Initially, tests for determining the low-frequency equivalent circuit (nominal) parameters of the motors were performed [27, 37]. The parameters were determined from characteristic tests using the two wattmeter method: test empty and locked rotor test with characteristic equations [26, 27]. The equivalent circuit parameters of the two induction motors 1 Hp shown in Table 1 were determined. These parameters are used in the simulation using PSPICE for analysis and comparison with the results obtained in the

The two three-phase induction motors used in this test are as follows: a) manufacturer: WEG, b) rated power: 1 Hp, c) nominal voltage: 220V (Δ) / 380V (Y) d) current nominal: 3,8A (Δ) and

The two three-phase induction motors used in this test are as follows: a) manufacturer: WEG, b) rated power: 1 Hp, c) nominal voltage: 220V (∆) / 380V (Y) d) current nominal: 3,8A (∆) and 2,4a (Y), e)

1 (IM1hp1) 8.55 5.62 16.95 346.31 1 (IM1hp2) 8.70 6.53 18.22 366.40

Figure 16: Equivalent circuit of low-frequency induction motor

Lmag

Using the application program MOVITOOLS [31], the PWM inverter is parameterized in terms of induction motor characteristics to be tested (plate data) as well as the drive and operating characteristics. PWM switching frequency and fundamental frequency of the induction motor can be changed in real time. The application program LabView [35] was set to adjust the frequencies of noise filters and band

After all measurements and calculations, the parasitic capacitance curves were constructed: a) capacitance as a function of motor drive frequency (Hz) to a fixed switching frequency, b) capacitance as a function of the switching frequency to drive 60 Hz motor, c) mean value of capacitance as a function of the switching frequency. The waveforms of the quantities of interest were also obtained by measuring with a

Table 1: The low-frequency equivalent circuit parameters determined from laboratory

1 (IM1hp1) 8.55 5.62 16.95 346.31 1 (IM1hp2) 8.70 6.53 18.22 366.40

**(Ω) L1= L2 (mH) Lmag(mH)**

R' 2

(Ω) L1= L<sup>2</sup> (mH) Lmag(mH)

L' 2

and comparison with the results obtained in the laboratory (Figure 16).

**Table 1.** The low-frequency equivalent circuit parameters determined from laboratory

R<sup>1</sup> L<sup>1</sup>

2,4a (Y), e) rated speed: 1710 rpm, f) number of poles: 4.

**Motor (Hp) R1(Ω) R2 '**

Motor (Hp) R1(Ω) R2'

V<sup>1</sup>

4.1.2. High-frequency parameters determination

**Figure 16.** Equivalent circuit of low-frequency induction motor

pass of the quantities of interest to the switching frequency of the PWM inverter.

rated speed: 1710 rpm, f) number of poles: 4.

The three-phase induction motor 1 Hp (IM1hp1) is connected to stator winding delta (Δ), and 220 V line voltage. A star configuration equivalent to the common mode voltage measurement (VCM) is well utilized. Table 2 shows the measured values of the quantities of interest. Table 3 shows the calculated values of the currents flowing between the stator and the motor frame (ICSF) and bearings (ICB). Table 4 shows the calculated values of the three-phase induction motor parasitic capacitances 1Hp IM1hp1.

Measurements and calculations of quantities of interest of parasitic capacitances of the two induction motors were made to switching frequencies of 12 and 16 kHz. The results for the switching frequencies of 4 and 8 kHz can be observed in [40].



**Table 2.** Measurement of quantities of interest of 1Hp motor IM1hp1


**Table 3.** Calculated currents – IM1hp1


Analysis and Methodology for Determining the Parasitic Capacitances in VSI-fed IM Drives Based on PWM Technique http://dx.doi.org/10.5772/61544 101


**Table 4.** Parasitic capacitances motor 1Hp IM1hp1

characteristics of the motor [1].

speed [10].

**Inverter Switching Frequency (kHz)**

> **Inverter Switching Frequency (kHz)**

> > 12

16

**Table 3.** Calculated currents – IM1hp1

**Motor Frequency (Hz)**

**Inverter Switching Frequency (kHz)**

12

16

**Motor Frequency (Hz)**

100 Induction Motors - Applications, Control and Fault Diagnostics

**Table 2.** Measurement of quantities of interest of 1Hp motor IM1hp1

**VCM (V)**

**VSHAFT (V)**

**Motor Frequency (Hz)**

> **CSF (pF)**

**ILEAKAGE (mA)**

50 51,77 2,53 10,50 0,302 0,257 60 33,71 1,67 7,03 0,202 0,175

**ISHAFT-OFF (mA)**

**IcSF (mA)**

 13,84 0,07 12,06 0,05 10,19 0,04 7,58 0,03 13,84 0,07

 18,86 0,10 16,81 0,08 13,80 0,06 10,20 0,05 6,83 0,03

> **CRF (pF)**

 1967,82 1387,17 67,99 268,72 1946,16 1346,89 66,57 191,85 2004,05 1430,60 70,82 188,86 1988,84 1382,29 67,97 183,88 2027,35 1427,71 71,07 149,30

20 1997,33 1199,87 60,53 283,61 30 1991,15 1194,67 61,00 226,18

**CSR (pF)**

**CB (pF)**

**ISHAFT-ON (mA)**

**IcB (mA)**

Figure 17 shows the values of each of the parasitic capacitances on the basis of the motor frequency (speed) specific to the switching frequency of the PWM inverter 12 kHz and 16 kHz. Figure 17 shows the values of each of the parasitic capacitances on the basis of the motor frequency (speed) specific to the switching frequency of the PWM inverter 12 kHz and 16 kHz.

a)

b)

The capacitances CSF, CRF, CSR are almost constant for the variation of the motor frequency and the switching frequency of the PWM inverter, indicating that they depend mainly on the geometric

In turn, the CB capacitance decreases with increasing motor frequency (increase the speed). This is because, besides being dependent on the dimensions of the bearing, this capacitance is also a function of

Figure 17: Parasitic capacitances due to motor frequency of 1 Hp (IM1hp1) for 12 kHz (a) and 16 kHz (b)

inverter switching frequency **Figure 17.** Parasitic capacitances due to motor frequency of 1 Hp (IM1hp1) for 12 kHz (a) and 16 kHz (b) inverter switching frequency

The capacitances CSF, CRF, CSR are almost constant for the variation of the motor frequency and the switching frequency of the PWM inverter, indicating that they depend mainly on the geometric characteristics of the motor [1].

In turn, the CB capacitance decreases with increasing motor frequency (increase the speed). This is because, besides being dependent on the dimensions of the bearing, this capacitance is also a function of speed [10].

Figure 18 shows the values of the parasitic capacitances on the basis of the switching frequency of the PWM inverter to the motor frequency of 60Hz. The results confirm that the parasitic capacitances depend exclusively on the physical constructive characteristics of the induction motor. Figure 18 shows the values of the parasitic capacitances on the basis of the switching frequency of the PWM inverter to the motor frequency of 60Hz. The results confirm that the parasitic capacitances depend exclusively on the physical constructive characteristics of the induction motor. Figure 18 shows the values of the parasitic capacitances on the basis of the switching frequency of the PWM inverter to the motor frequency of 60Hz. The results confirm that the parasitic capacitances depend exclusively on the physical constructive characteristics of the induction motor.

Figure 18: Capacitances due to the motor switching frequency of 1 Hp (IM1hp1) power frequency 60 Hz **Figure 18.** Capacitances due to the motor switching frequency of 1 Hp (IM1hp1) power frequency 60 Hz Figure 18: Capacitances due to the motor switching frequency of 1 Hp (IM1hp1) power frequency 60 Hz

Figure 19 presents the average parasitic capacitance values of the motor 1 Hp IM1hp1. Figure 19 presents the average parasitic capacitance values of the motor 1 Hp IM1hp1. Figure 19 presents the average parasitic capacitance values of the motor 1 Hp IM1hp1.

Figure 19: Average values of the capacitances for 1 Hp motor (IM1hp1)

Figure 19: Average values of the capacitances for 1 Hp motor (IM1hp1) **Figure 19.** Average values of the capacitances for 1 Hp motor (IM1hp1)

### *4.2.2. Motor IM1hp2*

The capacitances CSF, CRF, CSR are almost constant for the variation of the motor frequency and the switching frequency of the PWM inverter, indicating that they depend mainly on the

In turn, the CB capacitance decreases with increasing motor frequency (increase the speed). This is because, besides being dependent on the dimensions of the bearing, this capacitance is

Figure 18 shows the values of the parasitic capacitances on the basis of the switching frequency of the PWM inverter to the motor frequency of 60Hz. The results confirm that the parasitic capacitances depend exclusively on the physical constructive characteristics of the induction

MOTOR 1Hp – IM1hp1 – fmotor= 60Hz

MOTOR 1Hp – IM1hp1 – fmotor= 60Hz

Figure 18 shows the values of the parasitic capacitances on the basis of the switching frequency of the PWM inverter to the motor frequency of 60Hz. The results confirm that the parasitic capacitances

Figure 18 shows the values of the parasitic capacitances on the basis of the switching frequency of the PWM inverter to the motor frequency of 60Hz. The results confirm that the parasitic capacitances

Figure 18: Capacitances due to the motor switching frequency of 1 Hp (IM1hp1) power frequency 60 Hz

Figure 18: Capacitances due to the motor switching frequency of 1 Hp (IM1hp1) power frequency 60 Hz

Figure 19 presents the average parasitic capacitance values of the motor 1 Hp IM1hp1.

MOTOR 1Hp – IM1hp1 - Average Values

MOTOR 1Hp – IM1hp1 - Average Values

4 8 12 16 Switching frequency – f<sup>S</sup> (kHz)

4 8 12 16 Switching frequency – f<sup>S</sup> (kHz)

CSF CRF CSR C<sup>B</sup>

CSF CRF CSR C<sup>B</sup>

4 8 12 16 Switching frequency (kHz)

4 8 12 16 Switching frequency (kHz)

CSF CRF CSR C<sup>B</sup>

CSF CRF CSR C<sup>B</sup>

Figure 19: Average values of the capacitances for 1 Hp motor (IM1hp1)

Figure 19: Average values of the capacitances for 1 Hp motor (IM1hp1)

**Figure 19.** Average values of the capacitances for 1 Hp motor (IM1hp1)

Figure 19 presents the average parasitic capacitance values of the motor 1 Hp IM1hp1.

Figure 19 presents the average parasitic capacitance values of the motor 1 Hp IM1hp1.

**Figure 18.** Capacitances due to the motor switching frequency of 1 Hp (IM1hp1) power frequency 60 Hz

depend exclusively on the physical constructive characteristics of the induction motor.

depend exclusively on the physical constructive characteristics of the induction motor.

geometric characteristics of the motor [1].

102 Induction Motors - Applications, Control and Fault Diagnostics

also a function of speed [10].

Capacitance (pF)

Capacitance (pF)

0,00 500,00 1000,00 1500,00 2000,00 2500,00

0,00 500,00 1000,00 1500,00 2000,00 2500,00

Capacitance (pF)

Capacitance (pF)

0,00 500,00 1000,00 1500,00 2000,00 2500,00 3000,00

0,00 500,00 1000,00 1500,00 2000,00 2500,00 3000,00

motor.

The results for the second three-phase induction motor 1Hp, IM1hp2 are shown below. Table 5 presents the measured values of the quantities of interest.

Table 6 presents the calculated values of the currents flowing between the stator and the motor frame (ICSF) and bearings (ICB).

Table 7 presents the calculated values of the three-phase induction motor parasitic capacitances of 1 Hp IM1hp2.


**Table 5.** Measurement of quantities of interest – IM1hp2



**Table 6.** Calculated currents – IM1hp2


**Table 7.** Parasitic capacitances of motor 1 Hp IM1hp2

Figure 20 shows the values obtained for the parasitic capacitance depending on the motor frequency, for specific switching frequency of the PWM inverter 12 kHz and 16 kHz.

The same behaviors found in the motor 1Hp IM1hp1 were observed.

Figure 21 shows the values of the parasitic capacitances on the basis of the switching frequency of the PWM inverter to the motor frequency of 60Hz.

frequency, for specific switching frequency of the PWM inverter 12 kHz and 16 kHz. The same behaviors found in the motor 1Hp IM1hp1 were observed. Analysis and Methodology for Determining the Parasitic Capacitances in VSI-fed IM Drives Based on PWM Technique http://dx.doi.org/10.5772/61544 105

Figure 20 shows the values obtained for the parasitic capacitance depending on the motor

a)

Figure 20: a),b) Parasitic capacitances due to motor frequency for different inverter switching frequency (IM1hp2) **Figure 20.** a),b) Parasitic capacitances due to motor frequency for different inverter switching frequency (IM1hp2)

Figure 22 presents the average values of parasitic capacitance of motor 1 Hp IM1hp2. Figure 21 shows the values of the parasitic capacitances on the basis of the switching frequency of

#### **4.3. Simulations and measurements** the PWM inverter to the motor frequency of 60Hz.

**Inverter Switching Frequency (kHz)**

104 Induction Motors - Applications, Control and Fault Diagnostics

16

**Table 6.** Calculated currents – IM1hp2

**Motor Frequency (Hz)**

**Inverter Switching Frequency (kHz)**

12

16

**Table 7.** Parasitic capacitances of motor 1 Hp IM1hp2

**Motor Frequency (Hz)**

> **CSF (pF)**

Figure 20 shows the values obtained for the parasitic capacitance depending on the motor

Figure 21 shows the values of the parasitic capacitances on the basis of the switching frequency

frequency, for specific switching frequency of the PWM inverter 12 kHz and 16 kHz.

The same behaviors found in the motor 1Hp IM1hp1 were observed.

of the PWM inverter to the motor frequency of 60Hz.

**IcSF (mA)**

60 5,31 0,02

 19,47 0,20 17,98 0,15 14,78 0,09 10,80 0,04 7,46 0,03

> **CRF (pF)**

 2008,24 1239,80 57,09 1062,69 1977,10 1215,68 55,55 661,51 2013,30 1185,36 56,30 442,07 1995,63 1244,62 58,64 253,24 2032,70 1291,66 59,73 159,75

 2036,24 1212,65 58,06 749,66 2107,39 1196,70 58,72 554,36 2104,88 1212,93 60,35 349,10 2027,39 1215,36 59,69 196,66 2163,08 1280,51 64,68 172,38

**CSR (pF)**

**IcB (mA)**

> **CB (pF)**

> > The software Pspice [30, 36] was used to simulate the methodology and compare the wave‐ forms obtained in the simulations with actual measurements made using digital oscilloscope. The schematic circuit simulation is shown in Figure 23.

> > The schematic circuit comprises: a) inverter structure with three-phase supply, three-phase rectifier without control (diodes) with DC bus, and three-phase inverter bridge; b) equivalent

MOTOR 1Hp IM1hp2 – fmotor = 60Hz

Figure 21: Capacitances due to the motor switching frequency of 1 Hp (IM1hp2) motor frequency 60 Hz **Figure 21.** Capacitances due to the motor switching frequency of 1 Hp (IM1hp2) motor frequency 60 Hz Figure 22 presents the average values of parasitic capacitance of motor 1 Hp IM1hp2.

CSF CRF CSR C<sup>B</sup> Figure 22: Average values of capacitance for the motor 1 Hp IM1hp2 **Figure 22.** Average values of capacitance for the motor 1 Hp IM1hp2

circuit of low-frequency induction motor; c) equivalent circuit of high-frequency three-phase induction motor; and d) signal generator with pulse width modulation (PWM). Figure 22: Average values of capacitance for the motor 1 Hp IM1hp2

The charts below show waveforms that appear in the named graphs (a) are results of meas‐ urements by using digital oscilloscope. The forms of common mode voltage wave (VCM) are attenuated to match the oscilloscope's full-scale capacity. The waveforms that appear in the named graphs (b) are obtained by using PSPICE simulation application. Without loss of generality, in the simulation (Figure 23) are used ideal components of semiconductor switches that facilitate the process of solving differential equations reducing convergence problems.

The waveforms shown below are the quantities of interest with switching frequency of 16 kHz PWM inverter and frequency of 60 Hz motor to three-phase induction motors of 1 Hp (IM1hp1 and IM1hp2), respectively.

The software Pspice [30, 36] was used to simulate the methodology and compare the waveforms obtained in the simulations with actual measurements made using digital oscilloscope. The schematic Analysis and Methodology for Determining the Parasitic Capacitances in VSI-fed IM Drives Based on PWM Technique http://dx.doi.org/10.5772/61544 107

**Figure 23.** Schematic circuit used for simulation in Pspice [40]

4.3. Simulations and measurements

circuit simulation is shown in Figure 23.

circuit of low-frequency induction motor; c) equivalent circuit of high-frequency three-phase

MOTOR 1Hp IM1hp2 - Average Values

MOTOR 1Hp IM1hp2 - Average Values

4 8 12 16 Switching frequency – f<sup>S</sup> (kHz)

CSF CRF CSR C<sup>B</sup>

4 8 12 16 Switching frequency – f<sup>S</sup> (kHz)

CSF CRF CSR C<sup>B</sup>

4 8 12 16 Switching frequency (kHz)

CSF CRF CSR C<sup>B</sup>

4 8 12 16 Switching frequency (kHz)

CSF CRF CSR C<sup>B</sup>

The charts below show waveforms that appear in the named graphs (a) are results of meas‐ urements by using digital oscilloscope. The forms of common mode voltage wave (VCM) are attenuated to match the oscilloscope's full-scale capacity. The waveforms that appear in the named graphs (b) are obtained by using PSPICE simulation application. Without loss of generality, in the simulation (Figure 23) are used ideal components of semiconductor switches that facilitate the process of solving differential equations reducing convergence problems. The waveforms shown below are the quantities of interest with switching frequency of 16 kHz PWM inverter and frequency of 60 Hz motor to three-phase induction motors of 1 Hp (IM1hp1

induction motor; and d) signal generator with pulse width modulation (PWM).

**Figure 22.** Average values of capacitance for the motor 1 Hp IM1hp2

Figure 22: Average values of capacitance for the motor 1 Hp IM1hp2

Figure 22: Average values of capacitance for the motor 1 Hp IM1hp2

Figure 21: Capacitances due to the motor switching frequency of 1 Hp (IM1hp2) motor frequency 60 Hz

Figure 21: Capacitances due to the motor switching frequency of 1 Hp (IM1hp2) motor frequency 60 Hz

**Figure 21.** Capacitances due to the motor switching frequency of 1 Hp (IM1hp2) motor frequency 60 Hz

MOTOR 1Hp IM1hp2 – fmotor = 60Hz

MOTOR 1Hp IM1hp2 – fmotor = 60Hz

Figure 22 presents the average values of parasitic capacitance of motor 1 Hp IM1hp2.

Figure 22 presents the average values of parasitic capacitance of motor 1 Hp IM1hp2.

and IM1hp2), respectively.

0,00 500,00 1000,00 1500,00 2000,00 2500,00

0,00 500,00 1000,00 1500,00 2000,00 2500,00

Capacitance (pF)

Capacitance (pF)

0,00 500,00 1000,00 1500,00 2000,00 2500,00 3000,00

0,00 500,00 1000,00 1500,00 2000,00 2500,00 3000,00

Capacitance (pF)

Capacitance (pF)

106 Induction Motors - Applications, Control and Fault Diagnostics

Figures 24 and 25 show the waveforms of various quantities of interest for the three-phase induction motor 1Hp IM1hp1, Figures 26 and 27 show the waveforms for the three-phase induction motor of 1 Hp IM1hp2. without control (diodes) with DC bus, and three-phase inverter bridge; b) equivalent circuit of lowfrequency induction motor; c) equivalent circuit of high-frequency three-phase induction motor; and d) signal generator with pulse width modulation (PWM).

Figure 23: Schematic circuit used for simulation in Pspice [40]

The schematic circuit comprises: a) inverter structure with three-phase supply, three-phase rectifier

a)

b) Figure 25: VCM – CH1, ILEAKAGE – CH2; a) measured, b) simulated – (IM1hp1)

 Time 26.2489ms 26.2800ms 26.3200ms 26.3600ms 26.4000ms 26.4400ms 26.4753ms

t (ms) 0 0.25

b) t(ms)

Ifuga

Vcm

**Figure 24.** VCM – CH1, VSHAFT – CH2; a) measured, b) simulated (IM1hp1)




0-1.5

0 -200 ILEAKAGE(A) 1.5

VCM(V) 100

SEL>>



0

0V


200V

VCM(V) 200 0

SEL>>

Figure 25: VCM – CH1, ILEAKAGE – CH2; a) measured, b) simulated – (IM1hp1)

a)

Vcm

Veixo

Figure 24: VCM – CH1, VSHAFT – CH2; a) measured, b) simulated (IM1hp1)

b) t(ms)

**Figure 25.** VCM – CH1, ILEAKAGE – CH2; a) measured, b) simulated – (IM1hp1)

Figure 26: VCM – CH1, VSHAFT– CH2 - a) measured, b) simulated - (IM1hp2)

a)

b) Figure 27: VCM – CH 1, ILEAKAGE – CH 2 - a) measured, b) simulated - (IM1hp2)

Ifuga

 Time 93.3743ms 93.4000ms 93.4400ms 93.4800ms 93.5200ms 93.5600ms 93.6000ms

b) t(ms)


**Figure 26.** VCM – CH1, VSHAFT– CH2 - a) measured, b) simulated - (IM1hp2)


V(VCOM) -200V

200V VCM(V) 200 Vcm

0A

0

SEL>>

4.0A


0V

0

Figure 26: VCM – CH1, VSHAFT– CH2 - a) measured, b) simulated - (IM1hp2)

Veixo

a)

**Figure 27.** VCM – CH 1, ILEAKAGE – CH 2 - a) measured, b) simulated - (IM1hp2)


0

0V

0


V(VCOM) -200V

200V VCM(V) 200 Vcm

### **5. Results and conclusions**

a)

Vcm

Veixo

Figure 24: VCM – CH1, VSHAFT – CH2; a) measured, b) simulated (IM1hp1)

 Time 26.30ms 26.40ms 26.50ms 26.60ms 26.70ms 26.78ms

0 0.25

b) t(ms)

a)

b) Figure 25: VCM – CH1, ILEAKAGE – CH2; a) measured, b) simulated – (IM1hp1)

a)

Figure 26: VCM – CH1, VSHAFT– CH2 - a) measured, b) simulated - (IM1hp2)

Veixo

 Time 93.3743ms 93.4000ms 93.4400ms 93.4800ms 93.5200ms 93.5600ms 93.6000ms

b) t(ms)


a)

b) Figure 27: VCM – CH 1, ILEAKAGE – CH 2 - a) measured, b) simulated - (IM1hp2)

Ifuga

 Time 93.3743ms 93.4000ms 93.4400ms 93.4800ms 93.5200ms 93.5600ms 93.6000ms

b) t(ms)



V(VEIXO) -10V -5V 0V 5V

**Figure 26.** VCM – CH1, VSHAFT– CH2 - a) measured, b) simulated - (IM1hp2)

V(VCOM) -200V

VCM(V) 200 Vcm

SEL>>


V(VCOM) -200V

200V VCM(V) 200 Vcm

0A

0

SEL>>

4.0A


0V

0

0

0V

0


200V

**Figure 25.** VCM – CH1, ILEAKAGE – CH2; a) measured, b) simulated – (IM1hp1)



108 Induction Motors - Applications, Control and Fault Diagnostics


SEL>>

0 -15

0V


200V

VCM(V) 200 0

> -1.0A 0A 1.0A

0

0 -200 ILEAKAGE(A) 1.5

VCM(V) 100

SEL>>


 Time 26.2489ms 26.2800ms 26.3200ms 26.3600ms 26.4000ms 26.4400ms 26.4753ms

t (ms) 0 0.25

b) t(ms)

Ifuga

Vcm

In the comparison of results between the two 1Hp motors (IM1hp1 and IM1hp2), the following considerations are made: (a) Although the motors are of the same power and the same manufacturer, one of them underwent maintenance and the other still has its original compo‐ nents. This results in differences in the values of capacitances CSF, CRF, and CB. The exchange of maintaining consisted of stator conductors, insulating layer placed in the stator slots, and replacing the original bearings. These changes result in different values of capacitances, although they present very similar values. (b) The use of sensors of both voltage and current characteristics more suitable for this type of experiment such as precision operation range, frequency response, are necessary to avoid problems like those that occurred mainly in the measurements of the motors on the switching frequency of 4 kHz [40]. (c) There was no automation of measurements of quantities of interest according to the equipment available for this purpose. Thus, measurement errors were the same, but it can still be said that they were within a satisfactory tolerance, when comparing these two motors. In Table 8, comparisons are shown between the parasitic capacitances for two 1Hp motors.

The methodology for determining the parasitic capacitance of the induction motor, when driven by a PWM inverter presents consistent and coherent results.


The results of the tests have revealed that the parasitic capacitances of the induction motor are a function only of the geometric-constructive characteristics [40, 41].

**Table 8.** Comparison between the parasitic capacitances of 1Hp motors

The switching frequency variations almost do not change the values of the capacitances. In fact, the quantity which have their values changed due the variation of switching frequencies is the reactance of these capacitances. High switching frequency of the PWM inverter, despite improving the characteristic shape of the load current wave, causes the switching time of power electronic devices (IGBT or MOSFET) to be rather low, resulting in increased rates of growth of voltage (dV/dt) [7]. This reflects directly on the currents flowing through the parasitic capacitances and therefore the leakage current.

Also there is an increase of the amplitude of these currents due to the capacitive reactance parasites being substantially diminished in value due to the increase of the switching frequen‐ cy. So, the effects of electromagnetic interference are increased both on bearings (bearing currents) as on capacitive currents in the motor. It is also noticed that the bearing of capacitance values (CB) decrease with increasing induction motor speed [10].

Common mode filters are used to minimize the effects of currents flowing through the parasitic capacitances of the induction motor. The accurate determination of these capacitances values, using the methodology proposed in this section, has the main objective of optimizing the design of these filters.

This optimization implies a more accurate and reliable specification of the components used in filter design, thus providing a significant reduction of volume and weight of the filter; the number of components used, and thus cost reduction thereof.

### **Author details**

The results of the tests have revealed that the parasitic capacitances of the induction motor are

**CSF (pF)**

**Motor** 20 1997,33 1199,87 60,53 283,61 **1Hp** 30 1991,15 1194,67 61,00 226,18 **IM1hp1** 40 1982,45 1189,56 60,87 216,28

**Motor** 20 2036,24 1212,65 58,06 749,66 **1Hp** 30 2107,39 1196,70 58,72 554,36 **IM1hp2** 40 2104,88 1212,93 60,35 349,10

The switching frequency variations almost do not change the values of the capacitances. In fact, the quantity which have their values changed due the variation of switching frequencies is the reactance of these capacitances. High switching frequency of the PWM inverter, despite improving the characteristic shape of the load current wave, causes the switching time of power electronic devices (IGBT or MOSFET) to be rather low, resulting in increased rates of growth of voltage (dV/dt) [7]. This reflects directly on the currents flowing through the

Also there is an increase of the amplitude of these currents due to the capacitive reactance parasites being substantially diminished in value due to the increase of the switching frequen‐ cy. So, the effects of electromagnetic interference are increased both on bearings (bearing currents) as on capacitive currents in the motor. It is also noticed that the bearing of capacitance

Common mode filters are used to minimize the effects of currents flowing through the parasitic capacitances of the induction motor. The accurate determination of these capacitances values, using the methodology proposed in this section, has the main objective of optimizing the

**CRF (pF)**

50 1959,52 1187,41 61,01 207,91 60 2014,87 1203,23 62,72 185,64

50 2027,39 1215,36 59,69 196,66 60 2163,08 1280,51 64,68 172,38

**CSR (pF)**

**CB (pF)**

a function only of the geometric-constructive characteristics [40, 41].

**Motor Frequency (Hz)**

110 Induction Motors - Applications, Control and Fault Diagnostics

**Table 8.** Comparison between the parasitic capacitances of 1Hp motors

parasitic capacitances and therefore the leakage current.

values (CB) decrease with increasing induction motor speed [10].

**Inverter Switching Frequency (kHz)**

**16**

**16**

design of these filters.

Rudolf Ribeiro Riehl1\*, Fernando de Souza Campos1 , Alceu Ferreira Alves1 and Ernesto Ruppert Filho2

\*Address all correspondence to: rrriehl@feb.unesp.br

1 São Paulo State University, Unesp, Bauru, Brazil

2 State University of Campinas, Unicamp, Campinas, Brazil

### **References**


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## **Health Condition Monitoring of Induction Motors**

Wilson Wang and Derek Dezhi Li

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61110

### **Abstract**

Induction motors (IMs) are commonly used in various industrial applications. A spectrum synch (SS) technique is proposed in this chapter for early IM defect detection using electric current signals; fault detection in this work will focus on defects in rolling element bearings and rotor bars, which together account for more than half of IM imperfections. In bearing fault detection, the proposed SS technique will highlight the peakedness of the fault frequency components distributed over several fault related local bands. These bands are synchronized to form a fault information spectrum to accentuate fault features. A central kurtosis indicator is proposed to extract representative features from the fault information spectrum and formulate a fault index for incipient IM fault diagnosis. The effectiveness of the developed SS technique is tested on IMs with broken rotor bars and with damaged bearings.

**Keywords:** Induction motors, Bearing fault detection, Broken rotor bars, Current signal, Spectrum synch analysis

### **1. Introduction**

Induction motors (IMs) are the workhorse of many industries such as manufacturing, mining, and transportation; and more importantly, they consume up to 50% of the generated electrical energy in the world [1]. Due to these facts, a series of R&D activities have been directed, for decades, to improve the performance and efficiency of IMs. For example, in industrial applications, an effective and reliable condition monitoring system is very valuable in the detection of an IM fault at its earliest stage in order to prevent performance reduction and malfunction of the driven machinery. It could also be utilized to schedule predictive mainte‐

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

nance operations without periodically shutting down machines for manual inspections. Maintenance costs can be further reduced (especially for large expensive motors) by quickly identifying the faulty component(s) without inspecting all components in the IM.

As illustrated in Figure 1, a typical IM consists of a stator, a rotor, a shaft, rolling element bearings, and the related supplementary components. IM components could be damaged during operations due to reasons such as impacts, fatigue, insufficient lubrication, aging, and so on. Investigations have revealed that bearing faults account for approximately 75% of small and medium-sized motor defects and 41% of large motor imperfections in domestic and industrial applications [2]. Other IM defects include broken rotor bars (up to 10%), stator winding faults, shaft imbalance, and phase imperfection.

**Figure 1.** Structure of induction motors: 1-shaft, 2-bearings, 3-rotor, 4-stator.

The traditional IM fault diagnostic method, which is still widely practiced by maintenance crews in industry, relies on human diagnosticians for periodic inspections based on warning signs such as smell, temperature increase, excessive vibration, and increased acoustic noise level. However, these physical symptoms are prone to being contaminated with noise from other sources. The alternative is the use of signal processing techniques for fault detection. Signal processing is a process to extract representative features from the collected signals. Traditional machinery fault detection is based on thermal signals [3], acoustic signals, and vibration signals [4,5]. The local or bulk temperature can be used to diagnose IM defects, however the heat accumulation and progression are slow, which may not be suitable for incipient fault detection. The acoustic noise can indicate IM faults, especially for severe and distributed defects; however the acoustic signal is prone to contamination by background noise such as noise from other machines in the vicinity. Vibration signals can be collected by the use of the related vibration sensors mounted in the vicinity of the IM support bearings. Although vibration signals have relatively high signal-to-noise ratio, the vibration sensors are expensive and require a high degree of installation accuracy. The alternative is to use the stator current signal for analysis, which is non-invasive to the IM structure. In addition, electric current sensors are inexpensive and easy to install [6]. Thus, the proposed research in this work will focus on IM fault diagnosis using stator current signals.

Several motor current signature analysis techniques have been proposed in the literature for fault detection in IMs, mainly for rotors and bearings, which are briefly summarized next.

### **1.1. Fault detection of IM rotors**

nance operations without periodically shutting down machines for manual inspections. Maintenance costs can be further reduced (especially for large expensive motors) by quickly

As illustrated in Figure 1, a typical IM consists of a stator, a rotor, a shaft, rolling element bearings, and the related supplementary components. IM components could be damaged during operations due to reasons such as impacts, fatigue, insufficient lubrication, aging, and so on. Investigations have revealed that bearing faults account for approximately 75% of small and medium-sized motor defects and 41% of large motor imperfections in domestic and industrial applications [2]. Other IM defects include broken rotor bars (up to 10%), stator

identifying the faulty component(s) without inspecting all components in the IM.

winding faults, shaft imbalance, and phase imperfection.

118 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 1.** Structure of induction motors: 1-shaft, 2-bearings, 3-rotor, 4-stator.

The traditional IM fault diagnostic method, which is still widely practiced by maintenance crews in industry, relies on human diagnosticians for periodic inspections based on warning signs such as smell, temperature increase, excessive vibration, and increased acoustic noise level. However, these physical symptoms are prone to being contaminated with noise from other sources. The alternative is the use of signal processing techniques for fault detection. Signal processing is a process to extract representative features from the collected signals. Traditional machinery fault detection is based on thermal signals [3], acoustic signals, and vibration signals [4,5]. The local or bulk temperature can be used to diagnose IM defects, however the heat accumulation and progression are slow, which may not be suitable for incipient fault detection. The acoustic noise can indicate IM faults, especially for severe and distributed defects; however the acoustic signal is prone to contamination by background noise

Broken rotor bars are common rotor defects that will render asymmetries of an IM rotor. The rotor bar failures can be caused by several factors, such as overheating due to frequent starts under loading, unbalanced thermal load due to air gap eccentricity, manufacturing defects, and corrosion of rotor material caused by chemicals or moisture [7].

Because of the aforementioned reasons, the rotor bar(s) may be fully or partially damaged, which will cause the rotor cage asymmetry and result in asymmetrical distribution of the rotor currents. When a crack forms in a rotor bar, the cracked bar will overheat and tend to break. Then the adjacent bars have to carry higher currents and consequently they become prone to damage, leading to multiple bar fractures. Moreover, the broken parts from the faulty bars may hit the end winding of the motor and cause serious mechanical damage to the IM [8].

The Fast Fourier Transform (FFT) spectral analysis is a commonly used method for rotor bar breakage detection, by examining the characteristic frequency components in the spectrum. For example, Elkasabgy et al. [9] used spectral analysis of IM current signals to detect rotor bar breakage. It has been reported that the IM current signal becomes non-stationary if rotor bars are damaged. However, the FFT is useful for stationary signal analysis only, which lacks the capability of capturing the transitory characteristics such as drifts, abrupt changes, and frequency trends in non-stationary signals. To solve the problem, time-frequency methods, such as short time Fourier transform (STFT), can be used to process small segments of nonstationary signals for broken rotor bar defect detection. For example, Arabaci and Bilgin [10] applied the STFT to detect IM rotor bar faults. However, the STFT cannot provide the infor‐ mation corresponding to different time resolutions and frequency resolutions due to its fixed length windowing functions [11]. To solve this problem, the wavelet transform (WT) can be employed to explore the information associated with different frequency resolutions. For example, Daviu et al. [12] used discrete WT to detect IM broken rotor bars fault. The wavelet packet decomposition (WPD) was used to explore the whole frequency band with high resolution. For example, Sadeghian et al. [13] used WPD to extract features and applied neural networks to diagnose IM rotor bar breakage. Pineda-Sanchez et al. [14] employed polynomialphase transform to diagnose broken rotor bar fault in time-varying condition. Riera-Guasp et al. [15] extracted broken rotor bar fault features from transient state of IM using Gabor analysis. Although the WPD can explore details of the signal for some advanced signal analysis, it is usually difficult to recognize the real representative features from the map with redundant and misleading information. Akin et al. [16] performed real-time fault detection using the reference frame theory. Soualhi et al. [17] diagnosed broken rotor bar fault through the classification of selected fault features using the improved artificial ant clustering method. Gunal et al. [18] conducted IM broken rotor bar fault diagnosis by using fault indices in the time domain. Nevertheless, the aforementioned techniques only focus on limited fault information, thus their performance may be degraded.

### **1.2. Fault detection of IM bearings**

Rolling element bearings are commonly used not only in electric motors, but also in various types of rotating machinery facilities. As illustrated in Figure 2, a rolling element bearing is a system consisting of an outer ring (usually the fixed ring), an inner ring (usually the rotating ring), a number of rolling elements, and a cage.

**Figure 2.** Structure of a rolling element bearing. **Figure 2.** Structure of a rolling element bearing.

excessive misalignment errors.

*frd* are determined by

 Since bearing materials are subjected to dynamic loading, fatigue pitting is the most common defect in bearing components. The bearing defects can occur on the outer race, inner race, and rolling elements. Under normal operating conditions, after the load cycles exceed some threshold, fatigue pitting may occur on the fixed ring race first, and then on Since bearing materials are subjected to dynamic loading, fatigue pitting is the most common defect in bearing components. The bearing defects can occur on the outer race, inner race, and rolling elements. Under normal operating conditions, after the load cycles exceed some threshold, fatigue pitting may occur on the fixed ring race first, and then on the rotating race and rolling elements. Pitting defects not only deteriorate transmission accuracy, but also generate excessive vibration and noise. Other bearing defects, such as scoring and severe wear [7], can be generated by several external causes such as impacts, overloading and overheating, inadequate lubrication, contamination and corrosion from abrasive particles or acid, and improper installation of a bearing, which will introduce excessive misalignment errors.

the rotating race and rolling elements. Pitting defects not only deteriorate transmission When a bearing component is damaged, the corresponding characteristic frequencies will be associated with the bearing geometry, rotation speed, and defect location. Suppose the outer

accuracy, but also generate excessive vibration and noise. Other bearing defects, such as

scoring and severe wear [7], can be generated by several external causes such as impacts,

overloading and overheating, inadequate lubrication, contamination and corrosion from

abrasive particles or acid, and improper installation of a bearing, which will introduce

When a bearing component is damaged, the corresponding characteristic frequencies

will be associated with the bearing geometry, rotation speed, and defect location. Suppose

the outer race of a bearing is fixed and the inner race rotates with the shaft, which is

common case in most applications. The outer race defect characteristic frequency *fod*, inner

race defect characteristic frequency *fid*, and rolling element defect characteristic frequency

2

*<sup>D</sup> frd <sup>i</sup>*

*<sup>d</sup> <sup>f</sup> <sup>N</sup> fid <sup>i</sup>*

2

 *<sup>D</sup> <sup>d</sup> <sup>f</sup> <sup>N</sup> fod <sup>i</sup>*

 

2 *D <sup>d</sup> <sup>f</sup> <sup>d</sup>*

  (1)

(2)

(3)

 

 

2

)cos( <sup>1</sup>

)cos( <sup>1</sup>

*D*

cos <sup>1</sup>

race of a bearing is fixed and the inner race rotates with the shaft, which is common case in most applications. The outer race defect characteristic frequency *fod* inner race defect charac‐ teristic frequency *fid* and rolling element defect characteristic frequency *frd* are determined by

and misleading information. Akin et al. [16] performed real-time fault detection using the reference frame theory. Soualhi et al. [17] diagnosed broken rotor bar fault through the classification of selected fault features using the improved artificial ant clustering method. Gunal et al. [18] conducted IM broken rotor bar fault diagnosis by using fault indices in the time domain. Nevertheless, the aforementioned techniques only focus on limited fault

Rolling element bearings are commonly used not only in electric motors, but also in various types of rotating machinery facilities. As illustrated in Figure 2, a rolling element bearing is a system consisting of an outer ring (usually the fixed ring), an inner ring (usually the rotating

**Figure 2.** Structure of a rolling element bearing.

Since bearing materials are subjected to dynamic loading, fatigue pitting is the most

Since bearing materials are subjected to dynamic loading, fatigue pitting is the most common defect in bearing components. The bearing defects can occur on the outer race, inner race, and rolling elements. Under normal operating conditions, after the load cycles exceed some threshold, fatigue pitting may occur on the fixed ring race first, and then on the rotating race and rolling elements. Pitting defects not only deteriorate transmission accuracy, but also generate excessive vibration and noise. Other bearing defects, such as scoring and severe wear [7], can be generated by several external causes such as impacts, overloading and overheating, inadequate lubrication, contamination and corrosion from abrasive particles or acid, and improper installation of a bearing, which will introduce excessive misalignment errors.

common defect in bearing components. The bearing defects can occur on the outer race,

inner race, and rolling elements. Under normal operating conditions, after the load cycles

exceed some threshold, fatigue pitting may occur on the fixed ring race first, and then on

the rotating race and rolling elements. Pitting defects not only deteriorate transmission

When a bearing component is damaged, the corresponding characteristic frequencies will be associated with the bearing geometry, rotation speed, and defect location. Suppose the outer

accuracy, but also generate excessive vibration and noise. Other bearing defects, such as

scoring and severe wear [7], can be generated by several external causes such as impacts,

overloading and overheating, inadequate lubrication, contamination and corrosion from

abrasive particles or acid, and improper installation of a bearing, which will introduce

When a bearing component is damaged, the corresponding characteristic frequencies

will be associated with the bearing geometry, rotation speed, and defect location. Suppose

the outer race of a bearing is fixed and the inner race rotates with the shaft, which is

common case in most applications. The outer race defect characteristic frequency *fod*, inner

race defect characteristic frequency *fid*, and rolling element defect characteristic frequency

2

*<sup>D</sup> frd <sup>i</sup>*

*<sup>d</sup> <sup>f</sup> <sup>N</sup> fid <sup>i</sup>*

2

 *<sup>D</sup> <sup>d</sup> <sup>f</sup> <sup>N</sup> fod <sup>i</sup>*

 

2 *D <sup>d</sup> <sup>f</sup> <sup>d</sup>*

  (1)

(2)

(3)

 

 

2

)cos( <sup>1</sup>

)cos( <sup>1</sup>

*D*

cos <sup>1</sup>

excessive misalignment errors.

*frd* are determined by

information, thus their performance may be degraded.

ring), a number of rolling elements, and a cage.

**1.2. Fault detection of IM bearings**

120 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 2.** Structure of a rolling element bearing.

$$f\_{od} = \frac{N}{2} \left[ f\_i \left( 1 - \frac{d \cos \left( \theta \right)}{D} \right) \right] \tag{1}$$

$$f\_{id} = \frac{N}{2} \left[ f\_i \left( 1 + \frac{d \cos \left( \theta \right)}{D} \right) \right] \tag{2}$$

$$f\_{rd} = \frac{D}{2d} f\_i \left[ 1 - \left(\frac{d\cos\theta}{D}\right)^2 \right] \tag{3}$$

where *fi* is the inner race rotating speed or shaft speed in Hz; *d* is the diameter of the rolling element; *D* is the pitch diameter; *θ*is the contact angle.

When bearing defects occur, these bearing characteristic vibration frequencies *fv* (i.e., *fod* , *fid'* and *frd*) will be modulated with the power supply frequency *fp* in the spectrum of stator current signals, because of the air gap eccentricity and load torque variations. Thus, the characteristic stator current frequencies *fc* in terms of characteristic vibration frequencies *fv* will be calculated by [19]:

$$f\_c = \left| f\_p \pm mf\_v \right| \text{ / } m = \text{ 1, 2, 3} \dots \text{ } \tag{4}$$

For IM bearing fault detection, the characteristic stator current frequency components can be used as frequency domain indicators in spectrum analysis [20]. Several techniques have been proposed in the literature for IM bearing fault detection using stator current signals. For example, Devaney and Eren [21] applied IM stator current spectrum analysis for bearing defect detection. FFT can be used to conduct spectrum analysis, so as to detect IM bearing faults under deterministic motor conditions. Similar to the previous discussion regarding broken rotor bar analysis, the WT can be used to catch the transitory characteristics of the signal for IM bearing fault detection. For example, Konar and Vhattopadhyay [22] employed discrete WT to detect IM bearing faults. The WPD can also be employed to explore transient fault information for IM bearing fault detection [23]. Nevertheless, the WPD generates massive non-fault-related information that may mask the fault features in the map, and increase the difficulties in fault detection. Frosini and Bassi [24] used features from stator current signals and IM efficiency for bearing fault detection. Zhou et al. [25] utilized the Wiener filter for noise reduction, so as to detect IM bearing defect. Romero-Troncoso et al. [26] conducted online IM fault detection using information entropy and fuzzy inference. Pineda-Sanchez et al. [27] employed Teager-Kaiser energy operator to enhance fault features to detect IM bearing defect. Nevertheless, these available techniques conduct IM bearing fault detection based on limited fault information rather than comprehensively explore fault features from the time domain, the frequency domain, and the time-frequency domain. Therefore their performance may be degraded.

Typically, the onset of IM faults begins with small imperfections, and propagates to a severe stage as the operation progresses. The severe IM faults will cause machinery malfunction, and even catastrophic failures. Therefore, the detection of IM faults at their earliest stage is of great importance in IM condition monitoring. The IM fault features from stator current signals would be associated with fault size, motor type, supply frequency, load condition, and so on. To date, fault feature extraction from IM current signals, especially associated with bearing defects, still remains a challenging task due to the complex transmission path and environ‐ mental noise.

To tackle the aforementioned difficulties, a spectrum synch (SS) technique is proposed in this work to gather fault-related information and generate representative features of IM faults, such as broken rotor bar fault and outer race defect in a bearing. The SS will examine characteristic frequency components as well as their features over their neighborhood local bands, in order to comprehensively highlight fault features, and mitigate the effects of high amplitude outliers. The specific approaches in the proposed SS technique include the following: (1) a synch technique is proposed to form fault information spectrum (FIS) by synchronizing several faultrelated local bands, so as to accentuate the fault features and improve the SNR; (2) a central kurtosis technique is suggested to extract fault information from the resulting FIS and generate a fault indicator for incipient IM fault detection. The effectiveness of the proposed SS technique is verified by IM broken rotor bar fault detection and IM bearing fault detection.

The remainder of this chapter is organized as follows: the developed SS technique is described in Section 2. The effectiveness of the proposed diagnostic tool is examined in Section 3 by using two common types of IM fault conditions; finally, some concluding remarks of this study are summarized in Section 4.

### **2. The spectrum synch technique for IM health condition monitoring**

### **2.1. Theory of spectrum synch analysis**

The proposed SS technique is composed of two procedures: local band synch and central kurtosis analysis. The local band synch is used to form the fault information spectrum (FIS) and accentuate fault features. The central kurtosis is suggested to generate fault indices for IM health condition monitoring.

### *2.1.1. Local band synch*

The IM fault characteristic frequency components are distributed over the spectrum, which, however, are usually difficult to recognize due to their low amplitude. To highlight fault features in the spectrum, the FIS is used to enhance the local peakedness of the fault frequency components. Firstly, to mitigate the noise effect in the IM current signal, the spectrum averaging of *J* data sets *φ<sup>j</sup>* , *j* = 1, 2,..., *J*, is applied to improve the signal-to-noise ratio (SNR), computed by

information entropy and fuzzy inference. Pineda-Sanchez et al. [27] employed Teager-Kaiser energy operator to enhance fault features to detect IM bearing defect. Nevertheless, these available techniques conduct IM bearing fault detection based on limited fault information rather than comprehensively explore fault features from the time domain, the frequency domain, and the time-frequency domain. Therefore their performance may be degraded.

Typically, the onset of IM faults begins with small imperfections, and propagates to a severe stage as the operation progresses. The severe IM faults will cause machinery malfunction, and even catastrophic failures. Therefore, the detection of IM faults at their earliest stage is of great importance in IM condition monitoring. The IM fault features from stator current signals would be associated with fault size, motor type, supply frequency, load condition, and so on. To date, fault feature extraction from IM current signals, especially associated with bearing defects, still remains a challenging task due to the complex transmission path and environ‐

To tackle the aforementioned difficulties, a spectrum synch (SS) technique is proposed in this work to gather fault-related information and generate representative features of IM faults, such as broken rotor bar fault and outer race defect in a bearing. The SS will examine characteristic frequency components as well as their features over their neighborhood local bands, in order to comprehensively highlight fault features, and mitigate the effects of high amplitude outliers. The specific approaches in the proposed SS technique include the following: (1) a synch technique is proposed to form fault information spectrum (FIS) by synchronizing several faultrelated local bands, so as to accentuate the fault features and improve the SNR; (2) a central kurtosis technique is suggested to extract fault information from the resulting FIS and generate a fault indicator for incipient IM fault detection. The effectiveness of the proposed SS technique

The remainder of this chapter is organized as follows: the developed SS technique is described in Section 2. The effectiveness of the proposed diagnostic tool is examined in Section 3 by using two common types of IM fault conditions; finally, some concluding remarks of this study are

**2. The spectrum synch technique for IM health condition monitoring**

The proposed SS technique is composed of two procedures: local band synch and central kurtosis analysis. The local band synch is used to form the fault information spectrum (FIS) and accentuate fault features. The central kurtosis is suggested to generate fault indices for IM

The IM fault characteristic frequency components are distributed over the spectrum, which, however, are usually difficult to recognize due to their low amplitude. To highlight fault

is verified by IM broken rotor bar fault detection and IM bearing fault detection.

mental noise.

summarized in Section 4.

health condition monitoring.

*2.1.1. Local band synch*

**2.1. Theory of spectrum synch analysis**

122 Induction Motors - Applications, Control and Fault Diagnostics

$$\Phi = \frac{1}{I} \sum\_{j=1}^{I} \log \left( P(\varphi\_j) \right) \tag{5}$$

where Φ is the averaged spectrum over *J* spectra; *P*(*φ<sup>j</sup>* )represents the nonparametric power spectral density (PSD) estimate of the data set [28], given by

$$P\left(\boldsymbol{\varphi}\_{\boldsymbol{\upbeta}}\right) = \frac{2}{f\_s N} \sum\_{i=1}^{N/2 \times 1} \left| F\_{\boldsymbol{\upbeta}}\left(\boldsymbol{i}\right) \right|^2 \tag{6}$$

where *Fj* is the spectrum of *φ<sup>j</sup>* using the Fourier transform (FT); *N* is the length of *φ<sup>j</sup>* ; and *fs* is the sampling frequency.

The fault features are related to fault characteristic frequencies, most of which are masked over the local bands by some other higher level frequency components considered as noise. To tackle this problem, the local bands containing the fault characteristic frequencies are synchronized to reduce the noise effect and protrude the fault frequency components. In each selected local band, the fault frequency component *f <sup>c</sup>* is located in the center of the window, and the width of the local band is selected to properly reveal the peakedness of *f <sup>c</sup>*.

To synchronize the corresponding bands at different locations (frequencies) of the spectrum, the spectrum is transformed from the frequency domain Φ( *f* ) to discrete point representation Φ(*d*). Each frequency *f* can be represented by its nearest discrete point *d*. Then, fault charac‐ teristic frequency *f <sup>c</sup>* (*k*) is transformed into a discrete point, *dc*(*k*), whose corresponding frequency is the one closest to *f <sup>c</sup>*, where *k* = 1, 2,..., *K*, and *K* is the total number of fault characteristic frequencies considered. Thus, *K* local bands will be used for this synch operation. The widths of local bands are identical in this work to facilitate the synch operation. Given the bandwidth in frequency *fw* the length of the local band in discrete point representation, *dw* will be

$$d\_w = 2R \left\langle \frac{1}{2} f\_w \frac{D\_s}{f\_s} \right\rangle \tag{7}$$

where *fs* is the sampling frequency in Hz, *Ds* is the discrete point representing *fs*, and *R* ⋅ represents round-off operation. The *k*th local band *ψ<sup>k</sup>* in the discrete point representation can be determined by

$$\begin{split} \boldsymbol{\Psi}\_{k} &= \left\{ \boldsymbol{\Phi}(\boldsymbol{i}) \right\}\_{i} \boldsymbol{1}\_{-d\_{\boldsymbol{c}}(k)} \cdot \frac{1}{2} \boldsymbol{d}\_{w} \dots \boldsymbol{d}\_{\boldsymbol{c}}(k) \ast \frac{1}{2} \boldsymbol{d}\_{w} \\ &- \frac{1}{\boldsymbol{d}\_{w} + 1} \sum\_{l=d\_{\boldsymbol{c}}(k)}^{d\_{\boldsymbol{c}}(k) + \frac{1}{2} \boldsymbol{d}\_{w}} \boldsymbol{\Phi}(\boldsymbol{i}) \end{split} \tag{8}$$

The *i* th discrete point in the *k*th local band *ψ<sup>k</sup>* is denoted as *ψi*,*<sup>k</sup>* , *i* = 1, 2,..., *dw*+1; *k* = 1, 2,..., *K*. The *i* th discrete points over *K* local bands { *ψi*,*<sup>k</sup>* } are sorted in a descending order in terms of their values to generate *πi*,*<sup>k</sup> k* = 1, 2,..., *K*; the synchronized band FIS will be

$$\mathbf{g}\_{i} = \begin{cases} \frac{2}{\left(K - 1\right)} \sum\_{j=1}^{(K-1)/2} \pi\_{i,j} & \text{ $K$  is odd} \\ 2 \sum\_{j=1}^{K/2} \pi\_{i,j} & \text{ $K$  is even} \end{cases}, i = \frac{1}{2} d\_{w} + 1 \tag{9}$$

$$\log\_i = \xi \left( \pi\_{i,j} \right)\_{j=1,2,\dots,K}, i = 1,2,\dots,\frac{1}{2} d\_{w'} \frac{1}{2} d\_w + 2,\dots,d\_w + 1 \tag{10}$$

where *ξ* {⋅} represents the computation of median value. The top 50% high amplitude center frequency components in local bands are averaged in Equation (9) to enhance the fault feature. The median value calculation in Equation (10) will suppress other frequency components in local bands and reduce the amplitude of outliers. The processing procedures of the proposed FIS formation are illustrated in Figure 3, where the frequency resolution Δ*f* = 0.5 Hz.

#### **2.2. Central kurtosis analysis**

The classic kurtosis is a measure of the peakedness of a signal, computed as *χ* = *μ*4 *<sup>σ</sup>* <sup>4</sup> , where *<sup>σ</sup>* and *μ*4 are the standard deviation and the fourth moment of the signal distribution, respec‐ tively. The classic kurtosis measures all peaked frequency components of the FIS, which may not properly reveal the fault information. In this work, the fault detection aims to evaluate the peakedness of the center frequency component in the FIS. Therefore, a central kurtosis indicator is proposed to facilitate fault detection. Given the FIS *g*(*i*); *i* = 1, 2,..., *dw*+1, the relative amplitude of the center frequency components can be determined by

$$\mathbf{v}\_s = \mathbf{g}\_s - \xi \{ \mathbf{g} \} \tag{11}$$

where *gs* = {*gi* }*i*=*dw*/2+1 is the center discrete point in the FIS. The amplitude of fault frequency component over synchronized local bands (i.e., FIS), rather than the entire spectrum as in the classical methods, is used to examine fault information.

{ ( )} ( ) ( ) 1 1 ,... , 2 2

= F -

*<sup>k</sup> i dk d dk d dk d*

*c wc w*

=- +

*i*

th discrete point in the *k*th local band *ψ<sup>k</sup>* is denoted as *ψi*,*<sup>k</sup>* , *i* = 1, 2,..., *dw*+1; *k* = 1, 2,..., *K*. The

th discrete points over *K* local bands { *ψi*,*<sup>k</sup>* } are sorted in a descending order in terms of their

2 1 <sup>1</sup> , 1

*K is odd*

*K is even*

1 1 , 1 2 2 1

= = ++ (10)

<sup>2</sup> 2

<sup>+</sup> <sup>å</sup> (8)

(9)

*μ*4

*<sup>σ</sup>* <sup>4</sup> , where *<sup>σ</sup>*

<sup>1</sup> ( ) <sup>2</sup> <sup>1</sup> ( ) <sup>2</sup> <sup>1</sup> ( ) <sup>1</sup>

*id k d <sup>w</sup>*

values to generate *πi*,*<sup>k</sup> k* = 1, 2,..., *K*; the synchronized band FIS will be

( 1)/ 2


*j*

=

å

p

*i j j*

*K*

, 1 / 2 , 1

*g i d*

p

*i j*

*i w K*

2 2 *i ij w w <sup>w</sup> j K*

FIS formation are illustrated in Figure 3, where the frequency resolution Δ*f* = 0.5 Hz.

The classic kurtosis is a measure of the peakedness of a signal, computed as *χ* =

amplitude of the center frequency components can be determined by

classical methods, is used to examine fault information.

n

*i , , ... , d , d , ..., d* <sup>=</sup>

where *ξ* {⋅} represents the computation of median value. The top 50% high amplitude center frequency components in local bands are averaged in Equation (9) to enhance the fault feature. The median value calculation in Equation (10) will suppress other frequency components in local bands and reduce the amplitude of outliers. The processing procedures of the proposed

and *μ*4 are the standard deviation and the fourth moment of the signal distribution, respec‐ tively. The classic kurtosis measures all peaked frequency components of the FIS, which may not properly reveal the fault information. In this work, the fault detection aims to evaluate the peakedness of the center frequency component in the FIS. Therefore, a central kurtosis indicator is proposed to facilitate fault detection. Given the FIS *g*(*i*); *i* = 1, 2,..., *dw*+1, the relative

> x

component over synchronized local bands (i.e., FIS), rather than the entire spectrum as in the

*s s* = - *g g*{ } (11)

is the center discrete point in the FIS. The amplitude of fault frequency

<sup>ï</sup> - <sup>=</sup> <sup>í</sup> = +


*d*

( )

*K*

=

å

*K*

{ , } 1, 2, ...,

*g* x p

**2.2. Central kurtosis analysis**

where *gs* = {*gi*

}*i*=*dw*/2+1

ì ï

ï ï î

The *i*

*i*

y

124 Induction Motors - Applications, Control and Fault Diagnostics

*i*

*c w c w*

+ = -

**Figure 3.** The formulation of FIS: (a) is the original spectrum; (b)-(e) are respective extracted local **Figure 3.** The formulation of FIS: (a) is the original spectrum; (b)-(e) are respective extracted local bands corresponding to the four circled fault frequency components (red, green, pink, and black); (f) is the formulated FIS. The dotted lines in graph (a) represent the boundaries of the local bands; the dashed rectangular boxes represent outliers in the local bands.

bands corresponding to the four circled fault frequency components (red, green, pink, and black);

The variation of the FIS excluding center frequency component *gs* can be evaluated by (f) is the formulated FIS. The dotted lines in graph (a) represent the boundaries of the local bands;

$$\sigma\_s = \mathbb{E}\left\{ \left( \tilde{g} - \xi^\varepsilon \{ \tilde{g} \} \right)^2 \right\}^{\frac{1}{2}} \tag{12}$$

where *E*{⋅} represents the expectation function, and *g*˜ = {*gi* , *i* =1, 2, ..., *dw* / 2, *dw* / 2 + 2, ..., *dw* + 1}.

Then the peakedness of the fault frequency component in the FIS can be measured by the central kurtosis, determined by

$$\mathcal{X}\_s = \begin{cases} \nu\_s^4 / \sigma\_s^4 & \text{if } \nu\_s > 0 \\\\ 0 & \text{if } \nu\_s \le 0 \end{cases} \tag{13}$$

### **2.3. Implementation of Spectrum Synch Technique**

To recapitulate, the proposed SS technique is implemented for IM defect detection in the following steps:


### **3. Performance evaluation**

To evaluate the effectiveness of the proposed SS technique for IM fault detection, a series of tests have been conducted for the two common types of IM defects, IM broken rotor bar fault and IM bearing defect, using stator current signals. In rolling element bearings, defect occurs on the race of the fixed ring first since fixed ring material over the load zone experiences more cycles of fatigue loading than other bearing components (i.e., the rotating ring and rolling elements). Correspondingly, this test focuses on incipient bearing defect, or fault on the outer race (fixed ring in this case). The tests are conducted for two power supply frequencies *fp*: *fp* = 35 Hz and 50 Hz.

### **3.1. Experimental setup**

Figure 4 shows the experimental setup employed in the current work. The speed of the tested IM is controlled by a VFD-B AC speed controller (from Delta Electronics) with output frequency 0.1~400 Hz. A magnetic particle clutch (PHC-50 from Placid Industries) is used as a dynamometer for external loading. Its torque range is from 1 to 30 lb ft (1.356-40.675 N m). The motor used for this research is made by Marathon Electric, and its specifications are summarized in Table 1. The gearbox (Boston Gear 800) is used to adjust the speed ratio of the dynamometer. The current sensors (102-1052-ND) are used to measure different phase currents. A rotary encoder (NSN-1024) is used to measure the shaft speed with the resolution of 1024 pulses per revolution. Stator current signals are collected using a Quanser Q4 data acquisition board, which are then fed to a computer for further processing.

**Figure 4.** IM experimental setup: (1) tested IM, (2) speed controller, (3) gearbox, (4) load system, (5) encoder, (6) current sensors, (7) data acquisition system, and (8) computer.


**Table 1.** Motor specifications.

Then the peakedness of the fault frequency component in the FIS can be measured by the

4 4 / 0

*if*

 n

*if*

*s s s*

<sup>ï</sup> £ <sup>î</sup>

<sup>ì</sup> <sup>&</sup>gt; <sup>ï</sup> <sup>=</sup> <sup>í</sup>

ns

(10), in order to reduce the noise effect and highlight fault features.

*s*

c

the central kurtosis computed from Equation (13).

**2.3. Implementation of Spectrum Synch Technique**

**a.** Collect *J* electric current data sets *φ<sup>j</sup>*

**3. Performance evaluation**

35 Hz and 50 Hz.

**3.1. Experimental setup**

0 0

To recapitulate, the proposed SS technique is implemented for IM defect detection in the

**b.** Determine the spectrum average Φ over *J* spectra. Then extract characteristic local bands using Equation (8). Synchronize the local bands to form the FIS using Equations (9) and

**c.** Compute the center frequency representative feature using Equation (11), and the variation of the FIS using Equation (12). The fault diagnosis can be performed by analyzing

To evaluate the effectiveness of the proposed SS technique for IM fault detection, a series of tests have been conducted for the two common types of IM defects, IM broken rotor bar fault and IM bearing defect, using stator current signals. In rolling element bearings, defect occurs on the race of the fixed ring first since fixed ring material over the load zone experiences more cycles of fatigue loading than other bearing components (i.e., the rotating ring and rolling elements). Correspondingly, this test focuses on incipient bearing defect, or fault on the outer race (fixed ring in this case). The tests are conducted for two power supply frequencies *fp*: *fp* =

Figure 4 shows the experimental setup employed in the current work. The speed of the tested IM is controlled by a VFD-B AC speed controller (from Delta Electronics) with output frequency 0.1~400 Hz. A magnetic particle clutch (PHC-50 from Placid Industries) is used as a dynamometer for external loading. Its torque range is from 1 to 30 lb ft (1.356-40.675 N m). The motor used for this research is made by Marathon Electric, and its specifications are summarized in Table 1. The gearbox (Boston Gear 800) is used to adjust the speed ratio of the dynamometer. The current sensors (102-1052-ND) are used to measure different phase currents. A rotary encoder (NSN-1024) is used to measure the shaft speed with the resolution

*s*

, *j* = 1, 2,..., *J*, with the same time delay.

(13)

n

central kurtosis, determined by

126 Induction Motors - Applications, Control and Fault Diagnostics

following steps:

### **3.2. Broken rotor bar fault detection**

The fault detection of IM broken rotor bar defect is generally based on spectral analysis by inspecting fault-related sideband components in the spectrum:

$$\left(f\_{\mathbb{N}} = \left(1 - 2\,\mathrm{ks}\right)f\_p\right) \tag{14}$$

$$\left(f\_{br} = \left(1 + 2\,\mathrm{ks}\right)f\_p\right) \tag{15}$$

where *fbl* and *fbr* are the respective left sideband and right sideband of the IM broken rotor bar fault, *k* = 1, 2,... ; *fp* is the power supply frequency of the IM; *s* = *ns* −*na ns* ×100*%*is the slip of the IM. *ns* (rpm) is the speed of rotating magnetic field, and *na* (rpm) is the shaft rotating speed. In the following tests, an IM containing three broken rotor bars is used to evaluate the proposed SS technique.

To examine the effectiveness of the proposed SS technique, the power spectral density (PSD) based fault detection and the envelope analysis based fault detection are used for comparison. The PSD explores the energy distribution of the data over the spectrum; the envelope analysis performs amplitude demodulation to reveal fault features. In the PSD-based fault detection, the fault index can be represented as,

$$\mathcal{X}\_p = \begin{cases} \nu\_p^{\*4} / \sigma\_p^{\*4} & \text{if } \quad \nu\_p > 0\\ 0 & \text{if } \; \nu\_p \le 0 \end{cases} \tag{16}$$

The fault index of envelope analysis is given as

$$\mathcal{X}\_{\epsilon} = \begin{cases} \nu\_{\epsilon}^{4} / \sigma\_{\epsilon}^{4} & \text{if } \begin{array}{c} \nu\_{\epsilon} > 0 \\ \text{if } \begin{array}{c} \nu\_{\epsilon} \le 0 \end{array} \end{cases} \tag{17}$$

where *νp* and *ν<sup>e</sup>* represent the averages of the top 50% high amplitude fault frequency compo‐ nents from PSD and envelope analysis respectively; *σp*and *σ<sup>e</sup>* represent the standard deviations of the entire spectrum band of interests from PSD and envelope analysis respectively; *χp*and *χe* are the respective fault indices from PSD and envelope analysis. Therefore, these two techniques can be used to compare the local band synch method in the proposed SS technique, and the corresponding central kurtosis index.

### *3.2.1. 35 Hz supply frequency*

The first test aims to detect the IM with three adjacent broken rotor bars, 35 Hz power supply frequency, and a half load (50% of rated power). To reduce the noise effect in the spectrum, twenty data sets are collected for spectrum averaging (i.e., *J* = 20). Other settings are *fs* = 65,500 Hz and *fw* = 10 Hz. Since 1,024 low-to-high voltage transitions represent one shaft revolution in the encoder signal, the high sampling frequency *fs* is chosen to properly capture the encoder signal, so as to accurately estimate shaft speed (i.e., rotor speed). The frequency band [25 Hz, 45 Hz] is used to detect broken rotor fault, because the amplitudes of high order (i.e., *k* in Equations (14) and (15)) characteristic frequencies are not prominent in the spectrum. Figure 5 illustrates the PSD of a healthy IM (Figure 5a), the PSD of an IM with broken rotor bars (Figure 5b), the envelope analysis of a healthy IM (Figure 5c), and the envelope analysis of an IM with broken rotor bars (Figure 5d), respectively. From Figures 5(b) and5(d), it is seen that the broken rotor bar fault frequency components, although visible, do not prominently protrude in the spectrum. Therefore, a better fault detection technique is needed to extract useful information from multiple characteristic frequency components in the spectrum to generate a more reliable fault index.

where *fbl* and *fbr* are the respective left sideband and right sideband of the IM broken rotor bar

IM. *ns* (rpm) is the speed of rotating magnetic field, and *na* (rpm) is the shaft rotating speed. In the following tests, an IM containing three broken rotor bars is used to evaluate the proposed

To examine the effectiveness of the proposed SS technique, the power spectral density (PSD) based fault detection and the envelope analysis based fault detection are used for comparison. The PSD explores the energy distribution of the data over the spectrum; the envelope analysis performs amplitude demodulation to reveal fault features. In the PSD-based fault detection,

> 4 4 / 0 0 0 *p p p*

4 4 / 0 0 0 *e e e*

where *νp* and *ν<sup>e</sup>* represent the averages of the top 50% high amplitude fault frequency compo‐ nents from PSD and envelope analysis respectively; *σp*and *σ<sup>e</sup>* represent the standard deviations of the entire spectrum band of interests from PSD and envelope analysis respectively; *χp*and *χe* are the respective fault indices from PSD and envelope analysis. Therefore, these two techniques can be used to compare the local band synch method in the proposed SS technique,

The first test aims to detect the IM with three adjacent broken rotor bars, 35 Hz power supply frequency, and a half load (50% of rated power). To reduce the noise effect in the spectrum, twenty data sets are collected for spectrum averaging (i.e., *J* = 20). Other settings are *fs* = 65,500 Hz and *fw* = 10 Hz. Since 1,024 low-to-high voltage transitions represent one shaft revolution in the encoder signal, the high sampling frequency *fs* is chosen to properly capture the encoder signal, so as to accurately estimate shaft speed (i.e., rotor speed). The frequency band [25 Hz, 45 Hz] is used to detect broken rotor fault, because the amplitudes of high order (i.e., *k* in Equations (14) and (15)) characteristic frequencies are not prominent in the spectrum. Figure 5 illustrates the PSD of a healthy IM (Figure 5a), the PSD of an IM with broken rotor bars (Figure 5b), the envelope analysis of a healthy IM (Figure 5c), and the envelope analysis of an IM with broken rotor bars (Figure 5d), respectively. From Figures 5(b) and5(d), it is seen that the broken rotor bar fault frequency components, although visible, do not prominently

ìï <sup>&</sup>gt; <sup>=</sup> <sup>í</sup> ï £ î

*if if*

 n

<sup>ï</sup> <sup>&</sup>gt; <sup>=</sup> <sup>í</sup> £ ïî

*if if*

 n

*p*

*e*

n

n

*ns* −*na ns*

×100*%*is the slip of the

(16)

(17)

fault, *k* = 1, 2,... ; *fp* is the power supply frequency of the IM; *s* =

*p*

*e*

c

c

The fault index of envelope analysis is given as

and the corresponding central kurtosis index.

*3.2.1. 35 Hz supply frequency*

ns

ns

ì

SS technique.

the fault index can be represented as,

128 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 5.** The spectrum average corresponding to: (a) a healthy IM using PSD; (b) an IM with broken rotor bar fault using PSD; (c) a healthy IM using envelope analysis; and (d) an IM with **Figure 5.** The spectrum average Φ corresponding to: (a) a healthy IM using PSD; (b) an IM with broken rotor bar fault using PSD; (c) a healthy IM using envelope analysis; and (d) an IM with broken rotor bar fault using envelope analysis, at 35 Hz supply frequency and medium-load condition. The red solid rectangular boxes in (b) and (d) highlight fault frequency components.

condition. The red solid rectangular boxes in (b) and (d) highlight fault frequency components.

broken rotor bar fault using envelope analysis, at 35 Hz supply frequency and medium-load

The FIS, corresponding to a healthy IM (Figure 5a) and a broken rotor bar faulted IM

(Figure 5b), are given in Figures 6(a) and 6(b), respectively. The unit of amplitude of the

FIS is dB because the local bands are extracted from the PSD logarithmic spectrum. It is

seen from Figure 6 that the center frequency component (i.e., synchronized broken rotor

bar fault frequency components) in Figure 6(b) has higher relative amplitude than that in

*<sup>s</sup>* in the proposed SS technique. Figure 6(b)

Figure 6(a), which is evaluated by the index

The FIS, corresponding to a healthy IM (Figure 5a) and a broken rotor bar faulted IM (Figure 5b), are given in Figures 6(a) and 6(b),respectively. The unit of amplitude of the FIS is dB because the local bands are extracted from the PSD logarithmic spectrum. It is seen from Figure 6 that the center frequency component (i.e., synchronized broken rotor bar fault frequency components) in Figure 6(b) has higher relative amplitude than that in Figure 6(a), which is evaluated by the index *νs* in the proposed SS technique. Figure 6(b) has similar spectrum variation as in Figure 6(a), which is examined by the value *σ<sup>s</sup>* in the SS technique. Therefore, the fault information in the FIS can be characterized by the index *χ<sup>s</sup>* using the proposed SS technique. seen from Figure 6 that the center frequency component (i.e., synchronized broken rotor bar fault frequency components) in Figure 6(b) has higher relative amplitude than that in Figure 6(a), which is evaluated by the index *<sup>s</sup>* in the proposed SS technique. Figure 6(b) has similar spectrum variation as in Figure 6(a), which is examined by the value *<sup>s</sup>* in the SS technique. Therefore, the fault information in the FIS can be characterized by the index *<sup>s</sup>* using the proposed SS technique.

The FIS, corresponding to a healthy IM (Figure 5a) and a broken rotor bar faulted IM

FIS is dB because the local bands are extracted from the PSD logarithmic spectrum. It is

**Figure 6.** The FIS generated by the SS technique at 35 Hz and a half load condition: (a) from a healthy IM, (b) from an IM with broken rotor bar fault. **Figure 6.** The FIS generated by the SS technique at 35 Hz and a half load condition: (a) from a healthy IM, (b) from an IM with broken rotor bar fault.

 The values of IM speed *fr* (Hz) and indices corresponding to PSD, envelope analysis and the proposed SS are summarized in Table 2. It is seen from Table 2 that it is difficult to differentiate the IM broken rotor bar faulted condition from the IM healthy condition using envelope analysis, because the values of *<sup>e</sup>* corresponding to these two IM conditions are similar. The PSD has a relatively large difference of *<sup>p</sup>* of different IM conditions in this case; however, the PSD suffers from interference of non-fault-related high amplitude The values of IM speed *fr* (Hz) and indices corresponding to PSD, envelope analysis and the proposed SS are summarized in Table 2. It is seen from Table 2 that it is difficult to differentiate the IM broken rotor bar faulted condition from the IM healthy condition using envelope analysis, because the values of *χe* corresponding to these two IM conditions are similar. The PSD has a relatively large difference of *χ<sup>p</sup>* of different IM conditions in this case; however, the PSD suffers from interference of non-fault-related high amplitude frequency components and its *χp* values are too small to be relied on. The IM with broken rotor bar defect has considerably larger value of *χ<sup>s</sup>* than that of the healthy IM using the proposed SS technique. Consequently, the proposed SS technique associated with its index *χs* can be used as a fault index for IM broken rotor bar fault detection in the stator current spectrum.

proposed SS technique. Consequently, the proposed SS technique associated with its index

*<sup>p</sup>* values are too small to be relied on. The IM with broken

*<sup>s</sup>* than that of the healthy IM using the

frequency components and its

rotor bar defect has considerably larger value of


**Table 2.** Comparisons of central kurtosis indices for IM broken rotor bar fault detection.

### *3.2.2. 50 Hz supply frequency*

The FIS, corresponding to a healthy IM (Figure 5a) and a broken rotor bar faulted IM (Figure 5b), are given in Figures 6(a) and 6(b),respectively. The unit of amplitude of the FIS is dB because the local bands are extracted from the PSD logarithmic spectrum. It is seen from Figure 6 that the center frequency component (i.e., synchronized broken rotor bar fault frequency components) in Figure 6(b) has higher relative amplitude than that in Figure 6(a), which is evaluated by the index *νs* in the proposed SS technique. Figure 6(b) has similar spectrum variation as in Figure 6(a), which is examined by the value *σ<sup>s</sup>* in the SS technique. Therefore, the fault information in the FIS can be characterized by the index *χ<sup>s</sup>* using the proposed SS

has similar spectrum variation as in Figure 6(a), which is examined by the value

The FIS, corresponding to a healthy IM (Figure 5a) and a broken rotor bar faulted IM

(Figure 5b), are given in Figures 6(a) and 6(b), respectively. The unit of amplitude of the

FIS is dB because the local bands are extracted from the PSD logarithmic spectrum. It is

seen from Figure 6 that the center frequency component (i.e., synchronized broken rotor

bar fault frequency components) in Figure 6(b) has higher relative amplitude than that in

SS technique. Therefore, the fault information in the FIS can be characterized by the index

10 20 30 40 50 60

*<sup>p</sup>* values are too small to be relied on. The IM with broken

*<sup>e</sup>* corresponding to these two IM conditions are

*<sup>p</sup>* of different IM conditions in this

*<sup>s</sup>* than that of the healthy IM using the

10 20 30 40 50 60

Data Point

**Figure 6.** The FIS generated by the SS technique at 35 Hz and a half load condition: (a) from a

**Figure 6.** The FIS generated by the SS technique at 35 Hz and a half load condition: (a) from a healthy IM, (b) from an

The values of IM speed *fr* (Hz) and indices corresponding to PSD, envelope analysis and the proposed SS are summarized in Table 2. It is seen from Table 2 that it is difficult to differentiate the IM broken rotor bar faulted condition from the IM healthy condition using envelope analysis, because the values of *χe* corresponding to these two IM conditions are similar. The PSD has a relatively large difference of *χ<sup>p</sup>* of different IM conditions in this case; however, the PSD suffers from interference of non-fault-related high amplitude frequency components and its *χp* values are too small to be relied on. The IM with broken rotor bar defect has considerably larger value of *χ<sup>s</sup>* than that of the healthy IM using the proposed SS technique. Consequently, the proposed SS technique associated with its index *χs* can be used as a fault index for IM

The values of IM speed *fr* (Hz) and indices corresponding to PSD, envelope analysis

and the proposed SS are summarized in Table 2. It is seen from Table 2 that it is difficult to

differentiate the IM broken rotor bar faulted condition from the IM healthy condition using

case; however, the PSD suffers from interference of non-fault-related high amplitude

proposed SS technique. Consequently, the proposed SS technique associated with its index

*<sup>s</sup>* in the proposed SS technique. Figure 6(b)

*<sup>s</sup>* in the

technique.

Figure 6(a), which is evaluated by the index

130 Induction Motors - Applications, Control and Fault Diagnostics


healthy IM, (b) from an IM with broken rotor bar fault.

similar. The PSD has a relatively large difference of

rotor bar defect has considerably larger value of

broken rotor bar fault detection in the stator current spectrum.

envelope analysis, because the values of

frequency components and its


Amplitude (dB)

Amplitude (dB)

(a)

(b)

IM with broken rotor bar fault.

*<sup>s</sup>* using the proposed SS technique.

The proposed SS technique is then used for IM broken rotor bar fault detection with 50 Hz supply frequency and a half load condition (50% of rated power). Other settings remain the same as in the previous tests. The spectrum of frequency band [35, 65] Hz is used for fault diagnosis. The selected band is shown in Figure 7 using PSD in Figure 7(a) and the envelope analysis in Figure 7(b), respectively. It is seen from Figure 7 that most of the fault frequency components are masked by noise, which cannot be used effectively for reliable fault diagnosis.

The FIS, corresponding to a healthy IM and an IM with broken rotor bar fault are given in Figures 8(a) and 8(b), respectively. The related IM condition indices are summarized in Table 3. It is seen that the relative amplitude of fault frequency component in Figure 8(b) is greater than that in Figure 8(a). From Table 3, the IM with broken rotor bar fault has a larger value of *χ<sup>s</sup>* than that of a healthy IM, which indicates a broken rotor bar fault. The IM health condition with broken rotor bars cannot be differentiated from healthy condition using envelope analysis, associated with its fault index *χe*. Although the PSD index *χp* has a relatively large difference corresponding to different IM conditions, the performance of PSD may be degraded by the interference of non-fault-related high amplitude frequency components and its *χ<sup>p</sup>* values are too small to be relied on. Hence, the proposed SS technique associated with its fault index *χs* can accurately discern the health condition of IMs with broken rotor bar fault under different supply frequencies, when compared to the related two classical methods.

### **3.3. Incipient bearing defect detection**

As mentioned earlier, bearing defects are the most common faults in IMs, which also represent the most challenging task in IM health condition monitoring, especially when using stator current signals [29]. A small dent of diameter approximately 1/16-inch was introduced on the outer race of the bearing to simulate fatigue pitting defect. Whenever a rolling element rolls over the damaged region, impulses are generated, which then excite the resonance frequencies of the IM structures. The vibration-related outer race bearing defect characteristic frequency *f <sup>v</sup>* is given in Equation (1). The corresponding characteristic current frequency *fc* can be calculated using Equation (4).

**Figure 7.** The spectrum for an IM with broken rotor bar fault, 50 Hz supply frequency and half-**Figure 7.** The spectrum Φ for an IM with broken rotor bar fault, 50 Hz supply frequency and half-load condition, us‐ ing: (a) PSD; and (b) envelope analysis. The red solid rectangular boxes highlight fault frequency components. fault frequency components.

load condition, using: (a) PSD; and (b) envelope analysis. The red solid rectangular boxes highlight

Data Point **Figure 8.** The FIS generated by the SS technique at 50 Hz supply frequency and a half-load level (a) from a healthy IM; (b) from an IM with broken rotor bars. **Figure 8.** The FIS generated by the SS technique at 50 Hz supply frequency and a half-load level (a) from a healthy IM; (b) from an IM with broken rotor bars.

(a) from a healthy IM; (b) from an IM with broken rotor bars.

6.966e-4

0.008

0.195

49.089

0.653

Faulty

0.103

49.180

Methods PSD

0.634

Healthy

Conditions

fr

 *e s*

; ;

 *e s*

; ;

*e s*

**3.3 Incipient Bearing Defect Detection** 

; ;

 *p p p*

**Figure 8.** The FIS generated by the SS technique at 50 Hz supply frequency and a half-load level

**Table 3.** Comparisons of central kurtosis indices for IM broken rotor bar fault detection.

0.096

As mentioned earlier, bearing defects are the most common faults in IMs, which also

represent the most challenging task in IM health condition monitoring, especially when

using stator current signals [29]. A small dent of diameter approximately 1/16-inch was

0.441

0.777

522

0.325

0.068

Faulty

49.089

0.098

0.092

49.180

Healthy

SS

0.119

49.089

0.146

Faulty

0.083

49.180

0.149

Healthy

Envelope analysis

10 20 30 40 50 60


**Table 3.** Comparisons of central kurtosis indices for IM broken rotor bar fault detection.

### *3.3.1. 35 Hz supply frequency*

35 40 45 50 55 60 65

35 40 45 50 55 60 65

Frequency (Hz)

10 20 30 40 50 60

10 20 30 40 50 60

10 20 30 40 50 60

10 20 30 40 50 60

Data Point

Data Point

**Figure 8.** The FIS generated by the SS technique at 50 Hz supply frequency and a half-load level

**Table 3.** Comparisons of central kurtosis indices for IM broken rotor bar fault detection.

0.096

As mentioned earlier, bearing defects are the most common faults in IMs, which also

represent the most challenging task in IM health condition monitoring, especially when

using stator current signals [29]. A small dent of diameter approximately 1/16-inch was

0.441

0.777

522

0.325

0.068

Faulty

49.089

0.098

0.092

49.180

Healthy

SS

0.119

49.089

0.146

Faulty

0.083

49.180

0.149

Healthy

Envelope analysis

**Figure 8.** The FIS generated by the SS technique at 50 Hz supply frequency and a half-load level

**Figure 8.** The FIS generated by the SS technique at 50 Hz supply frequency and a half-load level (a) from a healthy IM;

**Figure 7.** The spectrum for an IM with broken rotor bar fault, 50 Hz supply frequency and halfload condition, using: (a) PSD; and (b) envelope analysis. The red solid rectangular boxes highlight

**Figure 7.** The spectrum for an IM with broken rotor bar fault, 50 Hz supply frequency and halfload condition, using: (a) PSD; and (b) envelope analysis. The red solid rectangular boxes highlight

**Figure 7.** The spectrum Φ for an IM with broken rotor bar fault, 50 Hz supply frequency and half-load condition, us‐ ing: (a) PSD; and (b) envelope analysis. The red solid rectangular boxes highlight fault frequency components.


1.4 1.6 1.8 2 2.2


(a) from a healthy IM; (b) from an IM with broken rotor bars.

6.966e-4

0.008

0.195

49.089

0.653

Faulty

0.103

49.180

Methods PSD

0.634

Healthy

(a) from a healthy IM; (b) from an IM with broken rotor bars.

0

0.2

0

0.2


0

0.2

Amplitude (dB)

Amplitude (dB)


(a)

0.4

0

0.2

0.4

Amplitude (dB)

Conditions

fr

 *e s*

; ;

 *e s*

; ;

*e s*

**3.3 Incipient Bearing Defect Detection** 

; ;

 *p p p*

Amplitude (dB)


(b)

(b) from an IM with broken rotor bars.

(b)

Amplitude (A)

(b)

fault frequency components.

(a)

fault frequency components.



Power (dB)

(a)




132 Induction Motors - Applications, Control and Fault Diagnostics

The proposed SS technique is first tested with stator current signals collected from an IM with the outer race defect, 35 Hz power supply frequency, and a light-load (20% of rated power). The settings for the proposed SS technique are selected as *J* = 20, *fs* = 65,500 Hz, *fw* = 10 Hz, and *f <sup>v</sup>* =3.066 *f <sup>r</sup>*. The high sampling frequency is used to accurately estimate the IM shaft speed. To obtain representative fault features, the frequency band [1000, 2000] Hz is selected for bearing fault detection.

To have a clear view of fault frequency components, the frequency band [1090, 1360] Hz from an IM with outer race bearing defect is shown in Figure 9 using PSD (Figure 9) and envelope analysis (Figure 9b). It is seen that the bearing fault frequency components are difficult to recognize due to the modulation of the signals with other IM frequency components.

The FIS, corresponding to a healthy IM and an IM with the outer race defect, are given in Figures 10(a) and 10(b), respectively. The values of indices corresponding to these three fault detection techniques are summarized in Table 4. It is seen from Figure 10 that the fault frequency component in Figure 10(b) protrudes more significantly than that in Figure 10(a). In Table 4, the fault index *χs* of the IM with faulty bearing is greater than that of a healthy IM using the proposed SS technique, whereas the envelope analysis, associated with its index *χe*, cannot recognize different IM health conditions. The PSD index *χ<sup>p</sup>* generates small values that cannot be relied on. Therefore, the SS technique can be used effectively for IM outer race bearing fault detection in this case, when compared to PSD and envelope analysis.

### *3.3.2. 50 Hz supply frequency*

In this test, the IM supply frequency is set as 50 Hz. The other settings remain the same as in previous test. The frequency band [1000, 2000] Hz of an IM with an outer race bearing defect is used for testing. The band [1400, 1750] Hz is shown in Figure 11, using PSD (Figure 11a) and envelope analysis (Figure 11b), respectively. From Figure 11, the bearing fault frequency components in the spectrum are masked by higher amplitude frequency components unre‐ lated to the bearings, which will degrade the fault detection reliability.

components.

[1000, 2000] Hz is selected for bearing fault detection.

rated power). The settings for the proposed SS technique are selected as *J* = 20, *fs* = 65,500 Hz, *fw* = 10 Hz, and *<sup>v</sup> <sup>r</sup> f* 3.066 *f* . The high sampling frequency is used to accurately estimate the IM shaft speed. To obtain representative fault features, the frequency band

 To have a clear view of fault frequency components, the frequency band [1090, 1360] Hz from an IM with outer race bearing defect is shown in Figure 9 using PSD (Figure 9) and envelope analysis (Figure 9b). It is seen that the bearing fault frequency components are difficult to recognize due to the modulation of the signals with other IM frequency

**Figure 9.** The spectrum average for an IM with outer race bearing defects, 35 Hz supply frequency, and light-load condition, using (a) PSD; and (b) envelope analysis. The rectangular boxes indicate bearing fault frequency components. **Figure 9.** The spectrum average Φ for an IM with outer race bearing defects, 35 Hz supply frequency, and light-load condition, using (a) PSD; and (b) envelope analysis. The rectangular boxes indicate bearing fault frequency compo‐ nents.

**Figure 10**. The FIS generated by the SS technique at 35 Hz supply frequency and with a light-load condition (a) from a healthy IM; (b) from an IM with outer race bearing defect. **Figure 10.** The FIS generated by the SS technique at 35 Hz supply frequency and with a light-load condition (a) from a healthy IM; (b) from an IM with outer race bearing defect.

*2) 50 Hz Supply Frequency:* 

reliability.

**Table 4.** Comparisons of central kurtosis indices for IM outer race bearing fault detection.

Faulty

In this test, the IM supply frequency is set as 50 Hz. The other settings remain the

0

0

0.396

185

Faulty

34.716

0.107 0.029

0.023 0.029

34.746

Healthy

SS

0 0.081

34.716

Faulty

0 0.102

34.746

Healthy

Envelope analysis

same as in previous test. The frequency band [1000, 2000] Hz of an IM with an outer race bearing defect is used for testing. The band [1400, 1750] Hz is shown in Figure 11, using PSD (Figure 11a) and envelope analysis (Figure 11b), respectively. From Figure 11, the bearing fault frequency components in the spectrum are masked by higher amplitude frequency components unrelated to the bearings, which will degrade the fault detection

1.929e-6

0.006 0.161

34.716

0

0 0.203

*fr* 34.746

Methods PSD

Healthy

Conditions

 *e s*

; ;

 *e s*

; ; ; ;

*e s*

 *p p p*

185

Faulty

34.716

0.107

0.396

0.023

34.746

Healthy

SS


1.929e-6

0

0

0

34.716

Faulty

0

34.746

Healthy

Envelope analysis

0.006 0.161

34.716

**Table 4.** Comparisons of central kurtosis indices for IM outer race bearing fault detection.

Faulty

reliability. *2) 50 Hz Supply Frequency:*  **Table 4.** Comparisons of central kurtosis indices for IM outer race bearing fault detection.

0

**Table 4.** Comparisons of central kurtosis indices for IM outer race bearing fault detection.

0 0.203

*fr* 34.746

Methods PSD

Healthy

Conditions

 *e s e s e s*

; ; ; ; ; ;

 *p p p*

reliability.

Power (dB)

(a)

rated power). The settings for the proposed SS technique are selected as *J* = 20, *fs* = 65,500 Hz, *fw* = 10 Hz, and *<sup>v</sup> <sup>r</sup> f* 3.066 *f* . The high sampling frequency is used to accurately estimate the IM shaft speed. To obtain representative fault features, the frequency band

 To have a clear view of fault frequency components, the frequency band [1090, 1360] Hz from an IM with outer race bearing defect is shown in Figure 9 using PSD (Figure 9) and envelope analysis (Figure 9b). It is seen that the bearing fault frequency components are difficult to recognize due to the modulation of the signals with other IM frequency

1100 1150 1200 1250 1300 1350

1100 1150 1200 1250 1300 1350

Frequency (Hz)

**Figure 9.** The spectrum average for an IM with outer race bearing defects, 35 Hz supply frequency, and light-load condition, using (a) PSD; and (b) envelope analysis. The rectangular

**Figure 9.** The spectrum average Φ for an IM with outer race bearing defects, 35 Hz supply frequency, and light-load condition, using (a) PSD; and (b) envelope analysis. The rectangular boxes indicate bearing fault frequency compo‐

 The FIS, corresponding to a healthy IM and an IM with the outer race defect, are given in Figures 10(a) and 10(b), respectively. The values of indices corresponding to these three fault detection techniques are summarized in Table 4. It is seen from Figure 10 that the fault frequency component in Figure 10(b) protrudes more significantly than that in Figure

10 20 30 40 50 60

10 20 30 40 50 60

Data Point

**Figure 10**. The FIS generated by the SS technique at 35 Hz supply frequency and with a light-load

**Figure 10.** The FIS generated by the SS technique at 35 Hz supply frequency and with a light-load condition (a) from a

**Table 4.** Comparisons of central kurtosis indices for IM outer race bearing fault detection.

Faulty

In this test, the IM supply frequency is set as 50 Hz. The other settings remain the

0

0

0.396

185

Faulty

34.716

0.107 0.029

0.023 0.029

34.746

Healthy

SS

0 0.081

34.716

Faulty

0 0.102

34.746

Healthy

Envelope analysis

same as in previous test. The frequency band [1000, 2000] Hz of an IM with an outer race bearing defect is used for testing. The band [1400, 1750] Hz is shown in Figure 11, using PSD (Figure 11a) and envelope analysis (Figure 11b), respectively. From Figure 11, the bearing fault frequency components in the spectrum are masked by higher amplitude frequency components unrelated to the bearings, which will degrade the fault detection

1.929e-6

0.006 0.161

34.716

condition (a) from a healthy IM; (b) from an IM with outer race bearing defect.

0

0 0.203

*fr* 34.746

Methods PSD

Healthy

[1000, 2000] Hz is selected for bearing fault detection.


1.6 1.7 1.8 1.9 2 2.1 2.2

boxes indicate bearing fault frequency components.


healthy IM; (b) from an IM with outer race bearing defect.

Conditions

 *e s*

; ;

 *e s*

; ; ; ;

*e s*

 *p p p*


Amplitude (dB)

(b)

*2) 50 Hz Supply Frequency:* 

reliability.

Amplitude (dB)

(a)

Amplitude (A)

(b)

nents.


Power (dB)

(a)


134 Induction Motors - Applications, Control and Fault Diagnostics

components.

**Figure 11.** The spectrum average Φ for an IM with outer race bearing defects, 50 Hz supply frequency, and light-load condition, using (a) PSD; and (b) envelope analysis. 1400 1450 1500 1550 1600 1650 1700 1750

The FIS of a healthy IM and an IM with outer race bearing defect are shown in Figure 12. The values of the shaft speed *fr* and indices of the PSD, the envelope analysis and the proposed SS technique are listed in Table 5. It is seen that peaked center frequency component can be highlighted in Figure 12(b) than in Figure 12(a). From Table 5, it is seen that the values of *χs* in the proposed SS technique are much greater than that from a healthy IM. Thus, the SS technique and its index *χs* can be used for IM outer race bearing defect detection at different supply frequencies. 1400 1450 1500 1550 1600 1650 1700 1750 1.6 1.8 2 2.2 Amplitude (A) (b)

Frequency (Hz)

**Figure 12.** The FIS generated by the SS technique at 50 Hz supply frequency and light-load **Figure 12.** The FIS generated by the SS technique at 50 Hz supply frequency and light-load condition (a) from a healthy IM; (b) from an IM with an outer race bearing defect.

condition (a) from a healthy IM; (b) from an IM with an outer race bearing defect.


0.176 0.173 0.087 0.086 0.055 *p e s* ; ; **Table 5.** Comparisons of central kurtosis indices for IM outer race bearing fault detection.

0.003

0

### **4. Conclusion**

*e s*

; ;

*p*

**4. Conclusion**  A spectrum synch, SS, technique has been proposed in this work for IM fault detection A spectrum synch, SS, technique has been proposed in this work for IM fault detection using electric current signals. This research focuses on broken rotor bar fault and outer race bearing fault detection. The local band synch technique is employed to synthesize bearing fault related features to form an FIS to enhance IM defect-related features. A central kurtosis analysis method is proposed to extract some features from the FIS, which are then used to formulate a

using electric current signals. This research focuses on broken rotor bar fault and outer race

bearing fault detection. The local band synch technique is employed to synthesize bearing

fault related features to form an FIS to enhance IM defect-related features. A central

kurtosis analysis method is proposed to extract some features from the FIS, which are then

used to formulate a fault indicator. The effectiveness of the proposed IM fault detection

technique is verified using IMs with the bearing defect and the broken rotor bar fault, under

different operating conditions. Test results have shown that the proposed SS technique and

1.091e-5

4.389e-5

7.170

202

0.052

fault indicator. The effectiveness of the proposed IM fault detection technique is verified using IMs with the bearing defect and the broken rotor bar fault, under different operating condi‐ tions. Test results have shown that the proposed SS technique and the related central kurtosis indicator can capture IM defect features effectively and can provide more accurate IM health condition monitoring information. Further research is underway to improve its robustness of the SS technique and adopt it for fault detection in other IM components such as bearings with defects on inner races and rolling elements.

## **Author details**

Wilson Wang1\* and Derek Dezhi Li2

\*Address all correspondence to: Wilson.Wang@Lakeheadu.ca

1 Dept. of Mechanical Engineering, Lakehead University, Canada

2 Dept. of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Ontario, Canada

### **References**

0 10 20 30 40 50 60

0 10 20 30 40 50 60

Data Point

**Figure 12.** The FIS generated by the SS technique at 50 Hz supply frequency and light-load

**Figure 12.** The FIS generated by the SS technique at 50 Hz supply frequency and light-load condition (a) from a healthy

**Table 5.** Comparisons of central kurtosis indices for IM outer race bearing fault detection.

Healthy

1.091e-5

A spectrum synch, SS, technique has been proposed in this work for IM fault detection

A spectrum synch, SS, technique has been proposed in this work for IM fault detection using electric current signals. This research focuses on broken rotor bar fault and outer race bearing fault detection. The local band synch technique is employed to synthesize bearing fault related features to form an FIS to enhance IM defect-related features. A central kurtosis analysis method is proposed to extract some features from the FIS, which are then used to formulate a

using electric current signals. This research focuses on broken rotor bar fault and outer race

bearing fault detection. The local band synch technique is employed to synthesize bearing

fault related features to form an FIS to enhance IM defect-related features. A central

kurtosis analysis method is proposed to extract some features from the FIS, which are then

used to formulate a fault indicator. The effectiveness of the proposed IM fault detection

technique is verified using IMs with the bearing defect and the broken rotor bar fault, under

different operating conditions. Test results have shown that the proposed SS technique and

4.389e-5

7.170

202

0.196

0.052

Faulty

49.705

0.090

202

0.196 0.052

49.757

0.055

Healthy

SS

Faulty

49.705

0.007

7.170

0.090 0.055

49.757

Healthy

SS

49.705

0.086

Faulty

0.005

1.091e-5

0.005 0.087

49.757

49.757

0.087

Healthy

Envelope analysis

Envelope analysis

49.705

0.007 0.086

Faulty

4.389e-5

condition (a) from a healthy IM; (b) from an IM with an outer race bearing defect.

0

0.003

0.041

0.003

0.041 0.173

49.705

49.705

0.173

Faulty

Faulty

0

0

*fr* 49.757

Methods PSD

*fr* 49.757

Methods PSD

0.176

**Table 5.** Comparisons of central kurtosis indices for IM outer race bearing fault detection.

Healthy

0 0.176

Healthy


IM; (b) from an IM with an outer race bearing defect.

Conditions

n *e* n*s*

; ; ; ; ; ;

s *e* s*s*

c*e* c*s*


0

0.1

Amplitude (dB)

(b)

Conditions

n *p* s *p* c*p*

 *e s*

; ;

 *e s*

; ;

*e s*

; ;

*p*

*p*

*p*

**4. Conclusion** 

**4. Conclusion**

0.2



0

0.1

Amplitude (dB)

(a)

0.2

136 Induction Motors - Applications, Control and Fault Diagnostics


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ny; 1999.


## **Failure Diagnosis of Squirrel-Cage Induction Motor with Broken Rotor Bars and End Rings**

Takeo Ishikawa

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60964

### **Abstract**

This chapter investigates the diagnosis of not only broken bar but also broken end ring faults in an induction motor. The difference between the broken bars and broken end ring segments is experimentally clarified by the Fourier analysis of the stator current. This difference is verified by two-dimensional finite element (FE) analysis that takes into consideration the voltage equation and the end ring. The electromag‐ netic field in the undamaged motor and the motor with broken bars and broken end ring segments is analyzed. The effect of the number of broken bars and broken end ring segments on the motor performance is clarified. Moreover, transient response is analyzed by the wavelet analysis.

**Keywords:** Failure diagnosis, finite element method, motor current signature analy‐ sis, wavelet analysis

### **1. Introduction**

Squirrel-cage induction motors are widely used in many industrial applications because they are cost effective and mechanically robust. However, production will stop if these motors fail. Therefore, early detection of motor faults is highly desirable. Induction motor faults are summarized in [1] and [2], and rotor failures account for approximately 10% of the total induction motor failures. Several studies have carried out diagnosis of induction machines using motor current signature analysis (MCSA). For example, Davio et al. proposed a method to diagnose rotor bar failures in induction machines based on the analysis of the stator current

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

during start-up using the discrete wavelet transform (DWT) [3]. Moreno et al. developed an automatic online diagnosis algorithm for broken-rotor-bar detection, which was optimized for single low-cost field-programmable gate array implementation [4]. Guasp et al. proposed a method based on the identification of characteristic patterns introduced by fault components in the wavelet signals obtained from the discrete wavelet transformation of transient stator currents [5]. Kia et al. proposed a time-scale method based on DWT to make the broken-bar fault diagnosis slip independent [6]. Gritli et al. carried out diagnosis of induction machines using DWT under a time-varying condition [7]. However, most of the literature has studied only broken-bar faults, and broken end ring faults have been marginally dealt with. For example, Bouzida et al. dealt with the fault diagnosis of induction machines with broken rotor bars and end ring segment and loss of stator phase during operation using DWT [8]. Con‐ cerning the FE analysis of rotor failures in induction motors, several papers have been presented. For example, Mohammed et al. studied the broken rotor bar and stator faults using FE and discrete wavelet analyses [9]. Weili et al. analyzed the flux distribution in the air gap of an induction motor with one and two broken rotor bars [10]. Faiz et al. analyzed the stator current under different numbers of broken bars and different loads of an induction motor [11]. They dealt with broken rotor bars but not a broken end ring.

This chapter addresses not only broken bar but also broken end ring faults. First, we manu‐ facture some rotors with broken bars or end rings [12]. Next, the difference between the broken end ring segments and broken bars is verified by MCSA [12]. The electromagnetic field in the rotor is analyzed to clarify the effect of the number of broken bars and broken end ring segments on the motor performance [13]. Moreover, the stator voltage and current waveforms in a transient response are analyzed by the wavelet analysis.

### **2. Induction motor with broken rotor and experimental system**

Figure 1 shows the photographs of a rotor with broken bars and a broken end ring segments that we have manufactured [13]. Figure 1(a) shows a rotor with one broken bar drilled at the center of the rotor, and Fig. 1(b) shows a rotor with two broken bars drilled at the adjacent aluminum bars. Figure 1(c) shows a rotor with a broken segment in the end ring, which is made by cutting aluminum. Figure 1(d) shows a rotor with two broken segments in the end ring, which are separated by two rotor bars. Figure 1(e) shows a rotor with two broken segments in the end ring whose distance is 45 degrees, that is, 90 electrical degrees. The experimental motor shown in Fig. 2 has the following specifications: 50 Hz, 200 V, 400 W, four poles, and 1,400 min-1 speed.

Figure 3 shows the experimental system for the failure diagnosis, which is composed of a 200- V 1.1-kVA 3-A inverter, an induction motor, a torque meter, and a servo motor used as load. Figure 4 shows the developed measurement system using NI cDAQ and Lab VIEW [14]. Lab VIEW is a system design platform and development environment for visual programming language and can be easily used for data acquisition in Microsoft Windows. Figure 4(a) shows the interface part, which is composed of a channel selector, *x* and *y* scales, trigger, and two Failure Diagnosis of Squirrel-Cage Induction Motor with Broken Rotor Bars and End Rings http://dx.doi.org/10.5772/60964 143

during start-up using the discrete wavelet transform (DWT) [3]. Moreno et al. developed an automatic online diagnosis algorithm for broken-rotor-bar detection, which was optimized for single low-cost field-programmable gate array implementation [4]. Guasp et al. proposed a method based on the identification of characteristic patterns introduced by fault components in the wavelet signals obtained from the discrete wavelet transformation of transient stator currents [5]. Kia et al. proposed a time-scale method based on DWT to make the broken-bar fault diagnosis slip independent [6]. Gritli et al. carried out diagnosis of induction machines using DWT under a time-varying condition [7]. However, most of the literature has studied only broken-bar faults, and broken end ring faults have been marginally dealt with. For example, Bouzida et al. dealt with the fault diagnosis of induction machines with broken rotor bars and end ring segment and loss of stator phase during operation using DWT [8]. Con‐ cerning the FE analysis of rotor failures in induction motors, several papers have been presented. For example, Mohammed et al. studied the broken rotor bar and stator faults using FE and discrete wavelet analyses [9]. Weili et al. analyzed the flux distribution in the air gap of an induction motor with one and two broken rotor bars [10]. Faiz et al. analyzed the stator current under different numbers of broken bars and different loads of an induction motor [11].

This chapter addresses not only broken bar but also broken end ring faults. First, we manu‐ facture some rotors with broken bars or end rings [12]. Next, the difference between the broken end ring segments and broken bars is verified by MCSA [12]. The electromagnetic field in the rotor is analyzed to clarify the effect of the number of broken bars and broken end ring segments on the motor performance [13]. Moreover, the stator voltage and current waveforms

Figure 1 shows the photographs of a rotor with broken bars and a broken end ring segments that we have manufactured [13]. Figure 1(a) shows a rotor with one broken bar drilled at the center of the rotor, and Fig. 1(b) shows a rotor with two broken bars drilled at the adjacent aluminum bars. Figure 1(c) shows a rotor with a broken segment in the end ring, which is made by cutting aluminum. Figure 1(d) shows a rotor with two broken segments in the end ring, which are separated by two rotor bars. Figure 1(e) shows a rotor with two broken segments in the end ring whose distance is 45 degrees, that is, 90 electrical degrees. The experimental motor shown in Fig. 2 has the following specifications: 50 Hz, 200 V, 400 W, four

Figure 3 shows the experimental system for the failure diagnosis, which is composed of a 200- V 1.1-kVA 3-A inverter, an induction motor, a torque meter, and a servo motor used as load. Figure 4 shows the developed measurement system using NI cDAQ and Lab VIEW [14]. Lab VIEW is a system design platform and development environment for visual programming language and can be easily used for data acquisition in Microsoft Windows. Figure 4(a) shows the interface part, which is composed of a channel selector, *x* and *y* scales, trigger, and two

They dealt with broken rotor bars but not a broken end ring.

142 Induction Motors - Applications, Control and Fault Diagnostics

in a transient response are analyzed by the wavelet analysis.

poles, and 1,400 min-1 speed.

**2. Induction motor with broken rotor and experimental system**

(a) One broken bar [1 bar] (b) Two broken bars [2 bars]

[1 ring] [2 rings] [2 rings (2)]

Fig. 1. Rotors with broken bars and end rings.

(c) One broken segment (d) Two broken segments (e) Two broken segments (90)

**Figure 1.** Rotors with broken bars and end rings.

displays that look like a multi-channel oscilloscope. Figure 4(b) shows a Lab VIEW block, which is composed of blocks for the acquisition and correction of data, trigger detection, and saving of data. Several physical variables, including the stator voltage *v*, stator current *i*, torque, and speed are measured by the NI cDAQ and Lab VIEW and are then analyzed by Fourier analysis.

Fig. 3. Experimental measurement system. **Figure 3.** Experimental measurement system.

Fig. 3. Experimental measurement system.

Lab VIEW

(a) Interface. (a) Interface.

(b) Block diagram using Lab VIEW Fig. 4. Developed measurement system [14].

File output

Fig. 4. Developed measurement system [14].

(b) Block diagram using Lab VIEW **Figure 4.** Developed measurement system [14].

### **3. Fourier analysis of the measured data**

Fig. 3. Experimental measurement system.

Fig. 3. Experimental measurement system.

Display and save of signals

Display and save of signals

Load Torque

Load Torque

meter

meter

Induction motor

Induction motor

> NI cDAQ Lab VIEW

NI cDAQ Lab VIEW

*v i* Torque Speed

*v i* Torque Speed

 Inverter

144 Induction Motors - Applications, Control and Fault Diagnostics

 Inverter

**Figure 3.** Experimental measurement system.

**Figure 4.** Developed measurement system [14].

(a) Interface.

(a) Interface.

Input of signals

Input of signals Correction of signals

Correction of signals

Trigger

Trigger

(b) Block diagram using Lab VIEW Fig. 4. Developed measurement system [14].

(b) Block diagram using Lab VIEW Fig. 4. Developed measurement system [14].

File output

File output

Figure 5 shows the Fourier analysis of the stator current at a rated speed of 1,400 min-1, where the Fourier component of several rotors is shown at every 0.33 Hz to easily compare the broken situations. Here, 1 bar, 2 bars, 1 ring, 2 rings, and 2 rings (2) mean one broken bar [see Fig. 1(a)], two adjacent broken bars [Fig. 1(b)], end ring broken at one position [Fig. 1(c)], end ring broken at two positions separated by two rotor bars [Fig. 1(d)], and end ring broken at two positions separated by five rotor bars, that is, 90 electrical degrees [Fig. 1(e)], respectively.

**Figure 5.** Fourier analysis of the measured stator current at the rated speed.

Therefore, three sets of measured results were slightly different.

In Fig. 3, the inverter rating is 1.1 kVA, which is a sufficient capacity for the 400-W experimental induction motor. Therefore, the Fourier analysis of the stator voltage did not include the (1 ± 2*s*)*f* Hz components, where *s* is the slip and *f* is the fundamental supply frequency. Because the servo motor is a synchronous motor with surface permanent magnets, the torque ripple is very small. Therefore, the effect of the inverter source and the load equipment on this measurement was very small. However, because the measured results are sensitive to the experimental setup, the experiment was performed three times. We expected a slight difference in the mechanical loss because the connection of the motor, the torque meter, and the servo motor could not be perfect even under the same situation. To take this slight difference into account, the experimental system was set up for every measurement. In Fig. 3, the inverter rating is 1.1 kVA, which is a sufficient capacity for the 400-W experimental induction motor. Therefore, the Fourier analysis of the stator voltage did not include the (1 ± 2*s*)*f* Hz components, where *s* is the slip and *f* is the fundamental supply frequency. Because the servo motor is a synchronous motor with surface permanent magnets, the torque ripple is very small. Therefore, the effect of the inverter source and the load equipment on this meas‐ urement was very small. However, because the measured results are sensitive to the experi‐ mental setup, the experiment was performed three times. We expected a slight difference in the mechanical loss because the connection of the motor, the torque meter, and the servo motor could not be perfect even under the same situation. To take this slight difference into account,

We found 50 ± 6.67 Hz components, that is, (1 ± 2*s*)*f* Hz as expected [15]. Let us explain the frequency of (1 ± 2*s*)*f* Hz. When the rotor is running at slip *s* and the supply frequency is *f*, the frequency of the forward current in the rotor is *sf*. If the rotor has a defect, such as a broken bar or broken end ring, a backward current frequency of -*sf* can flow in the rotor. The forward current frequency *sf* in the rotor is considered as frequency *f* at the stator. Because the rotor is running at (1 *s*)*f*, the frequency recognized at the stator is *sf* + (1 - *s*)*f* = *f*. In contrast, the backward current

Fig. 5. Fourier analysis of the measured stator current at the rated speed.

the experimental system was set up for every measurement. Therefore, three sets of measured results were slightly different.

We found 50 ± 6.67 Hz components, that is, (1 ± 2*s*)*f* Hz as expected [15]. Let us explain the frequency of (1 ± 2*s*)*f* Hz. When the rotor is running at slip *s* and the supply frequency is *f*, the frequency of the forward current in the rotor is *sf*. If the rotor has a defect, such as a broken bar or broken end ring, a backward current frequency of -*sf* can flow in the rotor. The forward current frequency *sf* in the rotor is considered as frequency *f* at the stator. Because the rotor is running at (1 - *s*)*f*, the frequency recognized at the stator is *sf* + (1 - *s*)*f* = *f*. In contrast, the backward current frequency of -*sf* is considered as a stator frequency of (1 - 2*s*)*f* because -*sf* + (1 - *s*)*f* = (1 - 2*s*)*f*. Then, a torque with a frequency of 2*sf* is developed because the stator current has two frequencies *f* and (1 - 2*s*)*f*. The torque produces a vibration of 2*sf*, and thus, the rotor speed becomes (1 - *s*)*f* ± 2*sf*. This speed vibration and the forward current produce a stator current frequency of (1 - *s*)*f* ± 2*sf* + *sf* = (1 ± 2*s*)*f*.

In each fault, the components at 50 - 6.67 Hz, that is, (1 - 2*s*)*f* Hz, are approximately the same as those at 50 + 6.67 Hz, that is, (1 + 2*s*)*f* Hz. Table 1 shows the average components at (1 ± 2*s*)*f* Hz. The order of the components for the different faults is as follows: [2 rings] > [1 ring] > [2 bars] > [1 bar] > [2 rings (2)] > [healthy]. Therefore, we have experimentally clarified that we can detect the fault of the rotor end ring segments and rotor bars from the (1 ± 2*s*)*f* Hz com‐ ponent of the stator current at the rated speed. In contrast, it is difficult to detect the failure type from the Fourier analysis of the stator current at (1 ± 2*s*)*f* Hz because no order of the components relative to the failure type is available.


**Table 1.** Fourier components of the measured stator current.

Figure 6 shows the Fourier analysis of the stator current under a no-load condition. The rotating speed of 1,495 min-1 was almost the same. We also find 50 ± 0.33 Hz components, that is, (1 ± 2*s*)*f* Hz components. However, because no order of the components relative to the failure types is available, it is difficult to detect the failure type by Fourier analysis of the stator current under the no-load condition.

Figure 7 shows the Fourier analysis of the torque at the rated speed of 1,400 min-1. We find 6.67 Hz components, that is, 2*sf* Hz. The order of the components for the 2*sf* for different faults was not clear. For the end ring fault, the order of the components is as follows: [2 rings] > [1 ring]

Failure Diagnosis of Squirrel-Cage Induction Motor with Broken Rotor Bars and End Rings http://dx.doi.org/10.5772/60964 147

(b) Enlarged around 49.7 Hz (b) Enlarged around 50.3 Hz

Fig. 6. Fourier analysis of the measured stator current at no load. **Figure 6.** Fourier analysis of the measured stator current at no load.

0.1

1

> [2 rings (2)]. However, the component of [2 rings (2)] is approximately the same as that of the healthy motor. For the bar fault, the component of [2 bars] was approximately the same as that of [1 bar]. Therefore, it is difficult to detect the difference in the faults of the rotor end rings and rotor bars by Fourier analysis of the torque even at the rated speed. Figure 7 shows the Fourier analysis of the torque at the rated speed of 1,400 min-1. We find 6.67 Hz components, that is, 2*sf* Hz. The order of the components for the 2*sf* for different faults was not clear. For the end ring fault, the order of the components is as follows: [2 rings] > [1 ring] > [2 rings (2)]. However, the component of [2 rings (2)] is approximately the same as that of the healthy motor. For

the bar fault, the component of [2 bars] was approximately the same as that of [1 bar]. Therefore, it is difficult to detect the difference in the faults of the rotor end rings and rotor bars by Fourier analysis

> : 2 bars : 1 ring : 2 rings : 2 rings (2)

#### **4. Simulation of induction motor with broken rotor bars and broken end ring segments** : Healthy : 1 bar

### **4.1. Analysis method**

of the torque even at the rated speed.

the experimental system was set up for every measurement. Therefore, three sets of measured

We found 50 ± 6.67 Hz components, that is, (1 ± 2*s*)*f* Hz as expected [15]. Let us explain the frequency of (1 ± 2*s*)*f* Hz. When the rotor is running at slip *s* and the supply frequency is *f*, the frequency of the forward current in the rotor is *sf*. If the rotor has a defect, such as a broken bar or broken end ring, a backward current frequency of -*sf* can flow in the rotor. The forward current frequency *sf* in the rotor is considered as frequency *f* at the stator. Because the rotor is running at (1 - *s*)*f*, the frequency recognized at the stator is *sf* + (1 - *s*)*f* = *f*. In contrast, the backward current frequency of -*sf* is considered as a stator frequency of (1 - 2*s*)*f* because -*sf* + (1 - *s*)*f* = (1 - 2*s*)*f*. Then, a torque with a frequency of 2*sf* is developed because the stator current has two frequencies *f* and (1 - 2*s*)*f*. The torque produces a vibration of 2*sf*, and thus, the rotor speed becomes (1 - *s*)*f* ± 2*sf*. This speed vibration and the forward current produce a stator

In each fault, the components at 50 - 6.67 Hz, that is, (1 - 2*s*)*f* Hz, are approximately the same as those at 50 + 6.67 Hz, that is, (1 + 2*s*)*f* Hz. Table 1 shows the average components at (1 ± 2*s*)*f* Hz. The order of the components for the different faults is as follows: [2 rings] > [1 ring] > [2 bars] > [1 bar] > [2 rings (2)] > [healthy]. Therefore, we have experimentally clarified that we can detect the fault of the rotor end ring segments and rotor bars from the (1 ± 2*s*)*f* Hz com‐ ponent of the stator current at the rated speed. In contrast, it is difficult to detect the failure type from the Fourier analysis of the stator current at (1 ± 2*s*)*f* Hz because no order of the

Healthy 0.0010 A 2.818 A 0.0009 A 1 bar 0.0135 A 2.755 A 0.0119 A 2 bars 0.0176 A 2.890 A 0.0193 A 1 ring 0.0286 A 2.872 A 0.0258 A 2 rings 0.0306 A 2.725 A 0.0333 A 2 rings (2) 0.0076 A 2.760 A 0.0072 A

Figure 6 shows the Fourier analysis of the stator current under a no-load condition. The rotating speed of 1,495 min-1 was almost the same. We also find 50 ± 0.33 Hz components, that is, (1 ± 2*s*)*f* Hz components. However, because no order of the components relative to the failure types is available, it is difficult to detect the failure type by Fourier analysis of the stator current

Figure 7 shows the Fourier analysis of the torque at the rated speed of 1,400 min-1. We find 6.67 Hz components, that is, 2*sf* Hz. The order of the components for the 2*sf* for different faults was not clear. For the end ring fault, the order of the components is as follows: [2 rings] > [1 ring]

**43.33 Hz 50 Hz 56.67 Hz**

results were slightly different.

146 Induction Motors - Applications, Control and Fault Diagnostics

current frequency of (1 - *s*)*f* ± 2*sf* + *sf* = (1 ± 2*s*)*f*.

components relative to the failure type is available.

**Table 1.** Fourier components of the measured stator current.

under the no-load condition.

The experimental motor has rotor skew of one slot pitch. Although a three-dimensional FE analysis is necessary to consider the rotor skew, it is very time consuming. This study calculates the electromagnetic field in the motor using a two-dimensional FE method, which considers the voltage equation and the rotor end ring. The cross section of the motor is shown in Fig. 8. The stator has 36 slots, and the rotor has 44 slots. The following assumptions have been made: Torque [Nm]0.001 0.01

**1.** Two-dimensional analysis is employed, and the skew in the rotor is ignored. Frequency [Hz] 0 10 20 30 40 50 0.0001

of the torque even at the rated speed.

However, the component of [2 rings (2)] is approximately the same as that of the healthy motor. For

difficult to detect the difference in the faults of the rotor end rings and rotor bars by Fourier analysis

Enlarged around (b) 6.67 Hz for the end ring and (c) 6.67 Hz for the bar. Fig. 7. Fourier analysis of the measured torque at the rated speed.

**Figure 7.** Fourier analysis of the measured torque at the rated speed.

**2.** Rotor bars and end ring are insulated from the rotor core, and no current flows from the rotor bars to the rotor core. **Simulation of Induction Motor with Broken Rotor Bars and Broken End Ring Segments**

electromagnetic field in the motor using a two-dimensional FE method, which considers the voltage

**3.** The rotating speed is constant. **4.1 Analysis Method**

to the rotor core.

**4.** The supply voltage is assumed to be sinusoidal. The experimental motor has rotor skew of one slot pitch. Although a three-dimensional FE analysis is necessary to consider the rotor skew, it is very time consuming. This study calculates the

Fig. 11. Distribution of the magnetic flux and eddy current in the healthy motor.

9

*NS* = 8.5

9.5

17 A/mm2

*NS* = 9

8

17 A/mm2

0

(b) Magnetic flux lines pass through the

position of the broken bars

0

9

10

*NS* = 9

Fig. 8. Cross section of the experimental induction motor. **Figure 8.** Cross section of the experimental induction motor.

9

9

(a) Magnetic flux lines do not pass through

the position of the broken bars

9.5

8.5

Although the motor is fed by a pulse width modulation (PWM) inverter, the Fourier compo‐ nents of the measured stator current around the switching frequency differ very slightly among the rotor fault types. Therefore, the PWM inverter does not affect the harmonic components of the stator current.

Figure 9 shows the FE analysis region and the connection of the end ring segments in the rotor where 44 bars are included in the FE analysis. Because the end ring is connected to each rotor bar, it is represented by 44 conductor segments whose resistance is *R*. For example, *R*1-2a represents the resistance of the end ring segment between bars 1 and 2, and its value is expressed by

$$R = \rho \frac{l}{S} \tag{1}$$

where of aluminum is. *l* is the length of conductor segment in the circumferential direction, and *S* is the area of cross section. Fins connected to the end ring for cooling are neglected. When rotor bar 1 is broken, its conductivity is set to zero. When part of the end ring is broken between bars 1 and 2, resistance *R*1-2a is set to infinity. The FE analysis was conducted for 3 s with 6,750 steps, where the number of nodes and elements were 34,909 and 60,866, respectively.

**Figure 9.** FE analysis region and end ring segments.

**2.** Rotor bars and end ring are insulated from the rotor core, and no current flows from the

The experimental motor has rotor skew of one slot pitch. Although a three-dimensional FE analysis is necessary to consider the rotor skew, it is very time consuming. This study calculates the electromagnetic field in the motor using a two-dimensional FE method, which considers the voltage equation and the rotor end ring. The cross section of the motor is shown in Fig. 8. The stator has 36

**Simulation of Induction Motor with Broken Rotor Bars and Broken End Ring** 

Enlarged around (b) 6.67 Hz for the end ring and (c) 6.67 Hz for the bar. Fig. 7. Fourier analysis of the measured torque at the rated speed.

6.67

10-3

10-2

(a) Fourier analysis

0 10 20 30 40 50 0.0001

Frequency [Hz]

6.67

10-3

10-2

: Healthy : 1 bar : 2 bars : 1 ring : 2 rings : 2 rings (2)

However, the component of [2 rings (2)] is approximately the same as that of the healthy motor. For the bar fault, the component of [2 bars] was approximately the same as that of [1 bar]. Therefore, it is difficult to detect the difference in the faults of the rotor end rings and rotor bars by Fourier analysis

<sup>V</sup> <sup>W</sup>

2) Rotor bars and end ring are insulated from the rotor core, and no current flows from the rotor bars

V

Fig. 8. Cross section of the experimental induction motor.

Fig. 11. Distribution of the magnetic flux and eddy current in the healthy motor.

9

*NS* = 8.5

9.5

U

17 A/mm2

*NS* = 9

8

17 A/mm2

0

(b) Magnetic flux lines pass through the

position of the broken bars

0

9

10

W

*NS* = 9

rotor bars to the rotor core.

**Segments**

**4.1 Analysis Method**

to the rotor core.

of the torque even at the rated speed.

148 Induction Motors - Applications, Control and Fault Diagnostics

Torque [Nm]

0.001

0.01

0.1

1

**3.** The rotating speed is constant.

3) The rotating speed is constant.

9

**Figure 8.** Cross section of the experimental induction motor.

9

(a) Magnetic flux lines do not pass through

the position of the broken bars

9.5

8.5

**4.** The supply voltage is assumed to be sinusoidal.

**Figure 7.** Fourier analysis of the measured torque at the rated speed.

U

slots, and the rotor has 44 slots. The following assumptions have been made: 1) Two-dimensional analysis is employed, and the skew in the rotor is ignored.

### **4.2. Analysis results**

Figure 10 shows the Fourier analysis of the calculated stator current at the rated speed of 1,400 min-1. We find the (1 ± 2*s*)*f* and (1 ± 4*s*)*f* components. Table 2 shows the calculated results of the Fourier analysis at the fundamental and (1 ± 2*s*)*f* components. By comparing these results with those in Table 1, we find that the calculated fundamental components are slightly smaller than the measured ones, and the calculated (1 ± 2*s*)*f* components are larger than the measured ones. We believe that these differences are attributed to the assumption where the skew is not taken into account in the calculation. We also verify from the calculated results that the (1 ± 2*s*)*f* components of the end ring faults are larger than those of the bar faults and that the (1 ± 2*s*)*f* component of the end ring broken at two positions separated by electrical radian is smaller than that of the other faults.

**Figure 10.** Fourier analysis of the calculated stator current.


**Table 2.** Fourier components of the measured stator current.

U

### **4.3. Electromagnetic field in the motor calculated by FEM**

**4.2. Analysis results**

than that of the other faults.

Stator

0.01

**Figure 10.** Fourier analysis of the calculated stator current.

**Table 2.** Fourier components of the measured stator current.

0.1

1

10

150 Induction Motors - Applications, Control and Fault Diagnostics

current [A]

Figure 10 shows the Fourier analysis of the calculated stator current at the rated speed of 1,400 min-1. We find the (1 ± 2*s*)*f* and (1 ± 4*s*)*f* components. Table 2 shows the calculated results of the Fourier analysis at the fundamental and (1 ± 2*s*)*f* components. By comparing these results with those in Table 1, we find that the calculated fundamental components are slightly smaller than the measured ones, and the calculated (1 ± 2*s*)*f* components are larger than the measured ones. We believe that these differences are attributed to the assumption where the skew is not taken into account in the calculation. We also verify from the calculated results that the (1 ± 2*s*)*f* components of the end ring faults are larger than those of the bar faults and that the (1 ± 2*s*)*f* component of the end ring broken at two positions separated by electrical radian is smaller

Frequency [Hz]

**43.33 Hz 50 Hz 56.67 Hz**

35 40 45 50 55 60 65 0.001

Healthy 0.0002 A 2.455 A 0.0003 A 1 bar 0.0326 A 2.434 A 0.0030 A 2 bars 0.0701 A 2.411 A 0.0079 A 1 ring 0.1637 A 2.390 A 0.0488 A 2 rings 0.1477 A 2.374 A 0.0618 A 2 rings (2) 0.0807 A 2.335 A 0.0222 A

: Healthy : 1 bar : 2 bars : 1 ring : 2 rings : 2 rings (2) An example of the magnetic flux and eddy current distribution in the healthy motor under the rated speed with rated-load condition is shown in Fig. 11. Because this motor is a four-pole machine, the magnetic flux distribution is periodic in every one-fourth region, that is, in every nine stator slots. Here, we denote the number of stator slots in the same group of magnetic flux lines as *NS*. Then, the *NS* for each pole is 9, 9, 9, and 9, and there is no distortion in the magnetic flux distribution. U V W Fig. 8. Cross section of the experimental induction motor.

Fig. 11. Distribution of the magnetic flux and eddy current in the healthy motor. **Figure 11.** Distribution of the magnetic flux and eddy current in the healthy motor.

*NS* = 8.5 9.5 *NS* = 9 9 17 A/mm2 Figure 12 shows the distribution of the magnetic flux and eddy current in the motor with two broken bars under different rotor positions, namely, that where the magnetic flux does not pass through the broken bars [Fig. 12(a)] and that where it passes through the broken bars [Fig. 12(b)]. In Fig. 12(a), the eddy current distribution in the rotor bars is approximately the same as that in the healthy motor shown in Fig. 11, and the *NS* under each pole is approximately 8.5, 9.5, 8.5, and 9.5, indicating that magnetic flux distortion occurs. On the other hand, Fig. 12(b) shows a rotor bar where the eddy current density is very high, and the *NS* for each pole is approximately 9, 9, 10, and 8. These magnetic distortions, shown in Figs. 12 (a) and (b), are repeated.

8.5 9.5 8 10 (a) Magnetic flux lines do not pass through the position of the broken bars (b) Magnetic flux lines pass through the position of the broken bars 0 Figure 13 shows the distribution of the magnetic flux and eddy current in the motor with a broken end ring segment under different rotor positions. No rotor bar exhibits a very high eddy current density, and the number of stator slots included in the flux lines for each pole is different. The *NS* for each pole is approximately 8.5, 9, 9, and 9.5 in Fig. 13(a) and approximately 8, 8.5, 10, and 9.5 in Fig. 12(b). These magnetic flux distortions are repeated. As explained in Chapter 3, these magnetic distortions produce a stator current frequency of (1 ± 2*s*)*f*.

### **4.4. Effect of the number of broken bars and end ring segments**

Next, we discuss the effect of the number of broken bars and broken end ring segments on the motor performance. Figure 14 shows the Fourier components of the stator current and torque 9

Fig. 11. Distribution of the magnetic flux and eddy current in the healthy motor.

U

17 A/mm2

0

9

W

*NS* = 9

<sup>V</sup> <sup>W</sup>

V

Fig. 8. Cross section of the experimental induction motor.

U

**Figure 12.** Distribution of the magnetic flux and eddy current in the motor with two broken bars under different rotor positions. different rotor positions.

Fig. 12. Distribution of the magnetic flux and eddy current in the motor with two broken bars under

(a) Magnetic flux lines do not pass through the position of the broken end (b) Magnetic flux lines pass through the position of the broken end ring

segment under different rotor positions. **Figure 13.** Distribution of the magnetic flux and eddy current in the motor with a broken end ring segment under dif‐ ferent rotor positions.

Fig. 13. Distribution of the magnetic flux and eddy current in the motor with a broken end-ring

for different numbers of broken bars. The fundamental components of the stator current and the average torque decrease, and the (1 ± 2*s*)*f* component of the stator current and the 2*sf* component of the torque increase when the number of broken bars increases. Figure 15 shows the Fourier components of the stator current and torque for different numbers of end ring segments. The fundamental components of the stator current and the average torque also decrease, and the (1 ± 2*s*)*f* component of the stator current and 2*sf* component of the torque approximately increase when the number of broken end ring segments increases. Tables 1 and *<sup>S</sup> <sup>l</sup> <sup>R</sup>* (1)

2 show that when the number of faults is small, the components for the different faults appear in the following order: [2 rings] > [1 ring] > [2 bars] > [1 bar] > [2 rings (2)] > [healthy]. In contrast, the comparison of Figs. 14 and 15 shows that the (1 ± 2*s*)*f* component of the stator current for the broken bars is larger than that for the broken end ring when the number of faults is greater than three. current and 2*sf* component of the torque approximately increase when the number of broken end ring segments increases. Tables 1 and 2 show that when the number of faults is small, the components for the different faults appear in the following order: [2 rings] > [1 ring] > [2 bars] > [1 bar] > [2 rings (2)] > [healthy]. In contrast, the comparison of Figs. 14 and 15 shows that the (1 ± 2*s*)*f* component of the stator current for the broken bars is larger than that for the broken end ring when the number of

Fig. 14. Stator current and torque for different numbers of broken bars. **Figure 14.** Stator current and torque for different numbers of broken bars.

### **5. Wavelet analysis**

Stator current [A]

0

0.5

1

1.5

2

2.5

faults is greater than three.

for different numbers of broken bars. The fundamental components of the stator current and the average torque decrease, and the (1 ± 2*s*)*f* component of the stator current and the 2*sf* component of the torque increase when the number of broken bars increases. Figure 15 shows the Fourier components of the stator current and torque for different numbers of end ring segments. The fundamental components of the stator current and the average torque also decrease, and the (1 ± 2*s*)*f* component of the stator current and 2*sf* component of the torque approximately increase when the number of broken end ring segments increases. Tables 1 and

**Figure 13.** Distribution of the magnetic flux and eddy current in the motor with a broken end ring segment under dif‐

Fig. 13. Distribution of the magnetic flux and eddy current in the motor with a broken end-ring

10

U

17 A/mm2

*NS* = 9

8

*NS* = 8

9.5

17 A/mm2

17 A/mm2

0

0

(b) Magnetic flux lines pass through the

position of the broken bars

(1)

(b) Magnetic flux lines pass through the

position of the broken end ring

0

9

10

**Figure 12.** Distribution of the magnetic flux and eddy current in the motor with two broken bars under different rotor

Fig. 12. Distribution of the magnetic flux and eddy current in the motor with two broken bars under

8.5

W

*NS* = 9

<sup>V</sup> <sup>W</sup>

V

Fig. 8. Cross section of the experimental induction motor.

Fig. 11. Distribution of the magnetic flux and eddy current in the healthy motor.

9

*NS* = 8.5

9.5

*NS* = 8.5

9.5

U

9

9

152 Induction Motors - Applications, Control and Fault Diagnostics

(a) Magnetic flux lines do not pass through the position of the broken bars

9.5

positions.

9

8.5

different rotor positions.

9

ferent rotor positions.

segment under different rotor positions.

(a) Magnetic flux lines do not pass through the position of the broken end

*<sup>S</sup>*

*<sup>l</sup> <sup>R</sup>* 

We have discussed about the failure diagnosis of broken end ring segments and broken bars in induction motor at the steady state using the Fourier analysis. In this section, the transient performance of an inverter-fed induction motor is discussed by using the wavelet analysis. There are two kinds of wavelet transform; continuous and discrete ones.

Number of broken end ring segments

0 4 8 12

50Hz

43.33Hz 56.67Hz faults is greater than three.

current and 2*sf* component of the torque approximately increase when the number of broken end ring segments increases. Tables 1 and 2 show that when the number of faults is small, the components for the different faults appear in the following order: [2 rings] > [1 ring] > [2 bars] > [1 bar] > [2 rings (2)] > [healthy]. In contrast, the comparison of Figs. 14 and 15 shows that the (1 ± 2*s*)*f* component of the stator current for the broken bars is larger than that for the broken end ring when the number of

Fig. 15. Stator current and torque for different numbers of broken end ring segments. **Figure 15.** Stator current and torque for different numbers of broken end ring segments.

#### **5.1. Continuous wavelet analysis Wavelet Analysis**

Let us make a brief introduction of continuous wavelet transform. Figure 16 shows the waveform of a signal and its wavelet analysis, which shows equipotential lines in the frequency and time plane. Although there are several kinds of Wavelet function – Morlet, Paul, and Derivative of Gaussian – Fig. 16 is the result of using the Morlet function, where the number of waves is 30. We can find high value region around 100 Hz and from 0.3 to 0.6 s and around 400 Hz and from 0.4 to 0.7 s.

We investigate transient response of an inverter-fed induction motor, where the control strategy is an open loop and the motor has no-load. The step responses of the stator voltage, stator current, and motor speed were measured when a start signal was input to the inverter. Figures 17 and 18 show the Wavelet analysis of the stator current *iu* and stator voltage *Vuv* using the Morlet function, where the number of waves is two, for the healthy motor and for the motor with two broken bars. We can find a very slight difference in the Wavelet analysis of the stator

**Figure 16.** An example of the continuous wavelet analysis using the Morlet mother function.

current between the healthy rotor and two broken bars. There are large components at high frequency before the motor starts, namely, time is from 0 to 0.05 s. As discussed before, the rotor fault produces the components of (1 ± 2*s*)*f*. The component becomes 150 Hz when the rotor is stopping, that is, *s* = 1. It is shown that there is no difference in the stator voltage. Therefore, it is difficult to distinguish the rotor defect by using the continuous wavelet transform of the stator current in the starting operation with no-load condition.

### **5.2. Discrete wavelet analysis**

**5.1. Continuous wavelet analysis**

**Wavelet Analysis** 

faults is greater than three.

Stator current [A]

Torque [Nm]

0 0.5 1 1.5 2 2.5 3

**Figure 15.** Stator current and torque for different numbers of broken end ring segments.

0

0.5

1

1.5

2

2.5

154 Induction Motors - Applications, Control and Fault Diagnostics

400 Hz and from 0.4 to 0.7 s.

Let us make a brief introduction of continuous wavelet transform. Figure 16 shows the waveform of a signal and its wavelet analysis, which shows equipotential lines in the frequency and time plane. Although there are several kinds of Wavelet function – Morlet, Paul, and Derivative of Gaussian – Fig. 16 is the result of using the Morlet function, where the number of waves is 30. We can find high value region around 100 Hz and from 0.3 to 0.6 s and around

(b) Torque Fig. 15. Stator current and torque for different numbers of broken end ring segments.

Number of broken end ring segments

0 4 8 12

current and 2*sf* component of the torque approximately increase when the number of broken end ring segments increases. Tables 1 and 2 show that when the number of faults is small, the components for the different faults appear in the following order: [2 rings] > [1 ring] > [2 bars] > [1 bar] > [2 rings (2)] > [healthy]. In contrast, the comparison of Figs. 14 and 15 shows that the (1 ± 2*s*)*f* component of the stator current for the broken bars is larger than that for the broken end ring when the number of

Fig. 14. Stator current and torque for different numbers of broken bars.

(a) Stator current

Number of broken end ring segments

0 4 8 12

50Hz

43.33Hz 56.67Hz

Average

6.67Hz

We investigate transient response of an inverter-fed induction motor, where the control strategy is an open loop and the motor has no-load. The step responses of the stator voltage, stator current, and motor speed were measured when a start signal was input to the inverter. Figures 17 and 18 show the Wavelet analysis of the stator current *iu* and stator voltage *Vuv* using the Morlet function, where the number of waves is two, for the healthy motor and for the motor with two broken bars. We can find a very slight difference in the Wavelet analysis of the stator

The discrete wavelet transform of a signal is calculated by passing it through a series of filters. As it is well known, the use of wavelet signals, that is, approximation and high-order details, resulting from discrete wavelet transform constitutes an interesting advantage because these signals act as filters. Moreover, the computational time of discrete wavelet transform is much shorter than that of continuous wavelet transform. Figure 19 shows the discrete wavelet analysis for the same signal as shown in Fig. 16. It is found that the component of 100 Hz appears in d6 and signal of 450 Hz component appears in d4 detail.

Table 3 shows frequency bands by decomposition in multi-levels. Figures 20 and 21 show discrete wavelet signals of stator current *iu* of the motor with the healthy rotor and two broken bars. It is shown that there are large components of d7 at *t* = 0.05 s, and a large component of

(c) Stator voltage.

Fig. 17. Continuous wavelet analysis of healthy rotor. **Figure 17.** Continuous wavelet analysis of healthy rotor.

Failure Diagnosis of Squirrel-Cage Induction Motor with Broken Rotor Bars and End Rings http://dx.doi.org/10.5772/60964 157

Fig. 18. Continuous wavelet analysis of the motor with two broken bars.

**Figure 18.** Continuous wavelet analysis of the motor with two broken bars.

(a) Speed response.

(b) Stator current.

(c) Stator voltage. Fig. 17. Continuous wavelet analysis of healthy rotor.

**Figure 17.** Continuous wavelet analysis of healthy rotor.

156 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 19.** An example of the discrete wavelet analysis.

d8 at *t* = 0.07 s and a large component of d9 at *t* = 0.12 s. These components correspond to the frequency of (1 + 2*s*)*f* Hz. We can find a slight difference of the components in these frequency bands between the healthy rotor and the rotor with two broken bars, especially in d2 through d6 details from 0 to 0.1 s.


**Table 3.** Frequency bands by decomposition in multi-levels.

### **6. Conclusions**

This study has analyzed the Fourier components of broken end ring segments and compared them with those of the broken bars. We have verified, by both experiment and simulation, that the components of (1 ± 2*s*)*f* of the broken end ring segments are larger than those of the broken bars when the number of faults is one or two. The electromagnetic field in the motor with two broken bars and a broken end ring has been analyzed. Moreover, the effect of the number of broken bars and broken end ring segments on the motor performance has been clarified. The discrete wavelet analysis has shown that there are slight differences in the detail signals in high frequency bands between healthy rotor and the rotor with two broken bars.

### **Author details**

Takeo Ishikawa

Address all correspondence to: ishi@el.gunma-u.ac.jp

Division of Electronics and Informatics, Faculty of Science and Technology, Gunma University, Japan

### **References**

d8 at *t* = 0.07 s and a large component of d9 at *t* = 0.12 s. These components correspond to the frequency of (1 + 2*s*)*f* Hz. We can find a slight difference of the components in these frequency bands between the healthy rotor and the rotor with two broken bars, especially in d2 through

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -10

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -5

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -5

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -2

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -0.5

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -0.5

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -0.2

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -0.5

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -1

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -2

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -2

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -5

t [s]

0 10 sig

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -2

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -2

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -2

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -2

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -2

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -2

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -2

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -2

t [s]

<sup>2</sup> sig

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -10

0

158 Induction Motors - Applications, Control and Fault Diagnostics

0 2

0 2

0 2

0 2

0 2

0 2

0 2

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -5

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -5

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -2

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -0.5

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -0.5

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -0.2

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -0.5

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -0.5

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -1

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -1

<sup>0</sup> 0.05 0.1 0.15 0.2 0.25 0.3 0.35 -5

t [s]

**Figure 19.** An example of the discrete wavelet analysis.

0 10 sig

> 0 5 a10

> 0 5 d10

> 0 2 d9

0 0.5 d8

0 0.5 d7

0 0.2 d6

0 0.5 d5

0 0.5 d4

> 0 1 d3

> 0 1 d2

> 0 5 d1

0 5 a10

0 5 d10

0 2 d9

0 0.5 d8

0 0.5 d7

0 0.2 d6

0 0.5 d5

> 0 1 d4

> 0 2 d3

> 0 2 d2

> 0 5 d1

d6 details from 0 to 0.1 s.

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160 Induction Motors - Applications, Control and Fault Diagnostics

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**Section 3**

**Control Strategies**

**Chapter 6**

## **Fuzzy Direct Torque-controlled Induction Motor Drives for Traction with Neural Compensation of Stator Resistance**

Mohammad Ali Sandidzadeh, Amir Ebrahimi and Amir Heydari

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/61545

### **Abstract**

In this chapter, a new method for stator resistance compensation in direct torque control (DTC) drives, based on neural networks, is presented. The estimation of electromagnetic torque and stator flux linkages using the measured stator voltages and currents is crucial to the success of DTC drives. The estimation is dependent only on one machine parame‐ ter, which is the stator resistance. Changes of the stator resistances cause errors in the es‐ timated magnitude and position of the flux linkage and therefore in the estimated electromagnetic torque. Parameter compensation by means of stator current phasor error has been proposed in literature. The proposed approach in this chapter is based on a principle that states the error between the measured current magnitude of the stator feed‐ back and the stator's command, verified with neural network, is proportional to the var‐ iation of the stator resistance and is mainly caused by the motor temperature and the varying stator frequency. Then the correction value of stator resistance is achieved by means of a fuzzy controller. For the first time, a combination of neural control and fuzzy control approach in stator resistance variations based on the stator current is presented. The presented approach efficiently estimates the correct value of stator resistance.

**Keywords:** Fuzzy direct torque control, neural compensation, induction motor drives

### **1. Introduction**

The direct torque control is one of the excellent control strategies available for torque control of induction machine. It is considered as an alternative to field oriented control (FOC) technique [1]. In fact, among all control methods for induction motor drives, direct torque

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

control (DTC) seems to be particularly interesting being independent of machine rotor parameters and requiring no speed or position sensors [2].

A basic concept of direct torque control of induction motor drives is simultaneous control of the stator flux and electromagnetic torque of a machine. Compared to the conventional vectorcontrolled drives, the torque and flux of a DTC-based drive are controlled in a closed-loop system that does not use the current loops.

In principle, DTC-based drives require only the knowledge of stator resistance and thereby decrease the associated sensitivity to parameter variations [3, 4]. Moreover, compared to the conventional vector-controlled drives, DTC-based drives do not require fulfilling the coordi‐ nate transformation between stationary and synchronous frames. Depending on how the switching sectors are selected, two different DTC schemes become possible [5].

Since a DTC-based drive selects the inverter switching states using a switching table, neither the current controllers nor the pulse-width modulation (PWM) modulator is required. As a result, the DTC-based drive provides a fast torque response [6]. The conventional direct torque control (CDTC) suffers from some drawbacks such as high current, flux and torque ripple, difficulties in torque, and flux control at very low speeds [7]. However, the switching-tablebased DTC approach has some disadvantages. If the switching frequency of the inverter is not high, the torque and flux pulsation could be high; moreover, there would be a sluggish response during the start-up or change of the reference flux or reference torque [8]. Hence, to improve the performance of the DTC drive during the start-up or changes in the reference flux and torque, a fuzzy-logic-based switching-vector process is developed in this chapter [9–15]. In DTC drives, the feedback of the electromagnetic torque and stator flux linkage is used as the input of controller. Using the measured stator currents and voltages, the electromagnetic torque and also stator flux linkages are estimated in stator reference frames [16, 17]. "The machine model is only dependent on stator resistance" [18]. There are different forms of direct torque control induction motor based on how currents and voltages are measured or estimated [19–21]. The stator current might be obtained using only the DC-link current sensor, and the motor line voltages could be reconstructed inexpensively using gate signals [22]. Nevertheless, all the measured values suffer from precision and low-speed operational problems caused by errors induced by the varying stator resistance in the flux and its angle calculator [23, 24]. The stator resistance change has a wide range, varying from 0.75 to 1.7 times the stator's nominal value. The variation is largely due to temperature variations, and to a small extent, due to the stator frequency variations [21]. The variation deteriorates the drive performance by intro‐ ducing errors in the estimated magnitude and position of the flux linkage and therefore in the electromagnetic torque estimation, particularly at low speeds [25]. Note that at low speeds, the voltage drops of the stator resistance constitute a significant portion of the applied voltages. Only a few control schemes have been proposed so far for overcoming the mentioned parameter sensitivity (which restricts the speed control range of the drives). The stator resistance has problems such as convergence and slowness of response. A partial operatingfrequency-dependent hybrid-flux estimator has been proposed for tuning the stator resistance [10]. Adjustment of the stator resistance, based on the difference between the flux current and its command, has problems in identifying the actual flux current [26, 27]. Finding the stator resistance based on the steady state voltage has the shortcoming of using direct axis flux linkages that are affected by the stator resistance variations.

In this chapter, a neural network estimator is developed to find the reference stator current values at each moment. Later, the error difference between the measured and the real stator current values is fed to a fuzzy logic controller, which then outputs the correct stator resistance value.

**Figure 1.** Block diagram of the fuzzy direct torque control of induction motor drives with a stator resistance estimator.

### **2. Fuzzy logic direct torque control**

control (DTC) seems to be particularly interesting being independent of machine rotor

A basic concept of direct torque control of induction motor drives is simultaneous control of the stator flux and electromagnetic torque of a machine. Compared to the conventional vectorcontrolled drives, the torque and flux of a DTC-based drive are controlled in a closed-loop

In principle, DTC-based drives require only the knowledge of stator resistance and thereby decrease the associated sensitivity to parameter variations [3, 4]. Moreover, compared to the conventional vector-controlled drives, DTC-based drives do not require fulfilling the coordi‐ nate transformation between stationary and synchronous frames. Depending on how the

Since a DTC-based drive selects the inverter switching states using a switching table, neither the current controllers nor the pulse-width modulation (PWM) modulator is required. As a result, the DTC-based drive provides a fast torque response [6]. The conventional direct torque control (CDTC) suffers from some drawbacks such as high current, flux and torque ripple, difficulties in torque, and flux control at very low speeds [7]. However, the switching-tablebased DTC approach has some disadvantages. If the switching frequency of the inverter is not high, the torque and flux pulsation could be high; moreover, there would be a sluggish response during the start-up or change of the reference flux or reference torque [8]. Hence, to improve the performance of the DTC drive during the start-up or changes in the reference flux and torque, a fuzzy-logic-based switching-vector process is developed in this chapter [9–15]. In DTC drives, the feedback of the electromagnetic torque and stator flux linkage is used as the input of controller. Using the measured stator currents and voltages, the electromagnetic torque and also stator flux linkages are estimated in stator reference frames [16, 17]. "The machine model is only dependent on stator resistance" [18]. There are different forms of direct torque control induction motor based on how currents and voltages are measured or estimated [19–21]. The stator current might be obtained using only the DC-link current sensor, and the motor line voltages could be reconstructed inexpensively using gate signals [22]. Nevertheless, all the measured values suffer from precision and low-speed operational problems caused by errors induced by the varying stator resistance in the flux and its angle calculator [23, 24]. The stator resistance change has a wide range, varying from 0.75 to 1.7 times the stator's nominal value. The variation is largely due to temperature variations, and to a small extent, due to the stator frequency variations [21]. The variation deteriorates the drive performance by intro‐ ducing errors in the estimated magnitude and position of the flux linkage and therefore in the electromagnetic torque estimation, particularly at low speeds [25]. Note that at low speeds, the voltage drops of the stator resistance constitute a significant portion of the applied voltages. Only a few control schemes have been proposed so far for overcoming the mentioned parameter sensitivity (which restricts the speed control range of the drives). The stator resistance has problems such as convergence and slowness of response. A partial operatingfrequency-dependent hybrid-flux estimator has been proposed for tuning the stator resistance [10]. Adjustment of the stator resistance, based on the difference between the flux current and its command, has problems in identifying the actual flux current [26, 27]. Finding the stator

switching sectors are selected, two different DTC schemes become possible [5].

parameters and requiring no speed or position sensors [2].

system that does not use the current loops.

166 Induction Motors - Applications, Control and Fault Diagnostics

In this section, the concept and principle of direct torque control approach of an induction motor is briefly introduced. A schematic diagram of the proposed drive is shown in Fig. 1. The feedback control of torque and stator flux linkages, which are estimated from the measured voltages and currents of the motor, is used in the proposed drive scheme. In this approach, stator-reference frame model of the induction motor is used. To avoid the trigonometric operations faced in coordinate transformations of other reference frames, the same reference frame is used in the implementation [22]. This can be considered as one of the advantages of the control scheme. Through the integration of the difference between the phase voltage and the voltage drop in the stator resistance, Stator *q* and *d* and axis flux linkages *λqs*, *λds* can be calculated as follows:

$$\mathcal{A}\_{\varphi} = \int (V\_{\varphi} - R\_s \mathbf{i}\_{\varphi}) dt \tag{1}$$

$$\mathcal{A}\_{ds} = \int (V\_{ds} - R\_s \mathbf{i}\_{ds}) dt \tag{2}$$

And the flux linkage phasor is as follows:

$$
\lambda\_s = \sqrt{\lambda\_{qs}^{'2} + \lambda\_{ds}^{'2}}\tag{3}
$$

The stator flux linkage phasor position is:

$$\theta\_s = \tan^{-1}(\frac{\mathcal{Z}\_{qs}}{\mathcal{Z}\_{ds}}) \tag{4}$$

And the electromagnetic torque is given by:

$$T\_e = \frac{3}{2} \frac{P}{2} (\dot{\mathbf{i}}\_{qs}\mathcal{A}\_{ds} - \dot{\mathbf{i}}\_{ds}\mathcal{A}\_{qs}) \tag{5}$$

According to Fig. 2, the inverter switching states are selected based on the errors of the torque and the flux (as indicated by Δ*Te* and Δ*λs*, respectively). Provided that

$$
\begin{aligned}
\Delta T\_e &= T\_e^\* - T\_e \\
\Delta \mathcal{X}\_s &= \mathcal{X}\_s^\* - \mathcal{X}\_s
\end{aligned}
\tag{6}
$$

The optimum switching vector is selected to decrease the errors [23, 25, 26]. Using a fuzzylogic-based switching-vector selection process, it would be possible to improve the perform‐ ance of the DTC drive during start-up or changes in the reference flux and torque. For this, a Mamdani fuzzy-logic-based system is used. Using the flux and torque deviation from reference ones and the position of the stator flux linkage space vector, it is possible to select different voltages. Then a rule-base has to be formulated based on these states. Thus the aim of the approach is to use a fuzzy logic system to expand the system performance (i.e., gives faster torque and flux response), outputs the zero and non-zero voltage switching states (*n*), and uses three quantities as its inputs: *e*Φ, the torque error (*eT* ), and the position of the stator flux space vector (*θs*). The stator flux linkage space vector can be located in any of the twelve sectors, each spanning a 60° wide region. These regions overlap each other as shown in Table 1.

Fuzzy Direct Torque-controlled Induction Motor Drives for Traction with Neural Compensation of Stator Resistance http://dx.doi.org/10.5772/61545 169

sectors, each spanning a 60 wide region. These regions overlap each other as shown in Table 1.

*<sup>s</sup>* ). The stator flux linkage space vector can be located in any of the twelve

The optimum switching vector is selected to decrease the errors [23, 25, 26]. Using a fuzzy-logic-based

switching-vector selection process, it would be possible to improve the performance of the DTC drive

during start-up or changes in the reference flux and torque. For this, a Mamdani fuzzy-logic-based

system is used. Using the flux and torque deviation from reference ones and the position of the stator

flux linkage space vector, it is possible to select different voltages. Then a rule-base has to be formulated

based on these states. Thus the aim of the approach is to use a fuzzy logic system to expand the system

performance (i.e., gives faster torque and flux response), outputs the zero and non-zero voltage

switching states (*n*), and uses three quantities as its inputs: *e* , the torque error ( *<sup>T</sup> e* ), and the position of

**Fig. 2.** Changes of flux linkage space vectors due to the switching vectors. **Figure 2.** Changes of flux linkage space vectors due to the switching vectors.



**Table 1.** Overlaps between sectors

the stator flux space vector (

( )

( )

2 2 ) *s qs ds*

<sup>1</sup> tan ( ) *qs*

<sup>3</sup> ( ) 2 2 *<sup>e</sup> qs ds ds qs <sup>P</sup> T ii* = l

According to Fig. 2, the inverter switching states are selected based on the errors of the torque

\* \* *ee e s ss*

 l

The optimum switching vector is selected to decrease the errors [23, 25, 26]. Using a fuzzylogic-based switching-vector selection process, it would be possible to improve the perform‐ ance of the DTC drive during start-up or changes in the reference flux and torque. For this, a Mamdani fuzzy-logic-based system is used. Using the flux and torque deviation from reference ones and the position of the stator flux linkage space vector, it is possible to select different voltages. Then a rule-base has to be formulated based on these states. Thus the aim of the approach is to use a fuzzy logic system to expand the system performance (i.e., gives faster torque and flux response), outputs the zero and non-zero voltage switching states (*n*), and uses three quantities as its inputs: *e*Φ, the torque error (*eT* ), and the position of the stator flux space vector (*θs*). The stator flux linkage space vector can be located in any of the twelve sectors, each

*TT T* ll

D= -

spanning a 60° wide region. These regions overlap each other as shown in Table 1.

*ds*

 l

l

l

 ll

*qs qs s qs* = - *V R i dt* ò (1)

*ds ds s ds* = - *V R i dt* ò (2)

= + (3)


D= - (6)

(5)

l

l

l

*s*

q

and the flux (as indicated by Δ*Te* and Δ*λs*, respectively). Provided that

And the flux linkage phasor is as follows:

168 Induction Motors - Applications, Control and Fault Diagnostics

The stator flux linkage phasor position is:

And the electromagnetic torque is given by:

**Table 2.** Fuzzy vector selection in sector 1

Since it was assumed that there were three and five fuzzy sets for the flux error and the torque error, respectively, there will be 15 rules for every sector. Table 2 shows the various rules for sector 1. In particular, the stator flux error (*e*Φ) can be positive (P), zero (ZE), or negative (N), corresponding to three overlapping fuzzy sets. The electromagnetic torque error can be positive large (PL), positive small (PS), zero (ZE), negative small (NS), or negative large (NL). This is because the intention is to make the torque variations smaller. Therefore, the universe of the torque is divided into five overlapping fuzzy sets. The various membership functions are shown in Fig. 3. Since there are 12 sectors, the total number of rules becomes 180. Each one of the rules can be described by the input variables and the control variable, which is the switching state (n). For example, Table 2 shows various rules for sector 1 as below:

Rule 1: If *e*Φ is positive (P), *eT* is positive large (PL) and *θs* is S1, then *n* is 1.

Rule 2: If *e*Φ is positive (P), *eT* is positive small (PS) and *θs* is S2, then *n* is 1.

Rule 3: If *e*Φ is positive (P), *eT* is ZE and *θs* is S3, then *n* is 0.

The goal of the fuzzy system is to obtain a crisp value (as the appropriate switching state) on its output. A general "*i*th rule" has the following form:

Rule *i*: If *e*Φ is *Ai* , *eT* is *Bi* and *θs* is *Ci* , then *n* is *Ni*

Thus, by using the minimum operation for the fuzzy *AND* operation and the firing strength of the *i*th rule, *α<sup>i</sup>* can be obtained from

$$\alpha\_{i} = \min \{ \mu\_{Al}(e\_{\phi}), \mu\_{\aleph}(e\_{T}), \mu\_{c}(\theta\_{s}) \} \tag{7}$$

where *μAi*(*e*Φ), *μBi*(*eT* ), *μci*(*θs*) are membership functions of fuzzy sets *Ai* , *Bi* , and *Ci* of the variables flux error, the torque error, and the flux position, respectively. The output form of the *i*th rule is obtained from

( ) min[ , ( )] *Ni i Ni* m am*n n* = (8)

where *μNi*(*n*) is the membership function of fuzzy set *Ni* of variable *n*. Therefore, the overall (or the combined) membership function of output *n* is gained by using the max operator as follows:

$$
\mu\_{\rm N}(n) = \max \{ \mu\_{\rm N}(n) \} \tag{9}
$$

In this case, the outputs include crisp numbers, switching states, and for defuzzification, the maximum used criteria.

### **3. Stator resistance compensation**

### **3.1. Scheme**

A mismatch between the controller-set stator resistance and its actual value in the machine can create the instability shown in Fig. 6a. This figure shows the simulations for the changes of the

Fuzzy Direct Torque-controlled Induction Motor Drives for Traction with Neural Compensation of Stator Resistance http://dx.doi.org/10.5772/61545 171

In this case, the outputs include crisp numbers, switching states, and for defuzzification, the maximum

flux error, the torque error, and the flux position, respectively. The output form of the *i*th rule is obtained

*Ni* is the membership function of fuzzy set *Ni* of variable *n*. Therefore, the overall (or the

combined) membership function of output *n* is gained by using the max operator as follows:

are membership functions of fuzzy sets *Ai* , *Bi* , and *Ci* of the variables

**Figure 3.** Membership functions.

 where ( ), ( ), )( *Ai Bi <sup>T</sup> ci <sup>s</sup> ee* 

*n*)( min[ (, *n*)]

*n*)( max[ (*n*)]

*Ni* (9)

*Ni* (8)

*Ni <sup>i</sup>*

where *n*)( 

used criteria.

**3.1 Scheme** 

from

*<sup>N</sup>*

of the torque is divided into five overlapping fuzzy sets. The various membership functions are shown in Fig. 3. Since there are 12 sectors, the total number of rules becomes 180. Each one of the rules can be described by the input variables and the control variable, which is the

The goal of the fuzzy system is to obtain a crisp value (as the appropriate switching state) on

Thus, by using the minimum operation for the fuzzy *AND* operation and the firing strength

min[ ( ), ( ), ( )] *<sup>i</sup> Ai Bi T ci s*

( ) min[ , ( )] *Ni i Ni*

( ) max[ ( )] *<sup>N</sup> Ni*

 am

(or the combined) membership function of output *n* is gained by using the max operator as

 m

In this case, the outputs include crisp numbers, switching states, and for defuzzification, the

A mismatch between the controller-set stator resistance and its actual value in the machine can create the instability shown in Fig. 6a. This figure shows the simulations for the changes of the

 m

variables flux error, the torque error, and the flux position, respectively. The output form of

 mq

*e e* <sup>F</sup> = (7)

*n n* = (8)

*n n* = (9)

, *Bi*

of variable *n*. Therefore, the overall

, and *Ci*

of the

 m

where *μAi*(*e*Φ), *μBi*(*eT* ), *μci*(*θs*) are membership functions of fuzzy sets *Ai*

m

m

where *μNi*(*n*) is the membership function of fuzzy set *Ni*

switching state (n). For example, Table 2 shows various rules for sector 1 as below:

, then *n* is *Ni*

Rule 1: If *e*Φ is positive (P), *eT* is positive large (PL) and *θs* is S1, then *n* is 1.

Rule 2: If *e*Φ is positive (P), *eT* is positive small (PS) and *θs* is S2, then *n* is 1.

Rule 3: If *e*Φ is positive (P), *eT* is ZE and *θs* is S3, then *n* is 0.

and *θs* is *Ci*

its output. A general "*i*th rule" has the following form:

can be obtained from

a

, *eT* is *Bi*

170 Induction Motors - Applications, Control and Fault Diagnostics

Rule *i*: If *e*Φ is *Ai*

of the *i*th rule, *α<sup>i</sup>*

follows:

**3.1. Scheme**

the *i*th rule is obtained from

maximum used criteria.

**3. Stator resistance compensation**

step stator resistance from 100% to 50% of its nominal value at second 0.5. The drive system becomes unstable if the controller-instrumented stator resistance is higher than its actual value in the motor [11]. An explanation for this could be as follows: when motor resistance decrease in machine and the applied voltage is the same, the current increases, resulting in increased flux and electromagnetic torque [28]. The opposite effect occurs in controller. In fact, by current increments, which are inputs of the system, the stator resistance voltage drops will increase in the calculator. Therefore, lower flux linkages and electromagnetic torque estimations will present. Compared with their command values, they give large torque and flux linkages deviations, which result in commanding larger voltages and currents and leading to a run off condition as shown in Fig. 6a. "The parameter mismatch between the controller and machine will result in a nonlinear relation between the torque and the torque's reference, making it a non-ideal torque amplifier" [29]. This will have undesirable effect in a torque drive and speedcontrolled drive systems. Therefore, it will be reasonable to design a motor resistance adaption law to overcome instability and to guarantee a linear torque amplifier in the DTC drive. A new approach is presented in the next section for stator resistance parameter adaption. 8 **3. Stator resistance compensation**  A mismatch between the controller-set stator resistance and its actual value in the machine can create the instability shown in Fig. 6a. This figure shows the simulations for the changes of the step stator

**Fig. 3.** Membership functions.

### **3.2. Stator current phasor command**

A diagram of the applied stator resistance compensation is shown in Fig. 4. The presented technique is based on the principle that the error between the measured stator feedback current-phasor magnitude *i <sup>s</sup>* and the stator's command *<sup>i</sup>* \* *s* is proportional to the stator resistance variation, which is mainly caused by the motor temperature and the varying stator frequency. The correction value is obtained by means of a fuzzy controller. The final estimated value of *Rs* ^ is obtained as the output of the limiter. The above algorithm requires the stator current phasor command, which is a function of the commanded torque and the commanded stator flux linkages.

**Figure 4.** Block diagram of the adaptive stator resistance compensator.

A neural network estimator, presented in the following, is designed to evaluate the stator current command from the torque and stator flux linkage commands.

The stator feedback current phasor magnitude *i <sup>s</sup>* is obtained from the *q* and *d* axis measured currents as

$$\dot{\mathbf{u}}\_s = \sqrt{\left(\dot{\mathbf{i}}\_{q\mathbf{s}}\,^2 + \dot{\mathbf{i}}\_{ds}\,^2\right)}\tag{10}$$

The stator command current phasor magnitude *i* \* *<sup>s</sup>* is derived from the dynamic equations of the induction motor in the synchronous-rotating reference frame, using the torque command *T* \* *e* and the stator flux linkage command *λ* \* *s* and aligning the *d* axis with the stator flux linkage phasor as

$$\mathcal{X}^{\epsilon}\_{\ \!\!\!\!\!\!\!\/]\_{\epsilon} = \mathbf{0}, \mathbf{p} \mathcal{X}^{\epsilon}\_{\ \!\!\!\/]\_{\epsilon}} = \mathbf{0}, \mathcal{X}^{\epsilon}\_{\ \!\!\!\/]\_{\epsilon}} = \mathcal{X}^{\epsilon}\_{\ \!\!\!\/]\_{\epsilon}} \tag{11}$$

where *p* is the number of poles. Substituting these equations in flux linkages and torque equations results in

Fuzzy Direct Torque-controlled Induction Motor Drives for Traction with Neural Compensation of Stator Resistance http://dx.doi.org/10.5772/61545 173

$$T\_e = \frac{3}{2} \frac{2}{p} \dot{\mathbf{l}}\_{q\mathbf{s}} \stackrel{\epsilon}{\lambda}\_s \tag{12}$$

Then the *q* axis current command is directly obtained by using the torque command *T* \* *e* and the stator flux linkage command *λ* \* *s* as

$$\left(\mathbf{i}^{\epsilon^\*}\right)\_{qs} = \frac{2}{3} \frac{2}{p} \frac{T\_\epsilon}{\lambda\_s^\*}^\* \tag{13}$$

It can be shown that *i <sup>e</sup>*\* *ds* is given by

**3.2. Stator current phasor command**

172 Induction Motors - Applications, Control and Fault Diagnostics

**Figure 4.** Block diagram of the adaptive stator resistance compensator.

The stator feedback current phasor magnitude *i*

The stator command current phasor magnitude *i* \*

l

and the stator flux linkage command *λ* \*

current command from the torque and stator flux linkage commands.

current-phasor magnitude *i*

value of *Rs*

currents as

*T* \* *e*

phasor as

equations results in

stator flux linkages.

A diagram of the applied stator resistance compensation is shown in Fig. 4. The presented technique is based on the principle that the error between the measured stator feedback

resistance variation, which is mainly caused by the motor temperature and the varying stator frequency. The correction value is obtained by means of a fuzzy controller. The final estimated

current phasor command, which is a function of the commanded torque and the commanded

A neural network estimator, presented in the following, is designed to evaluate the stator

2 2 ( ) *<sup>s</sup>*

the induction motor in the synchronous-rotating reference frame, using the torque command

 ll

where *p* is the number of poles. Substituting these equations in flux linkages and torque

*s*

\* 0, 0, *e ee qs qs ds s*

 l

^ is obtained as the output of the limiter. The above algorithm requires the stator

*s*

is proportional to the stator

*<sup>s</sup>* is obtained from the *q* and *d* axis measured

*<sup>s</sup>* is derived from the dynamic equations of

and aligning the *d* axis with the stator flux linkage

*<sup>i</sup> qs ds* = + *i i* (10)

= == *p* (11)

*<sup>s</sup>* and the stator's command *<sup>i</sup>* \*

$$\begin{split} L\_s(\dot{\mathbf{f}}\_{\rm dis}^{\boldsymbol{\epsilon}^\*})^2 - \dot{\mathcal{N}}\_{\rm s}^\* (1 - \frac{L\_s L\_r}{L\_m^2 - L\_s L\_r}) \dot{\mathbf{f}}\_{\rm dis}^{\boldsymbol{\epsilon}^\*} + \\ L\_s(\dot{\mathbf{f}}\_{\rm qs}^{\boldsymbol{\epsilon}^\*})^2 - \frac{(\dot{\mathcal{N}}\_{\rm s}^\*)^2 L\_r}{L\_m^2 - L\_s L\_r} = 0 \end{split} \tag{14}$$

Equation 14 gives two solutions for *i <sup>e</sup>*\* *ds* , and the appropriate solution is the one that outputs a smaller value. Finally, the stator current command is calculated from

$$\dot{\mathbf{u}}^{\*}\_{\ \ s} = \sqrt{\left(\dot{\mathbf{i}}^{\epsilon^\*}\,^2\_{qs} + \dot{\mathbf{i}}^{\epsilon^\*}\,^2\_{ds}\right)}\tag{15}$$

It is shown here that evaluation of the stator current command is a complicated and timeconsuming process. Instead of using the numerical solution for the system, it is possible to perform the stator current command by using an artificial neural network (ANN) since it is known that ANN is a general nonlinear function estimator. As a result, a multilayer feedforward back-propagation ANN, whose inputs are the torque and flux reference values, is trained to estimate the stator current command. A 2-8-8-1 structure, which has two hidden layers with 8 hidden nodes, is obtained by trial and error. The activation functions of the hidden layers are tan-sigmoid functions. Fig. 5 shows the structure of the ANN estimator. The neural estimator evaluates the reference stator current with less than 0.01% error. Furthermore, it is shown that more complicated ANN structures result in higher error rates.

### **4. Results**

Dynamic simulations are performed to validate the performance of the proposed technique. The induction motor details, used in the simulation, are given in the appendix. Fig. 6a and 6b show the simulations for a step change in the stator resistance parameter-uncompensated and compensated torque drive system respectively. The system controller has the nominal value of the stator resistance, and after half a second, the stator resistance is changed to ½ of its nominal value. Then the corresponding effects are studied. In the compensated system, it is observed that the estimation of stator resistance has experienced an initial transient state, and after a short time, it converges gradually to its final actual value in a steady state. The similar transitions are observed in other variables. However, all variables reach to their steady state situation. A step variation in the stator resistance is rather an extreme test and not a significant case encountered in practice. In real operating conditions, the temperature change rate is very slow and so is the stator resistance.

**Figure 5.** Neural network structure: (a) structure of layers and (b) structure of first hidden layer.

Stator flux linkages and the torque command are proportionally decreased and increased linearly from/to their original reference values. The tracking of motor variables and stator resistance is achieved, thus proving the effectiveness of the adaptive controller in the fluxweakening region. It also perfectly operates in stator resistance incremental case and in gradually stator resistance changes due to temperature changes. In these cases, there is not any oscillation even at the initial moments of resistance variations.

### **5. Conclusion**

of the stator resistance, and after half a second, the stator resistance is changed to ½ of its nominal value. Then the corresponding effects are studied. In the compensated system, it is observed that the estimation of stator resistance has experienced an initial transient state, and after a short time, it converges gradually to its final actual value in a steady state. The similar transitions are observed in other variables. However, all variables reach to their steady state situation. A step variation in the stator resistance is rather an extreme test and not a significant case encountered in practice. In real operating conditions, the temperature change rate is very

**Figure 5.** Neural network structure: (a) structure of layers and (b) structure of first hidden layer.

slow and so is the stator resistance.

174 Induction Motors - Applications, Control and Fault Diagnostics

A fuzzy direct torque-controlled drive was introduced, and an adaptive stator resistance compensation scheme was applied to a typical three-phase induction motor. With this approach, the elimination of parameter sensitivity of the stator resistance by using only the existing stator current feedback occurred. The scheme was simple to implement, and its realization was indirectly dependent on stator inductances. Since the flux was controlled in the machine, the inductances used in the computation of stator phasor current command were constants. A procedure for finding the phasor command of the stator current from the torque and stator flux linkage commands was derived to realize the complication of this method. The ANN estimator was designed to effectively evaluate the reference stator current value. The scheme was verified via dynamic simulation for various operating conditions, including the flux-weakening mode. The scheme was successful despite rapid changes in the stator resist‐ ance, such as step changes. It was observed that the scheme adapted very well without transients even for simultaneous variations of the torque and flux linkages command while the stator resistance was varying. Finally, a simple fuzzy controller was used to generate the exact stator resistance value.


(b) **Fig. 6a**. The step response for a parameter uncompensated system. Fig. 6b.The step response for a parameter compensated system. **Figure 6.** (a) The step response for a parameter uncompensated system. (b)The step response for a parameter compen‐ sated system.

## **6. Appendix**

### **Induction motor parameters**


## **Acknowledgements**

(a)

176 Induction Motors - Applications, Control and Fault Diagnostics

(b) **Fig. 6a**. The step response for a parameter uncompensated system. Fig. 6b.The step response for a parameter compensated system. **Figure 6.** (a) The step response for a parameter uncompensated system. (b)The step response for a parameter compen‐

sated system.

The authors would like to thank the school of railway engineering in Iran University of Science and Technology for the great support of this project. The assistance of Mr. H. Zafari for revising this paper is appreciated as well.

## **Author details**

Mohammad Ali Sandidzadeh1\*, Amir Ebrahimi1 and Amir Heydari2

\*Address all correspondence to: sandidzadeh@iust.ac.ir

1 School of Railway Engineering, Iran University of Science and Technology, Tehran, Iran

2 School of Railway Engineering, Iran university of Science and Technology, Tehran, Sepid Gatch Saveh, Saveh, Iran

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### **Chapter 7**
