**Electrical Parameter Identification of Single-Phase Induction Motor by RLS Algorithm**

Rodrigo Padilha Vieira, Rodrigo Zelir Azzolin, Cristiane Cauduro Gastaldini and Hilton Abílio Gründling

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/37664

## **1. Introduction**

274 Induction Motors – Modelling and Control

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This chapter addresses the problem of the electrical parameter identification of Single-Phase Induction Motor (SPIM). The knowledge of correct electrical parameters of SPIM allows a better representation of dynamic simulation of this machine. In addition, the identified parameters can improve the performance of the Field Oriented Control (FOC) and sensorless techniques used in these systems.

Controlled induction motor drives have been employed on several appliances in the last decades. Commonly, the control schemes are based on the FOC and sensorless techniques. These methods are mainly applied to three-phase induction machine drives, and a wide number of papers, such as [5, 9, 10, 15, 19, 23, 26] have described such drives. On the other hand, for several years the SPIM has been used in residential appliances, mainly in low power and low cost applications such as in freezers and air conditioning, consuming extensive rate of electrical energy generated in the world. In most of these applications, the SPIM operates at fixed speed and is supplied directly from source grid. However, in the last few years several works have illustrated that the operation with variable speed can enhance the process efficiency achieved by the SPIM ([1, 4, 8, 31]). Furthermore, some other studies have presented high performance drives for SPIM using vector control and sensorless techniques, such as is presented in [7, 12, 18, 24] and [29]. However, these schemes applied on single-phase and three-phase induction motor drives need an accurate knowledge of all electrical parameters machine to have a good performance.

As a consequence of the parameter variation and uncertainties of the machine, literature presents algorithms for computational parameter estimation of induction machines, mainly about three-phase induction machines ([3, 13, 20, 21, 27]). Some authors proposed an on-line

©2012 Vieira et al., licensee InTech. This is an open access chapter 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. ©2012 Vieira et al., licensee InTech. This is a paper 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.

### 2 Will-be-set-by-IN-TECH 276 Induction Motors – Modelling and Control Electrical Parameter Identification of Single-Phase Induction Motor

parameter estimation, for adaptive systems and self-tuning controllers due to the fact that the parameters of induction machine change with temperature, saturation, and frequency ([22]).

by RLS Algorithm 3

As in [14], in this chapter the squirrel cage SPIM mathematical model is described in a

<sup>0</sup> *Rsd isq*

<sup>0</sup> *Rrd irq*

 *φrq φrd* = 0 0

*isd* +

> *isd* +

> > *dωr*

where, the indexes *q* and *d* represent the main winding and auxiliary winding, respectively, the indexes *sq* and *sd* represent the stator variables, and the indexes *rq* and *rd* are used for the rotor variables. *Vsq*, *Vsd*, *Vrq*, *Vrd*, *isq*, *isd*, *irq*, *ird*, *φsq*, *φsd*, *φrq*, and *φrd* are the stator and rotor voltages, currents, and flux; *Rsq*, *Rsd*, *Rrq*, and *Rrd* are the stator and rotor resistances; *Llsq*, *Llsd*, *Llrq*, and *Llrd* are the leakage inductances; *Lmq* and *Lmd* are the mutual inductances; *Lsq*, *Lsd*, *Lrq*, and *Lrd* are the stator and rotor inductances, and are given by: *Lsq* = *Llsq* + *Lmq*, *Lsd* = *Llsd* + *Lmd*, *Lrq* = *Llrq* + *Lmq*, and *Lrd* = *Llrd* + *Lmd*; *Nq* and *Nd* represent the number of turns for the main and auxiliary windings, respectively; *p* is the pole pair number and *ωr* is the rotor speed, and *n* is the relationship between the number of turns for auxiliary and for main winding *Nd*/*Nq*. *Te* is the electromagnetic torque, *TL* is the load torque, *Bn* is the viscous

From (1) - (4) it is possible to obtain the differential equations that express the dynamical

*RrqLmq σq*

> *LrqLmd σd*

*irq*−*ω<sup>r</sup>*

*irq* +

*irq* + *ω<sup>r</sup>*

*LsdLrq σd*

1 *n*

1 *n*

*irq*<sup>−</sup> *LsdRrd σd*

*LrdLmq σq*

*RrdLmd σd*

> *LsqLrd σq*

*ird* +

*ird* +

*ird*<sup>−</sup> *Lmq σq*

*ird*<sup>−</sup> *Lmd σd*

*Lrq σq*

*Lrd σd*

*Vsq* (7)

*Vsd* (8)

*Vsq* (9)

*Vsd* (10)

*isd* +

*isd* + *ωrn*

*isd*<sup>−</sup> *LsqRrq σq*

*isd*−*ωrn*

*isd* + *d dt <sup>φ</sup>sq φsd*

*ird* + *d dt φrq φrd*

*Lmq* 0

*Lrq* 0

<sup>0</sup> *Lmd irq*

Electrical Parameter Identi cation of Single-Phase Induction Motor by RLS Algorithm 277

<sup>0</sup> *Lrd irq*

*Te* = *p*(*Lmqisqird* − *Lmdisdirq*) (5)

*ird*

*ird*

*dt* <sup>+</sup> *Bnω<sup>r</sup>* (6)

(1)

(3)

(4)

(2)

*Rsq* 0

*Rrq* 0

<sup>0</sup> *Lsd isq*

<sup>0</sup> *Lmd isq*

*p*(*Te* − *TL*) = *J*

stationary reference-frame by the following equations *Vsq Vsd* =

> *Vrq Vrd* =

 *φsq φsd* =

 *φrq φrd* =

friction coefficient, and *J* is the inertia coefficient.

*σq*

*isq*−*ω<sup>r</sup>*

*isq* + *ω<sup>r</sup>*

*LsdLmq σd*

*LmdLmq σd*

1 *n*

*isq*<sup>−</sup> *LrdRsd σd*

> 1 *n*

*isq* +

*LmqLmd σq*

> *LsqLmd σq*

> > *LmdRsd σd*

behavior of the SPIM, as follows,

*dtisq* <sup>=</sup> <sup>−</sup> *RsqLrq*

*dtisd* <sup>=</sup> *<sup>ω</sup>rn*

*dtirq* <sup>=</sup> *LmqRsq σq*

*dtird* <sup>=</sup> <sup>−</sup>*ωrn*

*d*

*d*

*d*

*d*

+*ω<sup>r</sup>* <sup>0</sup> <sup>−</sup><sup>1</sup> /*n n* 0

*Lsq* 0

*Lmq* 0

Differently from the three-phase induction motors, the SPIM is an asymmetrical and coupled machine; these features make the electrical parameter estimation by classical methods difficult, and these characteristics complicate the use of high performance techniques, such as vector and sensorless control. Thus, the use of Recursive Least Square (RLS) algorithm can be a solution for the parameter estimation or self-tuning and adaptive controllers, such as presented in [28] and [30]. Other studies have also been reported in literature describing the parameter estimation of SPIM ([2, 11, 17, 25]).

The aim of this chapter is to provide a methodology to identify a set of parameters for an equivalent SPIM model, and to obtain an improved SPIM representation, as consequence it is possible to design a high performance sensorless SPIM controllers. Here, from the machine model, a classical RLS algorithm is applied at *q* and *d* axes based on the current measurements and information of fed voltages with a standstill rotor. The automatized test with standstill rotor can be a good alternative in some applications, such as hermetic compressor systems, where the estimation by conventional methods is a hard task due the fact of the machine is sealed.

An equivalent SPIM behavior representation is obtained with this methodology in comparison with the SPIM model obtained by classical tests. However, some types of SPIM drives, for instance a hermetic system, it is impossible to carried out classical tests. In addition, the proposed methodology has a simple implementation.

This chapter is organized as follows: Section 2 presents the SPIM model, Section 3 gives the RLS parameter algorithm, Section 4 presents and discusses the experimental results obtained with the proposed methodology, and Section 5 gives the main conclusions of this study.
