
Variable Speed AC Drives with Inverter Output Filters
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Content
Foreword xi
Acknowledgments xiii
About the Authors xiv
Nomenclature xvi
1 Introduction to Electric Drives with LC Filters 1
1.1 Preliminary Remarks 1
1.2 General Overview of AC Drives with Inverter Output Filters 2
1.3 Book Overview 4
1.4 Remarks on Simulation Examples 5
References 6
2 Problems with AC Drives and Voltage Source Inverter Supply Effects 9
2.1 Effects Related to Common Mode Voltage 9
2.1.1 Capacitive Bearing Current 15
2.1.2 Electrical Discharge Machining Current 15
2.1.3 Circulating Bearing Current 15
2.1.4 Rotor Grounding Current 17
2.1.5 Dominant Bearing Current 17
2.2 Determination of the Induction Motor CM Parameters 18
2.3 Prevention of Common Mode Current: Passive Methods 20
2.3.1 Decreasing the Inverter Switching Frequency 20
2.3.2 Common Mode Choke 21
2.3.3 Integrated Common Mode and Differential Mode Choke 23
2.3.4 Common Mode Transformer 25
2.3.5 Machine Construction and Bearing Protection Rings 26
2.4 Active Systems for Reducing the CM Current 27
2.5 Common Mode Current Reduction by PWM Algorithm Modifications 28
2.5.1 Three Nonparity Active Vectors 30
2.5.2 Three Active Vector Modulation 32
2.5.3 Active Zero Voltage Control 32
2.5.4 Space Vector Modulation with One Zero Vector 36
2.6 Simulation Examples 39
2.6.1 Model of Induction Motor Drive with PWM Inverter and cmv 39
2.6.2 PWM Algorithms for Reduction of cmv 44
2.7 Summary 46
References 46
3 Model of AC Induction Machine 49
3.1 Introduction 49
3.1.1 T-Model of Induction Machine 50
3.2 Inverse-G Model of Induction Machine 53
3.3 Per-Unit System 54
3.4 Machine Parameters 56
3.5 Simulation Examples 59
References 63
4 Inverter Output Filters 65
4.1 Structures and Fundamentals of Operations 65
4.2 Output Filter Model 71
4.3 Design of Inverter Output Filters 74
4.3.1 Sinusoidal Filter 74
4.3.2 Common Mode Filter 80
4.4 dV/dt Filter 83
4.5 Motor Choke 85
4.6 Simulation Examples 86
4.6.1 Inverter with LC Filter 86
4.6.2 Inverter with Common Mode and Differential Mode Filter 90
4.7 Summary 95
References 96
5 Estimation of the State Variables in the Drive with LC Filter 97
5.1 Introduction 97
5.2 The State Observer with LC Filter Simulator 99
5.3 Speed Observer with Simplified Model of Disturbances 103
5.4 Speed Observer with Extended Model of Disturbances 106
5.5 Speed Observer with Complete Model of Disturbances 107
5.6 Speed Observer Operating for Rotating Coordinates 109
5.7 Speed Observer Based on Voltage Model of Induction Motor 114
5.8 Speed Observer with Dual Model of Stator Circuit 122
5.9 Adaptive Speed Observer 125
5.10 Luenberger Flux Observer 129
5.11 Simulation Examples 130
5.11.1 Model of the State Observer with LC Filter Simulator 130
5.11.2 Model of Speed Observer with Simplified Model of Disturbances 133
5.11.3 Model of Rotor Flux Luenberger Observer 136
5.12 Summary 138
References 138
6 Control of Induction Motor Drives with LC Filters 141
6.1 Introduction 141
6.2 A Sinusoidal Filter as the Control Object 141
6.3 Field Oriented Control 143
6.4 Nonlinear Field Oriented Control 148
6.5 Multiscalar Control 156
6.5.1 Main Control System of the Motor State Variables 157
6.5.2 Subordinated Control System of the Sinusoidal Filter State Variables 160
6.6 Electric Drive with Load-Angle Control 166
6.7 Direct Torque Control with Space Vector Pulse Width Modulation 178
6.8 Simulation Examples 186
6.8.1 Induction Motor Multiscalar Control with Multiloop Control of LC Filter 186
6.8.2 Inverter with LC Filter and LR Load with Closed-Loop Control 194
6.9 Summary 198
References 198
7 Current Control of the Induction Motor 201
7.1 Introduction 201
7.2 Current Controller 203
7.2.1 Predictive Object Model 207
7.2.2 Costs Function 208
7.2.3 Predictive Controller 208
7.3 Investigations 208
7.4 Simulation Examples of Induction Motor with Motor Choke and Predictive Control 210
7.5 Summary and Conclusions 216
References 217
8 Diagnostics of the Motor and Mechanical Side Faults 218
8.1 Introduction 218
8.2 Drive Diagnosis Using Motor Torque Analysis 218
8.3 Diagnosis of Rotor Faults in Closed-Loop Control 233
8.4 Simulation Examples of Induction Motor with Inverter Output Filter and Load Torque Estimation 235
8.5 Conclusions 239
References 239
9 Multiphase Drive with Induction Motor and an LC Filter 241
9.1 Introduction 241
9.2 Model of a Five-Phase Machine 243
9.3 Model of a Five-Phase LC Filter 246
9.4 Five-Phase Voltage Source Inverter 247
9.5 Control of Five-Phase Induction Motor with an LC Filter 253
9.6 Speed and Flux Observer 255
9.7 Induction Motor and an LC Filter for Five-Phase Drive 257
9.8 Investigations of Five-Phase Sensorless Drive with an LC Filter 257
9.9 FOC Structure in the Case of Combination of Fundamental and Third Harmonic Currents 262
9.10 Simulation Examples of Five-Phase Induction Motor with a PWM Inverter 266
References 269
10 General Summary, Remarks, and Conclusion 271
Appendix A Synchronous Sampling of Inverter Output Current 273
References 276
Appendix B Examples of LC Filter Design 277
B.1 Introduction 277
Appendix C Equations of Transformation 282
References 285
Appendix D Data of the Motors Used in Simulations and Experiments 286
Appendix E Adaptive Backstepping Observer 289
Marcin Morawiec
E.1 Introduction 289
E.2 LC Filter and Extended Induction Machine Mathematical Models 290
E.3 Backstepping Speed Observer 292
E.4 Stability Analysis of the Backstepping Speed Observer 298
E.5 Investigations 304
E.6 Conclusions 305
References 307
Appendix F Significant Variables and Functions in Simulation Files 308
Index 311
1
Introduction to Electric Drives with LC Filters
1.1 Preliminary Remarks
The basic function of electric drives is to convert electrical energy to mechanical form (in motor mode operation) or from mechanical form to electrical energy (in generation mode). The electric drive is a multidisciplinary problem because of the complexity of the contained systems (Figure 1.1).
Figure 1.1 General structure of an electrical drive
It is important to convert the energy in a controllable way and with high efficiency and robustness. If we look at the structure of global consumption of electrical energy the significance is plain. In industrialized countries, approximately two thirds of total industrial power demand is consumed by electrical drives [1, 2].
The high performance and high efficiency of electric drives can be obtained only in the case of using controllable variable speed drives with sophisticated control algorithms [3, 4].
In the industry, the widely used adjustable speed electrical drives are systems with an induction motor and voltage inverter (Figure 1.2). Their popularity results mainly from good control properties, good robustness, high efficiency, simple construction, and low cost of the machines [5].
Figure 1.2 Electrical drive with voltage inverter and AC motor
Simple control algorithms for induction motors are based on the V/f principle. Because the reference frequency changes, the motor supply voltage has to be changed proportionally. In more sophisticated algorithms, systems such as field-oriented, direct torque, or multiscalar control have to be applied [6, 7] . Simultaneously, because of the estimation possibilities of selected controlled variables, for example, mechanical speed, it is possible to realize a sensorless control principle [7-10]. The sensorless speed drives are beneficial to maintain good robustness. Unfortunately, for sophisticated control methods, knowledge of motor parameters as well as high robustness of the drives against changes in motor parameters is required.
1.2 General Overview of AC Drives with Inverter Output Filters
The inverter output voltage has a rectangular shape and is far from the sinusoidal one. Also, the use of semiconductor switches with short switching times causes high rates of rises of dV/dt voltages that initiate high levels of current and voltage disturbance [4, 11] . For this reason, it is necessary to apply filters between the inverter and the motor (Figure 1.3).
Figure 1.3 AC motor with voltage inverter and inverter output filter
The introduction of a filter at the inverter output disables the proper operation of advanced drive control systems because doing this introduces more passive elements (inductances, capacitances, and resistances), which are not considered in the control algorithm [4, 12, 13] . This irregularity is caused by amplitude changes and phase shifts between the first current component and the motor supply voltage, compared to the currents and voltages on the inverter output. This causes the appearance in the motor control algorithm of inaccurate measured values of current and voltage at the standard measuring points of the inverter circuit. A possible solution to this issue is the implementation of current and voltage sensors at the filter output. However, this solution is not applied in industry drive systems because the filter is an element connected to the output of the inverter. The implementation of external sensors brings an additional cable network and that increases the susceptibility of the system to disturbances, reduces the system reliability, and increases the total cost of the drive.
A better solution is to consider the structure and parameters of the filter in the control and estimation algorithms. This makes it possible to use the measurement sensors that are already installed in the classical voltage inverter systems.
The addition of the filter at the voltage inverter output is beneficial because of the limitation of disturbances at the inverter output by obtaining sinusoidal voltage and current waveforms. Noises and vibrations are reduced and motor efficiency is increased. Furthermore, output filters reduce overvoltages on the motor terminals, which are generated through wave reflections in long lines and can result in accelerated aging of insulation. Several filter solutions are also used for limiting motor leakage currents, ensuring a longer failure-free operation time of the motor bearings.
The application of an inverter output filter and its consideration in the control algorithm is especially beneficial for various drive systems such as cranes and elevators. In that application, a long connection between motor and inverter is common.
The limitation of disturbances in inverter output circuits is an important issue that is discussed in numerous publications [14-18]. To limit such current and voltage disturbances, passive or active filters are used [4, 15] . The main reasons for preferring passive filters are especially the economic aspects and the possibility of limiting current and voltage disturbances in drive systems with high dV/dt voltage.
The control methods presented so far in the literature (e.g., [8-10, 19-27]) for an advanced sensorless control squirrel cage motor are designed for drives with the motor directly connected to the inverter. Not using filters in many drives is the result of control problems because of the difference between the instantaneous current and voltage values at the filter output and the current and voltage values at the filter input. Knowledge of this values is needed in the drive system control [28, 29] . A sensorless speed control in a drive system with an induction motor is most often based on the knowledge of the first component of the current and voltage. The filter can be designed in such a way that it will not significantly influence the fundamental components and will only limit the higher harmonics. However, most output filter systems introduce a voltage drop and a current and voltage phase shift for the first harmonic [4, 30] . This problem is important especially for sinusoidal filters, which ensure sinusoidal output voltage and current waveforms.
Another problem that has received attention in the literature [16, 30-37] is the common mode current that occurs in drive systems with a voltage inverter. The common mode current flow reduces the motor durability because of the accelerated wear of bearings. This current might also have an effect on the wrong operation of other drives included in the same electrical grid and can cause rising installation costs, which could lead to the need for an increase in the diameter of earth wire. Such problems come from both the system topology and the applied pulse width modulation in the inverter, which are independent of the main control algorithms. Modifying the modulation method can cause a limitation of the common mode current [4, 30, 38].
This book presents the problems related to voltage-inverter-fed drive systems with a simultaneous output filter application. The authors have presented problems and searched for new solutions, which up to now, have not been presented in the literature. Therefore, this book introduces, among other topics, new state observer structures and control systems with LC filters.
The problem of drive systems with output filters, justifying the need for their application, is also explained. Moreover, the aim of this book is to present a way to control a squirrel cage induction motor and estimation of variables by considering the presence of the output filter, especially for drive systems without speed measurement.
Other discussed topics are several motor control structures that consider the motor filter as the control object. Such solutions are introduced for nonlinear-control drive systems and field-orientated control with load-angle control. Predictive current control with the presence of a motor choke is also analyzed. Solutions for systems with the estimation of state variables are presented, and the fault detection scheme for the mechanical part of the load torque transmission system is shown. Thus, for diagnostic purposes, state observer solutions were applied for drive systems with a motor filter.
The main points to be discussed are:
- A motor filter is an essential element in modern inverter drive systems.
- The introduction of a motor filter between the inverter and motor terminals changes the drive system structure in such a way that the drive system might operate incorrectly.
- The correct control of the induction motor, especially for sensorless drives, requires consideration of the filter in the control and state variable estimation process.
Some of the presented problems in the book also refer to drive systems without filters. Those problems are predictive current control using the state observer, fault diagnostics using a state observer in rotating frame systems, and decoupled field-orientated control with load-angle control.
1.3 Book Overview
Chapter 2 presents the problems of voltage and current common mode. The common mode is the result of voltage inverter operation with pulse width modulation in addition to the motor parasitic capacitances. The equivalent circuit of the common mode current flow is presented and explained extensively. Furthermore, attention is paid to the bearing current, whose types are characterized by a...
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