Off line and on line parameter estimation of induction machines

For off-line parameter estimation, two advanced particle swarm optimization PSO algorithms, known as the dynamic PSO and chaos PSO algorithms, are proposed for off-line parameter estimat

OFF-LINE AND ON-LINE PARAMETER ESTIMATION

OF INDUCTION MACHINES

DUY CHAU HUYNH

Thesis submitted for the Degree of Doctor of Philosophy

Heriot-Watt University

Department of Electrical, Electronic

and Computer Engineering

October 2010

The copyright in this thesis is owned by the author Any quotation from the thesis or use of any of the information contained in it must acknowledge this thesis as the source of the quotation or information

ABSTRACT

This thesis addresses off-line and on-line parameter estimations of an induction machine (IM) which are necessary to improve its control and operational performances For off-line parameter estimation, two advanced particle swarm optimization (PSO) algorithms, known as the dynamic PSO and chaos PSO algorithms, are proposed for off-line parameter estimation of the three-phase and single-phase IMs The experimental results obtained compare the estimated parameters with the IM parameters achieved using the

DC, no-load and locked-rotor tests for the three-phase IM and the load tests for the single-phase IM There is also a comparison of the solution quality between a genetic algorithm (GA), standard PSO, dynamic PSO and chaos PSO algorithms Additionally,

a recursive least-squares (RLS) algorithm with multiple time-varying forgetting factors

is proposed for on-line parameter estimation of the IM which can efficiently track the

IM parameter variations during operation Simulation results of the on-line estimated

IM parameters using the proposed RLS algorithm are compared with the IM parameters obtained using other RLS algorithm variants Energy efficient control of the IM is also

an important topic examined in this thesis A control strategy is proposed using an optimal IM rotor flux reference Two techniques, known as the derivative technique and the chaos PSO algorithm are proposed for obtaining the optimal IM rotor flux reference Furthermore, the on-line parameter estimator using the RLS algorithm with multiple time-varying forgetting factors is used in this application to update the IM parameter variations so that the optimal IM rotor flux reference is always accurate and the IM efficiency always remains optimal Simulations are implemented to confirm the effectiveness of the proposed strategy for energy efficient control of the IM

ACKNOWLEDGEMENTS

Firstly, I would like to express my deepest gratitude to my supervisor, Dr Matthew W Dunnigan for his enthusiasm, patience, guidance and support from the initial to the final level of the research and the writing of this thesis

Acknowledgement is also given to other members of the Power Electronics and Drives Laboratory, technicians of the Workshop and staff members in the Electrical, Electronic and Computer Engineering Department for their assistance and technical supports

I also would like to thank the Committee on Overseas Training Projects – Project No

322, Ministry of Education and Training, Government of Vietnam that supported the finance for me

Finally, I would also like to thank my dad, mum, all members of my family and my friends for their support and encouragement throughout the years of my PhD study

ACADEMIC REGISTRY

Research Thesis Submission

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1) the thesis embodies the results of my own work and has been composed by myself

2) where appropriate, I have made acknowledgement of the work of others and have made reference to

work carried out in collaboration with other persons

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TABLE OF CONTENTS

Abstract i Acknowledgements ii

2.5.1 Model reference adaptive systems 31

3.4 Comparison of the particle swarm optimization algorithm 70

with other evolutionary computation techniques

Chapter 4 Off-line parameter estimation of a three-phase induction machine

using particle swarm optimization algorithms

4.3 Off-line parameter estimation using particle swarm optimization algorithms 79

and a genetic algorithm 4.3.1 Standard particle swarm optimization algorithm 79

4.3.2 Dynamic particle swarm optimization algorithm 82

4.3.3 Chaos particle swarm optimization algorithm 85

4.3.4 Genetic algorithm 87

4.4 Experimental setup 90 4.5 Experimental results 91 4.6 Conclusion 98 4.7 References 99 Chapter 5 On-line parameter estimation of a three-phase induction machine using recursive least-squares algorithms 5.1 Introduction 102 5.2 Induction machine model for on-line parameter estimation 106

5.3 On-line parameter estimation using recursive least-squares algorithms 109

5.3.1 Standard recursive least-squares algorithm 109

5.3.2 Recursive least-squares algorithm with a constant forgetting factor 112

5.3.3 Recursive least-squares algorithm with a time-varying 114

forgetting factor 5.3.4 Recursive least-squares algorithm with multiple forgetting factors 118

5.3.5 Recursive least-squares algorithm with multiple time-varying 123

forgetting factors 5.4 Simulation results 127 5.4.1 Case 1 – Constant induction machine parameters 127 5.4.2 Case 2 – Time-varying induction machine parameters 130

with the same variation rate 5.4.3 Case 3 – Time-varying induction machine parameters 135

with different variation rates

5.5 Conclusion 139

optimization algorithm

using particle swarm optimization algorithms

7.2.2 Single-phase induction machine model with the core loss effect 170 7.2.3 Single-phase induction machine model with the rotor deep bar effect 171

7.3 Off-line parameter estimation using particle swarm optimization algorithms 173

Chapter 8 Conclusions and author’s contribution

LIST OF SYMBOLS

main windings in a single-phase induction machine

I s and I r stator and rotor RMS currents, A

I& and I& mb forward and backward complex currents of the main

winding in a single-phase induction machine, A

I& and I& a main and auxiliary winding complex currents in a

single-phase induction machine, A

m

I& and I& a complex magnitudes of the main and auxiliary winding

currents in a single-phase induction machine, A

mf

I& and I& mb complex magnitudes of the forward- and

backward-rotating field current components in the main winding of

a single-phase induction machine, A

af

I& and I& ab complex magnitudes of the forward- and

backward-rotating field current components in the auxiliary winding of a single-phase induction machine, A

L m , L s and L r magnetizing, stator and rotor inductances, H

single-phase induction machine

P lc and P ls and P lr core, stator and rotor copper losses, W

m

P and P a active powers of the main and auxiliary windings in a

single-phase induction machine, W

locked-rotor test, W

R s and R r Stator and rotor resistances, Ω

LR

m

a single-phase induction machine, Ω

V , V and bc V ac stator RMS line voltage, V

V& and V& a main and auxiliary winding complex voltages in a

single-phase induction machine, V

mf

V& and V& mb forward and backward complex voltages of the main

winding in a single-phase induction machine, V

X ′ , X ′ and ls X ′ lr locked-rotor, stator and rotor leakage reactances in the

locked-rotor test at a test frequency, Ω

m

single-phase induction machine, Ω

2

induction machine, Ω

Z 0 input impedance in the no-load test, Ω

e

m

in a single-phase induction machine, rad

However, in most high performance IM applications, accurate knowledge of the IM parameters is necessary This directly affects the operational and control characteristics

of the IM Thus, the question of how to estimate IM parameters is an important topic which merits research One approach is to estimate the IM parameters off-line which are then used for the initial setting of the IM controller

It is also a goal to improve the IM performance when its parameters vary during operation because of temperature variation, saturation phenomenon and skin effects In order to overcome these, the IM parameters need to be estimated continuously This means that they must be estimated on-line to update parameter variations in the control schemes of the IM

Additionally, energy efficient control of the IM is an important issue which has been researched recently due to the two main reasons of energy saving and environmental pollution reduction If the IM efficiency is improved by 1%, this will result in savings of over one billion USD per year in energy costs, 6-10 million tons less per year of combusted coal and approximately 15-20 million tons less carbon dioxide released into the atmosphere [1.2]

For these reasons, off-line and on-line parameter estimation and energy efficient control problems are examined in this thesis so that the IM can always exhibit high performance and good efficiency Novel solutions for off-line and on-line parameter estimation are presented in this thesis as well as an energy efficient control strategy for the IM

Off-line parameter estimation of the three-phase IM is one of the key issues for improving the IM performance Usually, some of the IM parameters are provided by the manufacturer However, manufacturers may not supply all the parameter information The parameters could be then estimated by using traditional tests such as the DC, no-load and locked-rotor tests [1.1], [1.3] In addition to the traditional tests, the parameters can also be estimated by using optimization algorithms The parameter estimation objective is then transformed into an optimization problem

Recently, a particle swarm optimization (PSO) algorithm [1.4] has been introduced as one of the relatively new stochastic optimization techniques which could be applied for parameter estimation This algorithm is simpler and easier to implement than other existing optimization algorithms, as it only has a few parameters to adjust This thesis proposes a novel application of the dynamic PSO and chaos PSO algorithms, known as variants of the standard PSO algorithm for parameter estimation of the IM The experimental results of the estimated parameters using the dynamic PSO and chaos PSO algorithms are compared with the parameters obtained from the traditional tests such as

DC, no-load and locked-rotor tests, and also a genetic algorithm (GA) and standard PSO algorithm Experimental results have demonstrated that the proposed approaches are effective in off-line parameter estimation of the IM

Parameter variations of the three-phase IM during operation occur and affect the IM performance Thus, this issue needs to be examined and resolved so that these influences can be reduced On-line parameter estimation of the IM is an effective solution which results in reducing the errors and oscillations in both the IM torque and speed responses

An advanced recursive least-squares (RLS) algorithm with multiple time-varying forgetting factors is proposed in this thesis for on-line parameter estimation of the IM

In this algorithm, each estimated parameter is assigned a different forgetting factor

which represents a different variation rate of that parameter Additionally, the forgetting factors are time-varying which can deal with the continuous variation of each parameter during the operational process By applying this algorithm for on-line parameter estimation of the IM, the control strategies can remain optimal Simulation results of the estimated parameters using the advanced RLS algorithm with multiple time-varying forgetting factors are compared with the parameters obtained from other related algorithms The comparison results confirm the presented algorithm has benefits for on-line parameter estimation of the IM

Energy saving and environmental pollution reduction are important issues which scientists are focusing on to resolve The three-phase IM is widely used in industry Energy efficient control of the IM can contribute to reduce energy consumption In order to resolve this problem, there are several developed solutions to enhance the IM efficiency such as using better materials for producing the IMs, improving the IM construction, adding power electronic converters for controlling the IM speed, as well as using multiple smaller machines instead of a single large one Also, the IM efficiency can be enhanced using on-line energy efficient controllers such as search and model-based controllers

This thesis proposes a novel energy efficient control strategy by optimizing the rotor flux reference of the IM in which the IM parameter variations are updated on-line to ensure an optimum solution The derivative technique and the chaos PSO algorithm are used in turn to determine the optimal rotor flux reference of the IM Simulation results demonstrate the validity of the described approach

If three-phase IMs are widely used in industrial systems, single-phase induction machines (SPIM) are popularly utilised in home appliances and in applications requiring less than 5 kW [1.5] This is due to the widespread availability of single-phase power supplies, simple mechanical and electrical structures, ruggedness, high reliability and low cost [1.6]

In most SPIM applications, its performance depends on the accuracy of the SPIM parameters Some of these parameters are usually provided by the manufacturer Nevertheless, manufacturers may not supply all the parameter information Thus, the

issue of how to estimate the SPIM parameters needs to be examined In [1.5], [1.8], the SPIM parameters are obtained using tests such as the DC, no-load and locked-rotor tests

[1.7]-This thesis proposes a novel application of the dynamic PSO and chaos PSO algorithms for off-line parameter estimation of the SPIM The experimental results of the estimated parameters using the dynamic PSO and chaos PSO algorithms are compared with the parameters obtained from the load test and the standard PSO algorithm The comparison results have confirmed the effectiveness of the proposed application in off-line parameter estimation of the SPIM

The thesis is presented in eight chapters

Chapter 1 – Introduction This chapter briefly introduces the IM and the motivation to

perform off-line and on-line parameter estimation as well as energy efficient control of the IMs These are the main objectives of the thesis The structure of the thesis is also presented in this chapter

Chapter 2 – Background theory and literature review This chapter presents the

background theory of three-phase IM modelling and the well-known field-oriented control techniques for the IM Several off-line parameter estimation algorithms for the three-phase IM and SPIM are discussed with emphasis on using optimization techniques Furthermore, various approaches for on-line parameter estimation of the three-phase IM are presented, including model reference adaptive systems (MRAS), Kalman filters (KF) and recursive least-squares (RLS) algorithms, neural networks (NN) Finally, energy efficient control strategies for the three-phase IM are introduced

including search and model-based control schemes

Chapter 3 – Background to and modifications of a particle swarm optimization algorithm This chapter presents the general background and modifications of the PSO

algorithm There have been several proposed PSO algorithm variants such as the PSO algorithm with a constriction factor, PSO algorithm with a time-varying inertia weight, dynamic PSO and chaos PSO algorithms Amongst these variants, the dynamic PSO and chaos PSO algorithms are more dominant than the others and are therefore adopted for off-line parameter estimation of the single- and three-phase IMs as well as energy

efficient control of the three-phase IM Some comparisons between the PSO algorithm and other evolutionary computation techniques are also provided in this chapter

Chapter 4 – Off-line parameter estimation of a three-phase induction machine using particle swarm optimization algorithms This chapter proposes a novel application of

the dynamic PSO and chaos PSO algorithms for off-line parameter estimation of the three-phase IM The off-line parameter estimation problem is based on the output error method The algorithms use the measurements of the three-phase stator currents, voltages and the rotor speed of the IM as the inputs to the parameter estimator The practical experiments are implemented by using the IM system, data acquisition PCI-

6251 card, block connector BNC-2110 together with LabVIEW software for sampling and recording the measurement data MATLAB is used to process the data and estimate the IM parameters The experimental results obtained compare the estimated parameters with the IM parameters achieved using traditional tests such as the DC, no-load and locked-rotor tests There is also a comparison of the solution quality between the GA, standard PSO, dynamic PSO and chaos PSO algorithms Conclusions about the

effectiveness of this approach for the proposed application are drawn

Chapter 5 – On-line parameter estimation of a three-phase induction machine using an advanced recursive least-squares algorithm This chapter proposes a novel RLS

algorithm with multiple time-varying forgetting factors for on-line parameter estimation

of the three-phase IM A regressive form of the IM mathematical model is introduced in this chapter as well The proposed RLS algorithm uses the measurements of the three-phase stator currents, voltages and the rotor speed of the IM as the inputs to the parameter estimators The simulation results obtained compare the estimated parameters with the IM parameters achieved using four versions of the RLS algorithm, specifically the standard RLS algorithm, RLS algorithm with a constant forgetting factor, RLS algorithm with a time-varying forgetting factor and RLS algorithm with multiple forgetting factors The comparison results show the advantages of the presented algorithm, especially in the case of time-varying IM parameters with different variation

reference is the optimized variable to improve the IM efficiency The derivative technique and the chaos PSO algorithm are used to optimize the rotor flux reference The energy efficient control scheme in this case is updated using on-line estimates of the IM parameter variations The on-line parameter estimation problem is used simultaneously with the energy efficient control strategy The simulation results using the derivative technique and the chaos PSO algorithm are compared with the case of using the rated rotor flux Furthermore, there is a comparison between the energy efficient control scheme using on-line updates and no updates of IM parameter variations Conclusions about the benefits of the proposed techniques are drawn

Chapter 7 – Off-line parameter estimation of a single-phase induction machine using particle swarm optimization algorithms This chapter proposes a novel application of

the dynamic PSO and chaos PSO algorithms for off-line parameter estimation of the SPIM This off-line parameter estimation problem is also based on the output error method as is used for off-line parameter estimation of the three-phase IM in Chapter 4 The algorithms use the measurements of the complex magnitudes of the currents and active powers in the SPIM main and auxiliary windings as the inputs to the parameter estimator

The experimental results obtained compare the estimated parameters with the parameters achieved using the load test There is also a comparison of the solution quality between the standard PSO, dynamic PSO and chaos PSO algorithms Conclusions about the effectiveness of the proposed technique are drawn from the experimental results

Chapter 8 – Conclusions This chapter summarizes the author’s main contributions and

their benefits Finally, future works are also suggested in this chapter

1.7 References

2002

“Efficiency optimization of induction motor using a fuzzy logic based optimum

flux search controller”, International Conference on Power Electronics, Drives

and Energy Systems, PEDES ’06, New Delhi, India, pp 1-6, 12-15 December

2006

[1.3] G McPherson and R D Laramore, An introduction to electrical machines and

transformers – Second Edition John Wiley & Sons, 1990

IEEE International Conference on Neural Networks, Perth, Australia, pp

1942-1948, 17 Nov-1 Dec 1995

single-phase induction machines”, 36th IEEE Industry Applications

Conference, IAS 2001, USA, pp 2280-2287, 30 September-4 October 2001

machine”, IEEE Transactions on Energy Conversion, vol 7, issue 4, pp

761-767, December 1992

constants”, Transactions of the American Institute of Electrical Engineers on

Power Apparatus and Systems, vol 71, issue 1, pp 221-227, January 1952

parameters of single-phase induction motors”, IEEE Transactions on Energy

Conversion, vol 10, issue 2, pp 248-253, June 1995

IMs are widely used in industry since they are economical, rugged, reliable and available over a large power range The IM consists of a wound stator and either a squirrel cage rotor or a wound rotor with slip rings When the wound stator is supplied with a sinusoidal balanced three-phase voltage, a synchronously rotating magnetic field

is created in the air gap This induces current in the rotor which generates the rotor magnetic field A torque is then produced from the interaction between the stator and rotor magnetic fields At the synchronous speed of the machine, the rotor cannot have any induction This means that torque cannot be produced This is why there must be a speed difference, known as the slip speed, between the stator magnetic field and rotor to induce rotor current In order to have a more detailed understanding about the IM as well as its applications, IM modelling techniques are presented in this section, including

the per-phase equivalent circuit and dynamic d-q models These are required for off-line

and on-line parameter estimation as well as the energy efficient control schemes

2.2.1 Per-phase equivalent circuit model

The three-phase IM is considered with the assumption of symmetrical windings In order to implement the IM analysis under steady-state conditions, this can be represented by the per-phase equivalent circuit as in Figure 2.1 [2.1]

In the equivalent circuit above, all the voltages and currents are RMS values The power expressions are then shown as follows, including the input and output powers, stator and rotor copper and core losses

The input power:

The core loss:

In fact, the per-phase equivalent circuit is only valid under steady-state conditions This

is useful for the calculation of the IM power and torque at a constant voltage, frequency and machine speed In high performance drive control, the transient behaviour of the IM

is required This leads to a different modelling technique which needs to be described

The dynamic d-q model which is introduced in the next section replaces the per-phase

equivalent circuit

2.2.2 Dynamic d-q model

In dynamic modelling of a three-phase IM, symmetrical windings are assumed and an axes transformation is required to reduce the complexity of the three-phase dynamic model This transforms the three-phase machine to a two-phase machine [2.1] Figure 2.2 shows both the transformation and inverse transformation between the three-phase

a-b-c and two-phase d-q stationary reference frames

stationary reference frames

v

s qs v

a

v as

θ

The transformation of the three-phase a-b-c voltage variables to two-phase d-q voltage

v

v

5.05

.05

0

)120sin(

)120sin(

sin

)120cos(

)120cos(

cos

3

0 0

0

θθ

θ

θθ

s qs

s ds

c

b

a

v v v v

v

v

0 0

0

0 0

1)120sin(

)120cos(

1)120sin(

)120cos(

1sin

cos

θθ

θθ

θθ

(2.8)

where

applied for the current and flux variables

component is assumed The transformations are then simplified as follows:

a s

qs

s

ds

v v

v v

v

3

13

1

0

00

s ds c

b

a

v

v v

v

v

2

32

32

1

01

(2.10)

In addition, it is also useful to model the IM in an arbitrary rotating reference frame as

in Figure 2.3 The rotating reference frame is usually chosen to rotate at synchronous

speed Then, the transformations from the two-phase d-q stationary reference frame to the two-phase d-q synchronously rotating reference frame and its inverse are:

s ds e e

e e

v

θθ

θθ

cossin

sincos

(2.11)

e ds e e

e e

v

θθ

θθ

cossin

sincos

(2.12)

d-q synchronously rotating reference frames

synchronously rotating reference frame

q s-axis

d e-axis

e ds

v

s qs v

θe

d s-axis

s ds

v

e qs v

q e-axis

i ds

R s

+ _

(ωe - ωr)ψdr R r

The two-phase IM equivalent circuits in an arbitrary synchronously rotating reference frame are then shown in Figure 2.4 [2.1] The effects of magnetic saturation, core loss and skin effect are neglected

The superscript e has been removed in the following equivalent circuits for

convenience

From the dynamic d e -q e equivalent circuits above, the voltage equations are as follows:

qs e ds ds

ls

ds =L i +L i +i =L i +L i

(qs qr) s qs m qr m

lr

dr =L i +L i +i =L i +L i

(qs qr) r qr m qs m

L e

The dynamic d-q model of the IM in an arbitrary synchronously rotating reference

frame is described by the electrical expressions, (2.13)-(2.22) and the mechanical expressions, (2.23)-(2.24)

In other applications, the IM is required to be modelled more accurately Then, the effects of the magnetic saturation, core loss and skin effect need to be considered In fact, when the flux in the IM varies such as in field weakening operation and energy efficient control problems, the magnetic saturation phenomenon appears This results in machine inductance variations In order to improve the performance of the IM applications with inductance variations, parameter estimation techniques are implemented to track these changes Additionally, this solution is also needed to deal with the skin effects which lead to variations in stator and rotor resistances with frequency Moreover, compensation techniques are applied to consider the core loss in the IM model as well

There are several IM control techniques, including voltage control, scalar control, oriented (vector) control and direct torque control Amongst these, the vector control technique is used in most high performance applications to achieve a quick and accurate torque response, large range of speed control and the ability to reduce the flux at low loads for energy efficient control For these reasons, vector control is chosen to be used

field-in this thesis for on-lfield-ine parameter estimation and energy efficient control

In vector control, the IM is controlled like a separately excited DC machine [2.1] This

is explained more clearly by considering the DC machine with the assumptions that the armature reaction and field saturation effects are neglected In the DC machine, the armature flux is produced by the armature current whereas the field flux is produced by the field current separately The armature flux is perpendicular to the field flux as in Figure 2.5 Because of decoupling, when the armature current controls the DC machine electrical torque, the field flux is not affected Otherwise, when the field current is controlled, this only affects the field flux and does not affect the armature flux

Figure 2.5 DC machine

Based on the DC machine performance, vector control is developed for the IM by splitting the current into two components rotating in a reference frame The IM is considered in an arbitrary synchronously rotating reference frame The IM control

scheme with the vector control technique and an inverter is shown in Figure 2.6 i ds * and

i qs * are the reference values of the two controlled currents which are the direct- and quadrature-axis components of the stator current respectively

In addition, i ds is chosen to align with the d-axis of the rotor flux and is perpendicular to

qs

i as in Figure 2.6 i ds is the IM flux producing current whereas i qs is the IM torque

producing current In the vector control technique, when i qs is controlled, this only

affects T e and does not affect ψr Similarly, when i ds is controlled, this only affects ψr

and does not affect T e This means that the vector control technique allows decoupled control of the IM flux and torque producing currents

IM

T e

In the rotor flux-oriented synchronously rotating reference frame, the d-axis voltage

expression is as follows:

( e r) qr

dr dr

where the q-axis rotor flux is zero in the rotor flux-oriented reference frame and (2.25)

is then re-written as follows:

dr dr

dr

dr

L

i L

m r dr r

r

L

L R L

The relationship between the rotor flux and the d-axis stator current is shown in (2.28)

Furthermore, in steady-state conditions, the derivative of the rotor flux is zero since the

rotor flux is constant The relationship between the rotor flux magnitude and the d-axis

stator current is then re-written as follows:

ds

m

dr =L i

Equations (2.28) and (2.29) show that the rotor flux magnitude can be controlled via the

d-axis stator current

Additionally, in the rotor flux-oriented synchronously rotating reference frame, the electrical torque expression is as follows:

Similarly, since the q-axis rotor flux is zero in the rotor flux-oriented reference frame,

(2.30) is then re-written as follows:

qs dr r

stator current as well

Thus, the rotor flux and torque can be separately controlled via controlling the rotor

flux-oriented d-q axis stator currents

However, in order to control the IM using the vector control technique, the axes transformation is required as illustrated in Figure 2.3 This means that the rotor flux position must be known There are two methods to achieve the rotor flux position known as the direct and indirect methods The main difference between them is how the rotor flux position is obtained These two vector control techniques are known as the direct and indirect vector control techniques

In the direct vector control technique, the rotor flux position is either measured using search coils or Hall effect transducers installed in the IM; calculated using the stator voltage or current model; or estimated using a flux observer, based on the Kalman filter

or Luenberger observer Using search coils or Hall effect transducers to obtain the rotor flux position is undesirable due to the high cost and reduced reliability When the rotor flux position is achieved using the other approaches, the stator voltages, currents and rotor speed of the IM are required These approaches are affected by the parameter variation effects of the stator resistance, stator and rotor inductances and magnetizing inductance

In the indirect vector control technique, the rotor flux position is obtained by adding the slip angle of the IM to the rotor angle as follows:

In the rotor flux-oriented reference frame, the q-axis rotor flux is zero One of the IM

voltage expressions then becomes as follows:

IM with the indirect vector control technique, the d-q axis stator currents and the rotor

speed or angle are required

In this case, it is obvious that the accuracy of the indirect vector control technique depends on the IM parameters This means that the IM parameter variations directly influence the performance of the control technique

Regarding the direct and indirect vector control techniques introduced, it can be realised that the performance of the indirect vector control technique is superior Therefore, the indirect vector control technique is chosen to be utilised in this thesis

2.4 Off-line parameter estimation approaches for a three-phase induction machine

In most high performance IM applications, accurate knowledge of the IM parameters is necessary This directly affects the operational and control characteristics of the IM Thus, the IM parameters need to be estimated during a commissioning procedure There are several approaches which have been proposed for off-line parameter estimation of the IM, including traditional tests such as the DC, no-load and locked-rotor tests There are also approaches using measurement of the IM variables such as model reference adaptive systems, artificial neural networks and optimization algorithms Amongst these approaches, the traditional tests and optimization algorithms are concentrated on and presented in detail in the next sections

2.4.1 DC, no-load and locked-rotor tests

Off-line parameter estimation using the DC, no-load and locked-rotor tests [2.2]-[2.3] is one of the common approaches to manually obtain IM parameters The procedure for each test is presented in detail in the following sections

A

B

C

I dc ≈ Irated

source supplying the IM stator windings Then, the stator winding resistance is

Under the no-load test condition, the IM is described by the per-phase equivalent circuit

V bc

mechanical load

Figure 2.9 Per-phase equivalent circuit of an IM under no-load test condition

In this case, the IM is almost run at synchronous speed This results in the slip being

s

s

R r 1−

is large, compared to R r and X lr Then, R r and X lr can be neglected

in the equivalent circuit

Additionally, the IM power factor is quite low in this test Thus, the circuit is essentially reactive This means that R s is small, compared to X m Then, R s can be neglected in the

Figure 2.10 Per-phase approximate equivalent circuit of an IM under no-load

From the equivalent circuit, Figure 2.10, the input impedance under no-load condition is

I

33

3

V V

A three-phase variac supplies the IM stator terminals so that rated current flows in the stator windings Full voltage at rated frequency should not be applied in this test since the stator current is then very large, five to eight more times than the rated value [2.2]

Figure 2.11 Locked-rotor test

The IM equivalent circuit for this test is shown in Figure 2.12 In this circuit, X m is many times greater than R r + jX lr [2.2] Thus, almost all the current flows through R r and X lr, instead of through the branch of R m and X m The equivalent circuit, Figure 2.12,

V bc

V ac

Locked rotor

becomes the simpler equivalent circuit as shown in Figure 2.13 which is a series

combination of R s, X ls, R r and X lr

Figure 2.12 IM equivalent circuit under the locked-rotor test

Figure 2.13 IM approximate equivalent circuit under the locked-rotor test at a

rated frequency

Figure 2.14 IM approximate equivalent circuit under the locked-rotor test at a

test frequency

At rated operating conditions of the IM with the stator frequency f s, the rotor frequency

f r is sf s, and is small since the slip is small In the locked-rotor test, the stator and rotor frequencies are the same since the slip is unity Thus, in order to obtain the rotor

R

=

X lr

resistance more exactly, this test is usually implemented using a test frequency less than the normal operating frequency The IEEE standard 112-1984 recommends that the locked-rotor test frequency is not more than 25% of the normal operating frequency [2.4]

The measurements from the locked-rotor test allow calculation of the IM parameters as follows:

The magnitude of the impedance looking into the per-phase equivalent circuit of the IM is:

s

LR

I

P R

R

2 2

2 2

LR LR

LR lr

ls

LR

I

P I

V R

Z X

a

LR

I I

From (2.45) and (2.48)-(2.49), the IM rotor resistance is determined as follows:

s LR

2.4.2 Optimization techniques

Besides using the traditional tests, the IM parameters can also be estimated utilising optimization techniques A genetic algorithm and a particle swarm optimization algorithm are two optimization algorithms which are introduced and applied to parameter estimation of a three-phase IM

Off-line parameter estimation techniques using optimization algorithms are based on the output error method which compares the response between the real system and an estimated parameter model using the same inputs Then, a performance function (or fitness function) is formed based on the real system response and the estimated parameter model response The fitness function is a function of the estimated parameter vector which obtains its minimum, zero, when the real parameter vector and the estimated parameter vector are the same Then, the parameters are estimated It can be realised that the parameter estimation problem becomes an optimization problem in this case

2.4.2.1 Genetic algorithms

The GA is a population-based search algorithm used in computing to find solutions for optimization and search problems This algorithm uses techniques inspired by the evolutionary biology processes such as inheritance, mutation, selection and crossover The GA behaviour and applications are introduced in detail in chapter 4 One of the GA applications is off-line parameter estimation of the IM which is presented in [2.5] The estimated parameters are derived from steady-state IM equivalent circuits such as the exact [2.5], [2.7], approximate [2.6], [2.10] and deep bar equivalent circuits [2.10] The

GA is used to minimize the error function between the measured and calculated values

of the terminal complex impedance at rated voltage and electrical torque of the IM [2.5] whereas the fitness function in [2.6], [2.7], [2.10] and [2.13] is a function of full-load, locked-rotor and breakdown torques

Furthermore, off-line parameter estimation of the IM was also performed using the IM models which are a set of non-linear differential equations for transient operation of the

IM from standstill to a steady-state speed for a set period followed by successive free motion to standstill [2.8]-[2.9], [2.11] In order to simplify the parameter estimation problem, the IM model is referred to the two-axis d-q stationary reference frame In this

case, the GA is used to minimize the error function between the responses of the real