Parameter Estimation of Permanent Magnet Synchronous Machines
Description
Comprehensive reference delivering basic principles and state-of-the-art parameter estimation techniques for permanent magnet synchronous machines (PMSMs)
Parameter Estimation of Permanent Magnet Synchronous Machines reviews estimation techniques of the parameters of PMSMs, introducing basic models and techniques, as well as issues and solutions in parameter estimation challenges, including rank deficiency, inverter nonlinearity, and magnetic saturation. This book is supported by theories, experiments, and simulation examples for each technique covered.
Topics explored in this book include:
- Electrical and mechanical parameter estimation techniques, including those based on current/voltage injection and position offset injection, under constant or variable speed and load for sensored or sensorless controlled PMSMs, accounting for magnetic saturation, cross-coupling, inverter nonlinearity, temperature effects, and more
- Recursive least squares, the Kalman filter, model reference adaptive systems, Adaline neural networks, gradient-based methods, particle swarm optimization, and genetic algorithms
- Applications of parameter estimation techniques for improvement of control performance, sensorless control, thermal condition monitoring, and fault diagnosis
This book is an essential reference for professionals working on the control and design of electrical machines, researchers studying electric vehicles, wind power generators, aerospace, industrial drives, automation systems, robots, and domestic appliances, as well as advanced undergraduate and graduate students in related programs of study.
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Persons
Zi Qiang Zhu is a Fellow of the Royal Academy of Engineering and the Head of the Electrical Machines and Power Research Group at the University of Sheffield, UK.
Kan Liu is the Assistant Dean of the College of Mechanical and Vehicle Engineering at Hunan University, China.
Dawei Liang is a Postdoctoral Research Associate with the University of Sheffield, UK.
Content
Authors xiii
Preface xv
List of Abbreviations xvii
List of Symbols xix
1 General Introduction 1
1.1 Introduction 1
1.2 Permanent Magnet Machines 2
1.3 Basic Equations and Machine Parameters 5
1.4 Drives and Control Strategies 11
1.5 Outline of Parameter Estimation Techniques 14
1.6 Scope of This Book 17
References 18
2 Critical Issues with Online Parameter Estimation 23
2.1 Rank-Deficient Problem 23
2.2 Non-linearity of VSI 29
2.3 Ill-Conditioned Problem 46
2.4 Summary 48
References 48
3 Online Estimation of Rotor Flux Linkage with the Aid of Thermocouples in Stator Windings 51
3.1 Introduction 51
3.2 Online Estimation of Rotor Flux Linkage with the Aid of Thermocouples in Stator Windings 52
3.3 Summary 57
References 57
4 Online Parameter Estimation Based on Current Injections 59
4.1 Introduction 59
4.2 Multi-parameter Estimation Based on Current Injection and Error Analysis 60
4.3 Winding Resistance and Rotor Flux Linkage Estimation Based on Current Injection under Constant Torque/Speed Control 68
4.4 Summary 72
References 73
5 Online Parameter Estimation Based on Position Offset Injection 75
5.1 Introduction 75
5.2 Phasor Analysis of Rotor Position Offset in PMSMs 76
5.3 Position Offset-based Estimation with ¿i¿d ¿= 0 ¿Under Constant Torque/Speed Control 77
5.4 Position Offset-based Estimation with i¿d¿¿ = 0¿ Under Variable Speed Control 89
5.5 Position Offset-based Estimation with i¿d¿ ¿ 0¿ Under Constant Torque/Speed Control 94
5.6 Position Offset-based Estimation with i¿d ¿= 0¿ and ¿ i¿d ¿¿ 0¿Under Constant and Variable Speed Control 99
5.7 Analysis of Amplitude of Position Offset Injection 103
5.8 Summary 108
References 109
6 Online Parameter Estimation Under Variable Speed Control 111
6.1 Introduction 111
6.2 Estimation of Stator Resistance, Inductances, and Rotor PM Flux Linkage 112
6.3 Estimation of dq-axis Flux Linkage Maps with Uncertainties of Circuit Resistance and Inverter Non-linearity 119
6.4 Summary 128
References 129
7 Estimation of Magnetic Saturation and Cross-coupling Based on High-frequency Signal Injection 131
7.1 Introduction 131
7.2 Magnetic Saturation Modelling and Time Delay Effect in HF Signal Injection 133
7.3 HF Rotating Voltage Injection Method 134
7.4 HF Pulsating Voltage Injection Method 137
7.5 Combined HF Rotating and Pulsating Voltage Injection Method 140
7.6 Experimental Results 142
7.7 Summary 146
References 147
8 Offline and Multi-step Parameter Estimation Methods 149
8.1 Introduction 149
8.2 Parameter Estimation at Standstill by Square Voltage Injection 150
8.3 Parameter Estimation at Standstill by HF Current Injection 153
8.4 Multi-step Parameter Estimation 158
8.5 Summary 163
References 163
9 Estimation of Mechanical Parameters 165
9.1 Introduction 165
9.2 Mechanical Parameter Estimation Methods 166
9.3 Experimental Results 170
9.4 Design of PI Speed Regulator 177
9.5 Summary 180
References 181
10 Modern Control and Optimization Theory-Based Parameter Estimation Algorithms 183
10.1 Introduction 183
10.2 Designed Parameter Estimation Scheme 183
10.3 Recursive Least-Squares 185
10.4 Kalman Filter 187
10.5 Model Reference Adaptive System 190
10.6 Adaline Neural Network 192
10.7 Gradient-Based Methods 195
10.8 Particle Swarm Optimization 198
10.9 Genetic Algorithm 201
10.10 Summary 203
References 205
11 Applications of Parameter Estimation 209
11.1 Introduction 209
11.2 Improvement in Control Performance 210
11.3 Improvement in Sensorless Control 216
11.4 Precise Torque Estimation 229
11.5 Thermal Condition Monitoring 232
11.6 Fault Diagnosis 234
11.7 Summary 237
References 238
Appendix A: Finite Element Calculation of Winding Inductances 243
Appendix B: Specifications of Prototype Machines and Experimental Platforms 251
Index 255
List of Symbols
Symbol Description Unit State transition matrix Control-input model Remanence T , Remanence at actual and reference temperatures T Maximum energy product kJ/m3 , Cognitive and social acceleration constants Condition number , -axis gain functions of VSI nonlinearity , Average values of -axis gain functions of VSI nonlinearity , -axis extended back-EMF V Friction coefficient Frequency of HF signal Hz First-order gradient Coercivity kA/m Intrinsic coercivity kA/m Identity matrix Three-phase currents A , , Three-phase currents A , -axis currents A , -axis HF currents A , -axis currents A , -axis HF currents A , Amplitudes of -axis HF currents A , Average values of -axis currents A Resolution of sampled current A Maximum current A , Amplitudes of positive and negative sequence currents A , Current perturbations in th and th coils A Variables of injected -axis current A Rotor moment of inertia kg m2 Index of discrete sampling instant , PI constants , , , , , Gains of cost functions Gain vector of RLS estimator Self-inductance H Mutual inductance H Phase self-inductance H Phase leakage inductance H Second-order harmonic of self-inductance H , -axis inductances H , -axis HF inductances H , -axis mutual inductances H , -axis HF mutual inductances H , -axis apparent inductances H , -axis incremental inductances H , -axis incremental self-inductances H , -axis apparent self-inductances H , -axis apparent mutual inductances H , -axis incremental mutual inductances H Average mutual inductance H Second-order harmonic of mutual inductance H Overall time error S Sampling number Pole pair number , Cost function Covariance matrix Model uncertainty matrix Measurement noise covariance Estimated synchronous rotating reference frame On-state resistance of IGBT O On-state resistance of freewheeling diode O Iron loss resistance O Stator winding resistance O Error of estimated stator winding resistance O , Winding resistance at actual and reference temperatures O Switching pattern of three-phase legs Clarke transformation Active durations of space vectors and S Actual duration of effective time S Commanded duration of effective time S Compensation time S Dead time of power device S Switch on/off time delay S Sampling time S Electromagnetic torque N m Estimated torque N m Load torque N m Control vector in KF , -axis voltages V , -axis voltages V , -axis reference voltages V , -axis HF voltages V , -axis HF reference voltages V Voltage vector reference V Maximum output phase voltage V HF voltage signal V System noise Observation/measurement noise Operator norm Voltage vectors V , , , Reference three-phase voltages V , , Distorted three-phase voltage caused by VSI nonlinearity V On-state voltage drop of IGBT V Threshold voltage drop of IGBT V On-state voltage drop of freewheeling diode V Threshold voltage drop of freewheeling diode V Variable of injected -axis voltage V dc bus voltage V , -axis distorted voltages due to VSI nonlinearity V Distorted voltage term due to VSI nonlinearity V Amplitude of injected HF voltage V Non-zero dc offset V Threshold voltage V Total stored energy J Weight in ANN estimator Zero-mean white Gaussian system noise Inertia weight in PSO estimator , Characteristic roots , Particle best and overall best locations in PSO estimator Step variation , Measured and predicted output variables Output matrix of RLS estimator Temperature coefficient of copper %/°C Temperature coefficient of magnet %/°C Step length of Newton algorithm Current advancing angle Deg. Finite positive constant Least-square error Optimal damping ratio Tuning factor Convergence...
