We are IntechOpen, the world's leading publisher of Open Access books Built by scientists, for scientists

3,600+

Open access books available

113,000+

International authors and editors

115M+

Downloads

151 Countries delivered to Our authors are among the

Top 1%

most cited scientists

12.2%

Contributors from top 500 universities

Selection of our books indexed in the Book Citation Index in Web of Science™ Core Collection (BKCI)

## Interested in publishing with us? Contact book.department@intechopen.com

Numbers displayed above are based on latest data collected. For more information visit www.intechopen.com

## **Meet the editors**

Abdel Ghani Aissaoui is a full Professor of Electrical Engineering at the University of Bechar (Algeria). He was born in 1969 in Naama, Algeria. He received his BS degree in 1993, MS degree in 1997, PhD degree in 2007, all from the Electrical Engineering Institute of Djillali Liabes, University of Sidi Bel Abbes (Algeria). He is an active member of IRECOM (Interaction Réseaux

Electriques - COnvertisseurs Machines) Laboratory and an IEEE senior member. He has edited many international journals (IJET, RSE, MER, IJECE, etc.) and serves as a reviewer in international journals (IJAC, ECPS, COMPEL, etc.). He serves as a member in a technical committee (TPC) and reviewer in international conferences (CHUSER 2011, SHUSER 2012, PECON 2012, SAI 2013, SCSE 2013, SDM 2014, SEB 2014, PEMC 2014, PEAM 2014, SEB (2014, 2015), ICRERA 2015, etc.). His current research interests include power electronics, control of electrical machines, artificial intelligence and renewable energies.

Ahmed Tahour was born in 1972 in Ouled Mimoun, Tlemcen, Algeria. He received his BS degree in electrical engineering in 1996, MS degree in 1999 and PhD degree in 2007, all from the Electrical Engineering Institute of the University of Sidi Bel Abbes (Algeria). He is currently a Professor of Electrical Engineering at the University of Mascara (Algeria). His current research interests include

power electronics, control of electrical machines and renewable energies.

Ilhami Colak was born in 1962 in Turkey. He received his diploma in electrical engineering from Gazi University, Turkey, in 1985. Then, he did his MSc degree in electrical engineering in the field of *Speed Control of Wound Rotor Induction Machines Using Semiconductor Devices* at Gazi University in 1991. After that, he received his MPhil degree from Birmingham University in

England by preparing a thesis on *High Frequency Resonant DC Link Inverters* in 1991. He received his PhD degree from Aston University in England on *Mixed Frequency Testing of Induction Machines Using Inverters* in 1994. He became an Assistant Professor, an Associate Professor, and a full Professor in 1995, 1999 and 2005, respectively.

He has published more than 225 papers on different subjects, including electrical machines, drive systems, machine learning, reactive power compensation, inverters, converters, artificial neural networks, distance learning, automation, renewable energy sources and smart grids. More than 86 of his papers have been cited in the SCI database of Thomson Reuters. His papers have received more than 445 citations. He has supervised 19 MSc students and 13 PhD students. He is a member of IEEE, IES, IAS, PELS and PES. He is also a member of the PEMC Council. He has organized 54 international conferences and workshops. In the last ten years, he has concentrated his studies on renewable energy and smart grids by publishing papers, journals (www.ijrer.org), and organizing international IEEE sponsored conferences (www.icrera.org). He is also the editor-in-chief of International Engineering Technologies (http://dergipark.ulakbim.gov.tr/ ijet) and one of the editors of the Journal of Power Electronics (http://www. jpels.org). He has 1 international and 3 national patents. He also spent around 3 years at the European Commission Research Centre (JRC) as an expert in the field of smart grids in the Netherlands. He is currently holding the positions of vice-rector and dean of the Engineering and Architecture Faculty of Nisantasi University.

Contents

**Preface VII**

Oliveira

**Section 1 Optimization Techniques in Electrical Systems 1**

**Control of Electrical Machines 3**

Chapter 3 **Optimal Design of Brushless Doubly Fed Reluctance Machine 33**

**Section 2 Control of Induction Machines 55**

**Torque Controlled DFIG 73**

**Excitation 57**

Abdel Ghani Aissaoui

Chapter 1 **Introductory Chapter: Introduction to the Design and the**

Chapter 2 **Multi-Objective Optimization Techniques to Solve the**

**Heuristic and Metaheuristic Algorithms 13**

**Economic Emission Load Dispatch Problem Using Various**

Jorge de Almeida Brito Júnior, Marcus Vinicius Alves Nunes, Manoel Henrique Reis Nascimento, Jandecy Cabral Leite, Jorge Laureano Moya Rodriguez, Carlos Alberto Oliveira de Freitas, Milton Fonseca Júnior, Edson Farias de Oliveira, David Barbosa de Alencar, Nadime Mustafa Moraes, Tirso Lorenzo Reyes Carvajal and Haroldo Melo de

Mandar Bhawalkar, Gopalakrishnan Narayan and Yogesh Nerkar

**Using Only Fundamental Pulse Width Modulation Waveform**

Chapter 4 **Zero and Low-Speed Sensorless Control of Induction Machines**

Chapter 5 **Rotor Flux Reference Generation Control Strategy for Direct**

Qiang Gao, Greg Asher and Mark Sumner

Gopala Venu Madhav and Y. P. Obulesu

## Contents

## **Preface XI**



Preface

operating mode.

Electrical drive systems were developed in the last century. The majority of all drive systems are electrical and this tendency is increasing. The main parts of these systems are electrical machines. With the advent of power electronics, there are new possibilities for the control of electrical machines with variable speed. The technical performance and economical design of electrical machines have opened a new philosophy of drive applications. Electrical ma‐ chines have undergone a huge development. New concepts in design and control allow for the expansion of their applications in different fields. Electrical machines are considered im‐ portant components in many industrial applications such as power systems, manufacturing

These machines are usually manufactured through mass-production techniques. Their per‐ formance can be affected by manufacturing processes and different operational conditions (e.g., temperature). As a requirement of quality control, an optimal design process is often applied to minimize the influence of uncertainties on the machine's performance. As a conse‐ quence, an optimal design system can be implemented for the analysis and design of electrical machines to minimize the effects of manufacturing errors in both iron and permanent magnets. Control is very important; it allows having a good functioning of the system. Different strat‐ egies of control can be applied to electrical machines depending on the necessary goals. The use of advanced control techniques and new technology brings the system into its optimal

The goal of this book is to present recent works on design and control related to electrical machines. The developments of this field happened quickly, accompanied with many diffi‐ culties that require solutions. Different solutions are proposed based on new techniques of

This book is divided into two parts. The first part is devoted to the design of different opti‐

• In the first main chapter of Part 1, several optimization techniques (e.g., Simulated Annealing, Ant-Lion, Dragonfly, NSGAII, and Differential Evolution) are analyzed and discussed to solve the economic-emission load dispatch problem. A comparison

• The second chapter highlights various optimization methods and discusses the suit‐ ability of non-linear programming methods and recent stochastic or populationbased methods for optimal design of brushless doubly fed reluctance machines

plants, power plants, electrical vehicles and home appliances.

control, design and advanced technology products.

• The introductory chapter describes electrical machines.

of all approaches and their results is offered through a case study.

mization techniques for electrical systems:

(BDFRM).

## Preface

Electrical drive systems were developed in the last century. The majority of all drive systems are electrical and this tendency is increasing. The main parts of these systems are electrical machines. With the advent of power electronics, there are new possibilities for the control of electrical machines with variable speed. The technical performance and economical design of electrical machines have opened a new philosophy of drive applications. Electrical ma‐ chines have undergone a huge development. New concepts in design and control allow for the expansion of their applications in different fields. Electrical machines are considered im‐ portant components in many industrial applications such as power systems, manufacturing plants, power plants, electrical vehicles and home appliances.

These machines are usually manufactured through mass-production techniques. Their per‐ formance can be affected by manufacturing processes and different operational conditions (e.g., temperature). As a requirement of quality control, an optimal design process is often applied to minimize the influence of uncertainties on the machine's performance. As a conse‐ quence, an optimal design system can be implemented for the analysis and design of electrical machines to minimize the effects of manufacturing errors in both iron and permanent magnets.

Control is very important; it allows having a good functioning of the system. Different strat‐ egies of control can be applied to electrical machines depending on the necessary goals. The use of advanced control techniques and new technology brings the system into its optimal operating mode.

The goal of this book is to present recent works on design and control related to electrical machines. The developments of this field happened quickly, accompanied with many diffi‐ culties that require solutions. Different solutions are proposed based on new techniques of control, design and advanced technology products.

This book is divided into two parts. The first part is devoted to the design of different opti‐ mization techniques for electrical systems:


The second part is dedicated to the control of induction machines:


The chapters of this book present recent works in the design, control, and applications of electrical machines and their importance. The aim of this book is to present the new trends of research on electrical machines.

We hope that the readers will find this book to be a significant source of knowledge and reference for the future years.

## **Prof. Dr. AbdelGhani Aissaoui**

Electrical Department Faculty of Technology University Tahri Mohamed of Bechar (UTMB) Bechar, Algeria

## **Prof. Dr. Ahmed Tahour**

**Section 1**

**Optimization Techniques in Electrical Systems**

Electrical Department Faculty of Technology University of Mascara Mascara, Algeria

## **Prof. Dr. Ilhami Colak**

Engineering and Architecture Faculty Nisantasi University Istanbul, Turkey **Optimization Techniques in Electrical Systems**

The second part is dedicated to the control of induction machines:

the DFIG to be connected to the grid even during a fault.

speeds.

VIII Preface

of research on electrical machines.

reference for the future years.

• The first chapter presents the zero and low speed sensorless control of induction machines using only fundamental pulse width modulation (PWM) waveform exci‐ tation. A position sensorless method is used, which only relies on the fundamental PWM waveforms to excite saliency. This method is essentially based on saliency de‐ tection, and therefore derivation of the rotor position is possible at low and zero

• In the second chapter, the development of a rotor flux reference generation control strategy is explained. This control strategy is used with the DTC scheme to elimi‐ nate the high peaks in torque with reduced stator and rotor currents and also to eliminate the necessity of a crowbar during low voltage dip. The scheme allows for

The chapters of this book present recent works in the design, control, and applications of electrical machines and their importance. The aim of this book is to present the new trends

We hope that the readers will find this book to be a significant source of knowledge and

**Prof. Dr. AbdelGhani Aissaoui**

University Tahri Mohamed of Bechar (UTMB)

Electrical Department Faculty of Technology

**Prof. Dr. Ahmed Tahour** Electrical Department Faculty of Technology University of Mascara Mascara, Algeria

**Prof. Dr. Ilhami Colak**

Nisantasi University Istanbul, Turkey

Engineering and Architecture Faculty

Bechar, Algeria

**Chapter 1**

**Provisional chapter**

**Introductory Chapter: Introduction to the Design and**

**Introductory Chapter: Introduction to the Design and** 

In the last century, electrical machines have been the subject of a huge development. New concepts in design and control allow expanding their applications in different fields. They are considered important components in many industrial applications as: power systems,

There are several types of electrical machines; we can find synchronous machines, induction machines, direct current (DC) machines, reluctance synchronous machines, transformers, etc.

The electrical machines are incorporated into the process of energy conversion in the generation, transmission, and consumption of electric power. In a power station, turbine generator converts the energy coming from the combustion of coal, natural gas, etc. into electric energy

manufactories, power plants, electrical vehicles, and home appliances.

© 2016 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.

© 2018 The Author(s). Licensee IntechOpen. 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.

DOI: 10.5772/intechopen.78772

**the Control of Electrical Machines**

**the Control of Electrical Machines**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78772

**Figure 1.** Different types of electrical machines.

Abdel Ghani Aissaoui

**1. Introduction**

(**Figure 1**).

Abdel Ghani Aissaoui

#### **Introductory Chapter: Introduction to the Design and the Control of Electrical Machines Introductory Chapter: Introduction to the Design and the Control of Electrical Machines**

DOI: 10.5772/intechopen.78772

Abdel Ghani Aissaoui Abdel Ghani Aissaoui

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78772

## **1. Introduction**

In the last century, electrical machines have been the subject of a huge development. New concepts in design and control allow expanding their applications in different fields. They are considered important components in many industrial applications as: power systems, manufactories, power plants, electrical vehicles, and home appliances.

There are several types of electrical machines; we can find synchronous machines, induction machines, direct current (DC) machines, reluctance synchronous machines, transformers, etc. (**Figure 1**).

The electrical machines are incorporated into the process of energy conversion in the generation, transmission, and consumption of electric power. In a power station, turbine generator converts the energy coming from the combustion of coal, natural gas, etc. into electric energy

**Figure 1.** Different types of electrical machines.

© 2016 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. © 2018 The Author(s). Licensee IntechOpen. 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.

that is transmitted to consumers: motors whose mechanical energy drive machines in industry, homes, traffics, etc.

The main part of these systems is electrical rotating machine. With the advent of power electronics, new possibilities appear for electrical machines with variable speed. Their technical

Introductory Chapter: Introduction to the Design and the Control of Electrical Machines

http://dx.doi.org/10.5772/intechopen.78772

5

The control of electrical power today is possible within short time for megawatts. It can be

The energy conversion between electrical and mechanical power is performed by the electri-

Electrical machines can be used for different ranges of speed. It can be used as motor particularly in traction, electrical vehicles, etc. or as generators in power station, wind turbines, etc.

The electrical machines are usually manufactured through mass-production techniques; their performances can be affected by manufacturing processes and different operational conditions (e.g., temperature). As a requirement of quality control, a robust design process is often

However, the conventional computer simulation cannot reflect the influences of the environmental uncertainties directly. The input data of the numerical model are usually the geometries of the modeled device, the material properties, and the uncertainties in both must be taken into account. While most of the works in the robust design of electromagnetic devices focus on the uncertainties in the geometries [2–4], only a few efforts have been conducted on the influences of the material uncertainties. In electromagnetic field computing, the nonlinear behavior of the constitutive laws of ferromagnetic materials is usually obtained by B-H curves. For ferromagnetic materials, [5] constructed a stochastic material model using the uncertainties of the measured points to characterize a nonlinear B-H curve. In [6], a global sensitivity analysis was applied to study the variance of the predicted behavior of a turbo-alternator with respect to material uncertainties.

All the above stochastic material models have formed a solid foundation for the study of material uncertainties in the electromagnetic design. A robust design system can then be implemented for the analysis and design of electrical machines in order to minimize the

There are some general design methods, which can be applied in terms of different disciplines/domains: electromagnetic design, thermal design, structural design, multi-physics

Electromagnetic design: The principle of operation of electrical machines is based on the electromagnetic theory. Electromagnetic design is based on the calculation of magnetic field and its distribution in the electrical machines, which allowed to compute some basic electromagnetic parameters including winding inductance and the evaluation of some performances, such as electromagnetic force, power loss, and efficiency. To obtain the magnetic field, there

effects of manufacturing errors in both iron and permanent magnets [7].

design, material design, and manufacturing process design.

applied to minimize the influence of uncertainties on the machine performance.

performance and economical design opened a new philosophy of drive applications.

controlled so fast than any other form of energy.

cal machine in both directions.

**2. Design**

Most applications are interested in rotating electrical machines. The rotating electrical machine can operate, without constructional changes, as a motor or generator, since the energy direction of an electrical machine is reversible (**Figure 2**).

Electrical machines can be classified according to the torque producing mechanism and their magnetic interactions. The first class based on the torque producing mechanism machines is classified into two types, one is alignment torque producing machines such as DC machines, induction, and synchronous machines and the second is the reluctance torque producing machine, for example, switched reluctance machines. The second class based on the magnetic interactions machines is classified as inductive-interactive type machines, for example, induction machines, synchronous machines, and DC machines, and variable reluctance type machines, for example, switched reluctance machines [1].

The electrical drive systems were developed based on the use of electrical machines. The majority of all drive systems are electrical drives with growing tendency. Electrical drive systems do not have a power density as high as pneumatic or hydraulic systems. Electrical motors are bulky and heavy in comparison to these competitors.

Electrical drives are considered for three reasons superior to other drive systems, such as pneumatic and hydraulic systems:


**Figure 2.** Conversion energy in electrical machines.

The main part of these systems is electrical rotating machine. With the advent of power electronics, new possibilities appear for electrical machines with variable speed. Their technical performance and economical design opened a new philosophy of drive applications.

The control of electrical power today is possible within short time for megawatts. It can be controlled so fast than any other form of energy.

The energy conversion between electrical and mechanical power is performed by the electrical machine in both directions.

Electrical machines can be used for different ranges of speed. It can be used as motor particularly in traction, electrical vehicles, etc. or as generators in power station, wind turbines, etc.

## **2. Design**

that is transmitted to consumers: motors whose mechanical energy drive machines in indus-

Most applications are interested in rotating electrical machines. The rotating electrical machine can operate, without constructional changes, as a motor or generator, since the energy direc-

Electrical machines can be classified according to the torque producing mechanism and their magnetic interactions. The first class based on the torque producing mechanism machines is classified into two types, one is alignment torque producing machines such as DC machines, induction, and synchronous machines and the second is the reluctance torque producing machine, for example, switched reluctance machines. The second class based on the magnetic interactions machines is classified as inductive-interactive type machines, for example, induction machines, synchronous machines, and DC machines, and variable reluctance type

The electrical drive systems were developed based on the use of electrical machines. The majority of all drive systems are electrical drives with growing tendency. Electrical drive systems do not have a power density as high as pneumatic or hydraulic systems. Electrical

Electrical drives are considered for three reasons superior to other drive systems, such as

try, homes, traffics, etc.

4 Optimization and Control of Electrical Machines

tion of an electrical machine is reversible (**Figure 2**).

machines, for example, switched reluctance machines [1].

• High efficiency of electromechanical power conversion

pneumatic and hydraulic systems:

• Cleanliness of the energy supply

**Figure 2.** Conversion energy in electrical machines.

• Dynamics of control

motors are bulky and heavy in comparison to these competitors.

The electrical machines are usually manufactured through mass-production techniques; their performances can be affected by manufacturing processes and different operational conditions (e.g., temperature). As a requirement of quality control, a robust design process is often applied to minimize the influence of uncertainties on the machine performance.

However, the conventional computer simulation cannot reflect the influences of the environmental uncertainties directly. The input data of the numerical model are usually the geometries of the modeled device, the material properties, and the uncertainties in both must be taken into account. While most of the works in the robust design of electromagnetic devices focus on the uncertainties in the geometries [2–4], only a few efforts have been conducted on the influences of the material uncertainties. In electromagnetic field computing, the nonlinear behavior of the constitutive laws of ferromagnetic materials is usually obtained by B-H curves. For ferromagnetic materials, [5] constructed a stochastic material model using the uncertainties of the measured points to characterize a nonlinear B-H curve. In [6], a global sensitivity analysis was applied to study the variance of the predicted behavior of a turbo-alternator with respect to material uncertainties.

All the above stochastic material models have formed a solid foundation for the study of material uncertainties in the electromagnetic design. A robust design system can then be implemented for the analysis and design of electrical machines in order to minimize the effects of manufacturing errors in both iron and permanent magnets [7].

There are some general design methods, which can be applied in terms of different disciplines/domains: electromagnetic design, thermal design, structural design, multi-physics design, material design, and manufacturing process design.

Electromagnetic design: The principle of operation of electrical machines is based on the electromagnetic theory. Electromagnetic design is based on the calculation of magnetic field and its distribution in the electrical machines, which allowed to compute some basic electromagnetic parameters including winding inductance and the evaluation of some performances, such as electromagnetic force, power loss, and efficiency. To obtain the magnetic field, there are three main kinds of analysis methods, analytical method, magnetic circuit method, and finite element method (FEM) [8–10, 14, 15]. Meanwhile, power losses and efficiency are two important performance indexes for electrical machines.

This can be explained and understood through the words of Miller [21]: "To a WISE engineer, optimal design means a compromise between conflicting factors, often producing an imper-

Introductory Chapter: Introduction to the Design and the Control of Electrical Machines

http://dx.doi.org/10.5772/intechopen.78772

7

Most of the metaheuristic techniques can be used to solve global optimization problems with nonlinear constraint by using metaheuristic algorithms; there is a high possibility to determine a near optimal solution, which can be considered by designer and engineering as a

One of the most promising algorithms from the class of evolutionary algorithms widely used in the field of electric machines is Differential Evolution (DE) [22–24] first introduced by Price and Storn [25] in 1995. The algorithm was later improved and named Generalized Differential Evolution (GDE) (extended DE for constrained multi-objective optimization) by Lampinen

Variety of other algorithms is used in electric machine design optimization: Genetic Algorithm (GA) [27, 28], Particle Swarm Optimization (PSO) [29, 30], Simulated Annealing (SA) [31], etc. Authors in [32] compared GA, SA, and DE on the design optimization of permanent magnet motor and authors in [32] compared DE, GA, and PSO on the design optimization of microstrip antennas. Both groups agree that the DE performance is the best. In [33, 34], PSO and GA were compared and PSO was found computationally more effective with slightly better objective function value reached. In [35], it is shown how PSO performs better than GA

The control of electrical machines has been the subject of great progress, due to the development and advancement in the field of power electronic devices, digital signal processing, the

The energy conversion between electrical and mechanical power is performed by the electrical machine in both directions. The control of this energy is very important. In the case of motors, we control the electric power consumed, and in the case of generator, we control the electric power generated. The control of electrical machines can be expanded to other variables as speed, voltages, currents, flux, torque, etc. **Figure 3** shows the control structure

so some authors decided to use hybrid GA-PSO method [36, 37].

**4. Control of electrical machines**

**Figure 3.** Control structure of electrical machines.

informatics tools, and advanced control techniques.

fect result from optimistic aspirations."

global optimum [22].

and Zelinka [25, 26].

of electrical machines.

Thermal design and structural design: these methods can be applied after the accomplishment of the electromagnetic design. The thermal design method aim is to compute the temperature distribution in the machine based on the heat obtained from the electromagnetic analysis. There are popular methods for the thermal analysis of electrical machines. They are computational fluid dynamics (CFD), FEM, and nodal method. Structural design aims to consider the stress and deformation of the machine under the electromagnetic and thermal analyses. Structural design can be conducted based on FEM as well [12, 13].

Multi-physics design: It aims to calculate the electromagnetic characteristics, temperature distribution, structural stress, vibration noise, and coupled performances of electrical machines based on a uniform model [8, 9, 10, 11]. The FEM has been widely employed as a powerful tool for the multi-physics design and analysis of electrical machines. It can be used to analyze the coupled field in machines, such as electromagnetic structure and thermal structure.

Material design: The type of material is important for the electromagnetic, thermal, and structural designs of electrical machines. Nowadays, new developed magnetic materials like soft magnetic composite (SMC), amorphous and grain-oriented silicon steel show better characteristics, such as high saturation flux density, low specific losses, and low manufacturing cost. They can be employed to design motors with new topologies, higher efficiency, and/or low manufacturing cost [16, 17].

Manufacturing process design: Manufacturing method design is also important in the design stage of electrical machines, which will influence their manufacturing quality and actual performances in operation. To obtain the best performances, some designs have complex structures which can be difficult for manufacturing.

With a good knowledge of the magnetic characteristics and manufacturing methods, we can fully exploit all the performances of the designed motors. A good motor design should be done in terms of both output performances and manufacturing abilities [18].

## **3. Optimization**

Optimization is a very popular term in modern design of electrical machines and devices due to the competition in the world markets, increased cost of electrical energy, and pressures for its conservation.

Optimization helps designers to push the existing invisible design boundaries while using available materials and technology. The objective of the optimization process is usually to minimize either the initial cost of the machine or its lifetime cost including the cost of lost energy. Other objectives such as mass minimization or efficiency maximization may also be appropriate in some situations [19, 20].

This can be explained and understood through the words of Miller [21]: "To a WISE engineer, optimal design means a compromise between conflicting factors, often producing an imperfect result from optimistic aspirations."

Most of the metaheuristic techniques can be used to solve global optimization problems with nonlinear constraint by using metaheuristic algorithms; there is a high possibility to determine a near optimal solution, which can be considered by designer and engineering as a global optimum [22].

One of the most promising algorithms from the class of evolutionary algorithms widely used in the field of electric machines is Differential Evolution (DE) [22–24] first introduced by Price and Storn [25] in 1995. The algorithm was later improved and named Generalized Differential Evolution (GDE) (extended DE for constrained multi-objective optimization) by Lampinen and Zelinka [25, 26].

Variety of other algorithms is used in electric machine design optimization: Genetic Algorithm (GA) [27, 28], Particle Swarm Optimization (PSO) [29, 30], Simulated Annealing (SA) [31], etc. Authors in [32] compared GA, SA, and DE on the design optimization of permanent magnet motor and authors in [32] compared DE, GA, and PSO on the design optimization of microstrip antennas. Both groups agree that the DE performance is the best. In [33, 34], PSO and GA were compared and PSO was found computationally more effective with slightly better objective function value reached. In [35], it is shown how PSO performs better than GA so some authors decided to use hybrid GA-PSO method [36, 37].

## **4. Control of electrical machines**

are three main kinds of analysis methods, analytical method, magnetic circuit method, and finite element method (FEM) [8–10, 14, 15]. Meanwhile, power losses and efficiency are two

Thermal design and structural design: these methods can be applied after the accomplishment of the electromagnetic design. The thermal design method aim is to compute the temperature distribution in the machine based on the heat obtained from the electromagnetic analysis. There are popular methods for the thermal analysis of electrical machines. They are computational fluid dynamics (CFD), FEM, and nodal method. Structural design aims to consider the stress and deformation of the machine under the electromagnetic and thermal

Multi-physics design: It aims to calculate the electromagnetic characteristics, temperature distribution, structural stress, vibration noise, and coupled performances of electrical machines based on a uniform model [8, 9, 10, 11]. The FEM has been widely employed as a powerful tool for the multi-physics design and analysis of electrical machines. It can be used to analyze the coupled field in machines, such as electromagnetic structure and thermal

Material design: The type of material is important for the electromagnetic, thermal, and structural designs of electrical machines. Nowadays, new developed magnetic materials like soft magnetic composite (SMC), amorphous and grain-oriented silicon steel show better characteristics, such as high saturation flux density, low specific losses, and low manufacturing cost. They can be employed to design motors with new topologies, higher efficiency, and/or low

Manufacturing process design: Manufacturing method design is also important in the design stage of electrical machines, which will influence their manufacturing quality and actual performances in operation. To obtain the best performances, some designs have complex struc-

With a good knowledge of the magnetic characteristics and manufacturing methods, we can fully exploit all the performances of the designed motors. A good motor design should be

Optimization is a very popular term in modern design of electrical machines and devices due to the competition in the world markets, increased cost of electrical energy, and pressures for

Optimization helps designers to push the existing invisible design boundaries while using available materials and technology. The objective of the optimization process is usually to minimize either the initial cost of the machine or its lifetime cost including the cost of lost energy. Other objectives such as mass minimization or efficiency maximization may also be

done in terms of both output performances and manufacturing abilities [18].

analyses. Structural design can be conducted based on FEM as well [12, 13].

important performance indexes for electrical machines.

6 Optimization and Control of Electrical Machines

structure.

manufacturing cost [16, 17].

**3. Optimization**

its conservation.

tures which can be difficult for manufacturing.

appropriate in some situations [19, 20].

The control of electrical machines has been the subject of great progress, due to the development and advancement in the field of power electronic devices, digital signal processing, the informatics tools, and advanced control techniques.

The energy conversion between electrical and mechanical power is performed by the electrical machine in both directions. The control of this energy is very important. In the case of motors, we control the electric power consumed, and in the case of generator, we control the electric power generated. The control of electrical machines can be expanded to other variables as speed, voltages, currents, flux, torque, etc. **Figure 3** shows the control structure of electrical machines.

**Figure 3.** Control structure of electrical machines.

The electrical drive systems are based mostly on electrical machines. These machines can be designed to operate at different speeds: high, medium, and low speed. According to these benefits, the use of electrical machines with variable speed is very important in the field of power station, wind turbine, electrical vehicles, etc.

The control of these machines is very complicated. We need to represent them by mathemati-

Introductory Chapter: Introduction to the Design and the Control of Electrical Machines

http://dx.doi.org/10.5772/intechopen.78772

9

Some mathematical transformations can be used to simplify the form of these models as Park transformation, Clark transformation, etc. The analytic approach of these equations is very complicated. To solve these systems of equations, the numerical methods are recommended. Following the obtained models many strategies of controls were developed such as vector control, direct torque control, direct power control, etc., and these strategies aim to give more

New techniques of control were developed based on the powerful control theory and artificial intelligence tools. Many control techniques were studied and applied to electrical machine, which we can find variable structure control, model reference adaptive control, adaptive pole placement control, predictive control, backstepping control, etc. The use of artificial intelligence techniques has been the subject of many recent researches. The most famous are the fuzzy logic control, the neuronal control, the neuro fuzzy control, etc. In the literature, we can

In [38], a model reference adaptive control-based estimated algorithm was proposed for online multi-parameter identification. In [39], MRAS observer was designed for the field oriented control of DFIG. Authors in [40] give an overview of model predictive control for induction motor drives. In [41], cascaded nonlinear predictive control was proposed for the control of induction motor. Backstepping controller was proposed in [42] for induction machine. An adaptive backstepping sliding mode controller was presented in [43]. A fuzzy logic controller

Electrical Department, Faculty of Technology, University of Tahri Mohamed of Bechar,

[1] Rajendran N. A survey on electrical machines for variable speed applications. Indian Journal of Science and Technology. 2015;**8**(31). DOI: 10.17485/ijst/2015/v8i31/84306 [2] Yoon S-B, Jung I-S, Hyun D-S, Hong J-P, Kim Y-J. Robust shape optimization of electro-

[3] Alotto P, Magele C, Renhart W, Weber A, Steiner G. Robust target functions in electromagnetic design. COMPEL: The International Journal for Computation and Mathematics

mechanical devices. IEEE Transactions on Magnetics. 1999;**35**:1710-1713

in Electrical and Electronic Engineering. 2003;**22**:549-560

cal models. Their models are defined by coupled and nonlinear equation systems.

flexibility to the control systems.

find many researches on these topics.

**Author details**

Algeria

**References**

Abdel Ghani Aissaoui

was developed for a switched reluctance motor in [44].

Address all correspondence to: irecom\_aissaoui@yahoo.fr

The electrical machines with high speed is in continuous evolution for a number of applications, including aero engine spools, electrical turbo-compounding systems, electrical spindles for milling cutters and grinding, helicopter and racing engines, turbochargers, fuel pumps, etc. These applications have typical operational speeds of over 10,000 r/min.

In the control design, we follow the next steps:


**Figure 4** shows different steps of control design.

**Figure 4.** The steps of control design.

The control of these machines is very complicated. We need to represent them by mathematical models. Their models are defined by coupled and nonlinear equation systems.

Some mathematical transformations can be used to simplify the form of these models as Park transformation, Clark transformation, etc. The analytic approach of these equations is very complicated. To solve these systems of equations, the numerical methods are recommended.

Following the obtained models many strategies of controls were developed such as vector control, direct torque control, direct power control, etc., and these strategies aim to give more flexibility to the control systems.

New techniques of control were developed based on the powerful control theory and artificial intelligence tools. Many control techniques were studied and applied to electrical machine, which we can find variable structure control, model reference adaptive control, adaptive pole placement control, predictive control, backstepping control, etc. The use of artificial intelligence techniques has been the subject of many recent researches. The most famous are the fuzzy logic control, the neuronal control, the neuro fuzzy control, etc. In the literature, we can find many researches on these topics.

In [38], a model reference adaptive control-based estimated algorithm was proposed for online multi-parameter identification. In [39], MRAS observer was designed for the field oriented control of DFIG. Authors in [40] give an overview of model predictive control for induction motor drives. In [41], cascaded nonlinear predictive control was proposed for the control of induction motor. Backstepping controller was proposed in [42] for induction machine. An adaptive backstepping sliding mode controller was presented in [43]. A fuzzy logic controller was developed for a switched reluctance motor in [44].

## **Author details**

The electrical drive systems are based mostly on electrical machines. These machines can be designed to operate at different speeds: high, medium, and low speed. According to these benefits, the use of electrical machines with variable speed is very important in the field of

The electrical machines with high speed is in continuous evolution for a number of applications, including aero engine spools, electrical turbo-compounding systems, electrical spindles for milling cutters and grinding, helicopter and racing engines, turbochargers, fuel pumps,

• Modeling: The plant can be described in the form of some mathematical equations. These equations constitute the mathematical model of the plant. A plant model should produce

• Controller design: The controller is designed to meet the performance requirements for the

• Implementation: The implementation can be done using a digital computer. Its efficiency depends on the type of computer available, the type of interface devices between the com-

etc. These applications have typical operational speeds of over 10,000 r/min.

the same output response as the plant for the same inputs.

power station, wind turbine, electrical vehicles, etc.

8 Optimization and Control of Electrical Machines

In the control design, we follow the next steps:

puter and the plant, software tools, etc.

**Figure 4** shows different steps of control design.

plant model.

**Figure 4.** The steps of control design.

Abdel Ghani Aissaoui

Address all correspondence to: irecom\_aissaoui@yahoo.fr

Electrical Department, Faculty of Technology, University of Tahri Mohamed of Bechar, Algeria

## **References**


[4] Steiner G, Weber A, Magele C. Managing uncertainties in electromagnetic design problems with robust optimization. IEEE Transactions on Magnetics. 2004;**40**:1094-1099

[17] Fan T, Li Q, Wen X. Development of a high power density motor made of amorphous alloy cores. IEEE Transactions on Industrial Electronics. 2014;**61**(9):4510-4518

Introductory Chapter: Introduction to the Design and the Control of Electrical Machines

http://dx.doi.org/10.5772/intechopen.78772

11

[18] Okamoto S, Denis N, Kato Y, Ieki M, Fujisaki K. Core loss reduction of an interior permanent-magnet synchronous motor using amorphous stator core. IEEE Transactions on

[19] Lei G, Zhu J, Guo Y, Liu C, Ma B. A review of design optimization methods for electrical

[20] Liu X, Slemon G. An improved method of optimization for electrical machines. IEEE

[21] Miller T. Optimal design of switched reluctance motors. IEEE Transactions on Industrial

[22] Andersen SB, Santos IF. Evolution strategies and multiobjective optimization of perma-

[23] Zarko D, Ban D, Lipo T. Design optimization of interior permanent magnet (IPM) motors with maximized torque output in the entire speed range. In: European Conference on

[24] Zhang P, Sizov G, Ionel D, Demerdash N. Establishing the relative merits of interior and spoke-type permanent magnet machines with ferrite or NdFeB through systematic

[25] Storn R, Price K. Differential Evolution—A simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Report TR-95-012. ICSI; March 1995

[26] Lampinen J, Zelinka I. Mixed integer-discrete-continuous optimization by differential evolution—Part 1: The optimization method. In: 5th International Mendel Conference

[27] Kukkonen S, Lampinen J. Performance assessment of generalized differential evolution 3 with a given set of constrained multi-objective test problems. In: IEEE Congress on

[28] Lukaniszyn M, JagieLa M, Wrobel R. Optimization of permanent magnet shape for minimum cogging torque using a genetic algorithm. IEEE Transactions on Magnetics.

[29] Bianchi N, Durello D, Fornasiero E. Multi-objective optimization of a PM assisted synchronous reluctance machine, including torque and sensorless detection capability. In: 6th IET International Conference on Power Electronics, Machines and Drives (PEMD

[30] Duan Y, Harley R, Habetler T. Multi-objective design optimization of surface mount permanent magnet machine with particle swarm intelligence. In: IEEE Swarm Intelligence

design optimization. IEEE Transactions on Industry Applications. 2015;**99**:1

Industrial Applications. 2016;**52**(3):2261-2268

Electronics. 2002;**49**(1):15-27

machines. Energies. 2017;**10**(12):1962. DOI: 10.3390/en10121962

nent magnet motor. Applied Soft Computing. 2012;**12**(2):778-792

Transactions on Energy Conversion. 1991;**6**(3):492-496

Power Electronics and Applications; 2005. 10pp

Evolutionary Computation, CEC 09; 2009. pp. 1943-1950

on Soft Computing; 1999. pp. 71-76

2004;**40**(2):1228-1231

2012); March 2012. pp. 1-6

Symposium; September 2008. pp. 1-5


[17] Fan T, Li Q, Wen X. Development of a high power density motor made of amorphous alloy cores. IEEE Transactions on Industrial Electronics. 2014;**61**(9):4510-4518

[4] Steiner G, Weber A, Magele C. Managing uncertainties in electromagnetic design problems with robust optimization. IEEE Transactions on Magnetics. 2004;**40**:1094-1099 [5] Bartel A, de Gersem H, Hulsmann T, Romer U, Schops S, Weiland T. Quantification of uncertainty in the field quality of magnets originating from material measurements.

[6] Mac D, Clenet S, Beddek K, Chevallier L, Korecki J, Moreau O, Thomas P. Influence of uncertainties on the B (H) curves on the flux linkage of a turboalternator. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields. 2014;**27**:385-399

[7] Li M, Mohammadi MH, Rahman T, Lowther D. Analysis and design of electrical machines with material uncertainties in iron and permanent magnet. COMPEL–The International Journal for Computation and Mathematics in Electrical and Electronic

[8] Lei G, Zhu JG, Guo YG. Multidisciplinary Design Optimization Methods for Electrical Machines and Drive Systems. Berlin/Heidelberg, Germany: Springer-Verlag; 2016. ISBN

[9] Lei G, Liu CC, Guo YG, Zhu JG. Multidisciplinary design analysis and optimization for a PM transverse flux machine with soft magnetic composite core. IEEE Transactions on

[10] Lei G, Liu CC, Zhu JG, Guo YG. Robust multidisciplinary design optimization of PM machines with soft magnetic composite cores for batch production. IEEE Transactions

[11] Kreuawan S, Gillon F, Brochet P. Optimal design of permanent magnet motor using multidisciplinary design optimization. In: Proceedings of the 18th International Conference

[12] Lin F, Zuo S, Wu X. Electromagnetic vibration and noise analysis of permanent magnet synchronous motor with different slot-pole combinations. IET Electric Power Appli-

[13] Li Y, Chai F, Song Z, Li Z. Analysis of vibrations in interior permanent magnet synchro-

[14] Pfister P-D, Perriard Y. Very-high-speed slotless permanent-magnet motors: Analytical modeling, optimization, design, and torque measurement methods. IEEE Transactions

[15] Luise F, Tessarolo A, Agnolet F, Pieri S, Scalabrin M, di Chiara M, de Martin M. Design optimization and testing of high-performance motors: Evaluating a compromise between quality design development and production costs of a Halbach-Array PM slotless motor.

[16] Krings A, Boglietti A, Cavagnino A, Sprague S. Soft magnetic material status and trends in electric machines. IEEE Transactions on Industrial Electronics. 2017;**64**(3):2405-2414

on Electrical Machines; Pattaya, Thailand; 25-28 October, 2015. pp. 1-6

nous motors considering air-gap deformation. Energies. 2017;**10**:1259

IEEE Transactions on Magnetics. 2013;**49**:2367-2370

Engineering. 2017;**36**(5):1326-1337

978-3-662-49269-7

Magnetics. 2015;**51**(11)

10 Optimization and Control of Electrical Machines

on Magnetics. 2016;**52**(3)

cations. 2016;**10**:900-908

on Industrial Electronics. 2010;**57**(1):296-303

IEEE Industry Applications Magazine. 2016;**22**(6):19-32


[31] Ma C, Qu L. Multiobjective optimization of switched reluctance motors based on design of experiments and particle swarm optimization. IEEE Transactions on Energy Conversion. 2015;**99**:1-10

**Chapter 2**

**Provisional chapter**

**Multi-Objective Optimization Techniques to Solve the**

**the Economic Emission Load Dispatch Problem Using** 

© 2016 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.

© 2018 The Author(s). Licensee IntechOpen. 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.

The main objective of thermoelectric power plants is to meet the power demand with the lowest fuel cost and emission levels of pollutant and greenhouse gas emissions, considering the operational restrictions of the power plant. Optimization techniques have been widely used to solve engineering problems as in this case with the objective of minimizing the cost and the pollution damages. Heuristic and metaheuristic algorithms have been extensively studied and used to successfully solve this multi-objective problem. This chapter, several optimization techniques (simulated annealing, ant lion, dragonfly, NSGA II, and differential evolution) are analyzed and their application to economic-emission load dispatch (EELD) is also discussed. In addition, a comparison of

**Keywords:** economic-emission load dispatch, optimization techniques, heuristic,

all approaches and its results are offered through a case study.

metaheuristic algorithms, power plants

DOI: 10.5772/intechopen.76666

**Economic Emission Load Dispatch Problem Using**

**Multi-Objective Optimization Techniques to Solve** 

**Various Heuristic and Metaheuristic Algorithms**

**Various Heuristic and Metaheuristic Algorithms**

Jorge de Almeida Brito Júnior, Marcus Vinicius Alves Nunes,

Jorge de Almeida Brito Júnior, Marcus Vinicius Alves Nunes,

Jandecy Cabral Leite,

Jandecy Cabral Leite,

Manoel Henrique Reis Nascimento,

Manoel Henrique Reis Nascimento,

Jorge Laureano Moya Rodriguez, Carlos Alberto Oliveira de Freitas,

Jorge Laureano Moya Rodriguez, Carlos Alberto Oliveira de Freitas,

Tirso Lorenzo Reyes Carvajal and

Tirso Lorenzo Reyes Carvajal and

http://dx.doi.org/10.5772/intechopen.76666

Haroldo Melo de Oliveira

**Abstract**

Milton Fonseca Júnior, Edson Farias de Oliveira, David Barbosa de Alencar, Nadime Mustafa Moraes,

Milton Fonseca Júnior, Edson Farias de Oliveira, David Barbosa de Alencar, Nadime Mustafa Moraes,

Additional information is available at the end of the chapter

Haroldo Melo de OliveiraAdditional information is available at the end of the chapter


#### **Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch Problem Using Various Heuristic and Metaheuristic Algorithms Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch Problem Using Various Heuristic and Metaheuristic Algorithms**

DOI: 10.5772/intechopen.76666

Jorge de Almeida Brito Júnior, Marcus Vinicius Alves Nunes, Manoel Henrique Reis Nascimento, Jandecy Cabral Leite, Jorge Laureano Moya Rodriguez, Carlos Alberto Oliveira de Freitas, Milton Fonseca Júnior, Edson Farias de Oliveira, David Barbosa de Alencar, Nadime Mustafa Moraes, Tirso Lorenzo Reyes Carvajal and Haroldo Melo de Oliveira Jorge de Almeida Brito Júnior, Marcus Vinicius Alves Nunes, Manoel Henrique Reis Nascimento, Jandecy Cabral Leite, Jorge Laureano Moya Rodriguez, Carlos Alberto Oliveira de Freitas, Milton Fonseca Júnior, Edson Farias de Oliveira, David Barbosa de Alencar, Nadime Mustafa Moraes, Tirso Lorenzo Reyes Carvajal and Haroldo Melo de OliveiraAdditional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76666

## **Abstract**

[31] Ma C, Qu L. Multiobjective optimization of switched reluctance motors based on design of experiments and particle swarm optimization. IEEE Transactions on Energy

[32] Mutluer M, Bilgin O. Comparison of stochastic optimization methods for design optimization of permanent magnet synchronous motor. Neural Computing and Applications.

[33] Deb A, Gupta B, Roy J. Performance comparison of differential evolution, genetic algorithm and particle swarm optimization in impedance matching of aperture coupled microstrip antennas. In: 11th Mediterranean Microwave Symposium (MMS); September

[34] Duan Y, Harley R, Habetler T. Comparison of particle swarm optimization and genetic algorithm in the design of permanent magnet motors. In: IEEE 6th International Power

[35] Mutluer M, Bilgin O. Design optimization of PMSM by particle swarm optimization and genetic algorithm. In: International Symposium on Innovations in Intelligent Systems

[36] Sarikhani A, Mohammed O. Hybrid GA-PSO multi-objective design optimization of coupled PM synchronous motor-drive using physics-based modeling approach. In: 14th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC); 2010. pp. 1-1

[37] Stipetic S, Miebach W, Zarko D.Optimization in design of electric machines: Methodology and workflow. In: International Aegean Conference on Electrical Machines & Power

[38] Zhong C, Lin Y. Model reference adaptive control (MRAC)-based parameter identification applied to surface-mounted permanent magnet synchronous motor. International

[39] Esmaeeli MR, Kianinejad R, Razzaz M. Field oriented control of DFIG based on modified MRAS observer. In: Proceedings of 17th Conference on Electrical Power Distribution

[40] Zhang Y, Xia B, Yang H, Rodriguez J. Overview of model predictive control for induction motor drives. Chinese Journal of Electrical Engineering. 2016;**2**(1):62-76

[41] Hedjar R, Toumi R, Boucher P, Dumur D. Cascaded nonlinear predictive control of

[42] Moutchou M, Moahmoudi H, Abbou A. Backstepping control of the induction machine, based on flux sliding mode observer, with rotor and stator resistances adaptation.

[43] Lin F-J, Shen P-H, Hsu S-P. Adaptive backstepping sliding mode control for linear induction motor drive. IEE Proceedings–Electric Power Applications. 2002;**149**(3):184-194 [44] Bolognani S, Zigliotto M. Fuzzy logic control of a switched reluctance motor drive. IEEE

Electronics and Motion Control Conference, IPEMC; 2009. pp. 822-825

Electronics (ACEMP); Side, Turkey. 2-4 September 2015. pp. 441-448

and Applications (INISTA), 2012; July 2012. pp. 1-4

Journal of Electronics. 2017;**104**(11):1854-1873

Networks (EPDC); Tehran, Iran. May 2012. pp. 2-3

induction motor. European Journal of Control. 2004;**10**(1):65-80

Transactions on Industry Applications. 1996;**32**(5):1063-1068

International Review of Automatic Control (IREACO). 2014;**7**(4):394-402

Conversion. 2015;**99**:1-10

12 Optimization and Control of Electrical Machines

2012;**21**(8):2049-2056

2011. pp. 17-20

The main objective of thermoelectric power plants is to meet the power demand with the lowest fuel cost and emission levels of pollutant and greenhouse gas emissions, considering the operational restrictions of the power plant. Optimization techniques have been widely used to solve engineering problems as in this case with the objective of minimizing the cost and the pollution damages. Heuristic and metaheuristic algorithms have been extensively studied and used to successfully solve this multi-objective problem. This chapter, several optimization techniques (simulated annealing, ant lion, dragonfly, NSGA II, and differential evolution) are analyzed and their application to economic-emission load dispatch (EELD) is also discussed. In addition, a comparison of all approaches and its results are offered through a case study.

**Keywords:** economic-emission load dispatch, optimization techniques, heuristic, metaheuristic algorithms, power plants

© 2016 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. © 2018 The Author(s). Licensee IntechOpen. 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.

## **1. Introduction**

The main problem of economic-emission load dispatch (EELD) is to reduce the emission level and total cost of generation at the same time accomplishing the demand for electricity from the power plant. Thermal power plants are among the maximum significant sources of contamination by sulfur dioxide (SO<sup>2</sup> ), carbon dioxide (CO<sup>2</sup> ), and nitrogen oxides (NOx), which create atmospheric pollution [1].

**2.1. Cost function (***F<sup>1</sup>*

where ai

where *Pi*

, bi

generators, and *Pi*

, and ci

**2.2. Economic emission function (***F<sup>2</sup>*

where di, ei, and fi are emission coefficients.

the actual power losses in transmission lines *PL*

The calculation of power losses *PL*

**2.3. Economical load dispatch constrains**

*2.3.1. Equality power balance constrain*

**)**

function of generator power output Pi [8, 22]:

The fuel cost is considered as an essential criterion for economics analysis in thermal power plants. The cost function of each generator can be assumed to be approximated by a quadratic

Emissions can be represented by a function that links emissions with power generated by each unit [23]. The emission function in ton/h, which normally represents the emission of SO<sup>2</sup>

NOx, is a function of the power output of the generator, and it can be expressed as follows [1]:

The real power of each generator is limited by the lower and upper limits. The following

is the output power of each *i* generator, *PD* is the load demand, and *PL*

equality constraints in the active and reactive power on each bar as follows [26]:

sion losses; in other words, the total power generation has to meet the total demand *PD* and

, i.e.

involves the solution of the load flow problem, which has

the active power of each generator (**Table 2**) .

**)**

The restrictions used in the problem were of three types as follows.

equation is the equality restriction of power balance [24, 25]:

are the fuel cost coefficients of the ith unit generating, *n* the number of

Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch…

http://dx.doi.org/10.5772/intechopen.76666

(2)

15

and

(3)

(4)

(5)

(6)

are transmis-

Some authors developed three approaches to solve the EELD problem [2–4]. The first one is using a single objective, considering emissions and pollution as restrictions with permissible limits [5]; the second one combines cost and emission functions into a single objective function with different weights, where cost and emission are minimized simultaneously [2]; and the third one uses the separated cost and emission functions in a multi-objective optimization [1, 6].

The solution of EELD problem is to minimize the total cost of fuel consumption and carbon emissions [7], considering power demand and operational restrictions [8]. Several techniques such as particle swarm optimization [9, 10], linear programming [11, 12], ant colony optimization [13], biogeography-based optimization [14], genetic algorithms (GA) [15, 16], Tabu search algorithm [17], simulated annealing (SA) [1], neural networks [18], differential evolution (DE) [19], harmony search algorithm [20], Lagrange functions [7], and others [19] have been used to fix the problem of EELD. In spite that all of them have been used, few are used with cost and emission functions in a multi-objective optimization.

This chapter, six multi-objective optimization approaches to solve the EELD problem are going to be presented, and a brief comparison among them is done.

In addition, the "shutdown" of the most inefficient generators is included in all multi-objective optimization approaches used [1, 8, 21].

## **2. Materials and methods**

To solve a problem of EELD, two important objectives in an electrical thermal power system must be considered; they are environmental and economy impacts [22].

The parameters of objective functions are determined by curve fitting techniques based on tests of engine performance.

The multi-objective optimization problem is defined as:

$$\underset{P}{\text{minimize}} \quad \left[F\_1(P), F\_2(P)\right] \tag{1}$$

where *F1(P)* and *F2(P)* are the objective functions to be minimized over the set of permissible decision vector *P*, as follow in the next Subsections 2.1 and 2.2.

#### **2.1. Cost function (***F<sup>1</sup>* **)**

**1. Introduction**

tion [1, 6].

tamination by sulfur dioxide (SO<sup>2</sup>

14 Optimization and Control of Electrical Machines

emission functions in a multi-objective optimization.

tive optimization approaches used [1, 8, 21].

**2. Materials and methods**

tests of engine performance.

going to be presented, and a brief comparison among them is done.

must be considered; they are environmental and economy impacts [22].

The multi-objective optimization problem is defined as:

decision vector *P*, as follow in the next Subsections 2.1 and 2.2.

create atmospheric pollution [1].

The main problem of economic-emission load dispatch (EELD) is to reduce the emission level and total cost of generation at the same time accomplishing the demand for electricity from the power plant. Thermal power plants are among the maximum significant sources of con-

), carbon dioxide (CO<sup>2</sup>

Some authors developed three approaches to solve the EELD problem [2–4]. The first one is using a single objective, considering emissions and pollution as restrictions with permissible limits [5]; the second one combines cost and emission functions into a single objective function with different weights, where cost and emission are minimized simultaneously [2]; and the third one uses the separated cost and emission functions in a multi-objective optimiza-

The solution of EELD problem is to minimize the total cost of fuel consumption and carbon emissions [7], considering power demand and operational restrictions [8]. Several techniques such as particle swarm optimization [9, 10], linear programming [11, 12], ant colony optimization [13], biogeography-based optimization [14], genetic algorithms (GA) [15, 16], Tabu search algorithm [17], simulated annealing (SA) [1], neural networks [18], differential evolution (DE) [19], harmony search algorithm [20], Lagrange functions [7], and others [19] have been used to fix the problem of EELD. In spite that all of them have been used, few are used with cost and

This chapter, six multi-objective optimization approaches to solve the EELD problem are

In addition, the "shutdown" of the most inefficient generators is included in all multi-objec-

To solve a problem of EELD, two important objectives in an electrical thermal power system

The parameters of objective functions are determined by curve fitting techniques based on

where *F1(P)* and *F2(P)* are the objective functions to be minimized over the set of permissible

), and nitrogen oxides (NOx), which

(1)

The fuel cost is considered as an essential criterion for economics analysis in thermal power plants. The cost function of each generator can be assumed to be approximated by a quadratic function of generator power output Pi [8, 22]:

$$F\_1(P\_l) = \sum\_{i=1}^{n} \left( a\_l + b\_l P\_l + c\_l P\_l^2 \right) \quad \text{S/h} \tag{2}$$

where ai , bi , and ci are the fuel cost coefficients of the ith unit generating, *n* the number of generators, and *Pi* the active power of each generator (**Table 2**) .

#### **2.2. Economic emission function (***F<sup>2</sup>* **)**

Emissions can be represented by a function that links emissions with power generated by each unit [23]. The emission function in ton/h, which normally represents the emission of SO<sup>2</sup> and NOx, is a function of the power output of the generator, and it can be expressed as follows [1]:

$$F\_2(P\_t) = \sum\_{t=1}^n \left( d\_t + e\_t \tilde{P}\_t + f\_t \tilde{P}\_t^2 \right) \quad \text{(kg/h)}\tag{3}$$

where di, ei, and fi are emission coefficients.

#### **2.3. Economical load dispatch constrains**

The restrictions used in the problem were of three types as follows.

#### *2.3.1. Equality power balance constrain*

The real power of each generator is limited by the lower and upper limits. The following equation is the equality restriction of power balance [24, 25]:

$$\sum\_{l=1}^{n} P\_l - P^D - P^L = 0\tag{4}$$

where *Pi* is the output power of each *i* generator, *PD* is the load demand, and *PL* are transmission losses; in other words, the total power generation has to meet the total demand *PD* and the actual power losses in transmission lines *PL* , i.e.

$$\sum\_{l=1}^{n} P\_l = P^\mathrm{D} + P^\mathrm{L} \tag{5}$$

The calculation of power losses *PL* involves the solution of the load flow problem, which has equality constraints in the active and reactive power on each bar as follows [26]:

$$P^{(L)} = \sum\_{l=1}^{L} B\_l \dot{P}\_l^2 \tag{6}$$

A simplification is applied to model the transmission losses, setting them as a function of the generator output through Kron's loss coefficient derivatives of the Kron formula for losses [21]:

$$P\_L = \sum\_{i=1}^{n} \sum\_{j=1}^{n} P\_i B\_{ij} P\_j + \sum\_{i=1}^{n} B\_{0i} P\_i + B\_{00},\tag{7}$$

where *Bij*, *B0i*, and *B00* are the energy loss coefficients in the transmission network and n is the number of generators. A reasonable accuracy can be obtained when the actual operating conditions are close to the base case, where the *B* coefficients were obtained [26].

## *2.3.2. Production capacity constraint*

The power capacity total generated from each generator is restricted by the lower limit and by the upper limit, so the constrain is [1]

$$P\_{\min,i} \le P\_{\hat{t}} \le P\_{\max,\hat{t}},\tag{8}$$

On **Figure 1**, the simulated annealing algorithm is shown.

**Figure 1.** Simulated annealing algorithm. Source: [28].

function:

is greater than a randomly generated number between 0 and 1 [27]:

where *v* is the iteration number and *r* is temperature reduction factor. *T0*

Starting from a high temperature, a molten metal is cooled slowly until it is solidified at a low temperature. The iteration number in the SA technique is analogous to the temperature level. In each iteration, a candidate solution is generated. If this solution is a better solution, it will be accepted and used to generate yet another candidate solution. If it is a deteriorated solution, the solution will be accepted when its probability of acceptance *Pr* (Δ) as given in Eq. (10)

Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch…

http://dx.doi.org/10.5772/intechopen.76666

17

where Δ is the amount of deterioration between the new and the current solutions and T is the temperature at which the new solution is generated. Accepting deteriorated solutions in the above manner enables the SA solution to "jump" out of the local optimum solution points and to seek the global optimum solution [1]. The last accepted candidate solution is then taken as the starting solution for the generation of candidate solutions in the next iteration. The reduction of the temperature in successive iterations is governed by the following geometric

ture; its value can be set arbitrarily or estimated [29]. A multi-objective simulated annealing optimization to fix a generation dispatch problem is analyzed in [30], and used too in [1], but

(10)

(11)

is the initial tempera-

where *Pi* is the output power of the *i* generator, *Pmin.i*, is the minimal power of the *i* generator, and *Pmax.i*, the maximal power of the *i* generator.

## *2.3.3. Fuel delivery constraint*

At each time interval, the amount of fuel supplied to all units must be less than or equal to the fuel supplied by the seller, i.e., the fuel delivered to each unit in each interval should be within its lower limit *Fmin,i* and its upper limit *Fmax,i* so that [21].

$$F\_{\min,i} \le F\_{\min} \le F\_{\max,i}, \ i \in N, m \in M,\tag{9}$$

where *Fi,m* is the fuel supplied to the engine *i* at the interval *m*, *Fi,min* is the minimum amount of fuel supplied to *i* generator, and *Fmax,i* is the maximum amount of fuel supplied to *i* generator.

## **3. Multi-objective optimization techniques to solve EELD**

There are a lot of multi-objective optimization approaches that can be used to solve the EELD problem [19], but implementations need to be made to solve EELD problem. On this chapter six metaheuristic algorithm methods that already have the implementation are going to be presented.

## **3.1. Simulated annealing (SA)**

SA is a powerful optimization technique which exploits the resemblance between a minimization process and the cooling of molten metal [1].

The physical annealing process is simulated in the SA technique for the determination of global or near-global optimum solutions for optimization problems. In this algorithm a parameter T, called temperature, is defined [27].


**Figure 1.** Simulated annealing algorithm. Source: [28].

A simplification is applied to model the transmission losses, setting them as a function of the generator output through Kron's loss coefficient derivatives of the Kron formula for losses [21]:

number of generators. A reasonable accuracy can be obtained when the actual operating con-

The power capacity total generated from each generator is restricted by the lower limit and by

At each time interval, the amount of fuel supplied to all units must be less than or equal to the fuel supplied by the seller, i.e., the fuel delivered to each unit in each interval should be within

where *Fi,m* is the fuel supplied to the engine *i* at the interval *m*, *Fi,min* is the minimum amount of fuel supplied to *i* generator, and *Fmax,i* is the maximum amount of fuel supplied to *i* generator.

There are a lot of multi-objective optimization approaches that can be used to solve the EELD problem [19], but implementations need to be made to solve EELD problem. On this chapter six metaheuristic algorithm methods that already have the implementation are going to be presented.

SA is a powerful optimization technique which exploits the resemblance between a minimiza-

The physical annealing process is simulated in the SA technique for the determination of global or near-global optimum solutions for optimization problems. In this algorithm a

**3. Multi-objective optimization techniques to solve EELD**

ditions are close to the base case, where the *B* coefficients were obtained [26].

, *B0i*, and *B00* are the energy loss coefficients in the transmission network and n is the

is the output power of the *i* generator, *Pmin.i*, is the minimal power of the *i* generator,

where *Bij*

where *Pi*

*2.3.2. Production capacity constraint*

16 Optimization and Control of Electrical Machines

*2.3.3. Fuel delivery constraint*

**3.1. Simulated annealing (SA)**

tion process and the cooling of molten metal [1].

parameter T, called temperature, is defined [27].

the upper limit, so the constrain is [1]

and *Pmax.i*, the maximal power of the *i* generator.

its lower limit *Fmin,i* and its upper limit *Fmax,i* so that [21].

(7)

(8)

(9)

#### On **Figure 1**, the simulated annealing algorithm is shown.

Starting from a high temperature, a molten metal is cooled slowly until it is solidified at a low temperature. The iteration number in the SA technique is analogous to the temperature level. In each iteration, a candidate solution is generated. If this solution is a better solution, it will be accepted and used to generate yet another candidate solution. If it is a deteriorated solution, the solution will be accepted when its probability of acceptance *Pr* (Δ) as given in Eq. (10) is greater than a randomly generated number between 0 and 1 [27]:

$$Pr(\Delta) = \exp\left(-\Delta/T\right) \tag{10}$$

where Δ is the amount of deterioration between the new and the current solutions and T is the temperature at which the new solution is generated. Accepting deteriorated solutions in the above manner enables the SA solution to "jump" out of the local optimum solution points and to seek the global optimum solution [1]. The last accepted candidate solution is then taken as the starting solution for the generation of candidate solutions in the next iteration. The reduction of the temperature in successive iterations is governed by the following geometric function:

$$
\ddot{T}\_v = r^{(v-1)} T\_0 \tag{11}
$$

where *v* is the iteration number and *r* is temperature reduction factor. *T0* is the initial temperature; its value can be set arbitrarily or estimated [29]. A multi-objective simulated annealing optimization to fix a generation dispatch problem is analyzed in [30], and used too in [1], but with the implementation of turning off the most inefficient generators, and this information will be used to compare with the new methods presented in this chapter.

*3.2.1. Initial population*

*3.2.2. Selection*

*3.2.3. Crossover*

*3.2.4. Mutation*

*3.2.5. Crowded tournament selection*

as in [37].

Initially, a parent random population is created. The population is ordered based on nondomination. For each solution, an aptitude equal to its level of non-domination is assigned (1 is the best level). Thus, a minimization of aptitude or fitness is assumed. Tournament selection, recombination, and mutation operators are used to create N size descendant populations [36]. The population is initialized based on the problem range and constraints, if any. This popula-

Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch…

http://dx.doi.org/10.5772/intechopen.76666

19

In the original NSGA II, the selection by binary tournament (BTS) is used, where tournament is disputed between two solutions and the best one is selected and placed in the crossing tank. Two other solutions are taken again, and another gap in the cross junction is filled. It is performed in such a way that each solution can participate in two tournaments exactly [35].

The NSGA II uses the simulated binary crossover (SBX), which works with two parent solu-

NSGA II uses polynomial mutation, which transforms each solution separately, that is, a stock solution gives offspring after being mutated. The mathematical formulation can be described

An estimate obtained of the density of solutions close to a particular solution *i* in the population, the average between the two solutions on both sides of solution i together with each one

The NSGA II presents an improved technique for the maintenance of the diversity of solutions, proposing a method of crowding classification distance. However, in its case the clas-

In NSGA II, all individuals are classified into combined populations (parents and descendants) based on the Pareto dominance ratio and then classified into several layers based on the front to which an individual is located. At each front, the individuals are arranged in descending order of magnitude of the crowding distance value. In the binary tournament selection process, the algorithm first selects an individual positioned on a better non-dominated front. In cases where the individuals with an identical front are compared, the tournament selection

The elitist strategy of NSGA II considers all combinations of non-dominated population solutions as the candidates for solutions to the next generation. If the number of non-dominated

of the targets is taken. This amount is the Crowding distance [35].

sification technique remained unchanged from its previous version.

operator chooses the winner based on the crowding distance value [38].

tions and generates two descendants. The step-by-step procedure is described in [35].

tion is initialized and ordered based on non-domination.

#### **3.2. NSGA II**

The Non-dominated Sorting Genetic Algorithm II (NSGA II) has been one of the algorithms most used to solve the multi-objective optimization (MOO) problems in general and EELD problem in particular [31–33]. It was proposed by Deb et al. in 2002 [34]. NSGA II uses a faster selection, an elitist preservation approach, and a less segmented operating parameter [35]. The operation of NSGA II is shown in **Figure 2**.

**Figure 2.** Operation of NSGA II. Source: [35].

## *3.2.1. Initial population*

with the implementation of turning off the most inefficient generators, and this information

The Non-dominated Sorting Genetic Algorithm II (NSGA II) has been one of the algorithms most used to solve the multi-objective optimization (MOO) problems in general and EELD problem in particular [31–33]. It was proposed by Deb et al. in 2002 [34]. NSGA II uses a faster selection, an elitist preservation approach, and a less segmented operating parameter [35].

will be used to compare with the new methods presented in this chapter.

The operation of NSGA II is shown in **Figure 2**.

**Figure 2.** Operation of NSGA II. Source: [35].

**3.2. NSGA II**

18 Optimization and Control of Electrical Machines

Initially, a parent random population is created. The population is ordered based on nondomination. For each solution, an aptitude equal to its level of non-domination is assigned (1 is the best level). Thus, a minimization of aptitude or fitness is assumed. Tournament selection, recombination, and mutation operators are used to create N size descendant populations [36].

The population is initialized based on the problem range and constraints, if any. This population is initialized and ordered based on non-domination.

## *3.2.2. Selection*

In the original NSGA II, the selection by binary tournament (BTS) is used, where tournament is disputed between two solutions and the best one is selected and placed in the crossing tank. Two other solutions are taken again, and another gap in the cross junction is filled. It is performed in such a way that each solution can participate in two tournaments exactly [35].

## *3.2.3. Crossover*

The NSGA II uses the simulated binary crossover (SBX), which works with two parent solutions and generates two descendants. The step-by-step procedure is described in [35].

## *3.2.4. Mutation*

NSGA II uses polynomial mutation, which transforms each solution separately, that is, a stock solution gives offspring after being mutated. The mathematical formulation can be described as in [37].

## *3.2.5. Crowded tournament selection*

An estimate obtained of the density of solutions close to a particular solution *i* in the population, the average between the two solutions on both sides of solution i together with each one of the targets is taken. This amount is the Crowding distance [35].

The NSGA II presents an improved technique for the maintenance of the diversity of solutions, proposing a method of crowding classification distance. However, in its case the classification technique remained unchanged from its previous version.

In NSGA II, all individuals are classified into combined populations (parents and descendants) based on the Pareto dominance ratio and then classified into several layers based on the front to which an individual is located. At each front, the individuals are arranged in descending order of magnitude of the crowding distance value. In the binary tournament selection process, the algorithm first selects an individual positioned on a better non-dominated front. In cases where the individuals with an identical front are compared, the tournament selection operator chooses the winner based on the crowding distance value [38].

The elitist strategy of NSGA II considers all combinations of non-dominated population solutions as the candidates for solutions to the next generation. If the number of non-dominated solutions is less than the size of the population, they are all maintained as the next-generation solutions. Otherwise, candidates for the next generation are selected by the criterion of crowding distance. This criterion has the advantage of maintaining the diversity of solutions in the population in order to avoid premature convergence [38, 39].

## **3.3. Dragonfly**

Recently new stochastic optimization technique was developed by Mirjaili in 2016 [40] named dragonfly optimizer. Dragonflies (Odonata) are fancy insects. There are nearly 3000 different species of this insect around the world. A dragonfly's lifecycle includes two main milestones: nymph and adult. They spend the major portion of their lifespan in nymph, and they undergo metamorphism to become adult [41].

On **Table 1** and **Figure 3**, the characteristics of dragonfly algorithm (DA) are shown.

Dragonflies are considered as small predators that hunt almost all other small insects in nature. Nymph dragonflies also predate on other marine insects and even small fishes. The interesting fact about dragonflies is their unique and rare swarming behavior. Dragonflies swarm for only two purposes: hunting and migration. The former is called static (feeding) swarm, and the latter is called dynamic (migratory) swarm [40].

The main inspiration of the DA algorithm originates from static and dynamic swarming behaviors. These two swarming behaviors are very similar to the two main phases of optimization using meta-heuristics: exploration and exploitation. Dragonflies create sub-swarms and fly over different areas in a static swarm, which is the main objective of the exploration phase. In the static swarm, however, dragonflies fly in bigger swarms and along one direction, which is favorable in the exploitation phase [40]. The dragonfly algorithm has been applied successfully to the environmental economic dispatch.


**3.4. Particle swarm optimization (PSO)**

**Figure 3.** Dragonfly pseudocode. Source: [43].

idea for multi-objective optimization in 1999 [44].

Particle swarm optimization (PSO) is a population-based stochastic optimization technique, inspired by the social behavior of birds or shoals of fishes. Moore and Chapman extended this

Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch…

http://dx.doi.org/10.5772/intechopen.76666

21

**Table 1.** Characteristics of the DA.


**Figure 3.** Dragonfly pseudocode. Source: [43].

solutions is less than the size of the population, they are all maintained as the next-generation solutions. Otherwise, candidates for the next generation are selected by the criterion of crowding distance. This criterion has the advantage of maintaining the diversity of solutions

Recently new stochastic optimization technique was developed by Mirjaili in 2016 [40] named dragonfly optimizer. Dragonflies (Odonata) are fancy insects. There are nearly 3000 different species of this insect around the world. A dragonfly's lifecycle includes two main milestones: nymph and adult. They spend the major portion of their lifespan in nymph, and they undergo

Dragonflies are considered as small predators that hunt almost all other small insects in nature. Nymph dragonflies also predate on other marine insects and even small fishes. The interesting fact about dragonflies is their unique and rare swarming behavior. Dragonflies swarm for only two purposes: hunting and migration. The former is called static (feeding)

The main inspiration of the DA algorithm originates from static and dynamic swarming behaviors. These two swarming behaviors are very similar to the two main phases of optimization using meta-heuristics: exploration and exploitation. Dragonflies create sub-swarms and fly over different areas in a static swarm, which is the main objective of the exploration phase. In the static swarm, however, dragonflies fly in bigger swarms and along one direction, which is favorable in the exploitation phase [40]. The dragonfly algorithm has been applied

Fitness function Distance from the food source, the predator, center of the swarm, velocity matching,

Flying with a specific velocity and direction

On **Table 1** and **Figure 3**, the characteristics of dragonfly algorithm (DA) are shown.

in the population in order to avoid premature convergence [38, 39].

swarm, and the latter is called dynamic (migratory) swarm [40].

successfully to the environmental economic dispatch.

Decision variable Dragonfly's position in each dimension

Initial solution Randomly selected position of a dragonfly

and collision avoidance

**General algorithm Dragonfly algorithm**

Solution Dragonfly's position Old solution Old position of a dragonfly New solution New position of a dragonfly Best solution Any dragonfly with the best fitness

Selection —

**Table 1.** Characteristics of the DA.

Process of generating new

solution

Source: [42].

**3.3. Dragonfly**

metamorphism to become adult [41].

20 Optimization and Control of Electrical Machines

## **3.4. Particle swarm optimization (PSO)**

Particle swarm optimization (PSO) is a population-based stochastic optimization technique, inspired by the social behavior of birds or shoals of fishes. Moore and Chapman extended this idea for multi-objective optimization in 1999 [44].

The simple PSO cannot be applied directly to multi-objective optimization since there are two issues to consider when extending PSO optimization to multi-objective problems [44].

The first one is how to select the best global and local particles (leaders) to guide the search, and the second one is how to keep good points found so far. For the latter, a secondary population is usually used to maintain non-dominated solutions.

PSO is one of the modern heuristic algorithms suitable for solving large-scale non-converting optimization problems. It is a population-based search algorithm and parallel search using a group of particles [45].

On **Figure 4**, the PSO flow chart is shown.

The main idea of the PSO is that "particles" (solutions) move through the search space with velocities that are adjusted dynamically according to their historical behavior. Therefore, the particles have a tendency to move to a better search area throughout the search process [47].

## **3.5. Differential evolution (DE)**

The DE algorithm was developed to be a promising heuristic optimization algorithm for numerical optimization problems. The DE was designed to meet the requirement of practical minimization techniques with consistent convergence to the global minimum in consecutive independent trials. It can solve non-differentiable, nonlinear functions and multimodal cost functions [48].

The DE algorithm is a simple stochastic optimization strategy. It uses a voracious and less stochastic approach with floating-point coding in problem solving, unlike other evolutionary algorithms [49].

DE uses the arithmetic operators to evolve from a randomly generated initial population to a final solution. Basically, the weighted difference between two individuals is added to a third individual in the population. Thus, no separate probability distribution has to be used, which makes the scheme completely self-organized [49]. There are several variant strategies of DE. In general expressions are divided into two parts: the first part represents a vector to be disturbed. The first part is "rand" (vector chosen at random) or "best" (best vector of the current population). The second part is the number of difference vectors (one or two) chosen for perturbation vectors of the first part, and the last part indicates the type of crossover to be used. The type of crossing can be "bin" (binomial) or "exp" (exponential) [49].

## *3.5.1. Initialization*

The initialization of DE can be done by randomly generating candidate solutions with *NP D*-dimensional vectors of real parameters evaluated [50].

*3.5.3. Crossover*

**Figure 4.** PSO flow chart. Source: [46].

*3.5.4. Selection*

rithms (GAs), use some form of selection.

The crossover increases the potential diversity of a population. In the case of binomial crossover, test vectors are produced. Crossover can be understood as a mutation rate or a probability of inheritance between successive generations. There are alternatives to binomial crossover. The most common is the exponential crossover. Both approaches are valid for all problems, although the success/improvement of one over the other varies according to the problem considered [50].

Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch…

http://dx.doi.org/10.5772/intechopen.76666

23

Selection can be understood as a form of competition, in line with many examples directly observable in nature. Many evolutionary optimization schemes, such as DE or genetic algo-

There are other approaches to determining the initial population, although random equality is the most common. In current optimization problems, a possible solution parameter is added to the initial population in order to improve convergence.

## *3.5.2. Mutation*

Differential mutation adds a scale, random sampling, of a difference vector to a third vector. Mutant vectors, also called donors, are obtained through the differential mutation operation [50].

Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch… http://dx.doi.org/10.5772/intechopen.76666 23

**Figure 4.** PSO flow chart. Source: [46].

#### *3.5.3. Crossover*

The simple PSO cannot be applied directly to multi-objective optimization since there are two

The first one is how to select the best global and local particles (leaders) to guide the search, and the second one is how to keep good points found so far. For the latter, a secondary popu-

PSO is one of the modern heuristic algorithms suitable for solving large-scale non-converting optimization problems. It is a population-based search algorithm and parallel search using a

The main idea of the PSO is that "particles" (solutions) move through the search space with velocities that are adjusted dynamically according to their historical behavior. Therefore, the particles have a tendency to move to a better search area throughout the search process [47].

The DE algorithm was developed to be a promising heuristic optimization algorithm for numerical optimization problems. The DE was designed to meet the requirement of practical minimization techniques with consistent convergence to the global minimum in consecutive independent trials. It can solve non-differentiable, nonlinear functions and multimodal cost functions [48]. The DE algorithm is a simple stochastic optimization strategy. It uses a voracious and less stochastic approach with floating-point coding in problem solving, unlike other evolutionary algorithms [49]. DE uses the arithmetic operators to evolve from a randomly generated initial population to a final solution. Basically, the weighted difference between two individuals is added to a third individual in the population. Thus, no separate probability distribution has to be used, which makes the scheme completely self-organized [49]. There are several variant strategies of DE. In general expressions are divided into two parts: the first part represents a vector to be disturbed. The first part is "rand" (vector chosen at random) or "best" (best vector of the current population). The second part is the number of difference vectors (one or two) chosen for perturbation vectors of the first part, and the last part indicates the type of crossover to be used. The type of crossing can be "bin" (binomial) or "exp"

The initialization of DE can be done by randomly generating candidate solutions with *NP* 

There are other approaches to determining the initial population, although random equality is the most common. In current optimization problems, a possible solution parameter is

Differential mutation adds a scale, random sampling, of a difference vector to a third vector. Mutant vectors, also called donors, are obtained through the differential mutation operation [50].

*D*-dimensional vectors of real parameters evaluated [50].

added to the initial population in order to improve convergence.

issues to consider when extending PSO optimization to multi-objective problems [44].

lation is usually used to maintain non-dominated solutions.

group of particles [45].

(exponential) [49].

*3.5.1. Initialization*

*3.5.2. Mutation*

On **Figure 4**, the PSO flow chart is shown.

**3.5. Differential evolution (DE)**

22 Optimization and Control of Electrical Machines

The crossover increases the potential diversity of a population. In the case of binomial crossover, test vectors are produced. Crossover can be understood as a mutation rate or a probability of inheritance between successive generations. There are alternatives to binomial crossover. The most common is the exponential crossover. Both approaches are valid for all problems, although the success/improvement of one over the other varies according to the problem considered [50].

#### *3.5.4. Selection*

Selection can be understood as a form of competition, in line with many examples directly observable in nature. Many evolutionary optimization schemes, such as DE or genetic algorithms (GAs), use some form of selection.

For a selection operation, the selection of pairs, also called avid selection or elite selection, is constantly used in the algorithm. As a stopping criterion, a maximum number of generations is defined [50].

(20, 30, 40, 50, 60, 70, 80, and 100% of the total power). For each one of these regimes, the data of fuel consumption of each engine were taken, and then the curve of power vs. cost of fuel for each motor was plotted. For clarity is convenient to say that each consume data was measured 10 times and was chosen the main. In a similar way, it was done for the emission case. The engines were set to work with different power values, the data of the emissions of NO2, CO, CO2, SO2, etc., were collected, besides the total volume of the emissions of each engine, and the curves of power vs. emissions were also plotted. In this section, comparisons of results obtained with different approaches for the same case study are presented. There are many algorithms used for the economic environmental load dispatch [55]. Results are compared

Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch…

http://dx.doi.org/10.5772/intechopen.76666

25

All algorithms were programmed in MATLAB to simulate and compare them with the predefined case studies. Besides, the shutdown of less efficient motors in all these metaheuristic

**Table 3** shows the emission coefficients of 10 gas engines of the power plant used as a case study. The coefficients "a," "b," "c," "d," "e," and "f" were determined by operating the engines of the power plant at different powers, measuring the consumption and emissions to obtain the power versus cost and power vs. emission curves of each engine. The quadratic equation of each curve of each motor was obtained by the regression methods using MATLAB's tool box curve fitting. In the same way, the coefficients "d," "e," and "f" were

On **Table 4**, the coefficients of losses of the ten motors that make up the case study are presented. In this chapter a reduction to the transmission loss model is applied as a function of

On **Table 5** cost and emission results with all metaheuristic algorithms used for comparison in this chapter are shown. Among these algorithms, applied in a plant with ten generators,

, NOX, and SO<sup>2</sup>

emissions of each engine at

using the following algorithms:

• Particle swarm optimization

The comparison was made with the following data:

obtained but in this case by measuring the CO<sup>2</sup>

the output of the generators through the Kron loss coefficients [26].

• Number of power plant generators, 10 • Minimum power of generators, 0.56 MW • Maximum power of generators, 3.9 MW

• Dragonfly optimizer

• Simulated annealing • Ant lion optimizer

• Power demand, 20 MW

algorithms was implemented.

**4.1. Motor data**

different powers.

• NSGA II

## **3.6. Ant lion**

Ant lion optimizer (ALO) [51] is a new algorithm inspired by nature proposed by Seyedali Mirjalili in 2015. The ALO algorithm mimics the mechanism of ant hunting in nature. It uses five main stages of prey hunting, such as random walking of ants, building traps, trapping ants in traps, catching prey, and rebuilding traps. All these steps are implemented.

The ant lions belong to the class of insects with wings and nerves (Neuroptera). The life cycle of the ants includes two main phases: larvae and adults. A natural shelf life can take up to 3 years, which occurs mainly in larvae (3–5 weeks into adulthood). The ant lion undergoes a metamorphosis into a cocoon to become an adult.

They hunt primarily on larvae, and the adult period is for breeding. A larva of ant lion digs a well of cones into sand, moving along a circular path and throwing the sands with the massive jaw. After digging the trap, the larvae hide under the bottom of the cone and wait for the insects (preferably ants) to be trapped in the well. The edge of the cone is sharp enough so that the insects fall easily into the bottom of the trap. Once that ALO realizes that a prey is in the trap, it tries to catch it. This is one of the algorithms that are also used for EELD, and it is one of the most recent discoveries [52–54].

The ALO is governed by the following rules [51]:


## **4. Results of the comparison among all approaches applied to a case study**

The power plant selected for the case study consists of 10 gas engines Jenbacher J620. In order to take the data of the power plant, its 10 motors were placed to work at different powers (20, 30, 40, 50, 60, 70, 80, and 100% of the total power). For each one of these regimes, the data of fuel consumption of each engine were taken, and then the curve of power vs. cost of fuel for each motor was plotted. For clarity is convenient to say that each consume data was measured 10 times and was chosen the main. In a similar way, it was done for the emission case. The engines were set to work with different power values, the data of the emissions of NO2, CO, CO2, SO2, etc., were collected, besides the total volume of the emissions of each engine, and the curves of power vs. emissions were also plotted. In this section, comparisons of results obtained with different approaches for the same case study are presented. There are many algorithms used for the economic environmental load dispatch [55]. Results are compared using the following algorithms:

• NSGA II

For a selection operation, the selection of pairs, also called avid selection or elite selection, is constantly used in the algorithm. As a stopping criterion, a maximum number of generations

Ant lion optimizer (ALO) [51] is a new algorithm inspired by nature proposed by Seyedali Mirjalili in 2015. The ALO algorithm mimics the mechanism of ant hunting in nature. It uses five main stages of prey hunting, such as random walking of ants, building traps, trapping

The ant lions belong to the class of insects with wings and nerves (Neuroptera). The life cycle of the ants includes two main phases: larvae and adults. A natural shelf life can take up to 3 years, which occurs mainly in larvae (3–5 weeks into adulthood). The ant lion undergoes a

They hunt primarily on larvae, and the adult period is for breeding. A larva of ant lion digs a well of cones into sand, moving along a circular path and throwing the sands with the massive jaw. After digging the trap, the larvae hide under the bottom of the cone and wait for the insects (preferably ants) to be trapped in the well. The edge of the cone is sharp enough so that the insects fall easily into the bottom of the trap. Once that ALO realizes that a prey is in the trap, it tries to catch it. This is one of the algorithms that are also used for EELD, and it is one of the most recent discoveries [52–54].

**3.** Ant lions can build pits proportional to their fitness (the higher the fitness, the larger the pit). **4.** Size of the pits is proportional to the probability of catching prey. Hence, ant lions with

**5.** Each ant can be caught by an ant lion as well as the elite (fittest ant lion) in each iteration. **6.** When ants try to escape from the pit, the ant lions throw sand toward the top of the trap to slide the ants inside the bottom of the trap. In order to simulate this behavior of sliding

**7.** If an ant becomes fitter than an ant lion, this means that it is caught and pulled under the

**8.** After each hunt, an ant lion repositions itself to the latest caught prey and builds a pit to

The power plant selected for the case study consists of 10 gas engines Jenbacher J620. In order to take the data of the power plant, its 10 motors were placed to work at different powers

**4. Results of the comparison among all approaches applied to a case** 

ants toward ant lions, the range of random walk is decreased adaptively.

ants in traps, catching prey, and rebuilding traps. All these steps are implemented.

metamorphosis into a cocoon to become an adult.

The ALO is governed by the following rules [51]:

**2.** Random walks are affected by the traps of ant lions.

larger pits have higher probability to catch ants.

improve its chance of catching another prey.

sand by the ant lion.

**study**

**1.** Ants move around the search space using different random walks.

is defined [50].

24 Optimization and Control of Electrical Machines

**3.6. Ant lion**


The comparison was made with the following data:


All algorithms were programmed in MATLAB to simulate and compare them with the predefined case studies. Besides, the shutdown of less efficient motors in all these metaheuristic algorithms was implemented.

## **4.1. Motor data**

**Table 3** shows the emission coefficients of 10 gas engines of the power plant used as a case study.

The coefficients "a," "b," "c," "d," "e," and "f" were determined by operating the engines of the power plant at different powers, measuring the consumption and emissions to obtain the power versus cost and power vs. emission curves of each engine. The quadratic equation of each curve of each motor was obtained by the regression methods using MATLAB's tool box curve fitting. In the same way, the coefficients "d," "e," and "f" were obtained but in this case by measuring the CO<sup>2</sup> , NOX, and SO<sup>2</sup> emissions of each engine at different powers.

On **Table 4**, the coefficients of losses of the ten motors that make up the case study are presented. In this chapter a reduction to the transmission loss model is applied as a function of the output of the generators through the Kron loss coefficients [26].

On **Table 5** cost and emission results with all metaheuristic algorithms used for comparison in this chapter are shown. Among these algorithms, applied in a plant with ten generators,

#### 26 Optimization and Control of Electrical Machines


**M 1 2 3 4 5 6 7 8 9 10** 0.14 0.17 0.15 0.19 0.26 0.22 0.34 0.38 0.43 0.45 0.17 0.6 0.13 0.16 0.15 0.2 0.23 0.56 0.23 0.51 0.15 0.13 0.65 0.17 0.24 0.19 0.25 0.38 0.43 0.45 0.19 0.16 0.17 0.71 0.3 0.25 0.43 0.56 0.23 0.51 0.26 0.15 0.24 0.3 0.69 0.32 0.18 0.37 0.42 0.48 0.22 0.2 0.19 0.25 0.32 0.85 0.97 0.55 0.27 0.58 0.22 0.2 0.19 0.25 0.32 0.85 0.67 0.38 0.43 0.45 0.19 0.7 0.13 0.18 0.16 0.21 0.28 0.56 0.23 0.51 0.26 0.15 0.24 0.3 0.69 0.32 0.18 0.37 0.42 0.48 0.15 0.13 0.65 0.17 0.24 0.19 0.25 0.38 0.43 0.45

Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch…

http://dx.doi.org/10.5772/intechopen.76666

27

**Results SA DE DA NSGA II PSO ALO** Emission (m3/h) 1757,39 1769,48 1765,34 2098,12 2113,33 1763,55 Cost (\$/h) 1556,61 1545,59 1548,28 1709,47 1685,18 1549,93

Fonte: [1, 21].

**Table 4.** Loss coefficients (all values have to be multiplied by 1e-4).

**Table 5.** Comparative table with all costs and emissions.

**Table 6.** Comparison between all results of the different programmed algorithms.

**Table 2.** Cost coefficients from the thermal plant case study.


**Table 3.** Emission coefficients from the thermal power plant used as case study.

it is possible to notice that the SA has the lowest emission of pollutants with 1757.39 (m<sup>3</sup> /h), however with a cost of 1556.61 (\$/h), while the DE algorithm has the lowest cost with 1545.59 (\$/h), however with emission of pollutants with 1769.48 (m<sup>3</sup> /h).

The comparison of all the results of the different metaheuristic algorithms is provided in **Table 6**.

Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch… http://dx.doi.org/10.5772/intechopen.76666 27


**Table 4.** Loss coefficients (all values have to be multiplied by 1e-4).


**Table 5.** Comparative table with all costs and emissions.

it is possible to notice that the SA has the lowest emission of pollutants with 1757.39 (m<sup>3</sup>

(\$/h), however with emission of pollutants with 1769.48 (m<sup>3</sup>

**Table 3.** Emission coefficients from the thermal power plant used as case study.

Source: [1].

**Motor** *ci*

Source: [1, 21].

 **(\$/Mw^2)** *bi*

26 Optimization and Control of Electrical Machines

**Motor f e d** 0.00419 1.32767 73.85932 0.00419 0.32767 13.85932 0.00683 −0.54551 40.2669 0.00683 −0.54551 40.2669 0.00461 −0.51116 42.89553 0.00461 −0.51116 42.8955 0.00461 −0.51116 42.8955 0.00461 −0.51116 42.8955 0.00061 −0.51116 10.8955 0.00461 −0.51116 42.8955

**Table 2.** Cost coefficients from the thermal plant case study.

 **(\$/Mw)** *ai*

 0.007 7 240 0.66 3.35 0.0095 10 200 0.9 3.7 0.009 8.5 220 0.8 3.6 0.009 11 200 0.66 3.35 0.008 10.5 220 0.72 3.45 0.0075 12 120 0.66 2.97 0.0075 14 130 0.88 3.5 0.0075 14 130 0.754 3.33 0.0075 14 130 0.9 3.9 0.0075 14 130 0.56 2.35

**(\$)** *Pmin***(Mw)** *Pmax* **(Mw)**

however with a cost of 1556.61 (\$/h), while the DE algorithm has the lowest cost with 1545.59

The comparison of all the results of the different metaheuristic algorithms is provided in **Table 6**.

/h).

/h),


**Table 6.** Comparison between all results of the different programmed algorithms.

## **5. Conclusion**

The model was implemented in MATLAB computing. Usually all algorithms have presented good results, because in all cases it is possible to switch off at least two motors, but some differences among results of the different algorithms were evidenced. It was possible to notice vantages in relation to cost and emission of two methods among all of them. The SA achieves the lowest emission of pollutants, while DE obtained the lowest cost for the power plant of ten generating units.

[2] Zhou J, Wang C, Li Y, Wang P, Li C, Lu P, et al. A multi-objective multi-population ant colony optimization for economic emission dispatch considering power system security.

Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch…

http://dx.doi.org/10.5772/intechopen.76666

29

[3] Roy PK, Bhui S. A multi-objective hybrid evolutionary algorithm for dynamic economic emission load dispatch. International Transactions on Electrical Energy Systems.

[4] Modiri-Delshad M, Kaboli SHA, Taslimi-Renani E, Rahim NA. Backtracking search algorithm for solving economic dispatch problems with valve-point effects and multiple

[5] Granelli G, Montagna M, Pasini G, Marannino P. Emission constrained dynamic dis-

[6] Gonçalves E. Métodos híbridos de pontos interiores/exteriores e de aproximantes de funções em problemas multiobjetivo de despacho econômico e ambiental; 2015

[7] Krishnamurthy S, Tzoneva R, editors. Comparative analyses of Min-Max and Max-Max price penalty factor approaches for multi criteria power system dispatch problem with valve point effect loading using Lagrange's method. 2011 International Conference on

[8] Nascimento MHR, Nunes MVA, Rodríguez JLM, Leite JC, Junior JAB. New solution for resolution of the economic load dispatch by different mathematical optimization methods, turning off the less efficient generators. Journal of Engineering and Technology for

[9] De M, Das G, Mandal S, Mandal K. Investigating economic emission dispatch problem using improved particle swarm optimization technique. Industry Interactive Innovations

[10] Mason K, Duggan J, Howley E. Multi-objective dynamic economic emission dispatch using particle swarm optimisation variants. Neurocomputing. 2017;**270**(Suppl C):188-197

[11] Mohan M, Kuppusamy K, Khan MA. Optimal short-term hydrothermal scheduling using decomposition approach and linear programming method. International Journal

[12] Farag A, Al-Baiyat S, Cheng T. Economic load dispatch multiobjective optimization procedures using linear programming techniques. IEEE Transactions on Power Systems.

[13] Huang S-J. Enhancement of hydroelectric generation scheduling using ant colony system based optimization approaches. IEEE Transactions on Energy Conversion.

[14] Ma H, Yang Z, You P, Fei M. Multi-objective biogeography-based optimization for dynamic economic emission load dispatch considering plug-in electric vehicles charg-

Applied Mathematical Modelling. 2017;**45**:684-704

patch. Electric Power Systems Research. 1992;**24**(1):55-64

Power and Energy Systems; 2011:22-24 Dec. 2011

in Science, Engineering and Technology: Springer. 2018:37-45

of Electrical Power & Energy Systems. 1992;**14**(1):39-44

Industrial Applications. 2017;**03**:37-46

1995;**10**(2):731-738

2001;**16**(3):296-301

ing. Energy. 2017;**135**(Suppl C):101-111

fuel options. Energy. 2016;**116**:637-649

2016;**26**(1):49-78

## **Acknowledgements**

The Institute of Technology and Education "Galileo" from Amazonia (ITEGAM), the Federal University of Para (UFPA), the Research Support Foundation State of Amazonas (FAPEAM), and the National Council of Research (CNPq) Productivity of Research Funds Process 301105/2016-2 for the financial support to this research.

## **Author details**

Jorge de Almeida Brito Júnior<sup>1</sup> \*, Marcus Vinicius Alves Nunes<sup>2</sup> , Manoel Henrique Reis Nascimento<sup>1</sup> , Jandecy Cabral Leite<sup>1</sup> , Jorge Laureano Moya Rodriguez3 , Carlos Alberto Oliveira de Freitas1 , Milton Fonseca Júnior<sup>4</sup> , Edson Farias de Oliveira1 , David Barbosa de Alencar<sup>1</sup> , Nadime Mustafa Moraes<sup>5</sup> , Tirso Lorenzo Reyes Carvajal<sup>1</sup> and Haroldo Melo de Oliveira1

\*Address all correspondence to: jorge.brito@itegam.org.br

1 Research Department Institute of Technology and Education Galileo da Amazônia (ITEGAM), Manaus, Brazil

2 Faculty of Electrical Engineering Institute of Technology, Federal University of Para (UFPA), Belém, Pará, Brazil

3 Federal University of Bahia (UFBA), Bahia, Brazil

4 Department of Generation of Mauá, Eletrobrás Amazonas GT, Manaus, Amazonas, Brazil

5 University of the State of Amazonas (UEA), Manaus, Amazonas, Brazil

## **References**

[1] Júnior JAB, Nunes MVA, Nascimento MHR, et al. Solution to economic emission load dispatch by simulated annealing: Case study. Electrical Engineering. 2017. https://doi. org/10.1007/s00202-017-0544-0

[2] Zhou J, Wang C, Li Y, Wang P, Li C, Lu P, et al. A multi-objective multi-population ant colony optimization for economic emission dispatch considering power system security. Applied Mathematical Modelling. 2017;**45**:684-704

**5. Conclusion**

28 Optimization and Control of Electrical Machines

ten generating units.

**Author details**

Milton Fonseca Júnior<sup>4</sup>

Nadime Mustafa Moraes<sup>5</sup>

(ITEGAM), Manaus, Brazil

(UFPA), Belém, Pará, Brazil

**References**

Jorge de Almeida Brito Júnior<sup>1</sup>

Manoel Henrique Reis Nascimento<sup>1</sup>

Jorge Laureano Moya Rodriguez3

**Acknowledgements**

301105/2016-2 for the financial support to this research.

\*Address all correspondence to: jorge.brito@itegam.org.br

3 Federal University of Bahia (UFBA), Bahia, Brazil

org/10.1007/s00202-017-0544-0

The model was implemented in MATLAB computing. Usually all algorithms have presented good results, because in all cases it is possible to switch off at least two motors, but some differences among results of the different algorithms were evidenced. It was possible to notice vantages in relation to cost and emission of two methods among all of them. The SA achieves the lowest emission of pollutants, while DE obtained the lowest cost for the power plant of

The Institute of Technology and Education "Galileo" from Amazonia (ITEGAM), the Federal University of Para (UFPA), the Research Support Foundation State of Amazonas (FAPEAM), and the National Council of Research (CNPq) Productivity of Research Funds Process

\*, Marcus Vinicius Alves Nunes<sup>2</sup>

, Jandecy Cabral Leite<sup>1</sup>

, Edson Farias de Oliveira1

5 University of the State of Amazonas (UEA), Manaus, Amazonas, Brazil

, Tirso Lorenzo Reyes Carvajal<sup>1</sup>

1 Research Department Institute of Technology and Education Galileo da Amazônia

2 Faculty of Electrical Engineering Institute of Technology, Federal University of Para

4 Department of Generation of Mauá, Eletrobrás Amazonas GT, Manaus, Amazonas, Brazil

[1] Júnior JAB, Nunes MVA, Nascimento MHR, et al. Solution to economic emission load dispatch by simulated annealing: Case study. Electrical Engineering. 2017. https://doi.

, Carlos Alberto Oliveira de Freitas1

,

, David Barbosa de Alencar<sup>1</sup>

,

and Haroldo Melo de Oliveira1

,

,


[15] Liu Hd, Ma Zl, Liu S, Lan H, editors. A new solution to economic emission load dispatch using immune genetic algorithm. 2006 IEEE Conference on Cybernetics and Intelligent Systems; 2006 7-9 June 2006

[29] Wong K, Fung C, editors. Simulated annealing based economic dispatch algorithm. IEE

Multi-Objective Optimization Techniques to Solve the Economic Emission Load Dispatch…

http://dx.doi.org/10.5772/intechopen.76666

31

[30] Ziane I, Benhamida F, Amel G. Simulated annealing optimization for multi-objective economic dispatch solution. Leonardo Journal of Sciences. 2014;**13**(25):43-56

[31] Abul'Wafa AR. Optimization of economic/emission load dispatch for hybrid generating systems using controlled elitist NSGA-II. Electric Power Systems Research.

[32] Basu M. Combined heat and power economic emission dispatch using nondominated sorting genetic algorithm-II. International Journal of Electrical Power & Energy Systems.

[33] Cococcioni M, Lazzerini B, Marcelloni F, Pistolesi F, editors. Solving the environmental economic dispatch problem with prohibited operating zones in microgrids using NSGA-II and TOPSIS. Proceedings of the 31st Annual ACM Symposium on Applied

[34] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation. 2002;**6**(2):182-197

[35] Golchha A, Qureshi SG. Non-dominated sorting genetic algorithm-II – A succinct survey. International Journal of Computer Science and Information Technologies - (IJCSIT).

[36] Kalaivani L, Subburaj P, Willjuice Iruthayarajan M. Speed control of switched reluctance motor with torque ripple reduction using non-dominated sorting genetic algorithm (NSGA-II). International Journal of Electrical Power & Energy Systems. 2013;**53**:69-77

[37] Golchha A, Qureshi SG. Non-dominated sorting genetic algorithm-II–A succinct survey. International Journal of Computer Science and Information Technologies.

[38] Suksonghong K, Boonlong K, Goh K-L. Multi-objective genetic algorithms for solving portfolio optimization problems in the electricity Market. Electrical Power and Energy

[39] Liu T, Gao X, Wang L. Multi-objective optimization method using an improved NSGA-II algorithm for oil–gas production process. Journal of the Taiwan Institute of Chemical

[40] Mirjalili S. Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Computing and

[41] Zolghadr-Asli B, Bozorg-Haddad O, Chu X. Dragonfly Algorithm (DA). Advanced

[42] Bozorg-Haddad O.Advanced Optimization by Nature-Inspired Algorithms. Springer; 2018

Optimization by Nature-Inspired Algorithms. Springer; 2018. pp. 151-159

proceedings C (generation, transmission and distribution). IET; 1993

2013;**105**:142-151

2013;**53**:135-141

Computing. ACM; 2016

2015;**6**(1):252-255

2015;**6**(1):252-255

Engineers 2015(0)

Systems, Elsevier Ltd All rights reserved; 2014

Applications. 2016;**27**(4):1053-1073


[29] Wong K, Fung C, editors. Simulated annealing based economic dispatch algorithm. IEE proceedings C (generation, transmission and distribution). IET; 1993

[15] Liu Hd, Ma Zl, Liu S, Lan H, editors. A new solution to economic emission load dispatch using immune genetic algorithm. 2006 IEEE Conference on Cybernetics and Intelligent

[16] Damousis IG, Bakirtzis AG, Dokopoulos PS. Network-constrained economic dispatch using real-coded genetic algorithm. IEEE Transactions on Power Systems.

[17] Kumarappan N, Mohan MR, editors. Hybrid genetic algorithm based combined economic and emission dispatch for utility system. International Conference on Intelligent

[18] Momoh JA, Reddy SS, editors. Combined Economic and Emission Dispatch using Radial Basis Function. 2014 IEEE PES General Meeting | Conference & Exposition; 2014 27-31

[19] Jebaraj L, Venkatesan C, Soubache I. Rajan CCA. Application of differential evolution algorithm in static and dynamic economic or emission dispatch problem: A review.

[20] Chatterjee A, Ghoshal S, Mukherjee V. Solution of combined economic and emission dispatch problems of power systems by an opposition-based harmony search algorithm.

[21] Nascimento MHR, Nunes MVA, Rodríguez JLM, et al. A new solution to the economical load dispatch of power plants and optimization using differential evolution. Electrical

[22] Basu M. Fuel constrained economic emission dispatch using nondominated sorting

[23] Miranda V, Hang PS. Economic dispatch model with fuzzy wind constraints and attitudes of dispatchers. IEEE Transactions on Power Systems. 2005;**20**(4):2143-2145 [24] Nwulu NI, Xia X. Multi-objective dynamic economic emission dispatch of electric power generation integrated with game theory based demand response programs. Energy

[25] Ashish D, Arunesh D, Surya P, Bhardwaj AK. A traditional approach to solve economic load dispatch problem of thermal generating unit using MATLAB programming. International Journal of Engineering Research & Technology (IJERT). 2013;**2**(9):2013 [26] Wang L, Singh C. Environmental/economic power dispatch using a fuzzified multiobjective particle swarm optimization algorithm. Electric Power Systems Research.

[27] Kamboj VK, Bath S, Dhillon J. Solution of non-convex economic load dispatch problem

[28] Fraga-Gonzalez LF, Fuentes-Aguilar RQ, Garcia-Gonzalez A, Sanchez-Ante G. Adaptive simulated annealing for tuning PID controllers. AI Communications. 2017;**30**(5):347-362

using Grey wolf optimizer. Neural Computing and Applications. 2015:1-16

Renewable and Sustainable Energy Reviews. 2017;**77**(Suppl C):1206-1220

International Journal of Electrical Power & Energy Systems. 2012;**39**(1):9-20

Engineering. 2017;**99**:561. https://doi.org/10.1007/s00202-016-0385-2

genetic algorithm-II. Energy. 2014;**78**:649-664

Conversion and Management 2015;**89**(0):963-974

2007;**77**(12):1654-1664

Sensing and Information Processing, 2004 Proceedings of; 2004

Systems; 2006 7-9 June 2006

30 Optimization and Control of Electrical Machines

2003;**18**(1):198-205

July 2014


[43] Daely PT, Shin SY, editors. Range based wireless node localization using dragonfly algorithm. Ubiquitous and Future Networks (ICUFN), 2016 Eighth International Conference on. IEEE; 2016

**Chapter 3**

Provisional chapter

**Optimal Design of Brushless Doubly Fed Reluctance**

DOI: 10.5772/intechopen.74805

Optimization techniques are widely used in the design of electrical machines to obtain maximum performance at minimal capital cost. After a brief overview of some of the optimization techniques employed in electrical machine design, this chapter highlights the features of brushless doubly fed reluctance machine (BDFRM) and its optimal design. The simple and robust construction, variable speed operation, better performance compared to traditional counterpart, and requirement of partially rated converter for speed control have made BDFRM an attractive alternative for variable speed applications such as pumps, blower, and wind generators. Due to unusual construction of BDFRM, conventional design procedures cannot be applied. A few critical issues in the design of BDFRM that greatly affect its performance are discussed. Design optimization is performed using nonlinear programming technique for 6-4-2 pole reluctance rotor and 8-6-4 pole ducted rotor configurations of BDFRM. 2 kW prototypes are then constructed for laboratory use. The performance of the prototypes is examined through finite element analysis (FEA)

Keywords: optimization, nonlinear programming, objective function, BDFRM, optimal

Many industrial applications demand efficient, robust, and cost-effective variable speed drives. Brushless doubly fed reluctance machine (BDFRM) is one of the better alternatives for induction motors due to simple and rugged construction, higher efficiency, absence of rotor winding, slip rings and brushes, and reduced maintenance cost. Last but not least, a partially

> © 2016 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 eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. 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.

employing Maxwell 16 software. The test results are also presented.

design of BDFRM, finite element analysis

Optimal Design of Brushless Doubly Fed Reluctance

Mandar Bhawalkar, Gopalakrishnan Narayan and

Mandar Bhawalkar, Gopalakrishnan Narayan and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74805

**Machine**

Machine

Yogesh Nerkar

Yogesh Nerkar

Abstract

1. Introduction


#### **Optimal Design of Brushless Doubly Fed Reluctance Machine** Optimal Design of Brushless Doubly Fed Reluctance Machine

DOI: 10.5772/intechopen.74805

Mandar Bhawalkar, Gopalakrishnan Narayan and Yogesh Nerkar Mandar Bhawalkar, Gopalakrishnan Narayan and Yogesh Nerkar

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74805

#### Abstract

[43] Daely PT, Shin SY, editors. Range based wireless node localization using dragonfly algorithm. Ubiquitous and Future Networks (ICUFN), 2016 Eighth International Conference

[44] Zhoua A, Bo-Yang Q, Shi-Zheng HLZ, Nagaratnam SP, Qingfu Z. Multiobjective evolutionary algorithms: A survey of the state of the art. Elsevier BV All rights reserved,

[45] Park JB, Jeong YW, Shin JR, Lee KY. An improved particle swarm optimization for nonconvex economic dispatch problems. IEEE Transactions on Power Systems.

[46] Armaghani DJ, Hajihassani M, Mohamad ET, Marto A, Noorani S. Blasting-induced flyrock and ground vibration prediction through an expert artificial neural network based on particle swarm optimization. Arabian Journal of Geosciences. 2014;**7**(12):5383-5396 [47] Idoumghar L, Chérin N, Siarry P, Roche R, Miraoui A.Hybrid ICA–PSO algorithm for continuous optimization. Applied Mathematics and Computation. 2013;**219**(24):11149-11170

[48] Behera S, Sahoo S, Pati BB. A review on optimization algorithms and application to wind energy integration to grid. Renewable and Sustainable Energy Reviews. 2015;**48**:214-227

[49] Coelho LS, Bora TC, Mariani VC. Differential evolution based on truncated Lévy-type flights and population diversity measure to solve economic load dispatch problems.

[50] Roque CMC, Martins PALS. Differential evolution for optimization of functionally

[52] Raju M, Saikia LC, Sinha N. Automatic generation control of a multi-area system using ant lion optimizer algorithm based PID plus second order derivative controller.

[53] Kamboj VK, Bhadoria A, Bath S. Solution of non-convex economic load dispatch problem for small-scale power systems using ant lion optimizer. Neural Computing and

[54] Mirjalili S, Jangir P, Saremi S. Multi-objective ant lion optimizer: A multi-objective optimization algorithm for solving engineering problems. Applied Intelligence. 2017;**46**(1):

[55] Qu B, Zhu Y, Jiao Y, Wu M, Suganthan P, Liang J. A survey on multi-objective evolutionary algorithms for the solution of the environmental/economic dispatch problems.

International Journal of Electrical Power & Energy Systems. 2014;**57**:178-188

[51] Mirjalili S. The ant lion optimizer. Advances in Engineering Software. 2015;**83**:80-98

International Journal of Electrical Power & Energy Systems. 2016;**80**:52-63

graded beams. Composite Structures. 2015;**133**:1191-1197

Applications. 2017;**28**(8):2181-2192

Swarm and Evolutionary Computation;**2017**

79-95

on. IEEE; 2016

32 Optimization and Control of Electrical Machines

2010;**25**(1):156-166

Swarm and Evolutionary Computation; 2011

Optimization techniques are widely used in the design of electrical machines to obtain maximum performance at minimal capital cost. After a brief overview of some of the optimization techniques employed in electrical machine design, this chapter highlights the features of brushless doubly fed reluctance machine (BDFRM) and its optimal design. The simple and robust construction, variable speed operation, better performance compared to traditional counterpart, and requirement of partially rated converter for speed control have made BDFRM an attractive alternative for variable speed applications such as pumps, blower, and wind generators. Due to unusual construction of BDFRM, conventional design procedures cannot be applied. A few critical issues in the design of BDFRM that greatly affect its performance are discussed. Design optimization is performed using nonlinear programming technique for 6-4-2 pole reluctance rotor and 8-6-4 pole ducted rotor configurations of BDFRM. 2 kW prototypes are then constructed for laboratory use. The performance of the prototypes is examined through finite element analysis (FEA) employing Maxwell 16 software. The test results are also presented.

Keywords: optimization, nonlinear programming, objective function, BDFRM, optimal design of BDFRM, finite element analysis

## 1. Introduction

Many industrial applications demand efficient, robust, and cost-effective variable speed drives. Brushless doubly fed reluctance machine (BDFRM) is one of the better alternatives for induction motors due to simple and rugged construction, higher efficiency, absence of rotor winding, slip rings and brushes, and reduced maintenance cost. Last but not least, a partially

© 2016 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 eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. 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.

rated converter is sufficient for control of speed in either direction of rated speed [1, 2]. These benefits are useful to BDFRM in generator mode in wind power applications.

The fierce competition in world market, increasing cost of energy supplies, and regulations for conservation of energy and resources are the key forces for design optimization of electrical machines. Electrical machine design is a complex process which can be realized as articulation or formulation subjected to restrictions imposed by various factors such as nonlinear characteristic of different material compositions, performance parameters, etc. and ability to achieve acceptable performance. The expected outcome of optimization is to minimize the capital and running costs and increased service life [3, 4]. The optimization is aimed at getting desirable solution of objective function(s) to maximize performance subjected to constraints. The design by analysis is based on estimation of performance of a machine from known variables and their inter-dependability. The known variables are usually design specifications or system parameters. In the design, the desired performance parameters are substituted in realistic mathematical model of machine which is then solved iteratively. However, the range of acceptable solutions may not necessarily yield optimum results with respect to cost, material requirements, and other factors, and hence machine design problem is linked to optimization and needs to be solved iteratively.

The organization of this chapter is as follows: Section 2 presents an overview of optimization techniques, and Section 3 gives a brief introduction to BDFRM to develop better understanding of machine. Section 4 discusses design considerations of BDFRM. An objective function is developed to minimize the active material requirements. Nonlinear programming is carried out for the optimal design of BDFRM. Section 5 presents the development of 2 kW prototypes. Section 6 discusses simulation results using Maxwell 16 (finite element software). This followed by test results of prototypes in Section 7. Section 8 presents conclusions.

## 2. Overview of optimization techniques

The optimization problems can be classified [5] as shown in Table 1. The classification of optimization problem depends on the nature of problem, operational constraints, and design limitations. The selection of algorithm for solving optimal problem depends not only on the types of objective function used but also on how its first and second derivatives are computed.

The optimization methods can be further classified broadly as classical methods and recent or advanced methods. The classical methods use continuous and differentiable functions [5], and these methods include single variable and multivariable optimization with and without constraints. Depending on the nature of objective function and design variables, optimization problem can be linear or nonlinear optimization with or without constraints. There is an inexhaustive list of different optimization techniques used for different applications looking into the aspects of various design/operational/environmental constraints. These methods are

given in Table 2 [3–9]. Classical optimization methods are found wanting due to increasing complexities, inter-dependability of design variables, and constraint functions. Therefore, nonlinear optimization methods with constraints are widely used along with newer methods

such as genetic algorithms, artificial neural networks, and fuzzy logic techniques.

design, Latin hypercube design

Based on Classification

Table 1. Classification of optimization problems.

One-dimensional nonlinear programing (NLP)

Table 2. Different optimization techniques.

Optimization Optimization methods

Existence of constraints Unconstrained/constrained optimization Nature of design variables Static/dynamic/trajectory optimization

Nature of variables Deterministic/stochastic programming Separable functions Separable/non-separable programming Number of objective functions Single objective/multiobjective programming

Fibonacci method, golden section search

Constrained NLP Direct methods—random search, heuristic search, complex, objective and constraint

Advanced optimization methods Geometric programming, dynamic programming, integer programming, stochastic

Jeeves, Rosenbrock, and simplex

Equations involved and objective function Linear/nonlinear/geometric/quadratic programming Permissible values of the design variables Integer programming/real-valued programming

Elimination methods—unrestricted search, exhaustive search, dichotomous search,

Optimal Design of Brushless Doubly Fed Reluctance Machine

http://dx.doi.org/10.5772/intechopen.74805

35

Descent methods—steepest descent, Fletcher-Reeves, Newton, Marquardt, quasi-Newton, Davidon-Fletcher-Powell, and Broyden-Fletcher-Goldfarb-Shanno

approximation, sequential linear programming, sequential quadratic programming, method of feasible directions, Zoutendijk, Rosen's gradient projection, generalized

minimization, interior penalty, exterior penalty, and augmented Lagrange multiplier

programming, simulated annealing method, genetic algorithm, artificial neural network, fuzzy system, particle swarm optimization, differential algorithm, filled function method, evolutionary algorithms, design of experiments—central composite

Indirect methods—transformation of variables, sequential unconstrained

Interpolation methods—quadratic interpolation, cubic interpolation Direct root methods—Newton, quasi-Newton, and Secant NLP with no constraint Direct search—random search, grid search, univariate, pattern search, Powell, Hooke-

Physical structure of problem Optimal/nonoptimal control

Classical Single variable, multivariable with or without constraints

LP Simplex, revised simplex, dual simplex method

reduced gradient


Table 1. Classification of optimization problems.

rated converter is sufficient for control of speed in either direction of rated speed [1, 2]. These

The fierce competition in world market, increasing cost of energy supplies, and regulations for conservation of energy and resources are the key forces for design optimization of electrical machines. Electrical machine design is a complex process which can be realized as articulation or formulation subjected to restrictions imposed by various factors such as nonlinear characteristic of different material compositions, performance parameters, etc. and ability to achieve acceptable performance. The expected outcome of optimization is to minimize the capital and running costs and increased service life [3, 4]. The optimization is aimed at getting desirable solution of objective function(s) to maximize performance subjected to constraints. The design by analysis is based on estimation of performance of a machine from known variables and their inter-dependability. The known variables are usually design specifications or system parameters. In the design, the desired performance parameters are substituted in realistic mathematical model of machine which is then solved iteratively. However, the range of acceptable solutions may not necessarily yield optimum results with respect to cost, material requirements, and other factors, and hence machine design problem

The organization of this chapter is as follows: Section 2 presents an overview of optimization techniques, and Section 3 gives a brief introduction to BDFRM to develop better understanding of machine. Section 4 discusses design considerations of BDFRM. An objective function is developed to minimize the active material requirements. Nonlinear programming is carried out for the optimal design of BDFRM. Section 5 presents the development of 2 kW prototypes. Section 6 discusses simulation results using Maxwell 16 (finite element software). This

The optimization problems can be classified [5] as shown in Table 1. The classification of optimization problem depends on the nature of problem, operational constraints, and design limitations. The selection of algorithm for solving optimal problem depends not only on the types of objective function used but also on how its first and second derivatives are

The optimization methods can be further classified broadly as classical methods and recent or advanced methods. The classical methods use continuous and differentiable functions [5], and these methods include single variable and multivariable optimization with and without constraints. Depending on the nature of objective function and design variables, optimization problem can be linear or nonlinear optimization with or without constraints. There is an inexhaustive list of different optimization techniques used for different applications looking into the aspects of various design/operational/environmental constraints. These methods are

followed by test results of prototypes in Section 7. Section 8 presents conclusions.

benefits are useful to BDFRM in generator mode in wind power applications.

34 Optimization and Control of Electrical Machines

is linked to optimization and needs to be solved iteratively.

2. Overview of optimization techniques

computed.


Table 2. Different optimization techniques.

given in Table 2 [3–9]. Classical optimization methods are found wanting due to increasing complexities, inter-dependability of design variables, and constraint functions. Therefore, nonlinear optimization methods with constraints are widely used along with newer methods such as genetic algorithms, artificial neural networks, and fuzzy logic techniques.

In the optimal design of electrical machines, the model of problem to be solved is to be selected along with choice of algorithms, variables, constraint functions, and objective functions. The classical methods such as random search method, simplex method, Hooke and Jeeves method, Powell and David-Fletcher-Powell method, and penalty function methods have been used in earlier decades. Most of them are nonlinear programing types as nonlinearities are imposed due to materials, operational issues, etc. Mathematically, these problems can be stated as.

$$\text{minimize} f(\mathbf{X}) \tag{1}$$

3. Brushless doubly fed reluctance machine (BDFRM)

number of poles on rotor and stator is given by Eq. (3):

windings, and representation of air gap by sine function.

control winding, respectively.

Figure 1. Schematic representation of BDFRM.

A BDFRM consists of two sets of three-phase sinusoidally distributed windings with 2p and 2q poles (p 6¼ q) embedded in the same slots of stator. The rotor has no winding. However, the

The schematic representation of BDFRM is shown in Figure 1. One of the two windings on stator is called as power/main winding, and the other is known as control/secondary winding. There is no direct magnetic coupling between two windings [1, 2]. The interaction between two windings takes place through rotor only. The power winding is directly excited by grid having frequency 50/60 Hz. The main role of power winding is to set up a magnetic field in the machine and deals with power exchange with grid. The control winding is excited by variable frequency, variable voltage obtained from a power electronic converter, or any other dedicated source. This winding controls torque developed and operating speed of the BDFRM. When two windings are excited, the MMFs are set up along the air gap. The MMFs Fp and Fc are the functions of rotor position where Fp and Fc are MMFS of power and

The interaction of two MMFs produces resultant air gap flux density and is responsible for development of electromagnetic torque which can be obtained analytically assuming infinite permeability of magnetic circuit, uniformly distributed windings, sinusoidal currents through

The MMFs produced by these two windings are given by Eqs. (4) and (5), and the spatial

Fp <sup>θ</sup>mg <sup>¼</sup> Fmp cos <sup>ω</sup>pt � <sup>p</sup>θmg <sup>þ</sup> <sup>φ</sup><sup>p</sup>

Fc <sup>θ</sup>mg <sup>¼</sup> Fmc cos <sup>ω</sup>ct � <sup>q</sup>θmg <sup>þ</sup> <sup>φ</sup><sup>c</sup> � <sup>α</sup>

distribution of power winding and control winding MMFs is shown in Figure 2:

Pr ¼ ð Þ p þ q (3)

Optimal Design of Brushless Doubly Fed Reluctance Machine

http://dx.doi.org/10.5772/intechopen.74805

37

(4)

(5)

$$\text{A subjected to } \operatorname{g}(\mathbf{X}) \succeq \mathbf{0} \tag{2}$$

where X is an n-dimensional vector, f(X) is an objective function, and g(X) represents design constraints. The bounded region enclosed by g(X) = 0 where X is feasible.

The multiobjective function optimization problems are more complex as the feasible solutions are conflicting and practically impossible to obtain optimal solution to all objective functions simultaneously. Hence, a set solutions providing tradeoff between objective functions are acceptable.

The recent methods such as differential evolutions (DE), genetic algorithms (GA), evolutionary algorithms (EA), and particle swarm optimization (PSO) are used in machine design optimization [7–9]. These methods use a set of populations as initial approximation unlike classical method and are stochastic in nature. As these methods can optimize nonlinear functions containing continuous and discrete variables, they are the most suited ones for machine design problems. A recent study [7] has shown that DE may not be always the fastest, but produces the best results. GA is based on principles of natural genetics and natural selection. It encodes parameters as bit string, and then manipulation is performed using logical operators [10]. Another technique design of experiments (DoE) is a statistical method that effectively quantifies the effect of changes in design variables or machine response. This method includes one factor at a time and is suitable for a limited number of variables. Hence, advanced DoE methods such as central composite design (CCD) and Latin hypercube design (LHD) are used [7]. EA encodes parameters as floating point arithmetic operators. These methods are usually linked to finite element analysis solvers to optimize the machine design. PSO is also gaining importance in electrical machine design as it is used to get appropriate fitness evaluation function, which represents the relationship between design variables and machine response. In PSO the potential solution (particles) flies through the problem space by following the current optimum particles after initialization with random particles. In addition ANN and fuzzy logic are also gaining wide-scale acceptance. ANN is used due its immense computational powers. Appropriate selection of network topology and layers is very important. This method also needs voluminous data for training neural networks. ANN can be trained to learn the relationship between input and output parameters of electrical machines [11]. Fuzzy logic is also being tried out for electrical machine design [12]. The fuzzy sets are formed from decision and controlled variables. A qualitative approach is used for deriving membership and objective functions. A combination of stochastic method such as such as neuro-fuzzy, fuzzy, and genetic algorithm is also used in optimization [13].

## 3. Brushless doubly fed reluctance machine (BDFRM)

In the optimal design of electrical machines, the model of problem to be solved is to be selected along with choice of algorithms, variables, constraint functions, and objective functions. The classical methods such as random search method, simplex method, Hooke and Jeeves method, Powell and David-Fletcher-Powell method, and penalty function methods have been used in earlier decades. Most of them are nonlinear programing types as nonlinearities are imposed due to materials, operational issues, etc. Mathematically, these problems can be stated as.

where X is an n-dimensional vector, f(X) is an objective function, and g(X) represents design

The multiobjective function optimization problems are more complex as the feasible solutions are conflicting and practically impossible to obtain optimal solution to all objective functions simultaneously. Hence, a set solutions providing tradeoff between objective functions are

The recent methods such as differential evolutions (DE), genetic algorithms (GA), evolutionary algorithms (EA), and particle swarm optimization (PSO) are used in machine design optimization [7–9]. These methods use a set of populations as initial approximation unlike classical method and are stochastic in nature. As these methods can optimize nonlinear functions containing continuous and discrete variables, they are the most suited ones for machine design problems. A recent study [7] has shown that DE may not be always the fastest, but produces the best results. GA is based on principles of natural genetics and natural selection. It encodes parameters as bit string, and then manipulation is performed using logical operators [10]. Another technique design of experiments (DoE) is a statistical method that effectively quantifies the effect of changes in design variables or machine response. This method includes one factor at a time and is suitable for a limited number of variables. Hence, advanced DoE methods such as central composite design (CCD) and Latin hypercube design (LHD) are used [7]. EA encodes parameters as floating point arithmetic operators. These methods are usually linked to finite element analysis solvers to optimize the machine design. PSO is also gaining importance in electrical machine design as it is used to get appropriate fitness evaluation function, which represents the relationship between design variables and machine response. In PSO the potential solution (particles) flies through the problem space by following the current optimum particles after initialization with random particles. In addition ANN and fuzzy logic are also gaining wide-scale acceptance. ANN is used due its immense computational powers. Appropriate selection of network topology and layers is very important. This method also needs voluminous data for training neural networks. ANN can be trained to learn the relationship between input and output parameters of electrical machines [11]. Fuzzy logic is also being tried out for electrical machine design [12]. The fuzzy sets are formed from decision and controlled variables. A qualitative approach is used for deriving membership and objective functions. A combination of stochastic method such as such as neuro-fuzzy,

constraints. The bounded region enclosed by g(X) = 0 where X is feasible.

fuzzy, and genetic algorithm is also used in optimization [13].

acceptable.

36 Optimization and Control of Electrical Machines

minimize f Xð Þ (1)

subjected to g Xð Þ ≥ 0 (2)

A BDFRM consists of two sets of three-phase sinusoidally distributed windings with 2p and 2q poles (p 6¼ q) embedded in the same slots of stator. The rotor has no winding. However, the number of poles on rotor and stator is given by Eq. (3):

$$P\_r = (p+q) \tag{3}$$

The schematic representation of BDFRM is shown in Figure 1. One of the two windings on stator is called as power/main winding, and the other is known as control/secondary winding. There is no direct magnetic coupling between two windings [1, 2]. The interaction between two windings takes place through rotor only. The power winding is directly excited by grid having frequency 50/60 Hz. The main role of power winding is to set up a magnetic field in the machine and deals with power exchange with grid. The control winding is excited by variable frequency, variable voltage obtained from a power electronic converter, or any other dedicated source. This winding controls torque developed and operating speed of the BDFRM. When two windings are excited, the MMFs are set up along the air gap. The MMFs Fp and Fc are the functions of rotor position where Fp and Fc are MMFS of power and control winding, respectively.

The interaction of two MMFs produces resultant air gap flux density and is responsible for development of electromagnetic torque which can be obtained analytically assuming infinite permeability of magnetic circuit, uniformly distributed windings, sinusoidal currents through windings, and representation of air gap by sine function.

The MMFs produced by these two windings are given by Eqs. (4) and (5), and the spatial distribution of power winding and control winding MMFs is shown in Figure 2:

$$F\_p\left(\theta\_{\text{mg}}\right) = F\_{\text{mp}}\cos\left(\omega\_p t - p\theta\_{\text{mg}} + q\_p\right) \tag{4}$$

$$F\_c \left( \theta\_{\text{mg}} \right) = F\_{\text{mc}} \cos \left( \omega\_c t - \eta \Theta\_{\text{mg}} + \varphi\_c - \alpha \right) \tag{5}$$

Figure 1. Schematic representation of BDFRM.

Figure 2. MMFs of power and control windings.

The resultant MMF acting along the air gap in BDFRM is the sum of MMFs produced by power and control windings. The interaction of two MMFs through rotor results in modulation of flux densities of both windings. These flux densities have fundamental frequency component along with two sidebands. Or, it can be interpreted that sinusoidal MMFs produced by two windings get modulated into a fundamental and two sidebands through inverse air gap function. The modulated frequency components are also time dependent and have spatial coordinates. Further, the coupling between two windings is decided by the pole numbers and sideband frequency component. The condition for torque production is that there is coupling between sidebands of one of the windings with fundamental frequency component of other windings. One of the sideband frequencies of power winding linking with fundamental frequency of control winding is given by Eq. (6):

$$
\omega\_m = \left(\omega\_\mathbf{p} + \omega\_\mathbf{c}\right) / \mathbf{P\_r} \tag{6}
$$

4. Design considerations in BDFRM

wound for different poles in stator?

and rotor core?

netic pull?

The reluctance machine has higher leakage inductances which lead to poor operational power factor. Incorporation of advanced rotors that orient flux in the preferred direction can improve the power factor [2, 14]. The other issues are smaller torque density and larger torque pulsation which can be improved by a careful design of BDFRM with higher saliency ratio. There are several considerations in design of BDFRM; the main issues are highlighted below [15, 16]: 1. What is the basis of selection of specific electric and magnetic loadings and stator slots?

Optimal Design of Brushless Doubly Fed Reluctance Machine

http://dx.doi.org/10.5772/intechopen.74805

39

3. Should there be two independent windings wound for different poles or one winding

6. What will be the practical range of control winding frequency and control winding voltage?

8. Is there any possibility of reduction of space harmonics, noise, losses in stator windings,

9. How to reduce or mitigate bearing currents due to PWM inverters and unbalanced mag-

The selection of specific loadings depends on permissible losses, overload capacity, magnetic saturation, forces acting on rotor surface, etc. Selection of the number of stator slots and rotor ducts is very important in elimination of space harmonics in resultant MMF waveform. As the resultant MMF wave along the air gap is superposition of two MMFs, it has large space

Proper selection of the number of poles on stator and rotor decides the magnetic coupling between stator and rotor which governs the torque production. The higher the coupling

hsp hsq

2. What are the criteria for the choice of the number of poles in stator and on rotor?

5. Which of the two windings should be selected as power winding/control winding?

7. Should the choice of air gap length based on magnetic pull or any other factor?

harmonics. Table 3 gives suitable combinations of stator slots and rotor ducts.

coefficient, the higher the torque production. This can be inferred from Figure 3.

S. no. Stator slots Rotor ducts Lower-order space harmonics

 48 54 104 104 48 60 52 56 48 66 136 140 48 72 136 140

Table 3. Minimum number of space harmonics for same stator and rotor slots [17, 18].

4. Do the stator windings have to be full pitched or short pitched?

The space phasor voltage equations of BDFRM are used to get electromagnetic torque Te developed which is given by Eq. (7):

$$T\_e = (3/2)(p+q)\left(\psi\_{dc}\dot{\imath}\_{qc} - \psi\_{qc}\dot{\imath}\_{dc}\right) \tag{7}$$

Three distinct modes of operations are possible depending upon the frequency of control winding:


BDFRM is therefore potentially useful as a variable speed drive.

## 4. Design considerations in BDFRM

The resultant MMF acting along the air gap in BDFRM is the sum of MMFs produced by power and control windings. The interaction of two MMFs through rotor results in modulation of flux densities of both windings. These flux densities have fundamental frequency component along with two sidebands. Or, it can be interpreted that sinusoidal MMFs produced by two windings get modulated into a fundamental and two sidebands through inverse air gap function. The modulated frequency components are also time dependent and have spatial coordinates. Further, the coupling between two windings is decided by the pole numbers and sideband frequency component. The condition for torque production is that there is coupling between sidebands of one of the windings with fundamental frequency component of other windings. One of the sideband frequencies of power winding linking with fundamental frequency of control winding is given by

ω<sup>m</sup> ¼ ω<sup>p</sup> þ ω<sup>c</sup>

The space phasor voltage equations of BDFRM are used to get electromagnetic torque Te

Te ¼ ð Þ 3=2 ð Þ p þ q ψdciqc–ψqcidc

Three distinct modes of operations are possible depending upon the frequency of control

1. If ω<sup>c</sup> = 0, control winding excitation is dc, and the machine operates as a conventional

2. If ω<sup>c</sup> > 0, this results in super synchronous operation. The phase sequence of power

3. If ω<sup>c</sup> < 0, this results in sub-synchronous operation. The phase sequence of power winding

=Pr (6)

(7)

Eq. (6):

winding:

developed which is given by Eq. (7):

Figure 2. MMFs of power and control windings.

38 Optimization and Control of Electrical Machines

synchronous machine.

winding is same as that of control winding.

is different from that of control winding.

BDFRM is therefore potentially useful as a variable speed drive.

The reluctance machine has higher leakage inductances which lead to poor operational power factor. Incorporation of advanced rotors that orient flux in the preferred direction can improve the power factor [2, 14]. The other issues are smaller torque density and larger torque pulsation which can be improved by a careful design of BDFRM with higher saliency ratio. There are several considerations in design of BDFRM; the main issues are highlighted below [15, 16]:


The selection of specific loadings depends on permissible losses, overload capacity, magnetic saturation, forces acting on rotor surface, etc. Selection of the number of stator slots and rotor ducts is very important in elimination of space harmonics in resultant MMF waveform. As the resultant MMF wave along the air gap is superposition of two MMFs, it has large space harmonics. Table 3 gives suitable combinations of stator slots and rotor ducts.

Proper selection of the number of poles on stator and rotor decides the magnetic coupling between stator and rotor which governs the torque production. The higher the coupling coefficient, the higher the torque production. This can be inferred from Figure 3.


Table 3. Minimum number of space harmonics for same stator and rotor slots [17, 18].

Figure 3. Coupling coefficient vs. pole combinations of BDFRM.

The selection of two or single winding in the stator is done on the basis of relative merits of both cases. Though it is costly, provision of two independent windings is more convenient for construction and control. With two independent windings, there is a great flexibility in winding pitches, and short pitching can be used to minimize the effect of space harmonics. The higher pole winding is generally considered as power winding [15] though there is no definite rule. There is no clarity over the voltage rating of control winding. It can be understood that in V/f control mode voltage will vary as frequency to avoid saturation in magnetic circuit. Is Vc/fc equal to Vp/fp? Or, can it be different? The length of air gap greatly affects the performance of the machine as MMF requirement increases with the length of air gap. Hence, selection of air gap needs a compromise.

Design of BDFRM is a complex process and involves various aspects of electromagnetism, thermal engineering, and machine design. The thermal and mechanical engineering aspects are similar to conventional machine design criteria. In BDFRM mechanical geometries differ from conventional machines, and hence conventional design procedures may have to be modified suitably. Therefore, analytical design approach is used. The voltage and current ratings of BDFRM decide the capacity of power electronic converter. The major consideration is the cost of machine which depends on the volume of active material used. For continuous operation the torque should be present over the designed range of speed, and the losses in BDFRM should be kept minimum for restricting temperature rise.

#### 4.1. Steps in the design of BDFRM

For the design of BDFRM rating of the machine (2 kW), a number of pole configurations on stator and rotor (8-6-4), rated synchronous speed (500 rpm), rotor construction (ducted), etc. are specified. With these inputs the design of the machine can be carried out on the guidelines suggested in [15, 16, 19]. After deciding the rating and the input data of BDFRM, the steps involved in the design are shown as a flow graph in Figure 4. Two configurations of BDFRM are short listed for prototype development: 6-4-2 with reluctance rotor, and the other one is 8-6-4 circular ducted rotor. Initial values of flux density (0.5 T), current density (4 A/mm2 ), integral slot, and full-pitched windings are assumed. A nonlinear programing (NLP) method is selected for design optimization of BDFRM as nonlinearities of materials and magnetic circuit have to be taken into considerations.

4.2. Objective function

Figure 4. Flow graph for design optimization.

1. Stator bore radius (x1)

2. Gross length of stator stack (x2)

A NLP problem involves the selection of independent variables, the development of objective function, and the constraint function for design of electrical machine. The objective function can be the cost of active materials or overall weight of machine or performance parameters, etc. The performance parameters of a machine can be used as constraints, e.g., pullout torque/full-load power factor/slot space factor/specific loadings/maximum flux density in stator tooth/temperature rise/shaft diameter. While designing BDFRM only a few

Optimal Design of Brushless Doubly Fed Reluctance Machine

http://dx.doi.org/10.5772/intechopen.74805

41

variables are considered as independent, and these are given below [6, 19]:

Optimal Design of Brushless Doubly Fed Reluctance Machine http://dx.doi.org/10.5772/intechopen.74805 41

Figure 4. Flow graph for design optimization.

#### 4.2. Objective function

The selection of two or single winding in the stator is done on the basis of relative merits of both cases. Though it is costly, provision of two independent windings is more convenient for construction and control. With two independent windings, there is a great flexibility in winding pitches, and short pitching can be used to minimize the effect of space harmonics. The higher pole winding is generally considered as power winding [15] though there is no definite rule. There is no clarity over the voltage rating of control winding. It can be understood that in V/f control mode voltage will vary as frequency to avoid saturation in magnetic circuit. Is Vc/fc equal to Vp/fp? Or, can it be different? The length of air gap greatly affects the performance of the machine as MMF requirement increases with the length of air gap. Hence, selection of air

Design of BDFRM is a complex process and involves various aspects of electromagnetism, thermal engineering, and machine design. The thermal and mechanical engineering aspects are similar to conventional machine design criteria. In BDFRM mechanical geometries differ from conventional machines, and hence conventional design procedures may have to be modified suitably. Therefore, analytical design approach is used. The voltage and current ratings of BDFRM decide the capacity of power electronic converter. The major consideration is the cost of machine which depends on the volume of active material used. For continuous operation the torque should be present over the designed range of speed, and the losses in BDFRM should be kept minimum for restricting tem-

For the design of BDFRM rating of the machine (2 kW), a number of pole configurations on stator and rotor (8-6-4), rated synchronous speed (500 rpm), rotor construction (ducted), etc. are specified. With these inputs the design of the machine can be carried out on the guidelines suggested in [15, 16, 19]. After deciding the rating and the input data of BDFRM, the steps involved in the design are shown as a flow graph in Figure 4. Two configurations of BDFRM are short listed for prototype development: 6-4-2 with reluctance rotor, and the other one is 8-6-4 circular ducted rotor. Initial values of flux density (0.5 T), current density (4 A/mm2

integral slot, and full-pitched windings are assumed. A nonlinear programing (NLP) method is selected for design optimization of BDFRM as nonlinearities of materials and magnetic

gap needs a compromise.

Figure 3. Coupling coefficient vs. pole combinations of BDFRM.

40 Optimization and Control of Electrical Machines

perature rise.

4.1. Steps in the design of BDFRM

circuit have to be taken into considerations.

A NLP problem involves the selection of independent variables, the development of objective function, and the constraint function for design of electrical machine. The objective function can be the cost of active materials or overall weight of machine or performance parameters, etc. The performance parameters of a machine can be used as constraints, e.g., pullout torque/full-load power factor/slot space factor/specific loadings/maximum flux density in stator tooth/temperature rise/shaft diameter. While designing BDFRM only a few variables are considered as independent, and these are given below [6, 19]:

1. Stator bore radius (x1)

),

2. Gross length of stator stack (x2)


The variables such as height of tooth lip, slot wedge thickness, slot opening, etc. have little effect on the overall performance. They are assumed to be known and constant and hence not considered in the optimization. The variables considered in BDFRM design are shown in Figure 5.

9. Temperature rise ≤ 50�C 10. Shaft diameter ≥ 25 mm

where Li = 0.9(x2 – ndbd).

(12), respectively:

active materials:

The objective function [20] for reluctance rotor configuration is derived as given below.

2 –πx1 2

<sup>2</sup> θg–sinθ<sup>g</sup> cosθ<sup>g</sup>

Vis ¼ Li πð Þ x1 þ x4 þ x6

2 –4x1

The volume of the copper required for power and control windings is given by Eq. (13):

For ducted rotor BDFRM, rotor iron volume is derived as given by Eq. (15):

2 –π dsh

The specifications of two 2 kW BDFRM configurations are given below:

speed 750 rpm, stator slots 36 with single winding in stator

Vir ¼ 0:9x2 πx1

angular distribution over a rotor pole.

Finally, the objective function is obtained as in Eq. (14) taking into account of the weights of

where A1–A6 represent duct areas and are calculated on the basis of width of the duct and

Eq. (15) is substituted in place of Vir in Eq. (14) to get the objective function for ducted rotor BDFRM.

a. Power winding poles—6, control winding poles—2, rotor poles(reluctance)—4, rated

Approximate mean length of turns for power and control windings are given by Eqs. (11) and

Sr ¼ ð Þ x1 þ x4 þ x6 (8)

Optimal Design of Brushless Doubly Fed Reluctance Machine

http://dx.doi.org/10.5772/intechopen.74805

43

–x3 x4x10 h i (9)

� � � � (10)

Lmtp ¼ 2x2 þ 2:3πð Þþ x1=p 0:152 (11)

Lmtc ¼ 2x2 þ 2:3πð Þþ x1=q 0:152 (12)

Vc <sup>¼</sup> 2 pmx5:x9:Lmtp <sup>þ</sup> qmx5x9Lmtc � � (13)

F ¼ Dið Þþ Vis þ Vir DcVc (14)

<sup>2</sup> � �–6 Að Þ <sup>1</sup> <sup>þ</sup> A2 <sup>þ</sup> A3 <sup>þ</sup> A4 <sup>þ</sup> A5 <sup>þ</sup> A6 (15)

The outer radius of stator (Sr) lamination is given by Eq. (8):

The volume of stator laminations is calculated by Eq. (9):

Thereafter, volume of rotor is calculated by using Eq. (10):

Vir ¼ 0:9x2 πx1

The constraint function limits considered in the design of BDFRM are:


Figure 5. Illustration of the design variables of BDFRM.

#### 9. Temperature rise ≤ 50�C

3. Width of stator slot (x3) 4. Depth of stator slot (x4)

42 Optimization and Control of Electrical Machines

6. Depth of stator core (x6)

7. Minimum length of air gap (x7) 8. Maximum length of air gap (x8)

10. Number of slots in stator (x10)

Figure 5.

5. Cross section of winding conductors (x5)

9. Number of turns per pole per phase (x9)

1. Maximum torque ≥ 1.5 time full-load torque

6. Maximum flux density in stator core and yoke ≤ 1.3 T 7. Specific electrical loading ≤ 25,000 ampere-conductor/m

2. Full-load power factor ≥ 0.5 lagging

5. Maximum tooth flux density ≤ 2 T

Figure 5. Illustration of the design variables of BDFRM.

3. Current density ≤ 4.5 A/mm<sup>2</sup>

8. Width of stator slot ≥ 6 mm

4. Slot fill factor ≤ 65%

The variables such as height of tooth lip, slot wedge thickness, slot opening, etc. have little effect on the overall performance. They are assumed to be known and constant and hence not considered in the optimization. The variables considered in BDFRM design are shown in

The constraint function limits considered in the design of BDFRM are:

10. Shaft diameter ≥ 25 mm

The objective function [20] for reluctance rotor configuration is derived as given below.

The outer radius of stator (Sr) lamination is given by Eq. (8):

$$\mathbf{S}\_{\mathbf{r}} = (\mathbf{x}\_1 + \mathbf{x}\_4 + \mathbf{x}\_6) \tag{8}$$

The volume of stator laminations is calculated by Eq. (9):

$$V\_{is} = L\_i \left[ \pi (\mathbf{x}\_1 + \mathbf{x}\_4 + \mathbf{x}\_6)^2 - \pi \mathbf{x}\_1 \mathbf{x}\_2^2 - \mathbf{x}\_3 \ge \mathbf{x}\_4 \mathbf{x}\_{10} \right] \tag{9}$$

where Li = 0.9(x2 – ndbd).

Thereafter, volume of rotor is calculated by using Eq. (10):

$$V\_{\rm ir} = 0.9 \text{x}\_2 \left( \pi \text{x}\_1^2 - 4 \text{x}\_1^2 \left( \Theta\_{\rm g} - \sin \Theta\_{\rm g} \cos \Theta\_{\rm g} \right) \right) \tag{10}$$

Approximate mean length of turns for power and control windings are given by Eqs. (11) and (12), respectively:

$$L\_{\rm mtp} = 2\mathbf{x}\_2 + 2.3\pi(\mathbf{x}\_1/p) + 0.152 \tag{11}$$

$$L\_{\rm mtc} = 2\mathbf{x}\_2 + 2.3\pi(\mathbf{x}\_1/q) + 0.152 \tag{12}$$

The volume of the copper required for power and control windings is given by Eq. (13):

$$V\_c = 2 \left( pmx \mathbf{5.x9.} L\_{mtp} + qmx\_5 x\_9 L\_{mtc} \right) \tag{13}$$

Finally, the objective function is obtained as in Eq. (14) taking into account of the weights of active materials:

$$F = D\_i(V\_{is} + V\_{ir}) + D\_c V\_c \tag{14}$$

For ducted rotor BDFRM, rotor iron volume is derived as given by Eq. (15):

$$V\_{\rm ir} = 0.9 \text{x}\_2 \left( \pi \text{x}\_1^{\; 2} - \pi \text{ } d\_{\rm sh} \right) - 6 (A\_1 + A\_2 + A\_3 + A\_4 + A\_5 + A\_6) \tag{15}$$

where A1–A6 represent duct areas and are calculated on the basis of width of the duct and angular distribution over a rotor pole.

Eq. (15) is substituted in place of Vir in Eq. (14) to get the objective function for ducted rotor BDFRM.

The specifications of two 2 kW BDFRM configurations are given below:

a. Power winding poles—6, control winding poles—2, rotor poles(reluctance)—4, rated speed 750 rpm, stator slots 36 with single winding in stator


b. Power winding poles—8, control winding poles—4, rotor poles(ducted)—6, rated speed

Sr. Description Initial values Optimized 8-6-4 BDFRM

Optimal Design of Brushless Doubly Fed Reluctance Machine

http://dx.doi.org/10.5772/intechopen.74805

Slot area 113 mm2 177.32 sq. mm

 Total slot space factor 0.45 0.35 (ac) Loading of power winding 10 kA/m 12.4 kA/m (ac) Loading of control winding 10 kA/m 9.04 kA/m Max flux density in stator tooth 1.2 T 1.48 T Max flux density in stator yoke 1.2 T 1.48 T Max flux density in rotor tooth 1.2 T 1.38 T Gap flux density 0.5 T 0.5 T Weight of copper 4.559 kg 3.783 kg Weight of stator core 4.989 kg 2.99 kg Weight of stator teeth 3.911 kg 2.86 kg Weight of rotor laminations 7.85 kg 6.8 kg

A nonlinear optimization technique is based on constrained optimization along with finite element analysis using Maxwell 15 2D software for design optimization of BDFRM. The key dimensions of BDFRM prototypes which are obtained after design optimization are given in Tables 4 and 5.

In optimized prototypes of 6-4-2 and 8-6-4 BDFRMs, requirements of active materials have reduced by 50 and 29% respectively. The considerable reduction in active material for 6-4-2 BDFRM is due to the use of single winding in stator. Even though material requirements have gone down, it hardly affects the performance parameters. This can be observed from Figures 6–8 where the plots for power factor, efficiency, and torque vs. weight of active materials used in

Figure 6. Variation of power factor with weight of active materials. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

500 rpm, stator slots 48 with two independent windings in stator

Table 5. Particulars of 8-6-4 configuration of BDFRM.

Table 4. Particulars of 6-4-2 configuration of BDFRM.



Table 5. Particulars of 8-6-4 configuration of BDFRM.

Sr. Description Initial values Optimized 6-4-2 BDFRM

Sr. Description Initial values Optimized 8-6-4 BDFRM

 Area of power winding conductor 0.506 mm2 0.653 sq.mm dia. 0.9118 mm Area of control winding conductor 0.506 mm2 0.653 sq.mm dia. 0.9118 mm

 Stator outer diameter 235 mm 210 mm Stator internal diameter (stator bore) 169 mm 144.24 mm Length of air gap (main) 0.45 mm 0.5 mm Rotor external diameter 168 mm 143 mm Effective axial length of machine 106 69 mm Stator yoke length 9 mm 14.5 mm Rotor pole pitch 85.37 mm 75.5 mm Rotor inner diameter 30 mm 35 mm

 Depth of stator slot 18 mm 26.88 mm Stator tooth width 5 mm 5.1278 mm

 Stator outer diameter 204 mm 165 mm Stator internal diameter (stator bore) 113.29 mm 91 mm Length of air gap (main) 0.45 mm 0.5 mm Rotor external diameter 112 mm 90 mm Effective axial length of machine 95 80 mm Stator yoke length 17 mm 15.3 mm Rotor inner diameter 40 mm 50 mm Conductor area for both windings 0.665 mm<sup>2</sup> 0.663 mm2 Depth of stator slot 21.9 mm 18.016 mm Stator tooth width 3 mm 4 mm Slot area 79.79 mm<sup>2</sup> 69.25 mm2 Total slot space factor 0.45 0.45 (ac) Loading of power/control winding 5000 A/m 5140 A/m Max flux density in stator tooth 1.46 T 1.3 T Max flux density in stator yoke 1.2 T 1.3 T Max flux density in rotor tooth 1.2 T 1.45 T Gap flux density 0.5 T 0.73 T Weight of copper 3.564 kg 2.494 kg Weight of stator core 4.84 kg 2.262 kg Weight of stator teeth 2.84 kg 2.123 kg Weight of rotor 2.8 kg 1.5 kg

Table 4. Particulars of 6-4-2 configuration of BDFRM.

Optimization and Control of Electrical Machines

b. Power winding poles—8, control winding poles—4, rotor poles(ducted)—6, rated speed 500 rpm, stator slots 48 with two independent windings in stator

A nonlinear optimization technique is based on constrained optimization along with finite element analysis using Maxwell 15 2D software for design optimization of BDFRM. The key dimensions of BDFRM prototypes which are obtained after design optimization are given in Tables 4 and 5.

In optimized prototypes of 6-4-2 and 8-6-4 BDFRMs, requirements of active materials have reduced by 50 and 29% respectively. The considerable reduction in active material for 6-4-2 BDFRM is due to the use of single winding in stator. Even though material requirements have gone down, it hardly affects the performance parameters. This can be observed from Figures 6–8 where the plots for power factor, efficiency, and torque vs. weight of active materials used in

Figure 6. Variation of power factor with weight of active materials. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

5.1. 6-4-2 Reluctance rotor configuration

Figure 9. Laminations used in 6-4-2 BDFRM.

Figure 10. Winding arrangement in 6-4-2 BDFRM.

Figure 11. Fabrication details of 6-4-2 BDFRM.

laminations (thickness 0.35 mm) used are shown in Figure 9.

The stator has 36 slots in which a single winding is embedded. The details of stator and rotor

Optimal Design of Brushless Doubly Fed Reluctance Machine

http://dx.doi.org/10.5772/intechopen.74805

47

The details of winding are shown in Figure 10. The winding is developed such that two different poles (6 and 2) are formed with single winding. The end connections and coil groups

Figure 7. Variation of efficiency with weight of active materials. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

Figure 8. Variation of developed torque (pu) with weight of active materials. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

BDFRM for all candidate machine designs were evaluated during optimization process, respectively. The data points for these variables form a cluster around the optimum value of active materials.

## 5. Prototypes of BDFRM

Two prototypes of BDFRM are fabricated based on optimum design, and details of which are given below [21].

## 5.1. 6-4-2 Reluctance rotor configuration

The stator has 36 slots in which a single winding is embedded. The details of stator and rotor laminations (thickness 0.35 mm) used are shown in Figure 9.

The details of winding are shown in Figure 10. The winding is developed such that two different poles (6 and 2) are formed with single winding. The end connections and coil groups

Figure 9. Laminations used in 6-4-2 BDFRM.

Figure 10. Winding arrangement in 6-4-2 BDFRM.

BDFRM for all candidate machine designs were evaluated during optimization process, respectively. The data points for these variables form a cluster around the optimum value of active

Figure 8. Variation of developed torque (pu) with weight of active materials. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

Figure 7. Variation of efficiency with weight of active materials. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

Two prototypes of BDFRM are fabricated based on optimum design, and details of which are

materials.

given below [21].

5. Prototypes of BDFRM

46 Optimization and Control of Electrical Machines

Figure 11. Fabrication details of 6-4-2 BDFRM.

are connected such that one end behaves as a 6-pole (power) winding and the other end acts as a 2-pole (control) winding. A short-pitched (short pitched by one slot) double-layer winding with 36 coils is designed primarily for two poles. Nine groups are formed with each group having four coils. The start and end terminals of each coil group are brought out for giving flexibility in winding connection. This has resulted in increased length of end connections than the normal case. Hence, special size end covers have to be designed. The actual photographs of 6-4-2 BDFRM during fabrication are shown in Figure 11.

Reluctance machines develop weak and pulsating torque. BDFRM is not different. This can be seen from Figure 14(a). However, the torque developed by ducted rotor BDFRM is higher with

Optimal Design of Brushless Doubly Fed Reluctance Machine

http://dx.doi.org/10.5772/intechopen.74805

49

reduced pulsation as shown in Figure 14(b).

Figure 13. Flux density distribution in BDFRM. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

Figure 14. Torque developed by BDFRM. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

Figure 15. Unbalanced magnetic pull acting on rotor surface. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

## 5.2. 8-6-4 Circular ducted rotor configuration

8-6-4 Circular ducted rotor BDFRM is fabricated. Stator consists of two independent windings one designed for eight poles (power) and the other for four poles (control). The windings are star connected. The stator windings are accommodated in 48 slots to get full-pitched windings. The lamination has deeper slots so that two double-layer windings can be fitted with a good slot space factor. The use of two double-layer windings facilitated the arrangement of end connections. All terminals of the windings are brought out so as to get flexibility in connection.

The number of ducts per rotor pole is selected as 10 as per the guidelines given in Table 3 [16, 17]. The fabrication details are shown in Figure 12.

Figure 12. Fabrication details of 8-6-4 BDFRM.

## 6. Finite element analysis of BDFRM

By using MAXWEL 16 software, the finite element models [22] are developed from the actual dimensions of stator and rotor laminations for 6-4-2 and 8-6-4 configurations. The models are simulated to get flux density distribution, torque, and surfaces forces. The flux density distribution in 6-4-2 BDFRM and 8-6-4 BDFRM is shown in Figure 13(a) and (b), respectively. It may be observed that flux density values are staying within saturation limit. The peak magnitude of flux density in prototype BDFRMs does not exceed 1.79 T.

Reluctance machines develop weak and pulsating torque. BDFRM is not different. This can be seen from Figure 14(a). However, the torque developed by ducted rotor BDFRM is higher with reduced pulsation as shown in Figure 14(b).

Figure 13. Flux density distribution in BDFRM. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

are connected such that one end behaves as a 6-pole (power) winding and the other end acts as a 2-pole (control) winding. A short-pitched (short pitched by one slot) double-layer winding with 36 coils is designed primarily for two poles. Nine groups are formed with each group having four coils. The start and end terminals of each coil group are brought out for giving flexibility in winding connection. This has resulted in increased length of end connections than the normal case. Hence, special size end covers have to be designed. The actual photographs of

8-6-4 Circular ducted rotor BDFRM is fabricated. Stator consists of two independent windings one designed for eight poles (power) and the other for four poles (control). The windings are star connected. The stator windings are accommodated in 48 slots to get full-pitched windings. The lamination has deeper slots so that two double-layer windings can be fitted with a good slot space factor. The use of two double-layer windings facilitated the arrangement of end connections. All terminals of the windings are brought out so as to get flexibility

The number of ducts per rotor pole is selected as 10 as per the guidelines given in Table 3 [16,

By using MAXWEL 16 software, the finite element models [22] are developed from the actual dimensions of stator and rotor laminations for 6-4-2 and 8-6-4 configurations. The models are simulated to get flux density distribution, torque, and surfaces forces. The flux density distribution in 6-4-2 BDFRM and 8-6-4 BDFRM is shown in Figure 13(a) and (b), respectively. It may be observed that flux density values are staying within saturation limit. The peak magnitude of

6-4-2 BDFRM during fabrication are shown in Figure 11.

5.2. 8-6-4 Circular ducted rotor configuration

48 Optimization and Control of Electrical Machines

17]. The fabrication details are shown in Figure 12.

6. Finite element analysis of BDFRM

Figure 12. Fabrication details of 8-6-4 BDFRM.

flux density in prototype BDFRMs does not exceed 1.79 T.

in connection.

Figure 14. Torque developed by BDFRM. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

Figure 15. Unbalanced magnetic pull acting on rotor surface. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

Figure 16. λ-I plots for BDFRM. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

Due to the absence of winding on rotor in BDFRM, there is no counterbalancing of MMF for stator MMF. This develops unbalanced magnetic forces on rotor surface. The magnitude of forces is quite large in reluctance rotor configuration, whereas they are considerably reduced in case of ducted rotor. This can be seen from Figure 15. The magnetic forces greatly reduce with advanced rotor configurations.

winding. The results are presented in Table 6. Because of the limitation of laboratory test

Optimal Design of Brushless Doubly Fed Reluctance Machine

http://dx.doi.org/10.5772/intechopen.74805

51

Figure 17. Performance curves of prototype BDFRMS. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

The capabilities of prototype BDFRMs can be judged from the performance curves shown in Figure 17. There is slight deviation of parameters from designed values. This may be due to practical difficulties during loading the machine. Additionally, there is an increase in losses due to the presence of harmonics in control winding excitation which has compromised efficiency and power factor. This advocates development of sophisticated control algorithm

This chapter highlights various optimization methods, suitability of nonlinear programming methods, and recent stochastic or population-based methods for optimal design of electrical machines. It also discusses briefly a few issues in the design of BDFRM. An objective function is developed for minimization of active material requirement, and an algorithm based on nonlinear programming is presented for optimal design of 2 kW BDFRMs. The analytical models developed based on optimized design are simulated in Maxwell 16 software. The simulation results closely agree with the design values, and there is no saturation in magnetic circuit. The field tests on the two prototypes have demonstrated the capabilities of BDFRMs. It is observed that the performance of 8-6-4 BDFRM is better than 6-4-2 BDFRM in all respects. Both the machines have attained rated speed. Speed control has been achieved on either side of it. Although efficiencies

of the prototypes are closer to design values, power factor is lower than expected.

Mandar Bhawalkar\*, Gopalakrishnan Narayan and Yogesh Nerkar \*Address all correspondence to: mandar\_bhawalkar@yahoo.co.in

PVG's College of Engineering and Technology, Pune, India

facilities, loading could be done up to 70%.

for BDFRM to get the desired performance.

8. Conclusion

Author details

The flux linkage-current plots (λ-i) for both configurations are shown in Figure 16. The performance of machine greatly depends on area of (λ-i) plot. The plots clearly indicate that 8-6-4 BDFRM has better performance due to larger area of (λ-i) plot.

## 7. Performance of prototypes

The performances of two prototype BDFRMs are obtained from load tests. BDFRM is coupled with a dc machine of rating 2 kW, 220 V, and 1500 rpm which acts as a load. A three-phase twolevel, 3 kW, IGBT variable voltage variable frequency inverter is used for exciting the control


Table 6. Performance details of prototype BDFRMs.

Figure 17. Performance curves of prototype BDFRMS. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

winding. The results are presented in Table 6. Because of the limitation of laboratory test facilities, loading could be done up to 70%.

The capabilities of prototype BDFRMs can be judged from the performance curves shown in Figure 17. There is slight deviation of parameters from designed values. This may be due to practical difficulties during loading the machine. Additionally, there is an increase in losses due to the presence of harmonics in control winding excitation which has compromised efficiency and power factor. This advocates development of sophisticated control algorithm for BDFRM to get the desired performance.

## 8. Conclusion

Due to the absence of winding on rotor in BDFRM, there is no counterbalancing of MMF for stator MMF. This develops unbalanced magnetic forces on rotor surface. The magnitude of forces is quite large in reluctance rotor configuration, whereas they are considerably reduced in case of ducted rotor. This can be seen from Figure 15. The magnetic forces greatly reduce

The flux linkage-current plots (λ-i) for both configurations are shown in Figure 16. The performance of machine greatly depends on area of (λ-i) plot. The plots clearly indicate that

The performances of two prototype BDFRMs are obtained from load tests. BDFRM is coupled with a dc machine of rating 2 kW, 220 V, and 1500 rpm which acts as a load. A three-phase twolevel, 3 kW, IGBT variable voltage variable frequency inverter is used for exciting the control

> Optimized machine (calculated)

Torque developed 38 N 30 N (from FEA

Temperature rise 34.45C 45C (by resistance

Actual value@60%

loading

analysis)

analysis)

method)

1.48 T 1.77 T (from FEA

6-4-2 Reluctance rotor BDFRM Description 8-6-4 Ducted rotor BDFRM

2 kW 1.2 kW Rated output 2 kW 1.6 kW 750 rpm 750 rpm Base speed 500 rpm 500 rpm 80% 75% Efficiency 83% 75% 0.7 0.54 Power factor 0.8 0.7

> Flux density in stator tooth

Actual value@60%

loading

analysis)

analysis)

method)

Table 6. Performance details of prototype BDFRMs.

25.46 N-m 15.27 N-m (from FEA

1.35 T 1.77 T (from FEA

34C 42C (by resistance

8-6-4 BDFRM has better performance due to larger area of (λ-i) plot.

Figure 16. λ-I plots for BDFRM. (a) 6-4-2 BDFRM and (b) 8-6-4 BDFRM.

with advanced rotor configurations.

50 Optimization and Control of Electrical Machines

7. Performance of prototypes

Optimized machine (calculated)

This chapter highlights various optimization methods, suitability of nonlinear programming methods, and recent stochastic or population-based methods for optimal design of electrical machines. It also discusses briefly a few issues in the design of BDFRM. An objective function is developed for minimization of active material requirement, and an algorithm based on nonlinear programming is presented for optimal design of 2 kW BDFRMs. The analytical models developed based on optimized design are simulated in Maxwell 16 software. The simulation results closely agree with the design values, and there is no saturation in magnetic circuit. The field tests on the two prototypes have demonstrated the capabilities of BDFRMs. It is observed that the performance of 8-6-4 BDFRM is better than 6-4-2 BDFRM in all respects. Both the machines have attained rated speed. Speed control has been achieved on either side of it. Although efficiencies of the prototypes are closer to design values, power factor is lower than expected.

## Author details

Mandar Bhawalkar\*, Gopalakrishnan Narayan and Yogesh Nerkar

\*Address all correspondence to: mandar\_bhawalkar@yahoo.co.in

PVG's College of Engineering and Technology, Pune, India

## References

[1] Betz R, Jovanovic M. Theoretical analysis of control properties for brushless doubly fed reluctance machine. IEEE Transactions on Energy Conversion. Sept 2002;17(1):332-339. DOI: 10.1109/TEC.2002.801997

[14] Liao Y, Xu L, Li Z. Design of a doubly fed reluctance motor for adjustable speed drive. IEEE Transactions on Industry Applications. Sept/Oct 1996;32(5):1195-1203. DOI: 10.1109/

Optimal Design of Brushless Doubly Fed Reluctance Machine

http://dx.doi.org/10.5772/intechopen.74805

53

[15] Knight A, Betz R, Dorrell D. Issues with the design of brushless doubly fed reluctance machines: Unbalanced magnetic pull, skew and iron losses. 2011 IEEE International Elec-

[16] Knight A, Betz R, Dorrell D. Design and analysis of brushless doubly fed reluctance machines. IEEE Transactions on Industry Applications. Jan/Feb 2013;49:50-57. DOI: 10.1109/

[17] Vagati A, Franceschini G, Marongiu I, Troglia G. Design criteria of high performance

[18] Vagati A, Pastorelli M, Francheschini G, Petrache S. Deign of low torque ripple synchronous reluctance motor. IEEE Transactions on Industry Applications. 1998;34(4):758-765.

[19] Boldea I. Reluctance Synchronous Machines and Drives. New York, USA: Oxford Science

[20] Kunte S, Bhawalkar M, Gopalakrishnan N, Nerkar Y. Optimal design and comparative analysis of different configurations of brushless doubly fed reluctance machine. IEEJ Transactions on Industry Applications. Nov. 2017;6(6):370-380. DOI: 10.1541/ieejjia.6.370

[21] Bhawalkar M. Studies in Wind Power Generation Systems [Ph.D. Thesis]. India: Savitribai

[22] Bianchi N. Electrical Machine Analysis Using Finite Elements. FL, USA: Taylor and Francis,

tric Machines & Drives Conference (IEMDC); 2011. pp. 663-668

synchronous reluctance motors. IAS Annual Meeting. 1992;1:66-73

28.536883

TIA.2012.2229451

DOI: 10.1109/IAS.1997.643040

Publications; 1996. ISBN: 0 19 85391 0

Phule Pune Univeristy; Oct. 2017

Special Indian reprints; 2015. ISBN 9780849333996


[14] Liao Y, Xu L, Li Z. Design of a doubly fed reluctance motor for adjustable speed drive. IEEE Transactions on Industry Applications. Sept/Oct 1996;32(5):1195-1203. DOI: 10.1109/ 28.536883

References

DOI: 10.1109/TEC.2002.801997

52 Optimization and Control of Electrical Machines

2000;36(4):1103-1110. DOI: 10.1109/28.855966

Electromotion Conference; 2015. pp. 441-448

232-239. DOI: 10.1109/TIA.2009.2036549

951-954

7:14-24. ISSN 0976-6545

[1] Betz R, Jovanovic M. Theoretical analysis of control properties for brushless doubly fed reluctance machine. IEEE Transactions on Energy Conversion. Sept 2002;17(1):332-339.

[2] Betz R, Jovanovic M. The brushless doubly fed reluctance machine and the synchronous reluctance machine—a comparison. IEEE Transactions on Industry Applications. Jul/Aug

[3] Stipetic S, Miebach W, Zarko D. Optimization in design of electrical machines: Methodology and workflow. In: Proceedings of the International Conference on ACEMP-OPTIM-

[4] Liu A, Xu W. A global optimization approach for electrical machine designs. IEEE Power

[5] Rao S. Engineering Optimization Theory and Practice. 3rd ed. New Delhi: New Age

[6] Ramamoorthy M. Computer Aided Design of Electrical Equipments. Reprint. New Delhi:

[7] Ma C, Qu L. Multiobjective optimization of switched reluctance motors based on design of experiments and particle swarm optimization. IEEE Transactions on Energy Conver-

[8] Jiang W, Jahns T, Lipo T, Taylor W, Suzuki Y. Machine design optimization based on finite element analysis in a high-throughput computing environment. In: Proceedings of IEEE Energy Conversion Congress and Exposition; Sept. 2012. 10.1109/ECCE.2012.6342727

[9] Legranger J, Friedrich G, Vivier S, Mipo J. Combination of finite-element and analytical models in the optimal multidomain design of machines: Application to an interior permanent magnet starter generator. IEEE Transactions on Industry Applications. Jan 2010;46(1):

[10] Ponmurugan P, Rengarajan N. Multiobjective optimization of electrical machines, a state of the art study. Journal of Computer Applications. Oct. 2012;56(13):26-30. DOI: 10.1.1.244.6959

[11] Idir K, Chang L, Dai H. A neural network based optimization approach for induction motor design. Canadian Conference on Electrical & Computer Engineering; May1996. pp.

[12] Bétin F, Yazidi A, Sivert A, Fuzzy CG. DOI n DOI logic control design for electrical machines. International Journal of Electrical Engineering and Technology. May–June 2016;

[13] Çuncaş M. Design optimization of electric motors by multiobjective fuzzy genetic algo-

rithm. Mathematical and Computational Applications. 2008;13(3):153-163

Affiliated East West Press Pvt Ltd; 2011, 2011. pp. 5-53. ISBN 81-85095-57-4

& Energy Society General Meeting. 2007:1-8. ISBN: 1-4244-1298-6

sion. Sept. 2015;30(3):1144-1153. DOI: 10.1109/TEC.2018.2411677

International Publisher; 2013. 722p. ISBN 978-81-224-2723-3


**Section 2**

**Control of Induction Machines**

**Control of Induction Machines**

**Chapter 4**

Provisional chapter

**Zero and Low-Speed Sensorless Control of Induction**

DOI: 10.5772/intechopen.75892

This chapter presents a position sensorless method for induction machines that only relies on the fundamental pulse width modulation (PWM) waveforms to excite saliency. Position signals can be synthesized through the measurement of the derivatives of the line currents induced by the PWM voltage vectors. This method is essentially saliency detection based, and therefore derivation of the rotor position is possible at low and zero speeds. In addition, it works also at higher speeds without the need of the knowledge of the machine's fundamental model. Experimental results showing fully sensorless induction motor control at low and higher speeds validate the principle of this method. Keywords: sensorless control, induction machine, saliency, PWM excitation, current

Due to the incapacity of the fundamental model-based sensorless rotor position estimation at zero and low frequencies, alternative methods have been intensively studied. These methods exploit the anisotropy or saliency of the machine resulting from either saturation or geometric variation on the rotor. They can be classified into two categories according to the detection method for the anisotropy (or saliency) position. One category relies on the continuous injection of high-frequency voltage signals and then measuring the response of the high-frequency (hf) current [1–7]. Demodulation of the hf current signal enables the extraction of the rotor angle. The second category makes use of the line-current transient response to a PWM switching state. This can be realized by injecting special voltage test vectors [8–13] or by modifying the normal pulse width modulation waveforms

> © 2016 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 eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. 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.

Zero and Low-Speed Sensorless Control of Induction

**Machines Using Only Fundamental Pulse Width**

Machines Using Only Fundamental Pulse Width

**Modulation Waveform Excitation**

Modulation Waveform Excitation

Qiang Gao, Greg Asher and Mark Sumner

Qiang Gao, Greg Asher and Mark Sumner

http://dx.doi.org/10.5772/intechopen.75892

Abstract

derivative

1. Introduction

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation Waveform Excitation** Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation Waveform Excitation

DOI: 10.5772/intechopen.75892

Qiang Gao, Greg Asher and Mark Sumner Qiang Gao, Greg Asher and Mark Sumner

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.75892

## Abstract

This chapter presents a position sensorless method for induction machines that only relies on the fundamental pulse width modulation (PWM) waveforms to excite saliency. Position signals can be synthesized through the measurement of the derivatives of the line currents induced by the PWM voltage vectors. This method is essentially saliency detection based, and therefore derivation of the rotor position is possible at low and zero speeds. In addition, it works also at higher speeds without the need of the knowledge of the machine's fundamental model. Experimental results showing fully sensorless induction motor control at low and higher speeds validate the principle of this method.

Keywords: sensorless control, induction machine, saliency, PWM excitation, current derivative

## 1. Introduction

Due to the incapacity of the fundamental model-based sensorless rotor position estimation at zero and low frequencies, alternative methods have been intensively studied. These methods exploit the anisotropy or saliency of the machine resulting from either saturation or geometric variation on the rotor. They can be classified into two categories according to the detection method for the anisotropy (or saliency) position. One category relies on the continuous injection of high-frequency voltage signals and then measuring the response of the high-frequency (hf) current [1–7]. Demodulation of the hf current signal enables the extraction of the rotor angle. The second category makes use of the line-current transient response to a PWM switching state. This can be realized by injecting special voltage test vectors [8–13] or by modifying the normal pulse width modulation waveforms

© 2016 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 eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. 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.

[14], which may increase the hazardous common mode current in the machine [15]. The induced current transient response during a test vector reflects the spatial variation of the stator leakage inductances due to the anisotropy. Therefore, it is possible to acquire the rotor position, or rotor flux angle, through the measurement of the transient current derivative in response to the test vector.

In this chapter, a method belonging to the second category is described. Instead of using extra test vectors or modifying the standard modulation scheme, this method integrates the test vectors with the standard PWM waveforms [16]. In the following paragraphs, the theory of the method will be presented first, then, its application on a 4-pole 30 kW Δ-connected cage machine having 56 open slots will be demonstrated. Other implementation issues related to the speed sensorless operation, such as the noise filter of the position signals, will also be introduced.

## 2. Position estimation with the fundamental wave PWM

When a three-phase, delta-connected induction machine has its stator leakage inductances modulated by the anisotropies introduced by either the main flux saturation or the rotor slotting, they can be assumed to vary according to:

$$l\_{\sigma a} = l\_0 + \Delta l \cos(n\_{am}\Theta\_{am}) \tag{1}$$

$$l\_{\sigma b} = l\_0 + \Delta l \cos(\eta\_{an}(\Theta\_{an} - 2\pi/3))\tag{2}$$

$$l\_{\sigma\varepsilon} = l\_0 + \Delta l \cos(n\_{am}(\Theta\_{am} - 4\pi/3))\tag{3}$$

where l0 is the average inductance and Δl is the amplitude of inductance variation caused by the anisotropy (nan = 2 for saturation-induced anisotropy or nan = nrs = Nr/p for rotor slotting, where Nr is rotor slot number and p the pole pairs).

The standard space vectors of Figure 1 are applied. Figure 2 shows the equivalent circuit when the machine is applied with vector u1 from which the following equations can be derived:

$$dL\_d = \dot{l}\_{ab}^{(u1)} r\_s + l\_{\sigma a} \frac{d\dot{l}\_{ab}^{(u1)}}{dt} + e\_a^{(u1)} \tag{4}$$

$$0 = \dot{l}\_{bc}^{(u1)} r\_s + l\_{cb} \frac{d\dot{i}\_{bc}^{(u1)}}{dt} + e\_b^{(u1)} \tag{5}$$

$$-\mathcal{U}\_d = \mathfrak{i}\_{ca}^{(u1)} r\_s + l\_{\sigma c} \frac{d\mathfrak{i}\_{ca}^{(u1)}}{dt} + \mathfrak{e}\_c^{(u1)} \tag{6}$$

By the application of the null vector u0 or u7, one has:

$$0 = \dot{l}\_{ab}^{(\mu 0)} r\_s + l\_{\sigma a} \frac{d\dot{i}\_{ab}^{(\mu 0)}}{dt} + e\_a^{(\mu 0)} \tag{7}$$

0 ¼ i ð Þ u0 ca rs þ l<sup>σ</sup> <sup>c</sup>

Figure 2. Equivalent circuit with u1 being applied.

Figure 1. Definition of space vectors.

If the instants of applying u1 and u0 are close enough, it is viable to assume that:

dið Þ <sup>u</sup><sup>0</sup> ca d t <sup>þ</sup> <sup>e</sup>

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation…

ð Þ u0

<sup>c</sup> (9)

http://dx.doi.org/10.5772/intechopen.75892

59

$$0 = i\_{bc}^{(u0)}r\_s + l\_{\sigma \flat} \frac{d i\_{bc}^{(u0)}}{dt} + e\_b^{(u0)} \tag{8}$$

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation… http://dx.doi.org/10.5772/intechopen.75892 59

Figure 1. Definition of space vectors.

[14], which may increase the hazardous common mode current in the machine [15]. The induced current transient response during a test vector reflects the spatial variation of the stator leakage inductances due to the anisotropy. Therefore, it is possible to acquire the rotor position, or rotor flux angle, through the measurement of the transient current derivative in response to the test vector. In this chapter, a method belonging to the second category is described. Instead of using extra test vectors or modifying the standard modulation scheme, this method integrates the test vectors with the standard PWM waveforms [16]. In the following paragraphs, the theory of the method will be presented first, then, its application on a 4-pole 30 kW Δ-connected cage machine having 56 open slots will be demonstrated. Other implementation issues related to the speed sensorless operation, such as the noise filter of the position signals, will also be introduced.

When a three-phase, delta-connected induction machine has its stator leakage inductances modulated by the anisotropies introduced by either the main flux saturation or the rotor

where l0 is the average inductance and Δl is the amplitude of inductance variation caused by the anisotropy (nan = 2 for saturation-induced anisotropy or nan = nrs = Nr/p for rotor slotting,

The standard space vectors of Figure 1 are applied. Figure 2 shows the equivalent circuit when the machine is applied with vector u1 from which the following equations can be derived:

> dið Þ <sup>u</sup><sup>1</sup> ab d t <sup>þ</sup> <sup>e</sup>

dið Þ <sup>u</sup><sup>1</sup> bc d t <sup>þ</sup> <sup>e</sup>

dið Þ <sup>u</sup><sup>0</sup> ab d t <sup>þ</sup> <sup>e</sup>

dið Þ <sup>u</sup><sup>0</sup> bc d t <sup>þ</sup> <sup>e</sup>

dið Þ <sup>u</sup><sup>1</sup> ca d t <sup>þ</sup> <sup>e</sup>

ð Þ u1

ð Þ u1

ð Þ u1

ð Þ u0

ð Þ u0

<sup>a</sup> (4)

<sup>b</sup> (5)

<sup>c</sup> (6)

<sup>a</sup> (7)

<sup>b</sup> (8)

l<sup>σ</sup> <sup>a</sup> ¼ l<sup>0</sup> þ Δlcosð Þ nanθan (1)

l<sup>σ</sup> <sup>b</sup> ¼ l<sup>0</sup> þ Δlcosð Þ nanð Þ θan � 2π=3 (2)

l<sup>σ</sup> <sup>c</sup> ¼ l<sup>0</sup> þ Δlcosð Þ nanð Þ θan � 4π=3 (3)

2. Position estimation with the fundamental wave PWM

Ud ¼ i ð Þ u1 ab rs þ l<sup>σ</sup> <sup>a</sup>

0 ¼ i ð Þ u1 bc rs þ l<sup>σ</sup> <sup>b</sup>

�Ud ¼ i

0 ¼ i ð Þ u0 ab rs þ l<sup>σ</sup> <sup>a</sup>

0 ¼ i ð Þ u0 bc rs þ l<sup>σ</sup> <sup>b</sup>

ð Þ u1 ca rs þ l<sup>σ</sup> <sup>c</sup>

slotting, they can be assumed to vary according to:

58 Optimization and Control of Electrical Machines

where Nr is rotor slot number and p the pole pairs).

By the application of the null vector u0 or u7, one has:

Figure 2. Equivalent circuit with u1 being applied.

$$0 = l\_{ca}^{(u0)}r\_s + l\_{\sigma \cdot c} \frac{d \dot{l}\_{ca}^{(u0)}}{dt} + e\_c^{(u0)} \tag{9}$$

If the instants of applying u1 and u0 are close enough, it is viable to assume that:

$$e\_a^{(\iota \bullet 0)} \approx e\_a^{(\iota \bullet 1)},\\ e\_b^{(\iota \bullet 0)} \approx e\_b^{(\iota \bullet 1)},\\ e\_c^{(\iota \bullet 0)} \approx e\_c^{(\iota \bullet 1)} \dots$$

Additionally, the voltage drops across the stator resistance and can be ignored due to their small values compared with Ud.

Hence, the subtraction of the Eqs. (4)–(7), (5)–(8) and (6)–(9) yields:

$$\frac{d\dot{\mathbf{i}}\_{ab}^{(u1)}}{dt} - \frac{d\dot{\mathbf{i}}\_{ab}^{(u0)}}{dt} = \frac{\mathbf{U}\_d}{l\_{\alpha a}}\tag{10}$$

pc ¼ 1 þ c<sup>1</sup>

pa ¼ �2 � c<sup>1</sup>

pb ¼ 1 � c<sup>1</sup>

pc ¼ 1 � c<sup>1</sup>

<sup>p</sup> <sup>¼</sup> <sup>p</sup><sup>α</sup> <sup>þ</sup> jp<sup>β</sup> <sup>¼</sup> pa <sup>þ</sup> apb <sup>þ</sup> <sup>a</sup><sup>2</sup>pc

dið Þ <sup>u</sup><sup>1</sup> b d t � dið Þ <sup>u</sup><sup>0</sup> b d t ! � <sup>a</sup>

�a<sup>2</sup> dið Þ <sup>u</sup><sup>2</sup> a dt � dið Þ <sup>u</sup><sup>0</sup> a dt !

dið Þ <sup>u</sup><sup>1</sup> b dt � dið Þ <sup>u</sup><sup>0</sup> b dt ! <sup>þ</sup>

> dið Þ <sup>u</sup><sup>2</sup> a dt � dið Þ <sup>u</sup><sup>0</sup> a dt !

þ 1 2

they are defined with the same terms, pa, pb and pc.

¼ c<sup>1</sup>

p<sup>α</sup> ¼ c<sup>1</sup>

where <sup>c</sup><sup>1</sup> <sup>¼</sup> <sup>l</sup>0=Ud. If both <sup>c</sup><sup>1</sup> and di

scalars can be defined as:

tion of (19), (24) and (25):

Therefore,

directly via:

dið Þ <sup>u</sup><sup>1</sup> c d t � dið Þ <sup>u</sup><sup>0</sup> c

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation…

where <sup>a</sup> <sup>¼</sup> ej<sup>2</sup>π=3. However, c1 consists of an unknown coefficient l0, which may vary with the saturation level of the main flux. This uncertainty can be avoided by looking at the current response to another voltage vector u2. Following the same as earlier, another three position

> dið Þ <sup>u</sup><sup>2</sup> c dt � dið Þ <sup>u</sup><sup>0</sup> c

dið Þ <sup>u</sup><sup>2</sup> b dt � dið Þ <sup>u</sup><sup>0</sup> b

dið Þ <sup>u</sup><sup>2</sup> a dt � dið Þ <sup>u</sup><sup>0</sup> a

It should be noted that because the application of u1 and u2 results in the same position scalars,

By referring to (19), (20), (21) and (23), (24), (25), it is possible to define p through the combina-

dið Þ <sup>u</sup><sup>2</sup> b dt � dið Þ <sup>u</sup><sup>0</sup> b dt !

1 2

dið Þ <sup>u</sup><sup>2</sup> b dt � dið Þ <sup>u</sup><sup>0</sup> b dt !

d t ! (21)

http://dx.doi.org/10.5772/intechopen.75892

61

dt ! (23)

dt ! (24)

dt ! (25)

(26)

(27)

dt are known, it is possible to construct the position vector p

<sup>p</sup> <sup>¼</sup> pa <sup>þ</sup> <sup>a</sup> � pb <sup>þ</sup> <sup>a</sup><sup>2</sup> � pc (22)

$$\frac{d\dot{i}\_{bc}^{(u1)}}{dt} - \frac{d\dot{i}\_{bc}^{(u0)}}{dt} = 0\tag{11}$$

$$\frac{d\dot{\mathbf{i}}\_{ca}^{(\mu 1)}}{dt} - \frac{d\dot{\mathbf{i}}\_{ca}^{(\mu 0)}}{dt} = -\frac{\mathbf{U}\_d}{\mathbf{I}\_{ca}}\tag{12}$$

From the relationship between phase currents and line currents, for example, ia = iab- ica, one has:

$$\frac{d\operatorname{i}\_{a}^{(\mu 1)}}{dt} - \frac{d\operatorname{i}\_{a}^{(\mu 0)}}{dt} = \frac{l\_{\sigma a} + l\_{\sigma c}}{l\_{\sigma a}l\_{\sigma c}} \mathcal{U}\_{d} \tag{13}$$

$$\frac{d\dot{i}\_b^{(u1)}}{dt} - \frac{d\dot{i}\_b^{(u0)}}{dt} = -\frac{1}{l\_{oa}}\mathcal{U}\_d\tag{14}$$

$$\frac{d\dot{l}\_c^{(u1)}}{dt} - \frac{d\dot{l}\_c^{(u0)}}{dt} = -\frac{1}{l\_{oc}}\mathcal{U}\_d\tag{15}$$

Considering Eqs. (1) to (3), one has:

$$\frac{d\dot{i}\_a^{(u1)}}{dt} - \frac{d\dot{i}\_a^{(u0)}}{dt} = \frac{\mathcal{U}\_d}{l\_0} \left( 2 + \frac{\Delta l}{l\_0} \cos \left( n\_{\text{on}} \left( \theta\_{\text{on}} - \frac{2\pi}{3} \right) \right) \right) \tag{16}$$

$$\frac{d\dot{i}\_b^{(u1)}}{dt} - \frac{d\dot{i}\_b^{(u0)}}{dt} = -\frac{\mathcal{U}\_d}{l\_0} \left(1 - \frac{\Delta l}{l\_0} \cos(n\_{\text{an}} \theta\_{\text{an}})\right) \tag{17}$$

$$\frac{d\dot{I}\_{\rm c}^{(u1)}}{dt} - \frac{d\dot{I}\_{\rm c}^{(u0)}}{dt} = -\frac{\mathcal{U}\_{\rm d}}{l\_0} \left( 1 - \frac{\Delta l}{l\_0} \cos \left( n\_{\rm an} \left( \Theta\_{\rm an} - \frac{4\pi}{3} \right) \right) \right) \tag{18}$$

from which three balanced position scalars pa, pb and pc can be defined as follows:

$$p\_a = 1 + c\_1 \left(\frac{d i\_b^{(u1)}}{dt} - \frac{d i\_b^{(u0)}}{dt}\right) \tag{19}$$

$$p\_b = -2 + c\_1 \left(\frac{d\dot{i}\_a^{(u1)}}{dt} - \frac{d\dot{i}\_a^{(u0)}}{dt}\right) \tag{20}$$

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation… http://dx.doi.org/10.5772/intechopen.75892 61

$$p\_c = 1 + c\_1 \left(\frac{d\dot{l}\_c^{(u1)}}{dt} - \frac{d\dot{l}\_c^{(u0)}}{dt}\right) \tag{21}$$

where <sup>c</sup><sup>1</sup> <sup>¼</sup> <sup>l</sup>0=Ud. If both <sup>c</sup><sup>1</sup> and di dt are known, it is possible to construct the position vector p directly via:

$$
\underline{p} = p\_a + a \cdot p\_b + a^2 \cdot p\_c \tag{22}
$$

where <sup>a</sup> <sup>¼</sup> ej<sup>2</sup>π=3. However, c1 consists of an unknown coefficient l0, which may vary with the saturation level of the main flux. This uncertainty can be avoided by looking at the current response to another voltage vector u2. Following the same as earlier, another three position scalars can be defined as:

$$p\_a = -2 - c\_1 \left(\frac{d i\_c^{(u2)}}{dt} - \frac{d i\_c^{(u0)}}{dt}\right) \tag{23}$$

$$p\_b = 1 - c\_1 \left(\frac{d i\_b^{(u2)}}{dt} - \frac{d i\_b^{(u0)}}{dt}\right) \tag{24}$$

$$p\_c = 1 - c\_1 \left(\frac{d\dot{i}\_a^{(u2)}}{dt} - \frac{d\dot{i}\_a^{(u0)}}{dt}\right) \tag{25}$$

It should be noted that because the application of u1 and u2 results in the same position scalars, they are defined with the same terms, pa, pb and pc.

By referring to (19), (20), (21) and (23), (24), (25), it is possible to define p through the combination of (19), (24) and (25):

$$\begin{aligned} \underline{p} &= p\_{\alpha} + jp\_{\beta} = p\_{a} + ap\_{b} + a^{2}p\_{c} \\ &= c\_{1} \left[ \left( \frac{di\_{b}^{(u1)}}{dt} - \frac{di\_{b}^{(u0)}}{dt} \right) - a \left( \frac{di\_{b}^{(u2)}}{dt} - \frac{di\_{b}^{(u0)}}{dt} \right) \right] \\ &- a^{2} \left( \frac{di\_{a}^{(u2)}}{dt} - \frac{di\_{a}^{(u0)}}{dt} \right) \end{aligned} \tag{26}$$

Therefore,

e ð Þ u0 <sup>a</sup> ≈ e ð Þ u1 <sup>a</sup> , eð Þ <sup>u</sup><sup>0</sup> <sup>b</sup> ≈ e ð Þ u1 <sup>b</sup> , eð Þ <sup>u</sup><sup>0</sup> <sup>c</sup> ≈ e ð Þ u1 <sup>c</sup> :

Hence, the subtraction of the Eqs. (4)–(7), (5)–(8) and (6)–(9) yields:

dið Þ <sup>u</sup><sup>1</sup> ab d t � dið Þ <sup>u</sup><sup>0</sup> ab d t <sup>¼</sup> Ud lσ a

dið Þ <sup>u</sup><sup>1</sup> bc d t � dið Þ <sup>u</sup><sup>0</sup> bc

dið Þ <sup>u</sup><sup>1</sup> ca d t � dið Þ <sup>u</sup><sup>0</sup> ca d t ¼ � Ud lσ a

dið Þ <sup>u</sup><sup>1</sup> a d t � dið Þ <sup>u</sup><sup>0</sup> a

> dið Þ <sup>u</sup><sup>1</sup> b d t � dið Þ <sup>u</sup><sup>0</sup> b d t ¼ � <sup>1</sup>

> dið Þ <sup>u</sup><sup>1</sup> c d t � dið Þ <sup>u</sup><sup>0</sup> c d t ¼ � <sup>1</sup>

> > 2 þ Δl l0

> > > <sup>1</sup> � <sup>Δ</sup><sup>l</sup> l0

> > > > dið Þ <sup>u</sup><sup>1</sup> b d t � dið Þ <sup>u</sup><sup>0</sup> b d t

dið Þ <sup>u</sup><sup>1</sup> a d t � dið Þ <sup>u</sup><sup>0</sup> a d t

!

!

d t ¼ � Ud l0

from which three balanced position scalars pa, pb and pc can be defined as follows:

pa ¼ 1 þ c<sup>1</sup>

pb ¼ �2 þ c<sup>1</sup>

d t ¼ � Ud l0

small values compared with Ud.

60 Optimization and Control of Electrical Machines

Considering Eqs. (1) to (3), one has:

dið Þ <sup>u</sup><sup>1</sup> a d t � dið Þ <sup>u</sup><sup>0</sup> a d t <sup>¼</sup> Ud l0

dið Þ <sup>u</sup><sup>1</sup> c d t � dið Þ <sup>u</sup><sup>0</sup> c

dið Þ <sup>u</sup><sup>1</sup> b d t � dið Þ <sup>u</sup><sup>0</sup> b

has:

Additionally, the voltage drops across the stator resistance and can be ignored due to their

From the relationship between phase currents and line currents, for example, ia = iab- ica, one

d t <sup>¼</sup> <sup>l</sup><sup>σ</sup> <sup>a</sup> <sup>þ</sup> <sup>l</sup><sup>σ</sup> <sup>c</sup> l<sup>σ</sup> al<sup>σ</sup> <sup>c</sup>

lσ a

lσ c

cos nan <sup>θ</sup>an � <sup>2</sup><sup>π</sup>

cosð Þ nanθan � �

cos nan <sup>θ</sup>an � <sup>4</sup><sup>π</sup>

� � � � � �

� � � � � �

<sup>1</sup> � <sup>Δ</sup><sup>l</sup> l0

3

3

(10)

(12)

(16)

(17)

(18)

(19)

(20)

d t <sup>¼</sup> <sup>0</sup> (11)

Ud (13)

Ud (14)

Ud (15)

$$p\_a = c\_1 \begin{bmatrix} \left(\frac{di\_b^{(u1)}}{dt} - \frac{di\_b^{(u0)}}{dt}\right) + \frac{1}{2} \left(\frac{di\_b^{(u2)}}{dt} - \frac{di\_b^{(u0)}}{dt}\right) \\\\ + \frac{1}{2} \left(\frac{di\_a^{(u2)}}{dt} - \frac{di\_a^{(u0)}}{dt}\right) \end{bmatrix} \tag{27}$$


Table 1. Definition of position scalars of all voltage vectors in a delta-connected IM.

$$p\_{\beta} = \frac{\sqrt{3}}{2} c\_1 \left[ \left( \frac{d\dot{l}\_a^{(u2)}}{dt} - \frac{d\dot{l}\_a^{(u0)}}{dt} \right) - \left( \frac{d\dot{l}\_b^{(u2)}}{dt} - \frac{d\dot{l}\_b^{(u0)}}{dt} \right) \right] \tag{28}$$

whereby the position can be derived through the arctan operation as shown in (29).

$$\theta\_{an} = \arctan\left(p\_{\beta}/p\_a\right) \tag{29}$$

3. Experimental implementation

in Figure 4 when the reference voltage lies in Sector I.

It can be seen that the correct position estimation relies on the precise measurement of the di/dt signals. For this aim, air-cored Rogowski [9], ferrite-cored Rogowski [18], or air-cored coaxial cable-typed [14] transducers can be used. Or direct digital calculation, di/dt = i(t2)i(t1)/(t2t1), can be employed instead. Figure 3 shows a typical di/dt signal along with ADC trigger signal when an air-cored coaxial cable-typed transducer

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation…

http://dx.doi.org/10.5772/intechopen.75892

63

Another important issue comes from the fact that due to the common/differential mode voltages produced by the inverter, high-frequency oscillation exists in the phase currents, which poses a challenge for accurate di/dt measurement. This is true when dwell times of the voltage vectors are too short or when the reference voltage vectors pass the boundaries of sectors. Therefore, a minimum dwell time, tmin, is imposed on voltage vectors for di/dt measurement. When the original dwell time of a voltage vector, t, is shorter than tmin, an opposite vector with a dwell time, tmin- t, is added to maintain the volt-second. This procedure can be realized simply by the edge-shifting technique, which is illustrated

Figure 5 shows the system schematic of the sensorless speed control. Three di/dt sensors are connected in series with the lines of the induction motor, whose parameters are given in Table 2. The position vector formation block synthesizes the position vector pαβ according to the measured di/dts and the sector index (Si) of the reference voltage vector. For example,

Figure 3. ADC trigger signal (1,V) and di/dt signal (2,V) measured by a air-cored coaxial cable type transducers.

3.1. Practical considerations

is used.

3.2. System schematic

Such a combination between two adjacent voltage vectors, and a null vector, also exists in other five sectors. Therefore, the position estimation is achievable using only the fundamental PWM sequence. Table 1 gives the position scalars corresponding to all the vectors.

## 3. Experimental implementation

## 3.1. Practical considerations

It can be seen that the correct position estimation relies on the precise measurement of the di/dt signals. For this aim, air-cored Rogowski [9], ferrite-cored Rogowski [18], or air-cored coaxial cable-typed [14] transducers can be used. Or direct digital calculation, di/dt = i(t2)i(t1)/(t2t1), can be employed instead. Figure 3 shows a typical di/dt signal along with ADC trigger signal when an air-cored coaxial cable-typed transducer is used.

Another important issue comes from the fact that due to the common/differential mode voltages produced by the inverter, high-frequency oscillation exists in the phase currents, which poses a challenge for accurate di/dt measurement. This is true when dwell times of the voltage vectors are too short or when the reference voltage vectors pass the boundaries of sectors. Therefore, a minimum dwell time, tmin, is imposed on voltage vectors for di/dt measurement. When the original dwell time of a voltage vector, t, is shorter than tmin, an opposite vector with a dwell time, tmin- t, is added to maintain the volt-second. This procedure can be realized simply by the edge-shifting technique, which is illustrated in Figure 4 when the reference voltage lies in Sector I.

## 3.2. System schematic

p<sup>β</sup> ¼

62 Optimization and Control of Electrical Machines

ffiffiffi 3 p <sup>2</sup> <sup>c</sup><sup>1</sup>

Table 1. Definition of position scalars of all voltage vectors in a delta-connected IM.

dið Þ <sup>u</sup><sup>2</sup> a dt � dið Þ <sup>u</sup><sup>0</sup> a dt

!

whereby the position can be derived through the arctan operation as shown in (29).

PWM sequence. Table 1 gives the position scalars corresponding to all the vectors.

θan ¼ arctan pβ=p<sup>α</sup>

Such a combination between two adjacent voltage vectors, and a null vector, also exists in other five sectors. Therefore, the position estimation is achievable using only the fundamental

� dið Þ <sup>u</sup><sup>2</sup> b dt � dið Þ <sup>u</sup><sup>0</sup> b dt

(28)

(29)

" # !

� �

Figure 5 shows the system schematic of the sensorless speed control. Three di/dt sensors are connected in series with the lines of the induction motor, whose parameters are given in Table 2. The position vector formation block synthesizes the position vector pαβ according to the measured di/dts and the sector index (Si) of the reference voltage vector. For example,

Figure 3. ADC trigger signal (1,V) and di/dt signal (2,V) measured by a air-cored coaxial cable type transducers.

Figure 4. Edge shifting of PWM waveforms when the dwell times of u1 and u2 are smaller than tmin.

does not require a pre-commissioning phase. Rather it initiates a learning type sequence in which the resolver disturbance signals are estimated and continually refined as the machine passes through the appropriate torque-speed space [17]. The pdαβ\_m disturbance signals are stored in memory and are subtracted from the uncompensated signals to give the compensated signal prsαβ. The resulting position vector prsαβ is fed to the Speed/Position Calculation

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation…

http://dx.doi.org/10.5772/intechopen.75892

65

The Speed/Position Calculation block further refines the position signals. Because the ADIcompensated rotor slot position still consists of a speed dependent disturbance signal rotating at Nrωr/p-2ωi, which is attributed to the inter-modulation effect between the slotting and saturation in the machine [11], and can be conveniently removed by a side band filter [11].

The position signals obtained so far can be used for position acquisition in the way shown in (29). However, a mechanical observer similar to [19] is utilized to reduce the noise. The

block for the speed and position estimation.

The filtered position signal is shown in Figure 6.

schematic is given in Figure 7.

Table 2. Parameters of the IM.

Figure 5. System schematic of the sensorless speed control (ADI).

when Si = 1, Eqs. (27) and (28) can be used. Each of the other five sectors has its own set of equations like (27) and (28) such that the continuous position signal pαβ can be constructed. Ideally, pαβ can be used for position/speed estimation, but due to the presence of disturbance signals, which are mainly due to the saturation of the machine, such as the 2fe and 4fe components [3], the estimated position will become distorted if pαβ is used directly. This disturbance cannot be eliminated by filtering since the disturbance frequencies converge to the wanted signal frequencies as the excitation frequency approaches zero. As a result, a memory-type filter is required. In this work, an adaptive disturbance identifier (ADI) [17] is employed to separate these disturbance signals, i.e., pdαβ\_m, which are filtered out from pαβ. This identifier

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation… http://dx.doi.org/10.5772/intechopen.75892 65


Table 2. Parameters of the IM.

when Si = 1, Eqs. (27) and (28) can be used. Each of the other five sectors has its own set of equations like (27) and (28) such that the continuous position signal pαβ can be constructed. Ideally, pαβ can be used for position/speed estimation, but due to the presence of disturbance signals, which are mainly due to the saturation of the machine, such as the 2fe and 4fe components [3], the estimated position will become distorted if pαβ is used directly. This disturbance cannot be eliminated by filtering since the disturbance frequencies converge to the wanted signal frequencies as the excitation frequency approaches zero. As a result, a memory-type filter is required. In this work, an adaptive disturbance identifier (ADI) [17] is employed to separate these disturbance signals, i.e., pdαβ\_m, which are filtered out from pαβ. This identifier

Figure 5. System schematic of the sensorless speed control (ADI).

64 Optimization and Control of Electrical Machines

Figure 4. Edge shifting of PWM waveforms when the dwell times of u1 and u2 are smaller than tmin.

does not require a pre-commissioning phase. Rather it initiates a learning type sequence in which the resolver disturbance signals are estimated and continually refined as the machine passes through the appropriate torque-speed space [17]. The pdαβ\_m disturbance signals are stored in memory and are subtracted from the uncompensated signals to give the compensated signal prsαβ. The resulting position vector prsαβ is fed to the Speed/Position Calculation block for the speed and position estimation.

The Speed/Position Calculation block further refines the position signals. Because the ADIcompensated rotor slot position still consists of a speed dependent disturbance signal rotating at Nrωr/p-2ωi, which is attributed to the inter-modulation effect between the slotting and saturation in the machine [11], and can be conveniently removed by a side band filter [11]. The filtered position signal is shown in Figure 6.

The position signals obtained so far can be used for position acquisition in the way shown in (29). However, a mechanical observer similar to [19] is utilized to reduce the noise. The schematic is given in Figure 7.

Figure 6. Position estimation at 15 rpm with 75% rated load (fe =1.0 Hz). Top: filtered position signal; and bottom: estimated rotor position (rad).

4. Experimental results

due to the losses involved.

The following experiments show the operation of the drive under sensorless speed control at low and higher speeds. The induction motor drive is under speed sensorless control. The load machine is under torque control. The rating of the dynamometer converter is such that only a loading of 80% rate can be applied to the induction motor. It is emphasized that all the

Figure 8. Rotor position estimation (rad) at 210 rpm, no load top: before the observer, bottom: after the observer.

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation…

http://dx.doi.org/10.5772/intechopen.75892

67

Figure 9 shows that under no load condition the IM is reversed at 6 rpm, corresponding to the excitation frequency fe = 0.2 Hz. Good rotor estimation can be seen. In Figure 10, the drive performs a speed reversal at 12 rpm under 70% rated load condition. At –12 rpm, this load condition corresponds to the drive under braking at zero excitation frequency. Since a constant torque is applied to the DC load machine, under speed reversal, the amplitude of isq changes

In Figure 11, the drive was taken between 210 rpm under no load. This test confirms the

experimental waveforms were recorded on an experiment rig.

capability of the drive to perform larger speed transients.

Figure 7. Schematic of the modified mechanical observer (J is the moment of inertial and k is a design constant, s = d/dt).

Figure 8 shows an improved estimated rotor position signal before and after the observer. An offset angle can be observed between these two rotor positions. This is due to the fact that the mechanical observer's estimation was aligned to the encoder's angle initially, whereas the estimate from the SBF only yields the incremental position.

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation… http://dx.doi.org/10.5772/intechopen.75892 67

Figure 8. Rotor position estimation (rad) at 210 rpm, no load top: before the observer, bottom: after the observer.

## 4. Experimental results

Figure 8 shows an improved estimated rotor position signal before and after the observer. An offset angle can be observed between these two rotor positions. This is due to the fact that the mechanical observer's estimation was aligned to the encoder's angle initially, whereas the

Figure 7. Schematic of the modified mechanical observer (J is the moment of inertial and k is a design constant, s = d/dt).

Figure 6. Position estimation at 15 rpm with 75% rated load (fe =1.0 Hz). Top: filtered position signal; and bottom:

estimate from the SBF only yields the incremental position.

estimated rotor position (rad).

66 Optimization and Control of Electrical Machines

The following experiments show the operation of the drive under sensorless speed control at low and higher speeds. The induction motor drive is under speed sensorless control. The load machine is under torque control. The rating of the dynamometer converter is such that only a loading of 80% rate can be applied to the induction motor. It is emphasized that all the experimental waveforms were recorded on an experiment rig.

Figure 9 shows that under no load condition the IM is reversed at 6 rpm, corresponding to the excitation frequency fe = 0.2 Hz. Good rotor estimation can be seen. In Figure 10, the drive performs a speed reversal at 12 rpm under 70% rated load condition. At –12 rpm, this load condition corresponds to the drive under braking at zero excitation frequency. Since a constant torque is applied to the DC load machine, under speed reversal, the amplitude of isq changes due to the losses involved.

In Figure 11, the drive was taken between 210 rpm under no load. This test confirms the capability of the drive to perform larger speed transients.

Figure 9. Speed reversal at 6 rpm, no load top: measured speed (rpm), bottom: estimated rotor position (rad).

5. Conclusion

rotor position (rad).

Author details

Qiang Gao<sup>1</sup>

over the entire torque-speed envelope.

\*, Greg Asher<sup>2</sup> and Mark Sumner<sup>2</sup>

\*Address all correspondence to: gaoqiang@sjtu.edu.cn

1 Shanghai Jiao Tong University, Shanghai, China

2 University of Nottingham, Nottingham, UK

A sensorless position scheme for AC machines is presented relying on the line-current derivative measurements in response to a fundamental PWM switching sequence. The rotor position angle is derived due to the tracking of rotor slotting and the signal is used for sensorless control. If the anisotropy caused by the main flux saturation is tracked, for example, in a permanent magnet machine, this method is applicable throughout a very wide speed range. If rotor slotting is tracked, then the maximum speed is limited by the Nyquist frequency associated with the rotor slot passing frequency. In principle, however, the method can work

Figure 11. Speed reversal at 240 rpm, no load top: measured speed (1, rpm) and filtered Isq (2, A); bottom: estimated

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation…

http://dx.doi.org/10.5772/intechopen.75892

69

Figure 10. Speed reversal at 12 rpm under 70% rated load top: measured speed (rpm), bottom: rotor flux angle (1, rad) and filtered Isq (2, A).

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation… http://dx.doi.org/10.5772/intechopen.75892 69

Figure 11. Speed reversal at 240 rpm, no load top: measured speed (1, rpm) and filtered Isq (2, A); bottom: estimated rotor position (rad).

## 5. Conclusion

Figure 9. Speed reversal at 6 rpm, no load top: measured speed (rpm), bottom: estimated rotor position (rad).

Figure 10. Speed reversal at 12 rpm under 70% rated load top: measured speed (rpm), bottom: rotor flux angle (1, rad)

and filtered Isq (2, A).

68 Optimization and Control of Electrical Machines

A sensorless position scheme for AC machines is presented relying on the line-current derivative measurements in response to a fundamental PWM switching sequence. The rotor position angle is derived due to the tracking of rotor slotting and the signal is used for sensorless control. If the anisotropy caused by the main flux saturation is tracked, for example, in a permanent magnet machine, this method is applicable throughout a very wide speed range. If rotor slotting is tracked, then the maximum speed is limited by the Nyquist frequency associated with the rotor slot passing frequency. In principle, however, the method can work over the entire torque-speed envelope.

## Author details

Qiang Gao<sup>1</sup> \*, Greg Asher<sup>2</sup> and Mark Sumner<sup>2</sup>


## References

[1] Jansen PL, Lorenz RD. Transducerless field orientation concepts employing saturation induced saliencies in induction machines. In: Proceedings of the IEEE IAS Annual Meeting; Nov/Dec 1995. p. 174-181

[14] Juliet J, Holtz J. Sensorless Acquisition of the rotor position angle for induction motors with arbitrary stator windings. In: Proceedings of the IEEE IAS Annual Meeting on CD-

Zero and Low-Speed Sensorless Control of Induction Machines Using Only Fundamental Pulse Width Modulation…

http://dx.doi.org/10.5772/intechopen.75892

71

[15] Erdman JM, Kerkman RJ, Schlegel DW, Skibinski GL. Effect of PWM inverters on AC motor bearing currents and shaft voltages. IEEE Transactions on Industrial Applications.

[16] Gao Q, Asher GM, Sumner M, Makyš P. Position estimation of AC machines at all frequencies using only space vector PWM based excitation. In: Proceedings of the IEE 3rd International Conference on Power Electronics, Machines and Drives (PEMD); 2006.

[17] Gao Q, Asher GM, Sumner M. Sensorless position and speed control of induction motors using high frequency injection and without off-line pre-commissioning. In: Proceedings of

[18] Wolbank TM, Machl JL, Hauser H. Closed-loop compensating sensors versus new current derivative sensors for shaft-sensorless control of inverter fed induction machines. IEEE Transactions on Instrumentation and Measurement. 2004;53(4):1311-1315. DOI: 10.1109/

[19] Jansen PL, Lorenz RD. Transducerless position and velocity estimation in induction and salient AC machines. IEEE Transactions on Industry Applications. 1995;31(2):240-247.

the 31st Annual Meeting of IEEE, IES 2005 on CD-ROM; 2005

ROM; 2004

p. 61-70

TIM.2004.830561

DOI: 10.1109/28.370269

1996;32(2):250-259. DOI: 10.1109/28.491472


[14] Juliet J, Holtz J. Sensorless Acquisition of the rotor position angle for induction motors with arbitrary stator windings. In: Proceedings of the IEEE IAS Annual Meeting on CD-ROM; 2004

References

ing; Nov/Dec 1995. p. 174-181

70 Optimization and Control of Electrical Machines

CD-ROM; 2002

CD-ROM; 2002

Meeting on CD-ROM; 2004

2002; Pittsburgh

[1] Jansen PL, Lorenz RD. Transducerless field orientation concepts employing saturation induced saliencies in induction machines. In: Proceedings of the IEEE IAS Annual Meet-

[2] Holtz J. Sensorless position control of induction motors – An emerging technology. IEEE Transactions on Industrial Electronics. 1998;45(6):840-852. DOI: 10.1109/41.735327

[3] Teske N, Asher GM, Sumner M, Bradley KJ. Encoderless position estimation for symmetric cage induction machines under loaded conditions. IEEE Transactions on Industrial

[4] Silva CA, Asher GM, Sumner M, Bradley KJ. Sensorless rotor position control in a surface mounted PM machine using HF voltage injection. In: Proceedings of the EPE –PEMC on

[5] Linke M, Kennel R, Holtz J Sensorless position control of permanent magnet synchronous machines without limitation at zero speed. In: Proceedings of the IEEE IECON 2002 on

[6] Corley MJ, Lorenz RD. Rotor position and velocity estimation for a salient-pole permanent magnet synchronous machine at standstill and high speeds. IEEE Transactions on Indus-

[7] Ha JI, Sul SK. Sensorless field orientation of an induction machine by high frequency signal injection. In: Proceedings of the IEEE IAS Annual Meeting; 1997. p. 426-432

[8] Schroedl M. Sensorless control of AC machines at low speed and standstill based on the INFORM method. In: Proceedings of the IEEE IAS Annual Meeting; 1996. p. 270-277

[9] Caruana C, Asher GM, Clare J. Sensorless flux position estimation at low and zero frequency by measuring zero-sequence current in delta connected cage induction machines.

[10] Staines CS, Asher GM, Sumner M. Sensorless control of induction machines at zero and low frequency using zero sequence currents. In: Proceedings of the IEEE IAS Annual

[11] Holtz J, Pan H. Elimination of saturation effects in sensorless position controlled induction motors. In: Proceedings of the IEEE IAS Annual Meeting on CD-ROM; 13–18 October

[12] Robeischl E, Schroedl M. Optimized INFORM measurement sequence for sensorless PM synchronous motor drives with respect to minimum current distortion. IEEE Transactions

[13] Wolbank T, Machl J. A modified PWM scheme in order to obtain spatial information of ac machines without mechanical sensor. In: Proceedings of the IEEE APEC; 2002. p. 310-315

on Industrial Applications. 2004;40(2):591-598. DOI: 10.1109/TIA.2004.824510

Applications. 2001;37(6):1793-1800. DOI: 10.1109/28.968193

try Applications. 1998;34(4):784-789. DOI: 10.1109/28.703973

In: Proceedings of the IEEE IAS Annual Meeting on CD-ROM; 2003


**Chapter 5**

Provisional chapter

**Rotor Flux Reference Generation Control Strategy for**

DOI: 10.5772/intechopen.75362

The wind turbines based Doubly Fed Induction Generator (DFIG) is not able to support the voltage and the frequency of the grid during and immediately following the grid failure. This would cause major problems for the systems stability, but the turbines should stay connected to the grid in case of a failure. This can be achieved by using crowbar protection in particularly during voltage dips. When low depth voltage dips occur, the necessity of crowbar protection can be eliminated by using proposed Direct Torque Control (DTC), with a proper rotor flux generation strategy, by which during the fault it will be possible to maintain the machine connected to grid, generating power from the wind, reducing the stator and rotor over currents, eliminating the torque oscillations that normally produce such voltage dips and fast dynamic response accompanies the overall control of the wind turbine. In this chapter, the DFIG performance is analyzed and the results are presented for with proposed control strategy with and without voltage dip, without control strategy with voltage dip, and control strategy during longer voltage dip.

Keywords: crowbar protection, direct torque control, doubly fed induction generator,

The main objective of the control strategy proposed for DFIG [1] in this chapter is to eliminate the necessity of the crowbar protection [2] when low voltage dips occur. Hence, by using Direct Torque Control (DTC), with a proper rotor flux generation control strategy, during the fault it is possible to maintain the machine connected to the grid [3, 4], generating power from the wind, reducing over currents, and eliminating the torque oscillations that normally produce over

> © 2016 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 eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. 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.

Rotor Flux Reference Generation Control Strategy for

**Direct Torque Controlled DFIG**

Direct Torque Controlled DFIG

Gopala Venu Madhav and Y. P. Obulesu

Gopala Venu Madhav and Y. P. Obulesu

http://dx.doi.org/10.5772/intechopen.75362

Abstract

1. Introduction

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

reference generation strategy, voltage dip

#### **Rotor Flux Reference Generation Control Strategy for Direct Torque Controlled DFIG** Rotor Flux Reference Generation Control Strategy for Direct Torque Controlled DFIG

DOI: 10.5772/intechopen.75362

Gopala Venu Madhav and Y. P. Obulesu Gopala Venu Madhav and Y. P. Obulesu

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.75362

#### Abstract

The wind turbines based Doubly Fed Induction Generator (DFIG) is not able to support the voltage and the frequency of the grid during and immediately following the grid failure. This would cause major problems for the systems stability, but the turbines should stay connected to the grid in case of a failure. This can be achieved by using crowbar protection in particularly during voltage dips. When low depth voltage dips occur, the necessity of crowbar protection can be eliminated by using proposed Direct Torque Control (DTC), with a proper rotor flux generation strategy, by which during the fault it will be possible to maintain the machine connected to grid, generating power from the wind, reducing the stator and rotor over currents, eliminating the torque oscillations that normally produce such voltage dips and fast dynamic response accompanies the overall control of the wind turbine. In this chapter, the DFIG performance is analyzed and the results are presented for with proposed control strategy with and without voltage dip, without control strategy with voltage dip, and control strategy during longer voltage dip.

Keywords: crowbar protection, direct torque control, doubly fed induction generator, reference generation strategy, voltage dip

## 1. Introduction

The main objective of the control strategy proposed for DFIG [1] in this chapter is to eliminate the necessity of the crowbar protection [2] when low voltage dips occur. Hence, by using Direct Torque Control (DTC), with a proper rotor flux generation control strategy, during the fault it is possible to maintain the machine connected to the grid [3, 4], generating power from the wind, reducing over currents, and eliminating the torque oscillations that normally produce over

© 2016 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 eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. 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.

voltage dips [5–9]. Elimination of crowbar protection is cost effective and reducing bulkiness and reducing circuitry besides the above mentioned advantages of the proposed strategy.

condition, i.e., during an voltage dip. During the voltage dip, if DFIG is maintained with constant electromagnetic torque and rotor flux amplitude, that means if no control strategy is been adopted then it leads to non-sinusoidal grid currents making the grid to be in unstabilized condition. The proposed control strategy eliminates the perturbations in electromagnetic torque, makes it to be within the stabilized limits, reduce the stator and rotor overcurrents produced leading to elimination of the crowbar protection during low voltage dips and generate sinusoidal grid currents without the necessity to change the hardware requirement and also the prevalent control philosophy adopted. The behavior of the DFIG during the voltage dip with and without

Rotor Flux Reference Generation Control Strategy for Direct Torque Controlled DFIG

http://dx.doi.org/10.5772/intechopen.75362

75

The DFIM is fed with back-to-back converter. It consists of two converters, i.e., machine-side converter and grid-side converter that are connected "back-to-back." Between the two converters a dc-link capacitor is placed, as energy storage, in order to keep the voltage variations (or ripple) in the dc-link voltage small. With the machine-side converter it is possible to control the torque or the speed of the DFIG and also the power factor at the stator terminals, the main objective for the grid-side converter is to keep the dc-link voltage constant. As the rotor current or voltage is lower, power is lower because of which the converter rating is 30% of the full-

In this chapter, a control strategy has been developed for the rotor side converter to generate rotor flux reference. The conventional Pulse Width Modulation (PWM) technique is adopted for grid-side converter; the converter maintains the dc-link voltage to be constant and also supplies the reactive power to the grid through it. As shown in Figure 1, the DFIM control is divided into two different control blocks. A DTC that controls the machine's torque (Tem) and the rotor flux amplitude (|ψr|) with high dynamic capacity, and a second block that generates the rotor flux amplitude reference, in order to handle with the voltage dips. The details of rotor flux reference generation are shown in Figure 2. The required rotor voltage vector is selected

When the wind turbine is affected by a voltage dip, it needs to address three main problems: the first problem is based on the view of the control strategy being adopted, the dip produces control difficulties, since it is a perturbation in the winding of the machine that is not being directly

proposed control strategy is validated with the results presented.

rated machine which makes to be the main advantage of DFIM.

based on the vector selection table as mentioned in Table 1.

Figure 2. Details of rotor flux reference generation control strategy.

This proposed control strategy gives fast dynamic response for voltage dips during electrical grid disturbances keeping the stator and rotor over currents within the considerable limits.

In Section 1, essence of the rotor flux reference generation scheme with Direct Torque Control (DTC) strategy of DFIM is briefly given.

In Section 2, description of the proposed control strategy is given.

In Section 3, the rotor flux reference generation strategy is described.

In Section 4, the results are presented for with and without fault condition for low and longer voltage dip.

In Section 5, the summary of the chapter is given.

## 2. Direct torque control strategy for rotor side converter

Figure 1 shows the wind turbine generation system with the DTC technique along with the rotor flux amplitude reference generation strategy to control the DFIG during the unbalanced

Figure 1. Block diagram of DTC of DFIM with rotor flux reference generation control strategy.

condition, i.e., during an voltage dip. During the voltage dip, if DFIG is maintained with constant electromagnetic torque and rotor flux amplitude, that means if no control strategy is been adopted then it leads to non-sinusoidal grid currents making the grid to be in unstabilized condition. The proposed control strategy eliminates the perturbations in electromagnetic torque, makes it to be within the stabilized limits, reduce the stator and rotor overcurrents produced leading to elimination of the crowbar protection during low voltage dips and generate sinusoidal grid currents without the necessity to change the hardware requirement and also the prevalent control philosophy adopted. The behavior of the DFIG during the voltage dip with and without proposed control strategy is validated with the results presented.

voltage dips [5–9]. Elimination of crowbar protection is cost effective and reducing bulkiness and

This proposed control strategy gives fast dynamic response for voltage dips during electrical grid disturbances keeping the stator and rotor over currents within the considerable limits.

In Section 1, essence of the rotor flux reference generation scheme with Direct Torque Control

In Section 4, the results are presented for with and without fault condition for low and longer

Figure 1 shows the wind turbine generation system with the DTC technique along with the rotor flux amplitude reference generation strategy to control the DFIG during the unbalanced

reducing circuitry besides the above mentioned advantages of the proposed strategy.

In Section 2, description of the proposed control strategy is given.

In Section 3, the rotor flux reference generation strategy is described.

2. Direct torque control strategy for rotor side converter

Figure 1. Block diagram of DTC of DFIM with rotor flux reference generation control strategy.

(DTC) strategy of DFIM is briefly given.

74 Optimization and Control of Electrical Machines

In Section 5, the summary of the chapter is given.

voltage dip.

The DFIM is fed with back-to-back converter. It consists of two converters, i.e., machine-side converter and grid-side converter that are connected "back-to-back." Between the two converters a dc-link capacitor is placed, as energy storage, in order to keep the voltage variations (or ripple) in the dc-link voltage small. With the machine-side converter it is possible to control the torque or the speed of the DFIG and also the power factor at the stator terminals, the main objective for the grid-side converter is to keep the dc-link voltage constant. As the rotor current or voltage is lower, power is lower because of which the converter rating is 30% of the fullrated machine which makes to be the main advantage of DFIM.

In this chapter, a control strategy has been developed for the rotor side converter to generate rotor flux reference. The conventional Pulse Width Modulation (PWM) technique is adopted for grid-side converter; the converter maintains the dc-link voltage to be constant and also supplies the reactive power to the grid through it. As shown in Figure 1, the DFIM control is divided into two different control blocks. A DTC that controls the machine's torque (Tem) and the rotor flux amplitude (|ψr|) with high dynamic capacity, and a second block that generates the rotor flux amplitude reference, in order to handle with the voltage dips. The details of rotor flux reference generation are shown in Figure 2. The required rotor voltage vector is selected based on the vector selection table as mentioned in Table 1.

When the wind turbine is affected by a voltage dip, it needs to address three main problems: the first problem is based on the view of the control strategy being adopted, the dip produces control difficulties, since it is a perturbation in the winding of the machine that is not being directly

Figure 2. Details of rotor flux reference generation control strategy.


Table 1. Selection of voltage vectors.

controlled (the stator); the second problem is the dip generates a disturbance in the stator flux, making necessary higher rotor voltage to maintain control on the machine currents; and the third problem is if there are no special improvements being adopted, the power delivered through the rotor by the back-to-back converter, will be increased due to the increase of voltage and currents [3, 5] in the rotor of the machine, provoking finally, an increase of the dc bus voltage [10, 11].

Taking into account this, depending on the dip depth and asymmetry, together with the machine operation conditions at the moment of the dip (speed, torque, mechanical power, etc.), implies that the necessity of the crowbar protection is inevitable in many faulty situations [12]. However, in this chapter, a control strategy that eliminates the necessity of the crowbar activation in some low depth voltage dips is proposed.

## 3. Rotor flux reference generation control strategy

The stator flux evolution of the machine is determined from the stator voltage equation as given by:

$$\mathbf{\overline{v}\_s^s} = \mathbf{R\_s}\mathbf{\overline{i}\_s^s} + \frac{\mathbf{d}\overline{\psi\_s^s}}{\mathbf{dt}} \tag{1}$$

Tem <sup>¼</sup> <sup>3</sup> 4 p Lm σLsLr

rotor fluxes and even the currents.

sinusoidal currents exchange with the grid.

voltage space vector [5] can be expressed as:

ψs � � � � 2 <sup>¼</sup> <sup>Ψ</sup><sup>2</sup>

> ψr � � � � 2 <sup>¼</sup> <sup>Ψ</sup><sup>2</sup>

mated as the addition of exponential and sinusoidal term.

<sup>α</sup><sup>s</sup> þ Ψ 2 βs 2

> <sup>α</sup><sup>r</sup> þ Ψ 2 βr 2

3 5 þ

> 3 5 þ

2 4

> 2 4

ΨβsΨα<sup>r</sup> þ ΨαsΨβ<sup>r</sup>

� �sinð Þþ <sup>δ</sup> ΨβsΨα<sup>r</sup> � ΨαsΨβ<sup>r</sup>

From Eq. (4), it can be observed that the torque expression consists of a constant term and an oscillating term. In general, for a given machine torque should be constant and it should not be oscillatory, if it is so it will lead to mechanical instability of the wind energy conversion system. Therefore, the oscillatory term has to be somehow canceled or make it zero. So, equating the oscillatory term to zero, it leads to condition, i.e., Eq. (5), wherein the ratio of the amplitudes of rotor and stator flux space vectors should be equal, which has to be maintained properly during the unbalanced condition. Otherwise, it will lead to oscillatory behavior of stator and

> Ψα<sup>r</sup> Ψβ<sup>r</sup>

<sup>¼</sup> Ψα<sup>s</sup> Ψβ<sup>s</sup>

From Eq. (5), one more inference is that the rotor flux reference generation should be in accordance to the above equation. Further, it can be deduced that during the unbalance condition as the stator flux space vector oscillates, likewise the rotor flux space vector should be made oscillatory, so that the torque with respect to the Eq. (2) is constant and sinusoidal currents exchange with the grid. If otherwise, it leads to oscillatory behavior in torque and leads to non-

As said previously, from Eq. (1), the unbalance grid voltage will produce an oscillatory behavior in stator flux space vector and further in rotor flux space vector. This oscillatory behavior in terms of the amplitudes of both stator and rotor flux space vectors similar to the unbalance

> Ψ2 <sup>α</sup><sup>s</sup> � Ψ 2 βs 2

2 4

Eq. (6) fulfill the Eq. (5), so in order to produce constant torque and sinusoidal currents to be exchanged with the grid, the rotor flux reference generation should be according to Eq. (6). Further discussion shows how this oscillatory rotor flux reference generation is created.

Stator flux equations are given in Eq. (7) (neglecting stator resistance, Rs) [1], it is approxi-

<sup>Ψ</sup>α<sup>s</sup> <sup>¼</sup> K1e�K2t <sup>þ</sup> K3cosð Þ <sup>ω</sup>St <sup>þ</sup> K4 <sup>Ψ</sup>β<sup>s</sup> <sup>¼</sup> K5e�K2t <sup>þ</sup> K3sinð Þ <sup>ω</sup>St <sup>þ</sup> K4

where K1 to K5 are constants which depends on nature and the moment when voltage dip occurs. In accordance to Eq. (5), the exponential term in Eq. (7) can be eliminated by producing

simultaneous oscillations in rotor flux as produced in stator flux due to unbalance.

Ψ2 <sup>α</sup><sup>r</sup> � Ψ 2 βr 2

3

3

5cos 2ð Þ ωt þ δ

5cos 2ð Þ ωt

2 4

� �sin 2ð Þ <sup>ω</sup><sup>t</sup> <sup>þ</sup> <sup>δ</sup> � � (4)

Rotor Flux Reference Generation Control Strategy for Direct Torque Controlled DFIG

http://dx.doi.org/10.5772/intechopen.75362

(5)

77

(6)

(7)

The torque can be estimated by using the following expression:

$$\mathbf{T\_{em}} = \frac{3}{2} \mathbf{p} \frac{\mathbf{L\_m}}{\sigma \mathbf{L\_s} \mathbf{L\_r}} \text{Im} \left\{ \overline{\boldsymbol{\psi}}\_\mathbf{r}^\*, \overline{\boldsymbol{\psi}}\_\mathbf{s}^\* \right\} \tag{2}$$

From the Eq. (1), considering the stator resistive drop as negligible, the unbalance in the grid voltage will directly affect the stator voltage and because of that it affects the stator flux space vector as the stator is directly connected to grid. That means, the oscillating behavior produced in the grid voltage due to unbalance will be reflected onto the stator flux space vector and further onto the rotor flux space vector [5]. The unbalance case of both the stator and the rotor flux space vectors can be represented mathematically as:

$$\begin{aligned} \overline{\psi}\_{\text{s}} &= \psi\_{\text{as}} + \text{j}\psi\_{\text{\beta}\text{s}} = \overline{\Psi}\_{\text{at}}\cos(\omega t + \delta) + \text{j}\overline{\Psi}\_{\text{\beta}\text{s}}\sin(\omega t + \delta) \\ \overline{\psi}\_{\text{r}} &= \psi\_{\text{ar}} + \text{j}\psi\_{\text{\beta}\text{r}} = \overline{\Psi}\_{\text{ar}}\cos(\omega \text{t}) + \text{j}\overline{\Psi}\_{\text{\beta}\text{r}}\sin(\omega \text{t}) \end{aligned} \tag{3}$$

Substituting Eq. (3) in Eq. (2), it leads to:

$$\mathbf{T\_{em}} = \frac{3}{4} \mathbf{p} \frac{\mathbf{L\_{m}}}{\sigma \mathbf{L\_{s}} \mathbf{L\_{r}}} \left[ (\overline{\Psi}\_{\beta \ast} \overline{\Psi}\_{\alpha \cdot} + \overline{\Psi}\_{\alpha \ast} \overline{\Psi}\_{\beta \ast}) \sin(\delta) + (\overline{\Psi}\_{\beta \ast} \overline{\Psi}\_{\alpha \cdot} - \overline{\Psi}\_{\alpha \ast} \overline{\Psi}\_{\beta \ast}) \sin(2\omega t + \delta) \right] \tag{4}$$

From Eq. (4), it can be observed that the torque expression consists of a constant term and an oscillating term. In general, for a given machine torque should be constant and it should not be oscillatory, if it is so it will lead to mechanical instability of the wind energy conversion system. Therefore, the oscillatory term has to be somehow canceled or make it zero. So, equating the oscillatory term to zero, it leads to condition, i.e., Eq. (5), wherein the ratio of the amplitudes of rotor and stator flux space vectors should be equal, which has to be maintained properly during the unbalanced condition. Otherwise, it will lead to oscillatory behavior of stator and rotor fluxes and even the currents.

controlled (the stator); the second problem is the dip generates a disturbance in the stator flux, making necessary higher rotor voltage to maintain control on the machine currents; and the third problem is if there are no special improvements being adopted, the power delivered through the rotor by the back-to-back converter, will be increased due to the increase of voltage and currents [3, 5] in the rotor of the machine, provoking finally, an increase of the dc bus voltage [10, 11].

Error of rotor flux 1 V(n�1) V0, V7 V(n+1)

Error of electromagnetic torque

Taking into account this, depending on the dip depth and asymmetry, together with the machine operation conditions at the moment of the dip (speed, torque, mechanical power, etc.), implies that the necessity of the crowbar protection is inevitable in many faulty situations [12]. However, in this chapter, a control strategy that eliminates the necessity of the crowbar activation in some

The stator flux evolution of the machine is determined from the stator voltage equation as given by:

From the Eq. (1), considering the stator resistive drop as negligible, the unbalance in the grid voltage will directly affect the stator voltage and because of that it affects the stator flux space vector as the stator is directly connected to grid. That means, the oscillating behavior produced in the grid voltage due to unbalance will be reflected onto the stator flux space vector and further onto the rotor flux space vector [5]. The unbalance case of both the stator and the rotor

ψ<sup>s</sup> ¼ ψα<sup>s</sup> þ jψβ<sup>s</sup> ¼ Ψαscosð Þþ ωt þ δ jΨβssinð Þ ωt þ δ

<sup>ψ</sup><sup>r</sup> <sup>¼</sup> ψα<sup>r</sup> <sup>þ</sup> <sup>j</sup>ψβ<sup>r</sup> <sup>¼</sup> Ψαrcosð Þþ <sup>ω</sup><sup>t</sup> <sup>j</sup>Ψβrsinð Þ <sup>ω</sup><sup>t</sup> (3)

Im ψ<sup>∗</sup> <sup>r</sup> :ψ<sup>s</sup> s n o

dt (1)

1 0 �1

�1 V(n�2) V0, V7 V(n+2)

(2)

vs <sup>s</sup> ¼ Rsi s <sup>s</sup> þ dψ<sup>s</sup> s

Tem <sup>¼</sup> <sup>3</sup> 2 p Lm σLsLr

low depth voltage dips is proposed.

Table 1. Selection of voltage vectors.

76 Optimization and Control of Electrical Machines

n = sector

3. Rotor flux reference generation control strategy

The torque can be estimated by using the following expression:

flux space vectors can be represented mathematically as:

Substituting Eq. (3) in Eq. (2), it leads to:

$$\frac{\overline{\Psi}\_{\rm ar}}{\overline{\Psi}\_{\beta \rm r}} = \frac{\overline{\Psi}\_{\rm os}}{\overline{\Psi}\_{\beta \rm s}} \tag{5}$$

From Eq. (5), one more inference is that the rotor flux reference generation should be in accordance to the above equation. Further, it can be deduced that during the unbalance condition as the stator flux space vector oscillates, likewise the rotor flux space vector should be made oscillatory, so that the torque with respect to the Eq. (2) is constant and sinusoidal currents exchange with the grid. If otherwise, it leads to oscillatory behavior in torque and leads to nonsinusoidal currents exchange with the grid.

As said previously, from Eq. (1), the unbalance grid voltage will produce an oscillatory behavior in stator flux space vector and further in rotor flux space vector. This oscillatory behavior in terms of the amplitudes of both stator and rotor flux space vectors similar to the unbalance voltage space vector [5] can be expressed as:

$$\begin{aligned} \left| \overline{\boldsymbol{\Psi}}\_{s} \right|^{2} &= \left[ \frac{\overline{\boldsymbol{\Psi}}\_{\alpha s}^{2} + \overline{\boldsymbol{\Psi}}\_{\beta s}^{2}}{2} \right] + \left[ \frac{\overline{\boldsymbol{\Psi}}\_{\alpha s}^{2} - \overline{\boldsymbol{\Psi}}\_{\beta s}^{2}}{2} \right] \cos(2\omega t + 8) \\\ \left| \overline{\boldsymbol{\Psi}}\_{r} \right|^{2} &= \left[ \frac{\overline{\boldsymbol{\Psi}}\_{ar}^{2} + \overline{\boldsymbol{\Psi}}\_{\beta r}^{2}}{2} \right] + \left[ \frac{\overline{\boldsymbol{\Psi}}\_{ar}^{2} - \overline{\boldsymbol{\Psi}}\_{\beta r}^{2}}{2} \right] \cos(2\omega t) \end{aligned} \tag{6}$$

Eq. (6) fulfill the Eq. (5), so in order to produce constant torque and sinusoidal currents to be exchanged with the grid, the rotor flux reference generation should be according to Eq. (6). Further discussion shows how this oscillatory rotor flux reference generation is created.

Stator flux equations are given in Eq. (7) (neglecting stator resistance, Rs) [1], it is approximated as the addition of exponential and sinusoidal term.

$$\begin{aligned} \overline{\Psi}\_{\rm as} &= \mathbf{K}\_1 \mathbf{e}^{-\mathbf{K}\_2 \mathbf{t}} + \mathbf{K}\_3 \cos(\omega\_3 \mathbf{t} + \mathbf{K}\_4) \\ \overline{\Psi}\_{\rm \beta} &= \mathbf{K}\_5 \mathbf{e}^{-\mathbf{K}\_2 \mathbf{t}} + \mathbf{K}\_3 \sin(\omega\_3 \mathbf{t} + \mathbf{K}\_4) \end{aligned} \tag{7}$$

where K1 to K5 are constants which depends on nature and the moment when voltage dip occurs. In accordance to Eq. (5), the exponential term in Eq. (7) can be eliminated by producing simultaneous oscillations in rotor flux as produced in stator flux due to unbalance.

The stator and rotor currents are given in Eq. (8).

$$
\overline{\mathbf{I}}\_s^s = \frac{\mathbf{L}\_{\rm m}}{\sigma \mathbf{L}\_{\rm r} \mathbf{L}\_s} \left( \frac{\mathbf{L}\_{\rm r}}{\mathbf{L}\_{\rm h}} \overline{\overline{\Psi}}\_s^s - \overline{\Psi}\_{\rm r}^s \right)
$$

$$
\overline{\mathbf{I}}\_{\rm r}^s = \frac{\mathbf{L}\_{\rm m}}{\sigma \mathbf{L}\_{\rm r} \mathbf{L}\_s} \left( \frac{\mathbf{L}\_{\rm s}}{\mathbf{L}\_{\rm h}} \overline{\overline{\Psi}}\_{\rm r}^s - \overline{\Psi}\_{\rm s}^s \right) \tag{8}
$$

will be the reference value of flux. The stator voltage waveform shown in Figure 3(a), from the

Rotor Flux Reference Generation Control Strategy for Direct Torque Controlled DFIG

http://dx.doi.org/10.5772/intechopen.75362

79

The torque is maintained at its generated value of 0.2 pu as there is no consideration of voltage

Figure 3. (a) Stator voltages of DFIM with proposed rotor flux reference generation without voltage dip, (b) torque of DFIM with proposed rotor flux reference generation without voltage dip, (c) stator and rotor flux of DFIM with proposed rotor flux reference generation without voltage dip, (d) rotor currents of DFIM with proposed rotor flux reference generation without voltage dip, (e) stator currents of DFIM with proposed rotor flux reference generation without voltage

dip, and (f) DC-link voltage of DFIM with proposed rotor flux reference generation without voltage dip.

figure, it is observed that the stator voltage is constant under normal operation.

dip, which is clearly shown in Figure 3(b).

As depicted in Figure 2, the proposed rotor flux amplitude reference generation strategy, adds a term (Δ|ψr|) to the required reference rotor flux amplitude according to the following expression:

$$
\Delta \left| \overline{\psi}\_{\mathbf{r}} \right| = \left| \overline{\psi}\_{\mathbf{s}} \right| - \frac{\left| \overline{\mathbf{v}}\_{\mathbf{s}} \right|}{\omega\_{\mathbf{s}}} \tag{9}
$$

with |ψs|, the estimated stator flux amplitude and |vs| voltage of the grid (not affected by the dip). This voltage can be calculated by several methods, for instance, using a simple small bandwidth low-pass filter, as illustrated in Figure 2. It must be highlighted that constants K1–K5 from Eq. (7) are not needed in the rotor flux reference generation reducing its complexity.

The stator and rotor fluxes and their magnitudes can be calculated by using:

$$\begin{aligned} \overline{\Psi}\_{\rm s} &= \mathcal{L}\_{\rm s} \overline{\mathcal{I}}\_{\rm s} + \mathcal{L}\_{\rm m} \overline{\mathcal{I}}\_{\rm r} \\ \overline{\Psi}\_{\rm r} &= \mathcal{L}\_{\rm m} \overline{\mathcal{I}}\_{\rm s} + \mathcal{L}\_{\rm r} \overline{\mathcal{I}}\_{\rm r} \\ |\psi\_{\rm s}| &= \sqrt{\psi\_{\rm ds}^{2}} + \psi\_{\rm qs}^{2} \\ |\psi\_{\rm r}| &= \sqrt{\psi\_{\rm dr}^{2}} + \psi\_{\rm qr}^{2} \end{aligned} \tag{10}$$

When there is voltage dip condition, the proposed control scheme makes the rotor flux produce the oscillations in similar to stator flux and when there is no dip the stator and rotor fluxes will be constant, which means the term Δ ψ<sup>r</sup> � � � � shown in Figure 2 is zero.

## 4. Results and discussion

The ratings of the DFIM and the wind turbine are 2.6 MW, 690 V, 50 Hz, 4-pole machine and 3 blades, rotor diameter of 70 m, hub height of 84.3 m, cut-in wind speed of 3 ms�<sup>1</sup> , cut-out wind speed of 25 ms�<sup>1</sup> and rated wind speed of 15 ms�<sup>1</sup> , respectively. The stator-to-rotor turns ratio, Ns/Nr is 0.34, and the rotor current is approximately 0.34 times smaller than the stator current, if the magnetizing current is neglected. The stator-to-rotor turns ratio of the DFIG is required to estimate the ohmic loss as it depends on current passing through it.

#### 4.1. Analysis of DFIG with rotor flux reference generation without voltage dip

The results are presented in the case of without symmetrical voltage dip as shown in Figure 3 that means, the value of Δ ψ<sup>r</sup> � � � � in Figure 2 will be zero, therefore the required value of rotor flux will be the reference value of flux. The stator voltage waveform shown in Figure 3(a), from the figure, it is observed that the stator voltage is constant under normal operation.

The stator and rotor currents are given in Eq. (8).

78 Optimization and Control of Electrical Machines

i s <sup>s</sup> <sup>¼</sup> Lm σLrLs

i s <sup>r</sup> <sup>¼</sup> Lm σLrLs

> Δ ψ<sup>r</sup> � � � � ¼ ψ<sup>s</sup> � � � � � vs j j ωs

Lr Lh Ψ s s � <sup>Ψ</sup><sup>s</sup> r

Ls Lh Ψ s r � <sup>Ψ</sup><sup>s</sup> s

As depicted in Figure 2, the proposed rotor flux amplitude reference generation strategy, adds a term (Δ|ψr|) to the required reference rotor flux amplitude according to the following expression:

with |ψs|, the estimated stator flux amplitude and |vs| voltage of the grid (not affected by the dip). This voltage can be calculated by several methods, for instance, using a simple small bandwidth low-pass filter, as illustrated in Figure 2. It must be highlighted that constants K1–K5

> ψ<sup>s</sup> ¼ LsIs þ LmIr ψ<sup>r</sup> ¼ LmIs þ LrIr

> > ffiffiffiffiffiffiffi ψ2 ds q

> > ffiffiffiffiffiffiffi ψ2 dr q

When there is voltage dip condition, the proposed control scheme makes the rotor flux produce the oscillations in similar to stator flux and when there is no dip the stator and rotor

The ratings of the DFIM and the wind turbine are 2.6 MW, 690 V, 50 Hz, 4-pole machine and

turns ratio, Ns/Nr is 0.34, and the rotor current is approximately 0.34 times smaller than the stator current, if the magnetizing current is neglected. The stator-to-rotor turns ratio of the DFIG is required to estimate the ohmic loss as it depends on current passing through it.

The results are presented in the case of without symmetrical voltage dip as shown in Figure 3

3 blades, rotor diameter of 70 m, hub height of 84.3 m, cut-in wind speed of 3 ms�<sup>1</sup>

4.1. Analysis of DFIG with rotor flux reference generation without voltage dip

� � �

<sup>þ</sup> <sup>ψ</sup><sup>2</sup> qs

<sup>þ</sup> <sup>ψ</sup><sup>2</sup> qr

� shown in Figure 2 is zero.

� in Figure 2 will be zero, therefore the required value of rotor flux

from Eq. (7) are not needed in the rotor flux reference generation reducing its complexity.

The stator and rotor fluxes and their magnitudes can be calculated by using:

ψs � � � � ¼

ψr � � � � ¼

fluxes will be constant, which means the term Δ ψ<sup>r</sup>

wind speed of 25 ms�<sup>1</sup> and rated wind speed of 15 ms�<sup>1</sup>

� � �

4. Results and discussion

that means, the value of Δ ψ<sup>r</sup>

� �

� �

(8)

(9)

(10)

, cut-out

, respectively. The stator-to-rotor

The torque is maintained at its generated value of 0.2 pu as there is no consideration of voltage dip, which is clearly shown in Figure 3(b).

Figure 3. (a) Stator voltages of DFIM with proposed rotor flux reference generation without voltage dip, (b) torque of DFIM with proposed rotor flux reference generation without voltage dip, (c) stator and rotor flux of DFIM with proposed rotor flux reference generation without voltage dip, (d) rotor currents of DFIM with proposed rotor flux reference generation without voltage dip, (e) stator currents of DFIM with proposed rotor flux reference generation without voltage dip, and (f) DC-link voltage of DFIM with proposed rotor flux reference generation without voltage dip.

The responses of the stator and rotor flux without the voltage dip are shown in Figure 3(c). Note that at the steady state, without the presence of a dip, the term Δ ψ<sup>r</sup> will be zero in Eq. (9).

Figure 3(d) shows the rotor currents response for without voltage dip, which clearly indicates the steady state operation of DFIM.

Figure 3(e) shows the normal operated result of stator currents under normal operation, that is, without any over currents.

The response of DC-link voltage is shown in Figure 3(f), it is noticed from the figure that the DClink voltage is maintained constant. When the wind energy system is operating under normal or abnormal condition, the DC-link voltage has to be maintained constant, but to mitigate the over currents in rotor and stator produced due to voltage dip by adopting the proposed control strategy, maintaining the constant value of DC-link voltage is lost. This is explained with the case of voltage dip with and without rotor flux reference generation scheme.

## 4.2. Analysis of DFIG without rotor flux reference generation with voltage dip

Results are presented for the proposed control strategy to show its effectiveness under low voltage dips, in this case 30%, as illustrated in Figure 4(a), symmetric voltage dip considered with and without the proposed flux reference generation strategy and at nearly constant speed. The symmetrical three phases to ground fault is created at 0.8 s and the fault is cleared off once the time reaches 0.9 s, after which the voltage starts to recover to normal value as shown in Figure 4(a).

From the Figure 4(b), it is observed that the generated torque before the voltage dip is maintained at 0.2 pu. When the dip occurs there are high transient peaks in it, this is because the value of the required rotor voltage is more than the DC-link voltage at that particular instant; otherwise the DTC technique tries to maintain the torque constant when the fault is cleared.

The response of the stator and rotor fluxes is shown in Figure 4(c). As it is the case of without rotor flux reference generation, the rotor flux doesn't follow the stator flux, which can be clearly seen because of which torque has perturbations as can be seen in Figure 4(b).

The response of rotor currents is shown in Figure 4(d). The Figure 4(d) clearly shows the high values of rotor currents are produced at the instant of voltage dip, but the DTC technique manages to control the rotor currents still within its limits.

It is observed from the Figure 4(e), high values of stator currents are produced due to abnormal condition, the values of stator currents crosses more than 0.9pu and settles back to steady state value once the fault is cleared.

4.3. Analysis of DFIG with rotor flux reference generation with voltage dip

on the wind energy system.

The response of the generated torque is shown in Figure 5(a). From the Figure 5(a), the high peaks produced in torque are eliminated, which were produced due to dip when without rotor flux reference generation scheme is considered. The high peaks are eliminated by producing the oscillations in rotor flux along with the oscillations produced in stator flux during dip due to poor damped poles. This torque response indicates that the mechanical stresses are reduced

Figure 4. (a) Stator voltages of DFIM without proposed rotor flux reference generation, (b) torque of DFIM without proposed rotor flux reference generation, (c) stator and rotor flux of DFIM without proposed rotor flux reference generation, (d) rotor currents of DFIM without proposed rotor flux reference generation, (e) stator currents of DFIM without proposed rotor flux reference generation, and (f) DC-link voltage of DFIM without proposed rotor flux reference generation.

Rotor Flux Reference Generation Control Strategy for Direct Torque Controlled DFIG

http://dx.doi.org/10.5772/intechopen.75362

81

The DC-link voltage oscillations for without reference generation for short duration of voltage dip can be clearly seen to be balanced and sinusoidal as shown in Figure 4(f). As in this case, there are no special improvements being adopted, the power delivered through the rotor by the ac-dc-ac converter will be increased due to the increase of voltage and currents in the rotor of the DFIM, provoking finally an increase in the DC-link voltage.

Rotor Flux Reference Generation Control Strategy for Direct Torque Controlled DFIG http://dx.doi.org/10.5772/intechopen.75362 81

The responses of the stator and rotor flux without the voltage dip are shown in Figure 3(c). Note

Figure 3(d) shows the rotor currents response for without voltage dip, which clearly indicates

Figure 3(e) shows the normal operated result of stator currents under normal operation, that

The response of DC-link voltage is shown in Figure 3(f), it is noticed from the figure that the DClink voltage is maintained constant. When the wind energy system is operating under normal or abnormal condition, the DC-link voltage has to be maintained constant, but to mitigate the over currents in rotor and stator produced due to voltage dip by adopting the proposed control strategy, maintaining the constant value of DC-link voltage is lost. This is explained with the

Results are presented for the proposed control strategy to show its effectiveness under low voltage dips, in this case 30%, as illustrated in Figure 4(a), symmetric voltage dip considered with and without the proposed flux reference generation strategy and at nearly constant speed. The symmetrical three phases to ground fault is created at 0.8 s and the fault is cleared off once the time reaches 0.9 s, after which the voltage starts to recover to normal value as

From the Figure 4(b), it is observed that the generated torque before the voltage dip is maintained at 0.2 pu. When the dip occurs there are high transient peaks in it, this is because the value of the required rotor voltage is more than the DC-link voltage at that particular instant; otherwise the DTC technique tries to maintain the torque constant when the fault is

The response of the stator and rotor fluxes is shown in Figure 4(c). As it is the case of without rotor flux reference generation, the rotor flux doesn't follow the stator flux, which can be

The response of rotor currents is shown in Figure 4(d). The Figure 4(d) clearly shows the high values of rotor currents are produced at the instant of voltage dip, but the DTC technique

It is observed from the Figure 4(e), high values of stator currents are produced due to abnormal condition, the values of stator currents crosses more than 0.9pu and settles back to steady

The DC-link voltage oscillations for without reference generation for short duration of voltage dip can be clearly seen to be balanced and sinusoidal as shown in Figure 4(f). As in this case, there are no special improvements being adopted, the power delivered through the rotor by the ac-dc-ac converter will be increased due to the increase of voltage and currents in the rotor

clearly seen because of which torque has perturbations as can be seen in Figure 4(b).

manages to control the rotor currents still within its limits.

of the DFIM, provoking finally an increase in the DC-link voltage.

state value once the fault is cleared.

 

will be zero in Eq. (9).

that at the steady state, without the presence of a dip, the term Δ ψ<sup>r</sup>

case of voltage dip with and without rotor flux reference generation scheme.

4.2. Analysis of DFIG without rotor flux reference generation with voltage dip

the steady state operation of DFIM.

80 Optimization and Control of Electrical Machines

is, without any over currents.

shown in Figure 4(a).

cleared.

Figure 4. (a) Stator voltages of DFIM without proposed rotor flux reference generation, (b) torque of DFIM without proposed rotor flux reference generation, (c) stator and rotor flux of DFIM without proposed rotor flux reference generation, (d) rotor currents of DFIM without proposed rotor flux reference generation, (e) stator currents of DFIM without proposed rotor flux reference generation, and (f) DC-link voltage of DFIM without proposed rotor flux reference generation.

#### 4.3. Analysis of DFIG with rotor flux reference generation with voltage dip

The response of the generated torque is shown in Figure 5(a). From the Figure 5(a), the high peaks produced in torque are eliminated, which were produced due to dip when without rotor flux reference generation scheme is considered. The high peaks are eliminated by producing the oscillations in rotor flux along with the oscillations produced in stator flux during dip due to poor damped poles. This torque response indicates that the mechanical stresses are reduced on the wind energy system.

The oscillations produced in rotor flux are clearly seen from the Figure 5(b), which follows close to stator flux oscillations. This is achieved by the proposed rotor flux reference generation scheme employed as shown in Figure 2.

The necessary rotor flux reference generation is to overcome the problems due to the longer

Rotor Flux Reference Generation Control Strategy for Direct Torque Controlled DFIG

http://dx.doi.org/10.5772/intechopen.75362

83

Figure 5. (a) Torque of DFIM with proposed rotor flux reference generation, (b) stator and rotor flux of DFIM with proposed rotor flux reference generation, (c) rotor currents of DFIM with proposed rotor flux reference generation, (d) stator currents of DFIM with proposed rotor flux reference generation, and (e) DC-link voltage of DFIM with

proposed rotor flux reference generation.

voltage dip along with the stator flux oscillations as shown in Figure 7(b).

Consequently, the proposed control scheme maintains the stator and rotor currents under their safety limits, avoiding high over currents, either in the voltage fall or rise. The proposed strategy is analyzed for three phase fault. However, as predicted in theory, it is hard to avoid a deterioration of the quality of these currents. The response of rotor currents of DFIM with proposed scheme is shown in Figure 5(c).

The response of the stator currents of DFIM is shown in Figure 5(d), wherein the stator currents are within the limits when compared to stator currents produced by without rotor flux reference generation scheme as shown in Figure 4(e).

Moreover, by mitigating the over currents of the rotor, the back-to-back converter is less affected by this perturbation, producing short dc bus voltage oscillations. The DC-link voltage oscillations for with rotor flux reference generation are shown in Figure 5(e). The DC-link voltage oscillations are unbalanced but sinusoidal and are constant as shown in Figure 5(e).

## 4.4. Analysis of DFIG without rotor flux reference generation during longer voltage dip

The results for continuous dip are shown in Figures 6 and 7 for both without and with reference rotor flux generation respectively. The duration of the longer voltage dip is from 0.2 to 1 s, which can be seen with three phase stator voltage in Figure 6(a).

As showed in Figure 6(b), there are number of perturbations in torque due to exceeding of requirement of rotor voltage compared to the actual DC-link voltage. This causes mechanical stresses on the wind energy conversion system, which is not good for the wind turbine.

The responses of the stator and rotor flux are shown in Figure 6(c), and it is observed from the figure that there are some oscillations in stator flux and no oscillations in rotor flux.

Figure 6(d) shows the response of rotor currents due to longer voltage dip. The rotor currents reach its limits and from the Figure 6(d), it can be clearly seen that there is complete unbalance in the rotor currents but as said they just reach the limits.

The over currents in the stator can be clearly seen in Figure 6(e), due to increase in the rotor currents.

The response of the DC-link voltage with balanced sinusoidal oscillations due to the fault is shown in Figure 6(f).

## 4.5. Analysis of DFIG with rotor flux reference generation during longer voltage dip

Figure 7(a) clearly shows the torque is maintained at its required value, without the high peaks caused due to longer voltage dip, which allows eliminating mechanical stresses on the wind turbine. The necessary rotor flux reference generation is to overcome the problems due to the longer voltage dip along with the stator flux oscillations as shown in Figure 7(b).

The oscillations produced in rotor flux are clearly seen from the Figure 5(b), which follows close to stator flux oscillations. This is achieved by the proposed rotor flux reference generation

Consequently, the proposed control scheme maintains the stator and rotor currents under their safety limits, avoiding high over currents, either in the voltage fall or rise. The proposed strategy is analyzed for three phase fault. However, as predicted in theory, it is hard to avoid a deterioration of the quality of these currents. The response of rotor currents of DFIM with

The response of the stator currents of DFIM is shown in Figure 5(d), wherein the stator currents are within the limits when compared to stator currents produced by without rotor

Moreover, by mitigating the over currents of the rotor, the back-to-back converter is less affected by this perturbation, producing short dc bus voltage oscillations. The DC-link voltage oscillations for with rotor flux reference generation are shown in Figure 5(e). The DC-link voltage oscillations are unbalanced but sinusoidal and are constant as shown in Figure 5(e).

4.4. Analysis of DFIG without rotor flux reference generation during longer voltage dip

to 1 s, which can be seen with three phase stator voltage in Figure 6(a).

in the rotor currents but as said they just reach the limits.

currents.

shown in Figure 6(f).

The results for continuous dip are shown in Figures 6 and 7 for both without and with reference rotor flux generation respectively. The duration of the longer voltage dip is from 0.2

As showed in Figure 6(b), there are number of perturbations in torque due to exceeding of requirement of rotor voltage compared to the actual DC-link voltage. This causes mechanical stresses on the wind energy conversion system, which is not good for the wind turbine.

The responses of the stator and rotor flux are shown in Figure 6(c), and it is observed from the

Figure 6(d) shows the response of rotor currents due to longer voltage dip. The rotor currents reach its limits and from the Figure 6(d), it can be clearly seen that there is complete unbalance

The over currents in the stator can be clearly seen in Figure 6(e), due to increase in the rotor

The response of the DC-link voltage with balanced sinusoidal oscillations due to the fault is

Figure 7(a) clearly shows the torque is maintained at its required value, without the high peaks caused due to longer voltage dip, which allows eliminating mechanical stresses on the wind turbine.

4.5. Analysis of DFIG with rotor flux reference generation during longer voltage dip

figure that there are some oscillations in stator flux and no oscillations in rotor flux.

scheme employed as shown in Figure 2.

82 Optimization and Control of Electrical Machines

proposed scheme is shown in Figure 5(c).

flux reference generation scheme as shown in Figure 4(e).

Figure 5. (a) Torque of DFIM with proposed rotor flux reference generation, (b) stator and rotor flux of DFIM with proposed rotor flux reference generation, (c) rotor currents of DFIM with proposed rotor flux reference generation, (d) stator currents of DFIM with proposed rotor flux reference generation, and (e) DC-link voltage of DFIM with proposed rotor flux reference generation.

Figure 6. (a) Stator voltages of DFIM without proposed rotor flux reference generation, (b) torque of DFIM without proposed rotor flux reference generation, (c) stator and rotor flux of DFIM without proposed rotor flux reference generation, (d) rotor currents of DFIM without proposed rotor flux reference generation, (e) stator currents of DFIM without proposed rotor flux reference generation, and (f) DC-link voltage of DFIM without proposed rotor flux reference generation.

Figure 7. (a) Torque of DFIM with proposed rotor flux reference generation, (b) stator and rotor flux of DFIM with proposed rotor flux reference generation, (c) rotor currents of DFIM with proposed rotor flux reference generation, (d) stator currents of DFIM with proposed rotor flux reference generation, and (e) DC-link voltage of DFIM with

Rotor Flux Reference Generation Control Strategy for Direct Torque Controlled DFIG

http://dx.doi.org/10.5772/intechopen.75362

85

proposed rotor flux reference generation.

Figure 7. (a) Torque of DFIM with proposed rotor flux reference generation, (b) stator and rotor flux of DFIM with proposed rotor flux reference generation, (c) rotor currents of DFIM with proposed rotor flux reference generation, (d) stator currents of DFIM with proposed rotor flux reference generation, and (e) DC-link voltage of DFIM with proposed rotor flux reference generation.

Figure 6. (a) Stator voltages of DFIM without proposed rotor flux reference generation, (b) torque of DFIM without proposed rotor flux reference generation, (c) stator and rotor flux of DFIM without proposed rotor flux reference generation, (d) rotor currents of DFIM without proposed rotor flux reference generation, (e) stator currents of DFIM without proposed rotor flux reference generation, and (f) DC-link voltage of DFIM without proposed rotor flux reference generation.

84 Optimization and Control of Electrical Machines

Compared to the rotor currents generated by without flux reference generation scheme for longer voltage dip as shown in Figure 6(d), the rotor currents for with reference generation scheme has lesser over currents, less severe and operate within the limits as shown in Figure 7(c).

[4] Slootweg JG, Kling WL. Modeling of large wind farms in power system simulations. In: Power Engineering Society Summer Meeting, 2002. IEEE, Jul 25, 2002. Vol. 1, pp. 503-508

Rotor Flux Reference Generation Control Strategy for Direct Torque Controlled DFIG

http://dx.doi.org/10.5772/intechopen.75362

87

[5] Abad G, Lopez J, Rodriguez M, Marroyo L, Iwanski G. Doubly Fed Induction Machine: Modeling and Control for Wind Energy Generation. New Jersey: IEEE Press, John Wiley

[6] Ekanayake JB, Holdsworth L, Wu X, Jenkins N. Dynamic modeling of doubly fed induction generator wind turbines. IEEE Transactions on Power Systems. 2003 May;18(2):803-809 [7] Holdsworth L, Wu XG, Ekanayake JB, Jenkins N. Comparison of fixed speed and doublyfed induction wind turbines during power system disturbances. IEEE Proceedings-

[8] Seman S, Niiranen J, Kanerva S, Arkkio A. Analysis of a 1.7 MVA doubly fed wind-power induction generator during power systems disturbances. Proceedings of NORPIE 2004.

[9] Morren J, De Haan SW. Short-circuit current of wind turbines with doubly fed induction

[10] Xiang D, Ran L, Tavner PJ, Yang S. Control of a doubly fed induction generator in a wind turbine during grid fault ride-through. IEEE Transactions on Energy Conversion. 2006

[11] López J, Gubía E, Olea E, Ruiz J, Marroyo L. Ride through of wind turbines with doubly fed induction generator under symmetrical voltage dips. IEEE Transactions on Industrial

[12] Pannell G, Atkinson DJ, Zahawi B. Minimum-threshold crowbar for a fault-ride-through grid-code-compliant DFIG wind turbine. IEEE Transactions on Energy Conversion. 2010

generator. IEEE Transactions on Energy Conversion. 2007 Mar;22(1):174-180

Generation, Transmission and Distribution. 2003 May 1;150(3):343-352

& Sons; 2011 Sep 28

Jun 2004;14:1-6

Sep;21(3):652-662

Sep;25(3):750-759

Electronics. 2009 Oct;56(10):4246-4254

Likewise, the stator currents are also within the limits as showed in Figure 7(d).

Figure 7(e) shows the DC-link voltage with oscillatory behavior due to fault and the oscillations are unbalanced and sinusoidal as mentioned previously.

## 5. Conclusions

In this chapter, rotor flux reference generation control strategy has been developed. Various cases have been considered such as: (a) with rotor flux reference generation without voltage dip, (b) without rotor flux reference generation with voltage dip, (c) with rotor flux reference generation with voltage dip, (d) without rotor flux reference generation during longer voltage dip, and (e) with rotor flux reference generation during longer voltage dip. Results are presented to validate the proposed scheme. From the results, it is observed that, during voltage dip, the rotor flux reference generation control scheme along with the DTC scheme eliminates the high peaks in torque with reduced stator and rotor currents, and also eliminates the necessity of crowbar during low voltage dip; the scheme makes the possibility of DFIG being connected to the grid even during fault.

## Author details

Gopala Venu Madhav<sup>1</sup> \* and Y. P. Obulesu<sup>2</sup>

\*Address all correspondence to: venumadhav.gopala@gmail.com


## References


[4] Slootweg JG, Kling WL. Modeling of large wind farms in power system simulations. In: Power Engineering Society Summer Meeting, 2002. IEEE, Jul 25, 2002. Vol. 1, pp. 503-508

Compared to the rotor currents generated by without flux reference generation scheme for longer voltage dip as shown in Figure 6(d), the rotor currents for with reference generation scheme has lesser over currents, less severe and operate within the limits as shown in Figure 7(c).

Figure 7(e) shows the DC-link voltage with oscillatory behavior due to fault and the oscilla-

In this chapter, rotor flux reference generation control strategy has been developed. Various cases have been considered such as: (a) with rotor flux reference generation without voltage dip, (b) without rotor flux reference generation with voltage dip, (c) with rotor flux reference generation with voltage dip, (d) without rotor flux reference generation during longer voltage dip, and (e) with rotor flux reference generation during longer voltage dip. Results are presented to validate the proposed scheme. From the results, it is observed that, during voltage dip, the rotor flux reference generation control scheme along with the DTC scheme eliminates the high peaks in torque with reduced stator and rotor currents, and also eliminates the necessity of crowbar during low voltage dip; the scheme makes the possibility of DFIG being connected to the grid even during fault.

[1] Lopez J, Gubia E, Sanchis P, Roboam X, Marroyo L. Wind turbines based on doubly fed induction generator under asymmetrical voltage dips. IEEE Transactions on Energy Con-

[2] Morren J, De Haan SW. Ridethrough of wind turbines with doubly-fed induction generator during a voltage dip. IEEE Transactions on Energy Conversion. 2005 Jun;20(2):435-441 [3] Seman S, Niiranen J, Arkkio A. Ride-through analysis of doubly fed induction windpower generator under unsymmetrical network disturbance. IEEE Transactions on Power

Likewise, the stator currents are also within the limits as showed in Figure 7(d).

tions are unbalanced and sinusoidal as mentioned previously.

\* and Y. P. Obulesu<sup>2</sup>

\*Address all correspondence to: venumadhav.gopala@gmail.com

2 VIT University, Vellore, Tamil Nadu, India

version. 2008 Mar;23(1):321-330

Systems. 2006 Nov;21(4):1782-1789

1 Anurag Group of Institutions, Hyderabad, Telangana State, India

5. Conclusions

86 Optimization and Control of Electrical Machines

Author details

References

Gopala Venu Madhav<sup>1</sup>


*Edited by Abdel Ghani Aissaoui, Ahmed Tahour and Ilhami Colak*

Electrical machines are used in the process of energy conversion in the generation, transmission and consumption of electric power. In addition to this, electrical machines are considered the main part of electrical drive systems. Electrical machines are the subject of advanced research. In the development of an electrical machine, the design of its different structures is very important. This design ensures the robustness, energy efficiency, optimal cost and high reliability of the system. Using advanced techniques of control and new technology products has brought electrical machines into their optimal functioning mode. Different techniques of control can be applied depending on the goals considered. The aim of this book is to present recent work on the design, control and applications of electrical machines.

Published in London, UK © 2018 IntechOpen © axeiz77 / iStock

Optimization and Control of Electrical Machines

Optimization and Control of

Electrical Machines

*Edited by Abdel Ghani Aissaoui,* 

*Ahmed Tahour and Ilhami Colak*