Fault Tolerant Control of Three Phase Induction Motor Drive System

Suez Canal University Faculty of Engineering Electrical Engineering Dept. Port said, Egypt.

Fault Tolerant Control of Three Phase Induction Motor Drive System By Eng. Mahmoud Fawzi Mahmoud Ahmed B.Sc., Electrical Engineering, Faculty of Engineering, Suez Canal University, 1997. Ms.c., Electrical Engineering, Faculty of Engineering, Suez Canal University, 2003. A Thesis Submitted for partial fulfillment for the requirements of the degree of Ph.D In Electrical Engineering Supervisors

Prof. Dr. Farouk M. Abdel-Kader

Prof Dr. Elwy Eissa El-Kholy

President of Sinai University

Prof. of Electrical Machines

Prof. of Electrical Machines

Faculty of Engineering- Shebeen Elkom

Faculty of Engineering- Port said

Menoufia University

Suez Canal University

Dr. Attia A. El-saadawi

Dr. Ahmed E. Kalas

Dept.of Electrical Engineering

Dept.of Electrical Engineering





2010

Contents

Table of Contents Page Table of contents

i

List of tables

iv

List of figures

v

Symbols and abbreviations

xiv

Abstract

xv

Chapter (1) Introduction 1.1 Introduction

1

1.2 Problem Definition

1

1.3 Literature Review

4

1.4 These Objectives

6

1.5 Theses Outlines

7

Chapter (2) Fault Tolerant Control Systems 2.1 Introduction

10

2.2 Fault Tolerance Concept

10

2.3 Fault tolerant control algorithms

11

2.3.1 (Method 1) Connecting the faulty phase terminal to the mid-point of the dc Link

11

2.3.2 (Method 2) Connecting the neutral point to the mid-point of the dc link 2.4 Fault Tolerant Control Procedure steps

13 15

2.4.1 Fault detection

16

2.4.2 Fault Isolation Technique

18

2.4.3 Fault Compensation

19

2.4.3.1 Four-leg Three Phase Inverter

20

2.4.3.2 Four switches three phase inverter (FSTPI)

22

Chapter (3) Modeling and Simulation of Induction Motor Drive System 3.1 Introduction

28

3.2 Induction Motor Dynamic d-q Model

28

3.2.1 Axis Transformation

29

3.2.2 Electrical Equations

30

3.2.3 Mechanical Equations

32 i

Contents 3.3 Induction Motor Model in ABC Reference Frame

36

3.3.1 Electrical Equations

36

3.3.2 Torque Equation in Machine Variables

39

3.4 Simulation Results

45

3.5 Modeling of Three Phase Sinusoidal PWM Inverter

48

3.5.1 Relation between Pole Voltage and Phase Voltage 3.6 Simulation Results

51 53

3.6.1 Inverter output voltage space vector

60

3.7 Inverter IGBT Gate Drive Open Circuit Fault

61

3.7.1 Simulation results under fault conditions

63

3.7.2 Stator Current Space Vector Approach to Fault Diagnosis

66

Chapter (4) Fault Tolerant Field Oriented Control Induction Motor Drive System 4.1 Introduction

68

4.2 Principle of Vector Control of Induction Motor

68

4.3 Indirect Field Oriented Vector Control Method

71

4.4 Derivation of Indirect Rotor Field Oriented Vector Control Equations

72

4.5 Implementation of Indirect Field Oriented Control System

77

4.6 The Current Regulated Pulse Width Modulation (CRPWM) Technique

76

4.6.1 Hysteresis Band Current Control PWM

76

4.7 System Simulation Using Matlab-Simulink

77

4.8 Fault Tolerant Control System Design Using Current RegulationTechnique

80

4.9 Implementation of Fault Tolerant Control System

83

4.10 Simulation results

87

4.10.1 Stator Current Space Vector Approach to Fault Diagnosis 4.11 Zero Current Switching Technique

93 97

Chapter (5) Fault Tolerant Direct Torque Control Induction Motor Drive System 5.1 Introduction

102

5.2 Principle of Direct Torque Control (DTC) method

102

5.2.1 Torque and Stator Flux Estimation in DTC

104

5.2.2 Control Strategy of DTC

104

5.3 The Proposed Fault Tolerant Control Algorithm 5.3.1 Four Switch Three Phase Inverter (FSTPI) Topology ii

107 107

Contents 5.3.2 Phase (a) is disconnected

109

5.3.3 Phase (c) is disconnected

112

5.4 Modeling of the Proposed System Using Matlab-Simulink

114

5.5 Simulation Results

117

Chapter (6) Experimental Test Setup 6.1 Introduction

125

6.2 Experimental setup

125

6.2.1 Power Circuit Design

127

6.2.2 Control system Design

129

6.2.2.1 The interface card (PCI 1711)

129

6.2.2.2 Current sensor circuit.

130

6.2.2.3 Voltage sensor circuit

132

6.2.2.4 The delay circuit

133

6.2.2.5 The Isolation circuit

136

6.2.2.6 The power supply circuits

138

6.3 Operating From Open Loop Sinusoidal PWM 6.3.1 Experimental Results

144 146

6.4 Open gate drive fault of upper MOSFET of phase (a)

153

6.5 Open gate drive fault of lower MOSFET of phase (a)

159

Chapter (7) Experimental Implementation of the Proposed Method 7.1 Experimental Implementation of Direct Torque Control (DTC) System

165

7.2 Experimental Results

167

7.3 Experimental Implementation of Four Switch Three Phase Inverter (FSTPI)

175

7.4 Experimental results of fault tolerant direct torque control system

177

Chapter (8) Comparison between Simulation and Experimental Results 8.1 Direct Torque Control Six Switch Three Phase Inverter DTC-SSTPI

195

8.2 Direct Torque Control Four Switch Three Phase Inverter DTC-FSTPI

200

Chapter (9) Conclusions and Future Works

207

References

211

Appendices

iii

List of Tables

List of Tables Page Table 2.I: Comparison between fault tolerant control methods

14

Table 2.II: DC Current Offset Polarity Corresponding To Faulty Open Circuit Transistor

17

Table2. III: Comparison between Fault Compensation Techniques

25

Table 3.I Summary of Inverter Switching States

60

Table.5.1: Switching table of inverter voltage vectors

107

TABLE 5.II: Stator space vectors if phase (a) is disconnected

110

TABLE 5.III: DTC Lookup Table

112

TABLE 5.IV: The switching states and the corresponding voltage space vectors

113

TABLE 5.V: DTC lookup table

113

iv

List of Figures

List of Figures Page Fig.1.1The most common faults in induction motor drive system

2

Fig.1.2 The percentage of the common faults in a switched mode power supply

3

Fig.1.3 Design procedures to improve the system reliability

4

Fig.2.1 Standard three phase AC drive system

10

Fig.2.2-a Connecting the faulty phase terminal to the mid-point of the dc link

11

Fig.2.2-b Connecting the neutral point to the mid-point of the dc link

11

Fig.2.3 Supplying three phase load from two voltages source with 60o phase shift

12

Fig.2.4 Phasor diagram of the stator current regulation technique

14

Fig.2.5 Faulty-leg isolation technique

18

Fig.2.6 Fault compensation techniques of three phase inverter

19

Fig.2.7 Phase-leg Redundant Topology

20

Fig.2.8 Double Switch Redundant Topology

21

Fig.2.9 Four switch three phase inverter topology

22

Fig.2.10 Connecting the neutral point to the mid-point of the dc link

23

Fig.2.11 Fault current path when isolating single switch short circuit fault

24

Fig.2.12 Numbers of electronic components in each topology

26

Fig.3.1 Stationary a-b-c to synchronously rotating d-q axis transformation

29

Fig.3.2 D-q dynamic equivalent circuits in synchronously rotating reference frame

31

Fig.3.3 Block diagram of induction motor d-q model.

33

Fig. 3.4 The overall system model in Matlab-Simulink

34

Fig.3.5 Inside the induction motor block

34

Fig.3.6 Inside the power supply block

35

Fig.3.7 Three phase symmetrical induction machine

36

Fig.3.8 Block diagram of induction motor a-b-c model.

41


42


42

Fig.3.11 Inside the stator current block

43

Fig.3.12 Inside the rotor current block

44

Fig.3.13 Developed torque at normal conditions

46

Fig.3.14 Speed at normal conditions

46

Fig.3.15 Stator currents at normal conditions

47 v

List of Figures Fig.3.16 Zoom in to the stator currents at normal conditions

47

Fig.3.17 Standard three phase inverter

48

Fig.3.18 Three phase inverter phase and line voltages

50

Fig.3.19 Relations between pole voltages and phase voltages

51

Fig.3.20 Three phase inverter block

52

Fig.3.21 Inside the three phase inverter block

52

Fig.3.22 Inside the load voltage block

52

Fig.3.23 The developed torque

53

Fig.3.24 Motor speed (rad/sec)

54

Fig.3.25 Stator currents

54

Fig.3.26 Zoom in to the stator currents

54

Fig.3.27 Inverter pole voltages Va0 , Vb0 , Vc0

55

Fig.3.28 Inverter phase voltages Van , Vbn , Vcn

56

Fig.3.29 Carrier and modulating signals (m=1.2) overmodulation

56


57


57


58


58


59

Fig.3.35 Carrier and modulating signals (m=0.9) undermodulation

59

Fig.3.36 Stator voltage space vector of three phase inverter

61

Fig.3.37 Inverter output voltage space vector in normal condition

61

Fig.3.38 Stator currents before and after opening gate drive of Q1

64

Fig.3.39 Phase A current before and after opening gate drive of Q1 with negative DC offset

64

Fig.3.40 Phase B current before and after opening gate drive of Q1 with positive DC offset

64

Fig.3.41 Phase C current before and after opening gate drive of Q1 with positive DC offset

65

Fig.3.42 The developed torque before, during the fault and after the fault clearance

66

Fig.3.43 Stator current space vector trajectory, before and after open gate drive fault of upper IGBT fault

67

Fig.3.44 Stator current space vector trajectory, before and after an open gate drive

vi

List of Figures fault of lower IGBT fault

67

Fig.4.1 DC motor currents relation

69

Fig.4.2 Torque and flux components in induction motor

70

Fig.4.3 vector control principle in induction motor

70

Fig.4.4 Indirect field oriented in phasor diagram

72

Fig.4.5 de-qe equivalent circuits of induction motor

72

Fig.4.6 Indirect vector control block diagram with open loop flux control

75

Fig.4.7 Inside IRFOC block

75

Fig.4.8 Hysteresis Band Current Control PWM

77

Fig.4.9 Indirect field oriented control system in Matlab-simulink

78

Fig.4.10 Inside torque command generator block

78

Fig.4.11 Inside Field Oriented control block

78

Fig.4.12 Inside three phase inverter block

79

Fig.4.13 Inside the inverter block

79

Fig.4.14 Stator currents phasor diagram before and after phase (a) disconnection

82

Fig.4.15 Stator currents phasor diagram before and after phase (b) disconnection

83

Fig.4.16 Stator currents phasor diagram before and after phase (c) disconnection

83

Fig.4.17. Fault isolation method using TRIACs

84

Fig.4.18 Current phasor diagram before and after phase (a) disconnection

85

Fig.4.19 Current vector loci in healthy and faulty drive

87

Fig.4.20 The developed torque during load changes

88


88

Fig.4.22 Stator currents Ias,Ibs,Ics

89

Fig.4.23 Inverter phase voltage Van , Vbn , Vcn

89


90

Fig.4.25 Phase (a) current Ias with its reference value Ias*

90

Fig.4.26 Zoom in to phase (a) current Ias with its reference value Ias*

91

Fig.4.27 Phase (a) current and DC offset value

91

Fig.4.28 Phase (b) current and DC offset value

92

Fig.4.29 Phase (c) current and DC offset value

92

Fig.4.30 DC offset current components in stator currents

92

Fig.4.31 Motor torque before and after phase disconnection at t=0.588 sec

93

Fig.4.32 Motor speed before and after phase disconnection at t=0.588 sec

93

Fig.4.33 Stator current space vector before and after the fault in phase (a)

94

vii

List of Figures Fig.4.34 Stator current space vector before and after the fault in phase (b)

94

Fig.4.35 Stator current space vector before and after the fault in phase (c)

95

Fig.4.36 The developed torque in normal, faulty and fault tolerant control periods

96

Fig.4.37 Speed in normal, faulty and fault tolerant control periods

96

Fig.4.38 Stator currents in normal, faulty and fault tolerant control periods

96

Fig.4.39 Phase Voltages in normal, faulty and fault tolerant control periods

97

Fig.4.40 Stator currents before and after phase disconnection at t=0.575 sec

97


98


98


98

Fig.4.44 Iqs, Ids and I0s before and after phase disconnection

99


100

Fig.5.1 Stator, rotor fluxes and stator current vectors on ds-qs plane

103

Fig.5.2 Direct Torque control block diagram

105

Fig.5.3 Stator flux vector trajectory in DTC control

106

Fig.5.4. Four Switch Three Phase Inverter (FSTPI) with phase (a) is connected to DC link mid-point

108

Fig.5.5. Fault isolation method using TRIACs

109

Fig.5.6. Stator voltage space vector if phase (a) is disconnected

110

Fig.5.7. Selection of suitable voltage vector (a) increasing s, (b) decreasing s

111

Fig.5.8.Stator flux space vector trajectory if phase (a) is disconnected

112

Fig.5.9. Phase (c) is disconnected

114

Fig.5.10. Modeling of DTC induction motor drive system using Matlab-Simulink

114

Fig.5.11 Look up tables and vector selection block

115

Fig.5.12 Determination of pole voltages according to the suitable voltage vector

115

Fig.5.13 Estimation of the developed torque

115

Fig.5.14 Estimation of the stator flux

115

Fig.5.15 Determination of sectors

116


117

Fig.5.17 Motor speed

117


118

Fig.5.19 Zoom in the stator currents

118

Fig.5.20 Stator flux magnitude

118

viii

List of Figures Fig.5.21 Zoom in the stator flux amplitude

119

Fig.5.22 Stator flux space vector trajectory with ±0.01 Wb hysteresis band controller

119

Fig. 5.23 Stator flux space vector and the voltage space vector when phase (a) is disconnected

120

Fig.5.24 Stator flux after phase (a) disconnection

120

Fig.5.25 The developed torque before and after phase disconnection at t=0.6 sec

120

Fig.5.26. Stator currents before and after phase disconnection at t=0.6 sec

121

Fig.5.27 Phase (a) voltage before and after phase disconnection at t=0.6 sec

121

Fig.5.28 Phase (b) voltage before and after phase disconnection at t=0.6 sec

121

Fig.5.29 Phase (c) voltage before and after phase disconnection at t=0.6 sec

122

Fig.5.30 Stator flux space vector and the voltage space vector when phase (C) is Disconnected

122

Fig.5.31Stator flux after phase (c) disconnection

123

Fig.5.32 The developed torque before and after phase disconnection at t=0.6 sec

123


123

Fig.5.34 Phase (a) voltage before and after phase disconnection at t=0.6 sec

124

Fig.5.35 Phase (b) voltage before and after phase disconnection at t=0.6 sec

124

Fig.5.36 Phase (c) voltage before and after phase disconnection at t=0.6 sec

124

Fig.6.1 Experimental setup block diagram

126

Fig.6.2 Real view of the diode bridge rectifier

127

Fig.6.3 Real view of the three phase MOSFET inverter

128

Fig.6.4 Real view of the PCI 1711 interface card

130

Fig.6.5 LA50-P current sensor circuit

131

Fig.6.6 Real view of LA50-P current sensor circuit

131

Fig.6.7 Per-phase voltage divider circuit

132

Fig.6.8 Real view of the voltage divider circuit

132

Fig.6.9 Real view of the delay circuit

133

Fig.6.10 Schematic diagram of the delay circuit

134

Fig.6.11 Printed circuit board (PCB) of the delay circuit

135

Fig.6.12 Schematic diagram of the isolation circuit

136

Fig.6.13 Printed circuit board (PCB) of the isolation circuit

137

Fig.6.14 Real view of the isolation circuit

138

Fig.6.15 Schematic diagram of the common power supply circuit

139

Fig.6.16 Printed circuit board (PCB) of the common power supply circuit

140

ix

List of Figures Fig.6.17 Real view of the common power supply circuit

140

Fig.6.18 Schematic diagram of the isolation circuit power supply

141

Fig.6.19 Printed circuit board (PCB) of the isolation circuit power supply

142

Fig.6.20 Real view of the isolation circuit power supply

143

Fig.6.21 Real view of the complete system

143

Fig.6.22 Block diagram of an open loop SPWM method

144

Fig.6.23 Block diagram of an open loop SPWM method

145

Fig.6.24 Pole voltage Va0 (experimental)

146

Fig.6.25 Pole voltage Va0 (simulation)

146

Fig.6.26 An oscillscope view of the line voltages (Vab, Vbc)

147

Fig.6.27 Phase voltage Van (experimental)

147

Fig.6.28 Phase voltage Van (simulation)

148

Fig.6.29 An oscillscope view of the phase voltages (Van, Vbn)

148

Fig.6.30 Phase current (experimental)

149

Fig.6.31 Phase current (simulation)

149

Fig.6.32 Zoom in to the stator currents (experimental)

149

Fig.6.33 Zoom in to the stator currents (simulation)

150

Fig.6.34 An oscillscope view of the phase current

150

Fig.6.35 The developed torque (experimental)

151

Fig.6.36 The developed torque (simulation)

151

Fig.6.37 Stator voltage space vector trajectory (experimental)

152

Fig.6.38 Stator voltage space vector trajectory (simulation)

152

Fig.6.39 Stator phase current Ia before and after the fault (experimental)

153

Fig.6.40 Stator phase currents before, during the fault and after the fault clearing (experimental)

154

Fig.6.41 Stator phase currents before, during the fault and after the fault clearing (simulation)

154

Fig.6.42 The developed torque before, during the fault and after the fault clearing (experimental)

155

Fig.6.43 The developed torque before, during the fault and after the fault clearing (simulation)

155

Fig.6.44 Line voltage Vab before and after the fault (Simulation)

156

Fig.6.45 An oscilloscope view of the line voltage Vab under the fault

156

Fig.6.46 Phase voltage Van before and after the fault (Simulation)

157

x

List of Figures Fig.6.47 An oscilloscope view of the phase voltage Van under the fault

157

Fig.6.48 Stator current space vector trajectory, before and after open gate drive fault of upper MOSFET fault (experimental)

158

Fig.6.49 Stator current space vector trajectory, before and after open gate drive fault of upper MOSFET fault (Simulation) Fig.6.50 Stator phase current Ia before and after the fault (experimental)

158 159

Fig.6.51 Stator phase currents before, during the fault and after the fault clearing (experimental)

160

Fig.6.52 Stator phase currents before, during the fault and after the fault clearing (simulation)

160

Fig.6.53The developed torque before, during the fault and after the fault clearing (experimental)

161

Fig.6.54 The developed torque before, during the fault and after the fault clearing (simulation)

161

Fig.6.55 Line voltage Vab before and after the fault (Simulation)

162

Fig.6.56 An oscilloscope view of the line voltage Van under the fault

162

Fig.6.57 Phase voltage Van before and after the fault (Simulation)

163

Fig.6.58 An oscilloscope view of the phase voltage Van under the fault

163

Fig.6.59 Stator current space vector trajectory, before and after open gate drive fault of lower MOSFET fault (experimental)

164

Fig.6.60 Stator current space vector trajectory, before and after open gate drive fault of lower MOSFET fault (simulation)

164

Fig.7.1 Block diagram of direct torque control system

165

Fig.7.2 MATLAB-Simulink file of direct torque control system

166

Fig.7.3 Pole voltage of phase (a) Va0

167

Fig.7.4 Phase voltage of phase (a) Van

168


168


169

Fig.7.7 D-axis flux

169

Fig.7.8 Q-axis flux

170


170

Fig.7.10 Zoom in to the stator flux magnitude with its reference value

171


171

Fig.7.12 Zoom in to the developed torque

172 xi

List of Figures Fig.7.13 Stator flux locus

172


173

Fig.7.15 Zoom in to the stator flux magnitude

173

Fig.7.16 Stator flux locus

174

Fig.7.17. Four Switch Three Phase Inverter (FSTPI) with phase (a) is connected to DC link mid-point

175

Fig.7.18. phase disconnection circuit

176

Fig.7.19. Real view of the phase disconnection circuit

176

Fig.7.20 Phase voltages before and after phase disconnection

177

Fig.7.21 Zoom in to the phase voltages in FSTPI

178

Fig.7.22 Stator currents before and after phase disconnection

179

Fig.7.23 Zoom in to the stator currents in FSTPI

179

Fig.7.24 The developed torque before and after phase disconnection

180

Fig.7.25 D-axis stator flux before and after phase disconnection

180

Fig.7.26 Zoom in to the d-axis stator flux in FSTPI

181

Fig.7.27 Q-axis stator flux before and after phase disconnection

181

Fig.7.28 Zoom in to the q-axis stator flux in FSTPI

182

Fig.7.29 Stator flux magnitude before and after phase disconnection

182

Fig.7.30 Zoom in to the stator flux magnitude in FSTPI

183

Fig.7.31 Stator flux space vector trajectory before and after phase disconnection

183

Fig.7.32 Stator flux space vector trajectory after phase disconnection

184


185

Fig.7.34 Zoom in to the phase voltages in FSTPI

186


187

Fig.7.36 Zoom in to the stator currents in FSTPI

187

Fig.7.37 The developed torque before and after phase disconnection

188

Fig.7.38 D-axis stator flux before and after phase disconnection

189

Fig.7.39 Zoom in to the d-axis stator flux in FSTPI

189

Fig.7.40 Q-axis stator flux before and after phase disconnection

190

Fig.7.41 Zoom in to the q-axis stator flux in FSTPI

190

Fig.7.42 Stator flux magnitude before and after phase disconnection

191

Fig.7.43 Zoom in to the stator flux magnitude before and after phase disconnection

191

Fig.7.44 Stator flux space vector trajectory before and after phase disconnection

192

Fig.8.1 Phase voltage Van (experimental)

193 xii

List of Figures Fig.8.2 Phase voltage Van (simulation)

193

Fig.8.3 Stator currents (experimental)

194

Fig.8.4 Stator currents (simulation)

194

Fig.8.8 D-axis flux (experimental)

195

Fig.8.8 D-axis flux (simulation)

195

Fig.8.7 Q-axis flux (experimental)

196

Fig.8.8 Q-axis flux (simulation)

196

Fig.8.8 The developed torque (experimental)

197

Fig. 8.18The developed torque (simulation)

197

Fig.8.11 Stator flux magnitude (experimental)

198

Fig.8.12 Stator flux magnitude (simulation)

198

Fig.8.13 Stator flux space vector trajectory (experimental)

199

Fig.8.14 Stator flux space vector trajectory (simulation)

199

Fig.8.15 Phase voltages in FSTPI (experimental)

200

Fig.8.16 Phase voltages in FSTPI (simulation)

200

Fig.8.17 Stator currents in FSTPI (experimental)

201

Fig.8.18 Stator currents in FSTPI (simulation)

201

Fig.8.18 Zoom in to the stator currents in FSTPI (experimental)

202

Fig.8.28 Zoom in to the stator currents in FSTPI (simulation)

202

Fig.8.21 The developed torque before and after phase disconnection (experimental)

203

Fig.8.22 The developed torque before and after phase disconnection (simulation)

203

Fig.8.23 D-q stator fluxes before and after phase disconnection (experimental)

204

Fig.8.24 D-q stator fluxes before and after phase disconnection (simulation)

204

Fig.8.28 Stator flux magnitude before and after phase disconnection (experimental)

205

Fig.8.28 Stator flux magnitude before and after phase disconnection (simulation)

205

Fig.8.27 Stator flux space vector trajectory before and after phase disconnection (experimental)

206

Fig.8.28 Stator flux space vector trajectory before and after phase disconnection (simulation)

206

xiii

Symbols and Abbreviations

SYMBOLS AND ABBREVIATIONS List of Symbols: idr : d axis rotor current ids : d axis stator current iqr : q axis rotor current iqs : q axis stator current J : combined rotor and load inertia Lm : mutual inductance p = number of pole pairs Rs, Lls : stator resistance and leakage inductance Rr , Llr : rotor resistance and leakage inductance Ls , Lr : total stator and rotor inductances Te : electromagnetic torque Tm : shaft mechanical torque V’dr : d axis rotor voltage Vds : d axis stator voltage V’qr : q axis rotor voltage Vqs : q axis stator voltage qs, dr : stator q and d axis fluxes ’qr, ’dr : rotor q and d axis fluxes r : angular velocity of the rotor e : electrical angular velocity of the rotor (r *p) : Rotor angular position List of Abbreviations: DTC: Direct Torque Control FSTPI: Four Switches Three Phase Inverter IRFOC: Indirect Rotor Field Oriented Control SSTPI: Six Switches Three Phase Inverter

xiv

ABSTRACT Power electronic systems are considered as one of the most important components in many applications, such as nuclear reactors, aerospace, military applications and life saving machines, In such applications the system should be high reliable. The reliability of adjustable speed drives is an area of great interest for all members of the drives community and marketplace. As a result, parallel redundancy is often employed for these systems, although at a high system cost. In many industrial drive applications the electrical machine is supplied by AC to AC converters with intermediate DC-link. These AC drive systems are sensitive to different types of failures occurring at the input rectifier, or at the power inverter stage, or at the control sub-system. In this thesis a new switching technique for fault tolerant control of induction motor drive is presented, this system firstly detects the fault, isolates the fault and then applies a current regulation technique to make the system operating in two phase mode with the same performance of three phase mode. Also, a new switching technique for Direct Torque Control (DTC) fault tolerant induction motor drive is presented, if one inverter leg is completely lost due to such abnormal condition, this system modifies the switching table of DTC system using the available stator voltage vectors in two phase mode with Four Switch Three Phase Inverter (FSTPI) topology to track the stator flux reference and directly control the torque and maintain the performance of induction motor as in the Six Switch Three Phase Inverter (SSTPI) mode.

xv

Chapter 1 Introduction

Chapter (1)

Introduction

1.1 Introduction The reliability of power electronics equipment is extremely important in general industrial applications. The fact that power electronics equipment is not adequately reliable prevents its wide spread application. Thus, the potential of power electronics for industrial productively and energy saving is not being fully explored. It has been predicted that voltage-fed inverters will eventually replace all other types of converters especially in AC motor drives in the near future [1]. The costs of unplanned stops are so high that fault detection, isolation, and even prediction are more and more economically viable [2]. Induction motors are a critical component of many industrial processes and are frequently integrated in commercially available equipment. Safety, reliability, efficiency, and performance are some of the major concerns of induction motor applications. With issues such as aging motors, high reliability requirements, and cost competitiveness, the issues of induction motors faults detection and diagnosis are of increasing importance. For these reasons, during the past twenty years, there has been a continually increasing interest and investigation into induction motors faults detection and diagnosis [3]. 1.2 Problem Definition The reliability of adjustable speed drives is an area of great interest for all members of the drives community and marketplace. This is particularly the case of military, aerospace and automotive industries that are increasingly adopting variable speed drives in order to improve overall system efficiency and performance. There are certain safety critical applications such as steering, fuel pumps, and brake-by-wire systems where operation of the drive is of paramount importance 1

Chapter (1)

Introduction

and continuous operation of the system must be insured. As a result, parallel redundancy is often employed for these systems, although at a high system cost [4]. The basic drive with voltage source inverter and squirrel cage induction machine can be subdivided into the power converter, consisting of the machine side PWM inverter, the dc bus capacitor and the mains side diode rectifier, induction machine with squirrel-cage rotor and the control for the power converter and the drive. The most common faults in voltage-fed inverters, either with mains side diode or transistor rectifier, for induction motor drives can be classified as following 1) AC line fault, single line to ground, line to line, Open one line; 2) DC link capacitor short-circuit fault; 3) Power semiconductor fault (IGBT or diode in inverter or rectifier) short circuit or open circuit; 4) Sensor faults, ac current sensor, dc bus voltage sensor; 5) Faults in the control circuit, gate signal disconnection. The previous classification can be shown in Fig.1.1. Induction Motor Drive System Faults

Single Line to Ground

AC Line Faults

DC Link Faults

Line to Line

Open One Line

Power Semiconductor Faults

Rectifier Diode Open or Short Circuit

Inverter Switch Open or Short Circuit

Sensor Faults

Current Sensor

Voltage Sensor

Fig.1.1The most common faults in induction motor drive system 2

Control Circuit Faults

Gate Signal Disconnect

Chapter (1)

Introduction

The percentage of these faults for a switch mode power supply calculated on the base of a military reliability handbook ( MIL-HDBK 217 F standard) are given here, they can give some idea about the possible distribution for the power converter: dc link capacitor 60%, power transistors 31%, inductive elements 6%, diodes 3% , as shown in Fig.1.2 [5],[6].

Percentage Of The Failure

70 60

60%

50 40 30

31%

20

6%

10 0

DC Link Capacitor Power Switches Inductive Elements

3% Diodes

Fig.1.2 The percentage of the common faults in a switched mode power supply Probably the high percentage for the capacitor is caused by the circuit design and the high frequency application, but in general this indicates, that the capacitor is to be taken into account concerning faults. Another previous report on faults of variable speed ac drives in industry from 1995, with a rougher classification shows 38 % faults in converter power part, 53,1 % in control circuits and 7,7 % in external auxiliaries. The high control circuit fault rate may be caused by limited reliability of early days PWM control. An investigation of the effects of these faults on complete drive systems is given in [1]. For these reasons, during the past twenty years, there has been a continually increasing interest and investigation into induction motors faults detection and diagnosis. As this interest has grown, the literature has also grown [3].

3

Chapter (1)

Introduction

Besides diagnosis there is another way to improve the fault behavior. To avoid faults or their consequences, according to the required reliability in the perspective application, for example higher reliability in space applications, the design concept has to be adapted, for higher reliability in general at higher costs, the procedures which can be used in these cases can be classified as follows 1- Fault free design, for example with redundancies, 2- Fault reduced design, for example with over dimensioning, for an increased mean time to repair, 3- Fault tolerant design of the drive, for example with possible emergency operation The previous classification can be shown in Fig.1.3

Drive System Design procedures With High Reliability

Fault Free Design

Fault Reduced Design

Fault Tolerant Design

Fig.1.3 Design procedures to improve the system reliability 1.3 Literature Review In this section previous work carried out in the area of fault tolerant control systems that applied on three phase induction motor drive system are reviewed.

4

Chapter (1)

Introduction

The first step of the fault tolerant control algorithm is to detect the fault and find the faulty device. The effect of different types of fault in voltage-fed PWM inverter induction motor drive that uses the open loop volts/hertz speed control method has been investigated in [1],[7],[8]. The previous system has been analyzed in single phasing mode which has been appeared due to fault isolation in [9]. The three phase induction motor drive system faults have been analyzed in time and frequency domain in [10],[11]. An on-line search algorithm for neutralization of low frequency harmonic torque for a variable frequency variable voltage induction motor has been described in [12]. Several diagnostic methods for open circuit IGBT faults in a voltage source inverter are discussed in [13],[14]. A knowledge-based expert system to fault diagnosis in three phase induction motor drive system has been developed in [2],[7],[8],[15]. A diagnostic method based on the wavelet transform of the stator currents has been proposed in [16],[17]. A literature review of IGBT fault diagnostic and protection methods of three phase power inverters have been investigated in [18],[19]. When a fault is occurred and detected, the second step of the fault tolerant algorithm is to isolate the faulty device to protect the overall system from damage. Some of fault isolation and compensation topologies on three phase inverter have been presented and a comparison between them has been carried out on the base of the cost in [4]. An approach to faulty switch isolation in a modern solid state inverter drive has been presented in [20]. A study on open circuit and short circuit fault isolation and compensation on ac-ac matrix converter drive has been presented in [21].

5

Chapter (1)

Introduction

The third step of fault tolerant control is to control the system under an unbalanced condition with an acceptable performance. A fault tolerant technique of a field oriented control three phase induction motor drive system based on a modification of the stator currents magnitude and angle has been introduced in [4], [22],[23]. Because of the increase of stator currents there is an overheating of the machine, the thermal performance during this technique has been analyzed in [24]. Another fault tolerant technique of a direct torque control (DTC) three phase induction motor drive system using a modified look up table has been developed in [25],[26],[27],[28]. A fault tolerant voltage-fed PWM inverter AC motor drive using parallel redundancies has been introduced in [29]. Another branch of literatures is related to the minimization of the system cost by using only four switches instead of six switches. A comparative investigation with a component minimized voltage-fed inverter under different control options are presented in [30],[31]. A space vector PWM and direct torque control for four switch three phase inverter-fed induction motor has been developed in [32],[33],[34],[35]. 1.4 These Objectives The objectives of this thesis are 1. Study of fault tolerant techniques of three phase induction motor drive system including fault isolation and compensation topologies. 2. Modeling and simulation of a voltage-fed inverter three phase induction motor drive in normal and faulty conditions using MATLABSIMULINK.

6

Chapter (1)

Introduction

3. Design a fault tolerant control using a field oriented control with a current regulation technique. 4. Design a fault tolerant control using a direct torque control system with a modified lookup table. 5. Practical implementation of a direct torque control of three phase induction motor drive. 6. Practical implementation of the proposed fault tolerant control algorithm. 7. Comparing simulation and experimental results. 1.5 Theses Outlines The thesis is composed of nine main chapters which are organized as follows: Chapter (1) is an introductory review of the three-phase induction motor drive system faults, a statistic of the most common faults has been introduced and the previous published work has been presented. Chapter (2) gives information about the fault tolerant control system topologies, the procedures of fault tolerant control technique have been presented including fault detection, fault isolation methods and fault compensation techniques. A comparison between various types of fault tolerant control methods has been made. Chapter (3) discuss in details modeling and simulation of three-phase induction motor drive system at normal and fault conditions using MATLAB-Simulink. Two mathematical models of three phase induction motor have been presented, one of them is the dynamic d-q reference frame model, and the other is a-b-c stationary reference frame model. The simulation results have been obtained in two cases:

7

Chapter (1)

Introduction

1-Direct on-line operation (feeding the induction motor via a pure three phase sinusoidal supply). 2- Open loop sinusoidal pulse width modulation (SPWM). An open gate drive fault of an inverter switch has been simulated.

Chapter (4) an indirect rotor field-oriented control system of induction motor has been modeled and simulated by MATLAB-Simulink and the results are shown at normal and fault conditions. A fault tolerant control system using a current regulation technique has been applied on the field oriented control system and the results are obtained before and after the fault isolation.

Chapter (5) a direct torque control (DTC) system of three phase induction motor has been modeled and simulated by MATLAB-Simulink and the results are shown at normal conditions. A fault tolerant control system using a modified direct torque control system has been proposed to operate the system in four switch three phase inverter (FSTPI) mode instead of six switch three phase inverter (SSTPI) normal mode and the results are obtained before and after the fault isolation.

Chapter (6) explains in details the implementation of the experimental setup of three phase induction motor drive system. The system has been operated with an open loop sinusoidal pulse width modulation (SPWM) and the experimental results have been compared with the simulation results in chapter (3).

8

Chapter (1)

Introduction

An open gate drive fault of an inverter switch has been applied on the upper and the lower MOSFET of phase (a) and the results have been compared with the simulation results in chapter (3).

Chapter (7) explains in details the implementation of the proposed fault tolerant algorithm using a modified direct torque control four switch three phase inverter (DTC-FSTPI) and the experimental results have been presented.

Chapter (8) gives a comparison between experimental and simulation results.

Chapter (9) presents the general conclusion and recommendation for the future work. Appendices and references have presented at the end of thesis.

9

Chapter 2

Chapter 2

Fault Tolerant Control Algorithms

Fault Tolerant Control of Induction Motor Drive System

Chapter 2

Fault Tolerant Control Systems

2.1 Introduction Several failures can afflict electrical motor drives and many different remedial techniques have been proposed. So far, redundant or conservative design has been used in every application where continuity of operation is a key feature [36]. A great deal of research has been done on intelligent control methods for standard three phase induction, permanent magnet or synchronous motors to achieve some degree of fault tolerance. These control techniques have been combined with modified versions of the standard three phase inverter configuration shown in Fig.2.1.

Fig.2.1 Standard three phase AC drive system 2.2 Fault Tolerance Concept The concept of a fault tolerant drive system is that it will continue to operate in a satisfactory manner after sustaining a fault. This implies a minimum level of performance after the fault occurrence, and will therefore be heavily influenced by system requirements [4]. 01

Chapter 2


2.3 Fault Tolerant Control Algorithms There are two main control algorithms to operate the three phase induction motor from a two pole three phase inverter , they are based on splitting the dc link into two identical parts each of them has a value of Vdc/2. The first method is connecting the faulty phase terminal to the mid-point of the dc link as shown in Fig.2.2-a, so the pole voltage of the faulty phase will be equal to zero and the motor can operate with a good performance by regulating the pole voltage of the two healthy phases. The second method is connecting the neutral point to the mid-point of the dc link as shown in Fig.2.2-b, so the motor will operate in two phase mode with two independent winding shifted by 120o , this allow an individual control of the amplitude and phase of the currents in the remaining two healthy phases.

Fig.2.2-a Connecting the faulty phase terminal to the mid-point of the dc link

Fig.2.2-b Connecting the neutral point to the mid-point of the dc link

The control principle of each method will be discussed in the following section. 2.3.1 (Method 1) Connecting the faulty phase terminal to the mid-point of the dc link Consider a three-phase load supplied by a three-phase voltage system Va, Vb, Vc, as in Fig. 2.3-a. Addition of a voltage Vz, opposite in phase and equal in 00

Chapter 2


amplitude to Vb (assume that the fault occurs in phase b) to all phases as shown in Fig.2.3-b will result to a new set of supply voltages VA, VC and VB = 0.0 as shown in Fig.2.3-c , Vz represents a zero sequence component and does not affect the current flow in the system as long as the star point remains floating. The new set of voltages VA and VC will be greater in amplitude by a factor of √

and shifted by 60o between each other, the phasor diagram is shown in

Fig.2.3-d.

(a)

(b)

(c)

(d)

Fig.2.3 Supplying three phase load from two voltages source with 60o phase shift 01

Chapter 2


The currents Ia, Ib, Ic, still represent a balanced positive sequence three phase system. If the load of the new system VA, VC is a balanced three-phase machine, only positive sequence torque will be produced, while it is worthwhile noting that the voltages responsible for the machine stator excitation per phase do not change and remain Va, Vb, Vc. The magnetic circuit of the machine consequently also operates under exactly the same conditions as with the balanced three-phase system. The four switches three phase inverter topology called B4 topology compared with the standard three phase inverter topology which called B6 topology [30]. 2.3.2 (Method 2) Connecting the neutral point to the mid-point of the dc link In this control algorithm the faulty phase has been disconnected from the motor terminal and the neutral point has been connected to mid-point of the dc link so the motor has been operated as a two phase motor with two independent winding, this allow an individual control of the amplitude and phase of the currents in the remaining two healthy phases. Now the control variables are the stator currents instead of the stator voltages in the previous method, so when the system detects a fault in an inverter leg (assume that the fault occurs in phase b), the faulty leg should be disconnected from the motor phase terminal so its current will be zero (IB=0.0) and the currents of the two healthy phases (IA, IC) should be regulated to be greater in amplitude by a factor of √ and shifted by 60o between each other as shown in Fig.2.4.

01

Chapter 2


This increase in phase currents is in the form of a non-torque producing zero sequence current and it is necessary to achieve the same MMF of the normal system [4],[20],[37],[38].

Fig.2.4 Phasor diagram of the stator current regulation technique A comparison between the two methods is shown in Table 2.I Table 2.I: Comparison between fault tolerant control methods Method

Advantages

Method 1

1No need to the neutral point so it can be Connecting the faulty used for star or delta phase terminal to the mid- connected motors. point of the dc link

2The stator current still represents a balanced positive sequence three phase system. 3There is no increase of the stator currents so there is no overheating problem.

Disadvantages 1- The dc bus voltage should be doubled to maintain the increase of the stator voltages by √ , which can be realized through using either a controlled rectifier or a dc-dc boost converter. 2- The circulating single phase current through the dc bus capacitor which will cause severe voltage variations and hence affect the system performance. 3-the imbalance of the

01

Chapter 2


Method 2 Connecting the neutral point to the mid-point of the dc link

1-This method based on that the MMF remains unchanged before and after the fault, so the developed torque does not change and it is suitable for industrial processes as in lifting cranes. 3-Regulating of the stator currents can be made simply using a Current Regulated Pulse Width Modulation CRPWM technique especially in drive systems that controlled via a field oriented control.

dc link mid-point voltages across the two capacitors can affect the system performance. 1-Required accessibility of the motor neutral, which is normally not provided by motor manufacturers, also this method would not be applicable to deltaconnected motors. 2-Increasing the currents of the healthy phases implies that the inverter and motor have to be overrated to withstand this higher level of current for at least a significant period of time. 3-The neutral current is no longer zero. It is the sum of the currents in the remaining two healthy phases which results in three times the value of the original phase current during the healthy operating mode.

2.4 Fault Tolerant Control Procedure steps. The fault tolerant technique consists of three main steps. 1- Fault detection 2- Fault isolation 3- Fault compensation 01

Chapter 2


Each part will be discussed in the following section 2.4.1 Fault detection Voltage source inverters (VSI’s) are widely used in motor drive and power quality applications. It is estimated that about 38% of the faults in variable speed ac drives in industry are due to failures of power devices [13]. Most of these inverters use IGBT’s as the power device for the following reasons. IGBT is available in high voltage and high current ratings. Its ability to handle shortcircuit currents for periods exceeding 10 microseconds has played a critical role in increasing the reliability of motor drive inverter circuits. Though IGBT’s are rugged, they suffer failures due to excess electrical and thermal stress that are experienced in many applications. IGBT failures can be broadly categorized as open-circuit faults, short-circuit faults, and intermittent gate- misfiring faults. In this thesis only gate drive open circuit fault has been taken into consideration. A gate-drive open-circuit fault may happen due to lifting of bonding wires caused by thermic cycling, which, in turn, may be caused by a driver fault or a short-circuit-fault-induced rupture of the IGBT. As referred to Fig.2.1, if an open gate drive fault has been occurred in the upper IGBT Q1 of phase (a), so this switch acts as an open circuit and the phase (a) of the induction machine is connected to the positive dc rail through the diode D1. The machine phase (a) voltage is then determined by the polarity of current and the switching pattern of Q4. The phase voltage Va will be clamped to the negative rail if phase (a) current is positive. On the other hand, if Ia is negative, 01

Chapter 2


the phase voltage Va will be clamped to the negative rail when Q4 is switch ON, and then to the positive rail when Q4 is OFF and D4 is ON. So an open gate drive fault leads to a dc current offset in both the faulty phase and in the healthy phase. The interaction between the dc component and the field generates a pulsating torque at the stator current frequency, which may substantially reduce the maximum average torque available to the drive [1]. The dc currents also generate unequal stress in the upper and lower IGBT. These effects may, in turn, cause secondary faults in the inverter, the motor, or the load [18]. The DC component of current is extracted by using a low pass filter. Its transfer function is like follow: (2.1) Where IDC is the DC component in IS and τ is the filter time constant Where fc is the cut off frequency of the low pass filter. An artificial intelligent system such as expert system is recommended to be used to identify the faulty device, as classified in Table 2.II. Table 2.II DC Current Offset Polarity Corresponding To Faulty Open Circuit Transistor. Faulty Device Tr1 Tr2 Tr3 Tr4 Tr5 Tr6

DC Current Offset Polarity Phase A -VE +VE +VE +VE -VE -VE

Phase B +VE -VE +VE -VE +VE -VE 01

Phase C +VE +VE -VE -VE -VE +VE

Chapter 2


2.4.2 Fault Isolation Technique The second step of fault tolerant algorithm is the isolation of the faulty phase leg from the dc bus in order to eliminate its influence over the drive behavior. The disconnection should be rapid, for a prompt start of the remedial algorithm and for a consequent limited torque transient. In addition, it has to be adequate to face either positive or negative faulty phase current, as well as to be able to interrupt unidirectional current. Such requirements make inadequate any electromagnetic switch or thyristor component, and call for a proper fuse protection of each inverter leg. The scheme that can be used is shown in Fig.5 Once a failure indicating a short or an open circuit of a switch is sensed, the whole inverter pole is disconnected by firing the two SCRs T1, T4, which, in turn, blow up the pole series-connected fuses F1,F4, the fault current path is shown as a dashed line in Fig.2.5. The value of Ci is chosen to have an energy transfer from the main dc-link capacitor sufficient to blow the fuses within a very short time [36].

Fig.2.5 Faulty-leg isolation technique 01

Chapter 2


2.4.3 Fault Compensation The third step of fault tolerant algorithm is the fault compensation process, it means that the system should take a proper action to keep the system still working with an acceptable performance. In order to achieve this target, some kinds of remedial strategies can be used. There are many remedial strategies have been introduced to achieve fault tolerant of induction motor drive they can be classified as follows: 1- Four-leg Three Phase Inverter. a) Phase Redundant Topology. b) Double switch redundant topology. 2- Four switch three phase inverter (FSTPI). a) Neutral point connected topology b) Faulty phase terminal connected topology The previous classification can be shown in Fig.2.6

Fault Compensation Techniques of Three Phase Inverter

Four Switch Three Phase Inverter FSTPI

Four-leg Three Phase Inverter

Phase-leg Redundant Topology

Double Switch Redundant Topology

Neutral point connected topology

Faulty phase terminal connected topology

Fig.2.6 Fault compensation techniques of three phase inverter

01

Chapter 2


2.4.3.1 Four-leg Three Phase Inverter In this topology a spare phase leg consists of two IGBTs can be used besides the standard three phase inverter, this fourth leg acts as a redundant leg and it can be connected to the faulty phase terminal or to the neutral point, as shown in the following sections. a) Phase-leg Redundant Topology This topology is based on the principle of redundancy. The circuit topology shown in Fig.2.7 incorporates the fault isolating SCRs and fuses in only the three active legs of the inverter. A spare fourth leg (Qn1 & Qn2) of the inverter is connected in place of the faulty phase leg after the fault isolation device has removed that leg from the system.

Fig.2.7 Phase-leg Redundant Topology During the normal operation, this spare phase leg is inactive and not switching. As a result the three TRIACs (TRa, TRb, TRc) shown in the topology act as a

11

Chapter 2


static transfer switches to connect this output to the faulty phase when needed [4],[38]. b) Double Switch-Redundant Topology The topology consists of a four-leg inverter with additional components for fault tolerance driving a four terminal motor as shown in Fig.2.8. The additional components needed for fault tolerance include two fuses and two SCRs per phase leg. Also one pair of capacitors Ci, is needed for isolation purposes as discussed earlier.

Fig.2.8 Double Switch Redundant Topology After detecting a fault (phase a for example), the control sends signals to T1 or T4 to turn on. This cause a transient short circuit through the main dc link, the auxiliary capacitor Ci, the SCR and fuse. Using the charge transferred to the auxiliary capacitor, the fuse clears and the faulted phase leg is removed from the

10

Chapter 2


circuit. The auxiliary capacitors need to be sized large enough that a sufficient amplitude and duration of current to clear the fuse is induced. The post fault control strategy is based on (method 2) of fault tolerant control algorithms which has been discussed in section 2.3.2. One difference however is the fact that the motor neutral is connected to a fourth inverter leg by firing the TRIAC TRn as opposed to a direct connection to the center point of the dc link in order to overcome the dc link mid-point balancing problems, so there is no need for splitting the dc bus. The fourth leg mid-point voltage can be regulated and adjusted by switching the two IGBTs using a PWM technique. 2.4.3.2 Four switches three phase inverter (FSTPI) This topology uses a simple isolation and compensation techniques, it incorporates four TRIACs and three fast acting fuses as shown in Fig.2.9. The fuses are connected in series with the load phases. This topology is a combination of two topologies: a) Neutral point connected Topology b) Faulty phase terminal connected Topology

Fig.2.9 Four switch three phase inverter topology 11

Chapter 2


a) Neutral point connected Topology In the case of an opened phase fault, only TRIAC TRn needs to be present in the topology of Fig.2.9, and the presence of the three series fuses is not required. When the system detects an opened phase fault, TRIAC TRn is fired in order to connect the neutral of the motor to the midpoint of the dc bus as in (method 2) in section 2.3.2. In order to maintain a constant flux trajectory and insure disturbance free operation of the system, the phase currents of the healthy phases need to be increased in magnitude by a factor of √3 and phase shifted 60о away from each other as discussed earlier. The post fault configuration is shown as a dashed line in Fig.2.10 [4],[20],[37].

Fig.2.10 Connecting the neutral point to the mid-point of the dc link

11

Chapter 2


b) Faulty phase terminal connected Topology This topology can be used in case of IGBT short circuit. If the switch Q4 is short circuited the circuit of Fig.2.9 operates as follows. It is assumed that some types of hardware based short circuit protection in the inverter will automatically open the complementary IGBT, Q1 in order to prevent a shoot through failure by short circuiting the dc bus. Using this signal and additional control logic, the controller turns on TRIAC TRa , this cause a short circuit through the lower half of the DC bus, the failed shorted switch, the TRIAC TRa and the fast blow fuse. As a result the fuse will open and clear the shorted switch out of circuit. The TRIAC TRa subsequently controlled to be continuously ON during this post fault condition, so the faulty phase terminal will be connected to the dc link mid-point (method 1) the fault current path is shown in Fig.2.11 [4],[20],[37].

Fig.2.11 Fault current path when isolating single switch short circuit fault 11

Chapter 2


A comparison between the standard three phase inverter and the previous topologies has been made on the basis of the dc link splitting and the number of auxiliary switches which have been used in table 2.III. TABLE 2.III Comparison between Fault Compensation Techniques

Standard Three Phase Inverter Fig.1.1 Phase-leg Redundant Topology Fig.2.7 Double Switch Redundant Topology Fig.2.8 FSTPI- Neutral Point Connected Topology Fig.2.10 FSTPI- Faulty Phase Terminal Connected Topology Fig.2.11

Auxiliary Fuse Capacitor s s

Split DC bus

Topology

TRIACs

IGBTs

SCR s

N

0

6

0

0

0

N

3

8

6

6

2

N

1

8

8

8

2

Y

1

6

0

0

0

Y

3

6

0

3

0

The number of electronic components of each topology can be presented in a graphical method as shown in Fig.2.12.

11

Chapter 2


8 7 6 5 4 3 2 1 0

Fig.2.12 Numbers of electronic components in each topology As shown in Fig.2.12, it is clear that the cost of Four Switch Three Phase Inverter (FSTPI) with its two topologies is not far from that of the standard three phase inverter. Taking into consideration that the cost of the IGBT is very high compared with the other electronic components. So in this thesis a Four Switch Three Phase Inverter (FSTPI) has been used and a fault tolerant control algorithm (method 2) has been designed to supply a three phase induction motor controlled with an Indirect Rotor Field Oriented Control (IRFOC) system in case of detecting an open gate drive fault. The system has been modeled using Matlab-Simulink, the simulation results have been analyzed, the advantages and the disadvantages will be proposed.

11

Chapter 2


A new fault tolerant control technique has been proposed using (method 1) to supply a three phase induction motor by a Four Switch Three Phase Inverter (FSTPI) controlled via a Direct Torque Control (DTC) system to overcome the disadvantages of the previous system. The proposed system has been modeled using Matlab-Simulink and the simulation results have been analyzed and experimentally verified using an experimental setup.

11

Chapter 3

Modeling and Simulation of Induction Motor Drive System

Chapter 3


3.1 Introduction Among all types of AC machines, the induction machine, particularly the cage type is most commonly used in industry. These machines are very economically, rugged and reliable, and are available in the ranges of Fractional Horse Power (FHP) to multi-megawatt capacity. Low-power FHP machines are available in single-phase, but poly-phase (three phase) are used most often in variable speed drives [39]. Usually, when an electrical machine is simulated in circuit simulators such as PSpice, its steady state model is used; but for electrical drive studies, the transient behavior is also important. One advantage of Matlab-Simulink over circuit simulators is the ease in modeling the transients of electrical machines and drives and in including drive controls in the simulation [39]. In this chapter a Matlab-Simulink model of three phase induction motor has been presented, the three phase induction motor has been modeled in two ways for fault tolerant control purposes. The first model is the dynamic d-q reference frame model which can be used with fault tolerant control method 1, in this method. The second model is the dynamic a-b-c reference frame model which can be used with fault tolerant control method 2. 3.2 Induction Motor Dynamic d-q Model The dynamic machine model in state-space form is important for transient analysis, particularly for computer simulation study. Although the rotating frame model is generally preferred, the stationary frame model can also be used. The electrical variables in the model can be chosen as fluxes, currents, or a mixture of both. 82

Chapter 3


3.2.1 Axis Transformation Consider a three phase induction machine with stationary a-b-c- axis at 120o phase shift. The variables in this frame such as voltages, currents or fluxes can be transformed into two phase stationary reference frame variables ds,qs , as shown in Fig.3.1a assuming the quadrature axis is aligned with the axis of phase (a) and the direct axis is perpendicular to it, then transform these to synchronously rotating reference frame de,qe as shown in Fig.3.1b using Park's transformation as in (3.1),(3.3) respectively [40],[41],[42].

(a)

(b)

Fig.3.1 Stationary a-b-c to synchronously rotating d-q axis transformation.

[

]

[

] [ √

]

……….. (3.1)

√

And inversely

82

Chapter 3

[


√

] [

[

]

[

√

[

]

……….. (3.2)

] ] [

]

……….. (3.3)

] [

]

……….. (3.4)

And inversely [

]

[

3.2.2 Electrical Equations The induction machine d-q or dynamic equivalent circuit is shown in Fig.3.1a and b. One of the most popular induction motor models derived from this equivalent circuit is Krause’s model. In this model the state space equations of the machine in rotating frame have been developed with flux linkages as the main variables.

03

Chapter 3


Fig.3.2 D-q dynamic equivalent circuits in synchronously rotating reference frame. Let's define the flux linkage variables as follows:

……….. (3.5) } Where b = the base frequency of the machine.

qs, ds = q and d axis stator fluxs. qr, dr = q and d axis rotor fluxs. According to this model, the modeling equations in flux linkage form are as follows [Bose, Krause]: [

(

)]

……….. (3.6)

[

(

)]

……….. (3.7)

(

)]

……….. (3.8)

[

(

[

)

(

)

(

)] 03

……….. (3.9)

Chapter 3


Where [

]

[

……….. (3.10)

]

……….. (3.11)

(

)

……….. (3.12)

(

)

……….. (3.13)

(

)

……….. (3.14)

(

)

……….. (3.15)

( )

(

)

……….. (3.16)

For squirrel cage induction motor vdr = vqr = 0.0 3.2.3 Mechanical Equations The rotor speed r cannot be treated as a constant. It can be related to the torque as in (3.17) ……….. (3.17) Where TL is the load torque, J is the rotor inertia and m is the mechanical speed so the previous equation can be rewritten as in (3.18). ( )

……….. (3.18)

For a squirrel cage induction machine the rotor voltages vqr and vdr are set to zero. An induction machine model can be represented with five differential equations as seen above. To solve these equations, they have to be rearranged in the state-space form, is the state vector. 08

Chapter 3


Note that Fij =( ψij*ωb) where Fij is the flux linkage (i=q or d and j=s or r) and ψij is the flux. In this case, state-space form can be achieved by inserting (3.10) and (3.11) in (3.6-3.9) and collecting the similar terms together so that each state derivative is a function of only other state variables and model inputs. Then equations (3.6-3.9 and 3.18) of a squirrel cage induction motor in state-space become as follow.

[

( [ (

[ [

(

( )(

) )

(

(

)

)]

……….. (3.19)

(

(

)

)]

……….. (3.20)

(

(

)

)]

……….. (3.21)

(

)

)

)]

……….. (3.22) ……….. (3.23)

Fig.3.3 Block diagram of induction motor d-q model. 00

Chapter 3


The block diagram of the induction motor d-q dynamic model is shown in Fig.3.3. The previous system can be simulated using Matlab-Simulink, Fig.3.4 shows the overall system model it consists of two main blocks, the induction motor block and the three phase power supply block, the blocks details can be shown in Figs.3.5,3.6.



03

Chapter 3


Fig.3.6 Inside the power supply block

This method is applicable in fault tolerant control systems when fault tolerant method 1 is used, because the input of this model is the stator voltages Va,Vb,Vc and when the fault tolerant algorithm is applied the voltage of the faulty phase (for example phase C) will be zero. So it can be accomplished by setting Vc =0.0 in the simulation at any time. But when fault tolerant control method 2 is used, this model could not be used because in this method the faulty phase should be disconnected it means that its current will be zero and it is clear from the block diagram in Fig.3.3 that the stator current are not accessible in this model. They can be calculated through (dq/abc) transformation block but it is impossible to set I a or Ib or Ic equal to zero it absolutely not affect the simulation. It is the fact in this model the induction motor has been simulated as a two phase machine, so the three phase induction motor should be modeled as a real three phase machine using the stationary a-b-c reference frame in order to use it with fault tolerant control method 2 as mentioned earlier.

03

Chapter 3


3.3 Induction Motor Model in ABC Reference Frame Winding arrangement for a 3-phase, wye-connected symmetrical induction machine is shown in Fig.3.7.[41]. Stator windings are identical, sinusoidal distributed windings, displaced by120, with Ns equivalent turns and resistance Rs.

Fig.3.7 Three phase symmetrical induction machine Consider the case when rotor windings are also three identical sinusoidally distributed windings, displaced by120, with Nr equivalent turns and resistance Rr. 3.3.1 Electrical Equations In a-b-c reference frame, voltage equations can be written as

}

……….. (3.24)

s: denotes variables and parameters associated with the stator circuits. r: denotes variables and parameters associated with the rotor circuits. The flux linkage equations can be written as 03

Chapter 3

  


  Ls   ( L )T abcr   sr

Lsr  iabcs  Lr  iabcr 

abcs

……….. (3.25)

Where   Lls  Lms  1 L s    Lms  2 1L  2 ms   Llr  Lmr  1 L r    Lmr  2 1L  2 mr

1   Lms  2  1  Lms , 2  Lls  Lms  

1  Lms 2 Lls  Lms 1  Lms 2 1  Lmr 2 Llr  Lmr 1  Lmr 2

……….. (3.26)

     Llr  Lmr   1  Lmr 2 1  Lmr 2

……….. (3.27)

Lls and Lms are, respectively, the leakage and magnetizing inductance of the stator windings. Llr and Lmr are, respectively, the leakage and magnetizing inductance of the rotor windings. ( Lsr = Lrs = [

(

)

(

)

)

(

(

)

(

)

)

……….. (3.28) ]

Where (Lsr ) is the amplitude of the mutual inductances between stator and rotor windings. So, the stator currents can be derived from the previous equations as in (3.29)

[ [

]

]

[

]

[

[

] [

] 03

]

[ [

]

][

]

….. (3.29)

Chapter 3


Where ( Lsr1 = [

Lsr2 = [

(

)

(

)

(

)

(

)

)

(

)

(

)

(

(

)

(

), ]

(

)

(

)

)

]

Rotor variables can be referred to the stator windings by appropriate turns ratio.

 iabcr

N N   s Vabcr ,  r iabcr , Vabcr Ns Nr



abcr

N  s Nr

abcr

, Lms

N   s  Nr

2

  Lsr 

2 2   cos( r  ) cos( r  )  cos  r 3 3   2  Lsr   N s L sr   Lms cos( r  2 ) cos  r cos( r  ) , Nr 3 3   cos(  2 ) cos(  2 )  cos  r r r   3 3

……….. (3.30)

……….. (3.31)

Also 2

N  Lmr   r  Lms ,  Ns 

2

  Lr    N r  L r   Ns 

……….. (3.32)

Where   Llr  Lmr  Lr     1 Lms  2 1L  2 ms

1  Lms 2 Llr  Lms 1  Lms 2

1   Lms  2  1  Lms  2  Llr  Lms  

……….. (3.33)

02

Chapter 3


And 2

N  Llr   s  Llr  Nr 

……….. (3.34)

Flux linkage may be expressed as  abcs   L s     (L )T  abcr   sr

Lsr  iabcs    Lr  iabcr

……….. (3.35)

Voltage equations expressed in terms of machine variables referred to the stator windings may be written as [

]

[

][ (

]

……….. (3.36)

)

Where ( )

……….. (3.37)

For squirrel cage induction motor var = vbr = vcr = 0.0 So, the rotor currents can be derived from the previous equations as in (3.38)

[ [

]

]

[

[

] [

]

]

[ [

][

] ……….. (3.38)

]

3.3.2 Torque Equation in Machine Variables Energy stored in the coupling field may be written as 1 (iabcs ) T (L s  L ls I)iabcs  2 1   (iabcr  ) T (Lr  Llr I)iabcr  (iabcs ) T (L sr )iabcr 2

Wc  W f 

02

……….. (3.39)

Chapter 3


Where, I: identity matrix Voltage equations expressed in terms of machine variables referred to the stator windings may be written as Te (i j , r ) 

P Wc (i j , r ) 2  r

……….. (3.40)

Since Ls and Lr are functions of r, the above equation for the electromagnetic torque yields. p   Lsr iabcr Te  ( )(iabcs )T 2  r   1 1 1 1 1 1   ibr   icr  )  ibs (ibr   iar   icr  )  ics (icr   ibr   iar  ) sin  r  ias (iar   2 2 2 2 2 2 P      Lms   2  3         2 ias (ibr  icr )  ibs (icr  iar )  ics (iar  ibr )cos  r 

.. (3.41)

The torque and rotor speed are related by 2 Te  J   pr  TL P

……….. (3.42)

33

Chapter 3


Fig.3.8 Block diagram of induction motor a-b-c model. The block diagram of the induction motor d-q dynamic model is shown in Fig.3.8. The previous system can be simulated using Matlab-Simulink, Fig.3.9 shows the overall system model, it consists of two main blocks, the induction motor block and the three phase power supply block, the blocks details can be shown in Figs.3.10,3.11,3.12.

33

Chapter 3



Fig.3.10 Inside the induction motor block 38

Chapter 3


Fig.3.11 Inside the stator current block

30

Chapter 3


Fig.3.12 Inside the rotor current block

33

Chapter 3


3.4 Simulation Results The simulation results of the previous systems have been obtained using MatlabSimulink with the following simulation parameters. Solver: Fixed step Ode4 (Rung-Kutta) Step Time: 0.0001s Simulation Time: 2sec. And the induction motor parameters are as follows Rated power: 1.1 Kw Rated line voltage: 380 Volts No. of pole pairs: 2 Stator resistance: 7.4826 Ohm Rotor resistance: 3.6840 Ohm Mutual inductance: 0.4114 Henry Stator leakage inductance: 0.0221 Henry Rotor leakage inductance: 0.0221 Henry Supply frequency: 50 Hz Motor speed: 1400 r.p.m. Moment of Inertia: 0.004 Kg.m2 Rated load torque: 7.5 N. m. A step function load torque starting with 2 N.m and increased to 5 N.m at t= 1 sec is applied to the machine. As a result the stator currents have been increased according to the load torque change and the motor speed has been decreased. 33

Chapter 3


The simulation results of the induction motor d-q model have been presented as shown in Figs.3.13,3.14,3.15, 3.16.

Fig.3.13 Developed torque at normal conditions

Fig.3.14 Speed at normal conditions

33

Chapter 3


Fig.3.15 Stator currents at normal conditions

Fig.3.16 Zoom in to the stator currents at normal conditions

33

Chapter 3


3.5 Modeling of Three Phase Sinusoidal PWM Inverter One of the most common converter topologies that are very widely used in industry is shown in this Fig.3.17. It consists of a three-phase bridge inverter with a three-phase diode rectifier in the front end. The rectifier (which can be single or three-phase) converts AC to uncontrolled DC.

Fig.3.17 Standard three phase inverter The harmonics in the dc link are filtered by an LC or C filter to generate smooth voltage Vdc for the inverter. The inverter consists of three half-bridges or phase legs to generate three-phase ac for industrial motor drives or other applications. In all such cases, Vdc is usually unregulated. The battery-fed inverter drive is commonly used for electric/hybrid vehicle drives. The filter capacitor sinks the harmonics from the rectifier as well as inverter sides. Because an inverter contains electronic switches, it is possible to control the output voltage as well as optimize the harmonics by performing multiple switching within the inverter with the constant DC link voltage Vdc. The Pulse Width Modulation 84

Chapter 3


(PWM) principle to control the output voltage is explained in Fig.3.18. The fundamental voltage V1 has the maximum amplitude 4Vd/π at a square wave mode. Sinusoidal Pulse Width Modulation (SPWM) technique is very popular for industrial converters. Fig.3.18 explains the general principle of SPWM, where a triangle carrier wave with frequency fc is compared with the fundamental frequency fs sinusoidal modulating wave, and the points of intersection determine the switching points of power devices. The same carrier wave can be used for all three phases, as shown in Fig.3.18, the typical wave shape of line and phase voltages for an isolated neutral load. The Fourier analysis of the Vao is somewhat involved and can be shown to be of the following form (

)

(

84

)

….. (3.43)

Chapter 3


Fig.3.18 Three phase inverter phase and line voltages Where m = modulation index, ω = fundamental frequency in rad/sec and φ = phase shift of output. The modulation index m is defined as

Where VP = peak value of modulating wave, VT = peak value of carrier wave. Ideally (m) can be varied between 0 and 1 to give a linear relation between the modulating and output wave (usually called Undermodulation region). If (m) is larger than 1 it is called Overmodulation region.

05

Chapter 3


3.5.1 Relation between Pole Voltage and Phase Voltage If the three phase load neutral point (n) is connected to the center tap of the dc link voltage Vdc then the load phase voltage are Va0 , Vb0 , Vc0 (usually called the pole voltages) . With an isolated neutral load the equivalent circuit is as shown in Fig.3.19 here the triplen harmonic that is, the zero sequence component of the supply will appear across points (n) and (0). We can write the following relations:

Fig.3.19 Relations between pole voltages and phase voltages

}

……….. (3.44)

Since the load phase voltages are balanced so

Therefore

05

Chapter 3


……….. (3.45) } The system can be simulated in Matlab-Simulink as shown in Figs.3.20, 3.21,3.22.

Fig.3.21 Inside the three phase inverter block

Fig.3.20 Three phase inverter block

Fig.3.22 Inside the load voltage block 05

Chapter 3


3.6 Simulation Results The simulation results of PWM three phase inverter are obtained with the following parameters [42]: Solver: Fixed step Ode4 (Rung-Kutta) Step Time: 0.0001s Simulation Time: 1sec. DC Link Voltage: 2*150 V Modulation Index (m): 1.2 (Overmodulation) The developed torque contains an amount of ripples according to the switching process as shown in Fig.3.23, Fig.3.24 shows the motor speed, it increase to a such level according to the inverter output voltage, so it can be controlled by varying the modulation index (m). In this system an open loop PWM has been used. The stator currents also contain an amount of ripples according to the switching process as shown in Figs.3.25, 3.26.


05

Chapter 3





08

Chapter 3


Related to Fig.3.18, the inverter output voltages are a pulsating waves, the width of the pulses depends on the modulation index. As in Eqs.3.44,3.45, the pole voltages Va0 , Vb0 , Vc0 are a one level waves and their values are changed from +Vdc /2 , Vdc/2 as shown in Fig.3.27


According to Eq.3.45 and Fig.3.18, the phase voltages Van , Vbn , Vcn are a two level waves and their values are changed from +Vdc/3, +2Vdc/3 and -Vdc/3, 2Vdc/3 as shown in Fig.3.28.

00

Chapter 3


Fig.3.28 Inverter phase voltages Van , Vbn , Vcn The modulating waves and the triangle wave are shown in Fig.3.29

Fig.3.29 Carrier and modulating signals (m=1.2) overmodulation

05

Chapter 3


When the modulation index (m) has been changed to be 0.9 the system has been operated in Undermodulation region which is the common case because of the linear relation between the modulating and output wave the system gives the following results. Since the modulation index has been reduced, the r.m.s value of the output voltage has been reduced also. This reduction in output voltage decreases the developed torque and increases the starting time as shown in Fig.3.30.

Fig.3.30 The developed torque The motor speed reaches its rated value after a long time compared with the overmodulation region as shown in Fig.3.31.

Fig.3.31 Motor speed (rad/sec) 05

Chapter 3


The stator currents also contain an amount of ripples due to the switching process as shown in Fig.3.32.

Fig.3.32 Stator currents The inverter pole voltages Va0 , Vb0 , Vc0 and phase voltages Van , Vbn , Vcn are shown in Figs.3.33, 3.34 respectively.

Fig.3.33 Inverter pole voltages Va0 , Vb0 , Vc0 04

Chapter 3



The modulating waves and the triangle wave are shown in Fig.3.35

Fig.3.35 Carrier and modulating signals (m=0.9) undermodulation

04

Chapter 3


3.6.1 Inverter output voltage space vector The three phase inverter as shown in Fig.3.17 has a 23 = 8 switching states, Table 3.I gives a summary of the switching states and the corresponding phase to neutral voltages of an isolated neutral machine. Table 3.I Summary of Inverter Switching States State

ON Devices

Van

Vbn

Vcn

0 1 2 3 4 5 6 7

(Q4,Q6,Q2) (Q1,Q6,Q2) (Q1,Q3,Q2) (Q4,Q3,Q2) (Q4,Q3,Q5) (Q4,Q6,Q5) (Q1,Q6,Q5) (Q1,Q3,Q5)

0 2Vdc/3 Vdc/3 . . . . 0

0 -Vdc/3 Vdc/3 . . . . 0

0 -Vdc/3 -2Vdc/3 . . . . 0

Space Voltage Vector V0 (000) V1(100) V2(110) V3(010) V4(011) V5(001) V6(101) V7(111)

Consider, for example, state 1, when switches Q1, Q6 and Q2 are closed. In this state phase (a) is connected to the positive bus and phases (b) and (c) are connected to the negative bus, the simple circuit solution indicates that V an = 2Vdc/3, Vbn = Vdc/3 and Vcn = -Vdc/3. The inverter has a six active states (1-6) when voltage is impressed across the load, and two zero states (0,7) when the machine terminals are shorted through the lower switches or the upper switches respectively as shown in Fig.3.36 [39].

55

Chapter 3


Fig.3.36 Stator voltage space vector of three phase inverter The voltage space vector of three phase inverter that obtained from the simulation is shown in Fig.3.37.

Fig.3.37 Inverter output voltage space vector in normal condition 3.7 Inverter IGBT Gate Drive Open Circuit Fault A PWM-VSI inverter induction motor drive system is shown in Fig.3.16. Firstly a single transistor base drives open-circuit fault of power converter will be 55

Chapter 3


considered. This fault will only reduce the operating conditions of the drive without involving the short circuit protection of the system. The drive system can operate for a considerable period of time but with degraded performance and low efficiency. The injected dc offset in the machine phase currents caused by a base drive open-circuit fault, worsen the current stress of the inverter healthy switching devices. Continuous operation in such faulty condition may lead to the catastrophic breakdown of the drive system. To operate power transistors such as MOSFET or IGBT, an appropriate gate voltage must be applied in order to drive transistors into the saturation mode for low on-state voltage. Malfunctioning of gate drive circuit can lead to the transistor base drive open- circuit fault. Since the transistor Q1 has now an open-circuit fault, the phase A of the induction machine is connected to the positive dc rail through the diode D1. The machine phase A voltage is then determined by the polarity of current and the switching pattern of transistor Q4. The phase voltage (Va) will be clamped to the negative rail if stator current phase A, (Ia) is positive. On the other hand, if Ia is negative, the phase voltage VA will be clamped to the negative rail when transistor Q4 is switch on, and then to the positive rail when transistor Q4 is off and D4 is on. The phase currents will be balanced and sinusoidal with a dc offset after the fault because the phase voltages (Va, Vb, Vc) are balanced with the sinusoidal PWM modulation before and after the fault. The dc offset current in phase A will be equally divided between the phase B and phase C and of opposite sign. This

55

Chapter 3


conclusion is only valid under the assumption of magnetic linearity and infinite rotor inertia. A change in stator current waveform is defined as the instant at which a sudden increase or decrease is observed in the DC offset component of the current. A change is considered to have occurred in the stator current DC offset component of the current exceeds or falls below a given band. If the open circuit faulty IGBT is one of the upper IGBTs of the inverter, the current of the phase linked to that leg will have a negative DC component and the two other phases currents will have a positive ones. If the open circuit faulty IGBT is one of the lower IGBTs of the inverter, the current of the phase linked to that leg will have a positive DC component and the two other phases currents will have a negative ones as shown below. The DC component of current is extracted by using a low pass filter. Its transfer function is like follow: ……….. (3.46) Where IDC is the DC component in IS and τ is the filter time constant

where

fc is the cutoff frequency of the low pass filter. 3.7.1 Simulation results under fault conditions An open gate drive of the upper IGBT of phase (a) Q1 fault is simulated in MatlabSimulink, the stator currents and its dc offset level are shown in Figs.3.38,3.39,3.40,3.41.

55

Chapter 3


Fig.3.38 Stator currents before and after opening gate drive of Q1

Fig.3.39 Phase A current before and after opening gate drive of Q1 with negative DC offset

Fig.3.40 Phase B current before and after opening gate drive of Q1 with positive DC offset

58

Chapter 3


Fig.3.41 Phase C current before and after opening gate drive of Q1 with positive DC offset An artificial intelligent system such as Expert system is recommended to be used to identify the faulty device, as classified in Table 3.II. Table 3.II : DC Current Offset Polarity Corresponding to Faulty Open Circuit Transistor. Faulty Device Q1 Q2 Q3 Q4 Q5 Q6

DC Current Offset Polarity Phase A -VE +VE +VE +VE -VE -VE

Phase B +VE -VE +VE -VE +VE -VE

Phase C +VE +VE -VE -VE -VE +VE

The developed torque has been distorted according to the interaction between the AC and DC components of the stator currents as shown in Fig.3.42

50

Chapter 3

Modeling and Simulation of Induction Motor Using Matlab-Simulink

Fig.3.42 The developed torque before, during the fault and after the fault clearance 2.7.3 Stator Current Space Vector Approach to Fault Diagnosis The stator current space vector can be expressed as in Eq. 4.34. ̅

() (

)

…….. (34.3)

The stator current space vector trajectory at normal conditions has a circular shape. If an open gate drive fault has been occurred at the Upper IGBT of phase (a) the DC offset components in each phase will change the circular shape to an elliptic shape shifted its center has been shifted from (0,0). Figs.3.43, 3.44 show the stator currents space vector trajectory in case of open gate drive fault of the upper and lower IGBTs respectively, and it can be used to compare between the system performance before, during and after the fault moment [5].

55

Chapter 3

Modeling and Simulation of Induction Motor Using Matlab-Simulink

Fig.3.43 Stator current space vector trajectory, before and after open gate drive fault of upper IGBT fault

Fig.3.4. Stator current space vector trajectory, before and after an open gate drive fault of lower IGBT fault 55

Chapter 4

Fault Tolerant Field Oriented Control Induction Motor Drive System

Chapter (4)


4.1 Introduction The invention of vector control in the beginning of 1970s, and the demonstration that an induction motor can be controlled like a separately excited dc motor, brought a renaissance in the high-performance control of ac drives. Because of dc machine-like performance, vector control is also known as decoupling, orthogonal, or transvector control. Vector control is applicable to both induction and synchronous motor drive. Undoubtedly, vector control and the corresponding feedback signal processing, particularly for modern sensorless vector control, are complex and the use of powerful microcomputer or DSP is mandatory [39]. In this chapter a new switching technique for fault tolerant control of a field oriented control induction motor drive is presented, the system firstly detects the fault, isolates the fault and then applies a current regulation technique to make the system operating in two phase mode with the same performance of three phase mode. 4.2 Principle of Vector Control of Induction Motor. With a vector control, an induction motor can operate as a separately excited dc motor. In a dc machine, the developed torque is given by ……….. (4.1) Where Ia is the armature current and If is the field current. The construction of a dc machine is such that the field flux linkage ψf produced by If is perpendicular to the armature flux linkage ψa produced by Ia as shown in Fig.4.1.

86

Chapter (4)


Fig.4.1 DC motor currents relation These flux vectors that are stationary in space are orthogonal or decoupled in nature. As a result, the dc motor has fast transient response. However, an induction motor cannot give such fast response due to its inherent coupling problem. However an induction motor can exhibit the dc machine characteristic if the machine is controlled in a synchronously rotating reference frame (de-qe) , where the sinusoidal machine variables appear as dc quantities in the steady state [43],[44],[45]. With vector control, i*ds is analogous to the field current If and i*qs is analogous to the armature current Ia as shown in Fig.4.2. Therefore, the developed torque of an induction motor is given by ……….. (4.2) Where ψr is the absolute peak value of the sinusoidal space flux linkage vector Ids is the field component Iqs is the torque component

86

Chapter (4)


Fig.4.2 Torque and flux components in induction motor Implementation of a vector control is shown in Fig.4.3. The inverter generates currents ia , ib, ic in response to the corresponding command currents i *a , i*b , i*c from the controller . the machine terminal currents ia , ib, ic are converted to isds and isqs components by three phase to two phase transformation.

Fig.4.3 vector control principle in induction motor These are then converted to synchronously rotating frame by the unit vector components cosθe and sinθe before applying them to the machine.

07

Chapter (4)


The controller makes two stages of inverse transformation so that the line control currents i*ds and i*qs

correspond to the machine currents ids and iqs ,

respectively. There are essinsially two general methods of vector control. One called direct or feedback method was invented by Blaschke, and the other, known as the indirect or feedforward method, was invented by Hasse . The methods are different essentially by how the unit vector (cosθe and sinθe) is generated for the control. In direct method , the flux vector is computed from the terminal quantities of the motor, but in indirect method the unit vector is generated from the summation of slip speed and the rotor speed as discussed in the following section. 4.3 Indirect Field Oriented Vector Control Method The indirect method which is our case uses the motor slip frequency ω sl to compute the desired flux vector . indirect vector control is very popular in industrial applications. Fig.4.4 explains the fundamental principle of indirect vector control with the help of a phasor diagram. The ds-qs axes are fixed on the stator, but the dr-qr axes, which are fixed on the rotor, are moving at speed ωr. Synchronously rotating axes de-qe are rotating ahead of the

dr-qr axes by a positive slip angle θsl corresponding to slip

frequency ωsl . since the rotor pole is directed on the de axis and ωe= ωr+ ωsl ∫

∫(

)

……….. (4.3)

07

Chapter (4)


Fig.4.4 Indirect field oriented in phasor diagram 4.4 Derivation of Indirect Rotor Field Oriented Vector Control Equations For decoupling control, a derivation of control equations can be made with the help of de-qe equivalent circuit shown in Fig.4.5

Fig.4.5 de-qe equivalent circuits of induction motor The rotor circuit equations can be written as (

)

……….. (4.4)

07

Chapter (4)


(

)

……….. (4.5)

Where The rotor flux linkage expressions can be given as ( (

)

) ……….. (4.6)

Where ( (

)

) ……….. (4.7)

So ……….. (4.8) ……….. (4.9) Substituting rotor currents in Eqs. (4.4,4.5) will yields ……….. (4.10) ……….. (4.11)

Substituting the following conditions in the above equations

So that the rotor flux ψr is directed on the de axis and. 07

Chapter (4)


And Substituting these conditions in Eqs. 4.10, 4.11 we can get. ……….. (4.12) If the rotor flux is constant which is usually the case, then Eq.4.12 can be written as ……….. (4.13) And ……….. (4.14)

4.5 Implementation of Indirect Field Oriented Control System To implement the indirect vector control strategy, it is necessary to take Eqs.4.3, 4.12,4.14 into consideration.Figs.4.6,4.7 show the block diagram of indirect field oriented control system of three phase induction motor. The power circuit consists of a front end diode rectifier and a PWM inverter. A hysteresis- band current control PWM is shown. The speed control loop generates the torque component of current iqs* as in Eq.4.15. ……….. (4.15) The flux component of current ids*for the desired rotor flux ψr is determined from Eq.4.13 and is maintained constant here in an open loop manner for simplicity. The variation of magnetizing inductance Lm will cause some drift in the flux. The slip frequency ωsl* is generated from iqs* in feedforward manner as in Eq.4.14 to satisfy the phasor diagram in Fig.4.4.

07

Chapter (4)


Fig.4.6 Indirect vector control block diagram with open loop flux control Signal ωsl* is added to the speed signal ωr to generate frequency signal ωe. the unit vector signals cose and sine are then generated from ωe by integration as shown in Fig.4.7.

Fig.4.7 Inside IRFOC block

07

Chapter (4)


4.6 The Current Regulated Pulse Width Modulation (CRPWM) Technique. The three phase PWM inverters are widely used for ac motor drives. The inverter can be voltage or current controlled, each method has a technique to fire each switch a specific period, in our case a current controlled PWM inverter is used.

4.6.1 Hysteresis Band Current Control PWM Hysteresis band PWM is basically an instantaneous feedback current control method of PWM where the actual current continually tracks the command current within a hysteresis band. As indicated in Fig.4.8, if the actual current exceeds the Hysteresis Band (HB), the upper device of the half-bridge is turned off and the lower device is turned on. As the current decays and crosses the lower band, the lower device is turned off and the upper device is turned on. If the HB is reduced, the harmonic quality of the wave will improve, but the switching frequency will increase, which will in turn cause higher switching losses. Basically, the current loop error signal generates the PWM voltage wave through a comparator with a hysteresis band. Although the technique is simple, control is very fast, and device current is directly limited, the disadvantages are a harmonically non-optimum waveform and slight phase lag that increases with frequency. There is, of course, additional distortion in the isolated neutral threephase load.

08

Chapter (4)


Fig.4.8 Hysteresis Band Current Control PWM

4.7 System Simulation Using Matlab-Simulink.

An indirect rotor field oriented control of three phase induction motor drive system has been simulated in MATLAB-Simulink . A fixed band hysteresis current controller has been used to control the stator currents and give the gating signals of the three phase inverter [42] .The simulation results at normal conditions are shown in the following figures.

00

Chapter (4)


Fig.4.9 Indirect field oriented control system in Matlab-simulink

Fig.4.10 Inside torque command generator block

Fig.4.11 Inside Field Oriented control block 06

Chapter (4)


Fig.4.12 Inside three phase inverter block

Fig.4.13 Inside the inverter block

06

Chapter (4)


4.8 Fault Tolerant Control System Design Using Current Regulation Technique It is assumed that before any phase is disconnected, the currents feeding the induction motor are regulated to be three balanced positive sequence sinusoidal currents as follows: (

)

(

⁄ )

(

⁄ )

……….. (4.16)

}

The rotating mmf generated by the armature currents is the sum of the mmfs caused by each phase,this mmf can be expressed by the complex vector. ……….. (4.17) ……….. (4.18) Where a =11200 , a2 =12400 and N is the number of turns per stator phase , √

So [

√

, (

⁄ )

(

⁄ )] …….. (4.19)

Where Substituting a and a2 in Eq.4.19 it will lead to [⏟

⏟]

……….. (4.20)

Or in vector form Assume that at any instance (t), the current in phase (a) is suddenly drops to zero. In this case, the rotating m.m.f. will be the sum of mmfb and mmfc so 67

Chapter (4)


……….. (4.21) √

(

[⏟

)

(

√

( √

)

⏟(

)

……….. (4.22)

)]

……….. (4.23)

To maintain the same m.m.f. after phase (a) is disconnected Eq.4.20 should be equal to Eq.4.23, solving for real and imaginary parts will lead to Real parts: [(

)]

Imaginary parts: √

[(

)] √

Solving for I'bs and I'cs √

(

)

√

(

√

√ (

) )

……….. (4.24) (

√

) .. (4.25)

And √

(

)

√

(

√

√ (

) )

√

……….. (4.26) (

By comparing Eqs.4.25,4.27 With standard three phase currents (

)

(

)

67

)….. (4.27)

Chapter (4)


So, in order to maintain the same m.m.f. and insure disturbance free operation of the system, the phase currents of the unfaulted phases need to be increased in magnitude by a factor of √ and phase shifted 30о away from the axis of the axis of the faulted phase The phasor diagram for an open one phase fault (a) is shown in Fig.4.14.

Fig.4.14 Stator currents phasor diagram before and after phase (a) disconnection The same analysis can be implemented on the other two phases and the same results can be shown as follows If phase (b) is disconnected so And √ ( √ (

) } )

……….. (4.28)

And If phase (c) is disconnected so √ ( √ (

) } )

……….. (4.29)

And the phasor diagram of the stator currents before and after the fault in the two cases is shown in Figs.4.15,4.16.

67

Chapter (4)


Fig.4.15 Stator currents phasor diagram before and after phase (b) disconnection

Fig.4.16 Stator currents phasor diagram before and after phase (c) disconnection 4.9 Implementation of Fault Tolerant Control System As mentioned before the fault tolerant control technique consists of three main parts 1- Fault Detection. 2- Fault Isolation. 3- Fault compensation. The first and second steps have been discussed earlier in sections 2.4.1, 2.4.2 respectively.

67

Chapter (4)


The third step (fault compensation) has been mentioned in section 2.4.3, in case of field oriented controlled induction motor drives, the current regulation technique can be implemented with the fault compensation topology of Fig.4.17 by changing the equations of reference current calculation as follows.

Fig.4.17. Fault isolation method using TRIACs when the system detects an abnormal condition (for example open IGBT gate drive fault) the system firstly disconnect the faulty phase leg by firing Thyristors (TR1 and TR4) as discussed in section 2.4.3 as shown in Fig.4.17. Then the third step (fault compensation) should be started which can be divided into two steps. a) Connecting the neutral point to the mid-point of the DC link by firing TRn TRIAC to operate the machine as a balanced two phase motor. b) Applying the current regulation technique. The current regulation technique can be implemented by changing the equations of reference current calculation in (de-qe/ a-b-c) block in Fig.4.7 as follows.

67

Chapter (4)


Normal Mode: In normal case the reference currents (Ia*,Ib*,Ic*) can be calculated from the reference d,q currents in stationary reference frame as shown in Fig.4.18.

Fig.4.18 Current phasor diagram before and after phase (a) disconnection

√ √ ( √ (

……….. (4.30)

) )

}

Fault Mode: In fault mode (phase (a) is disconnected), the new reference currents can be calculated as a function of d,q components in stationary reference frame as

67

Chapter (4)


√ [√ (

)]

√ [√ (

)]

……….. (4.31) }

So a general formula for reference currents can be generated depending on a control logic signal (X) which describe the normal or fault case. ( [(

)

√

] √ [

[(

)

√

] √ [

) √ (

) (

)

(

)]

(

)]

…….. (4.32) }

Where X=0 in normal conditions and X=1for fault condition. Note that this increase in phase currents is in the form of a non-torque producing zero sequence current (i0s) , so the new current regulation technique does not affect the field orientation because the direct and quadrature axis components have not been changed. Since the zero sequence component current can be calculated as (

)

……….. (4.33)

So in normal conditions it will be zero but in the case of loss one phase it will be one third of the summation of the currents in healthy phases. This fact has been clarified from the stator current space vector loci in ds-qs-0s frame shown in Fig.4.19.

68

Chapter (4)


Fig.4.19 Current vector loci in healthy and faulty drive It is clear that the stator currents space vector in ds-qs-0s frame has a circular shape in healthy conditions and the zero sequence component does not appear. If one phase is lost, the zero sequence component of the stator current must arise, and the current vector trajectory in the faulty drive departs from d s-qs plane, where it moves during healthy operation as shown in the threedimensional (3-D) space of Fig.4.19. To obtain the same performance, the current locus after a fault has to be an ellipse, whose projection on ds-qs plane coincides with the healthy current circle [36].

4.10 Simulation results The simulation results of a field oriented control system with three phase current regulated PWM inverter are obtained with the following parameters: Solver: Fixed step Ode4 (Rung-Kutta) Step Time: 0.0001s Simulation Time: 1 sec. DC Link Voltage: 2*200 V 60

Chapter (4)


A step function load torque is applied starting with 5 N.m and increased to 10 N.m at t= 0.3 sec, the current regulated PWM minimizes the ripples of stator currents, so, the torque ripples have been minimized as shown in Fig.4.20, the speed has been changed from 0 to 100 rad/sec with 100 rad/ sec reference value as shown in Fig.4.21 according to the speed controller loop which includes a PI controller. The stator currents have been changed according to the load torque

The Developed Torque (N.m)

change as shown in Fig.4.22. 40 30 20 10 0 -10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time (sec)

Fig.4.20 The developed torque during load changes The Speed (rad/sec)

150 100 50 0 -50

0

0.1

0.2

0.3

0.4

0.5

Time (sec)


66

0.6

0.7

0.8

Chapter (4)


Fig.4.22 Stator currents Ias,Ibs,Ics

The inverter output voltages are a pulsating waves, the width of the pulses depends on the hysteresis bands of the CRPWM. The phase voltages V an , Vbn , Vcn are a two level waves and their values are changed from +Vdc/3, +2Vdc/3 and -Vdc/3, -2Vdc/3 as shown in Fig.4.23, the pole voltages Va0 , Vb0 , Vc0 are a pulsating waves and their values are changed from +Vdc /2 , -Vdc/2 as shown in Fig.4.24.

Fig.4.23 Inverter phase voltage Van , Vbn , Vcn 98

Chapter (4)


Fig.4.24 Inverter pole voltages Va0 , Vb0 , Vc0 The actual stator currents track the reference signals within a fixed hysteresis band (HB= 0.05) as shown in Figs.4.25, 4.26.

Fig.4.25 Phase (a) current Ias with its reference value Ias*

89

Chapter (4)


Fig.4.26 Zoom in to phase (a) current Ias with its reference value Ias* An open gate drive fault of the upper IGBT in phase (a) is simulated in MatlabSimulink at (t = 0.7 Sec), this fault leads to cancellation of the current in the faulty phase during half of the current period which causes a DC current offset in the faulty phase as discussed before (see Table 3.II), the stator currents and

Phase A Current (Amp)

their associated DC offset value are shown in Figs.4.27, 4.28, 4.29, 4.30. 6 4 2 0 -2 -4 -6 0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

time (sec)

Fig.4.27 Phase (a) current and DC offset value

89

1.3

1.4

Chapter (4)


Phase B current (Amp)

8 6 4 2 0 -2 -4 -6 0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

time (sec)

Fig.4.28 Phase (b) current and DC offset value phase C current (amp)

10

5

0

-5

-10 0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

time (sec)

DC offset component of stator currents

Fig.4.29 Phase (c) current and DC offset value 3

IbDC

2 1

IaDC

0

IcDC

-1 -2 -3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

time (sec)

Fig.4.30 DC offset current components in stator currents The developed torque has been distorted according to the interaction between the AC and DC components of the stator currents as shown in Fig.4.31. 89

Chapter (4)


Fig.4.31 Motor torque before and after phase disconnection at t=0.588 sec A little distortion has been appeared in the motor speed around the reference value which set by the speed controller as shown in Fig.4.32.

Fig.4.32 Motor speed before and after phase disconnection at t=0.588 sec 4.10.1 Stator Current Space Vector Approach to Fault Diagnosis

The stator current space vector can be expressed as in Eq. 4.34. ̅

() (

)

…….. (4.34)

The stator current space vector trajectory at normal conditions has a circular shape. If an open gate drive fault has been occurred at the Upper IGBT of phase 89

Chapter (4)


(a) its associated phase current is clamped to zero during the positive period, so the stator current space vector trajectory has a semi-circular shape with its center line is perpendicular to the direction of the faulty phase as shown in Figs.4.33, 4.34, 4.35 and it can be used to compare between the system performance before, during and after the fault moment [5].

Fig.4.33 Stator current space vector before and after the fault in phase (a)

Fig.4.34 Stator current space vector before and after the fault in phase (b)

89

Chapter (4)


Fig.4.35 Stator current space vector before and after the fault in phase (c) The current regulation fault tolerant control technique has been simulated and applied to operate the system in two phase mode as discussed before. Phase (a) has been disconnected due to an open gate drive fault of the upper IGBT of phase (a) at (t =0.32 Sec) and the current regulation technique has been applied at (t =0.6 Sec). The developed torque and the motor speed return to their pre-


fault value with only two healthy phases, as shown in Figs.4.36, 4.37. 40 30 20 10 0 -10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time (sec)

Fig.4.36 The developed torque in normal, faulty and fault tolerant control periods

89

The Speed (rad/sec)

Chapter (4)


150 100 50 0 -50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time (sec)

Fig.4.37 Speed in normal, faulty and fault tolerant control periods When the fault tolerant control technique is applied, the faulty phase has been disconnected, so, its current has been reduced to zero and the currents of the healthy phases have been increased in magnitude by a factor of 1.73 and shifted 300 apart from each other as shown in Fig.4.38.

Fig.4.38 Stator currents in normal, faulty and fault tolerant control periods Also, when the fault tolerant control technique is applied, the neutral terminal has been connected to the mid-point of dc link. So, the phase voltages of the healthy phases (Vbn,Vcn) are equal to the pole voltages (Vb0,Vc0) as shown in Fig.4.39.

89

Chapter (4)


Fig.4.39 Phase Voltages in normal, faulty and fault tolerant control periods 4.11 Zero Current Switching Technique It can be shown from the simulation results that there is a distortion of the torque at the instant of applying this technique; this distortion depends on the instant at which the fault tolerant algorithm is applied. If the faulty phase has been disconnected at a moment at which its current has a nonzero value, it results in large switching losses, the torque will disturb and the transient period has a large overshoot values. Fig.4.40. shows the stator currents if phase (a) disconnected at (t= 0.575) at which the current has a negative value.

Stator Current (Amp)

And the developed torque disturbance is shown in Fig.4.41. 20 10 0 -10 -20 0.5

0.55

0.6

0.65

0.7

Time (sec) Fig.4.40 Stator currents before and after phase disconnection at t=0.575 sec 89

0.75


Chapter (4)


12 10 8 6 4 2 0 0.5

0.55

0.6

0.65

0.7

0.75

0.8

Time (sec)

Fig.4.41 Motor torque before and after phase disconnection at t=0.575 sec To overcome this problem it is required to disconnect the faulty phase when its current reaches zero (zero current soft switching technique), as shown in Figs.4.42, 4.43.



89

Chapter (4)


The direct and quadrature axis currents (Ids, Iqs) have been not changed, so the field orientation process has been not affected by the fault tolerant control technique. Besides the zero sequence current component I 0s has been appeared when the faulty phase is disconnected and the neutral point has been connected to the mid-point of the dc link as shown in Fig.4.44.

Fig.4.44 Iqs, Ids and I0s before and after phase disconnection Due to the increase in zero sequence current, the stator current space vector in stationary reference frame changed from it circular shape in ds-qs plane. The current locus after a fault has to be an ellipse, whose projection on d s-qs plane coincides with the healthy current circle as shown in Fig.4.45.

88

Chapter (4)



Advantages: 1- The developed torque does not change and it is suitable for industrial processes as in lifting cranes. 2- Regulating of the stator currents can be made simply using a Current Regulated Pulse Width Modulation CRPWM technique especially in drive systems that controlled via a field oriented control. Disadvantages: 1- Required accessibility of the motor neutral, which is normally not provided by motor manufacturers, also this method would not be applicable to delta-connected motors. 2- Increasing the currents of the healthy phases implies that the inverter and motor have to be overrated to withstand this higher level of current for at least a significant period of time. 3- Increasing the currents of the healthy phases result in an overheating of the machine. So, it may affect the motor insulation and increase the ambient temperature

999

Chapter (4)


4- The neutral current is no longer zero. It is the sum of the currents in the remaining two healthy phases which results in three times the value of the original phase current during the healthy operating mode. The next chapter presents the proposed method for fault tolerant control to overcome some of disadvantages of this method.

999

Chapter 5

Fault Tolerant Direct Torque Control Induction Motor Drive System

Chapter (5)


5.1 Introduction In the mid-1980s, an advanced scalar control technique, known as Direct Torque and Flux Control (DTFC) or Direct Torque Control (DTC) or direct self-control (DSC), was introduced for voltage-fed PWM inverter drives. This technique was claimed to have nearly comparable performance with vector controlled drives. Recently, the scheme was introduced in commercial products by a major company and therefore created wide interest. The scheme, as the name indicates, is the direct control of the torque and stator flux of a drive by inverter voltage space vector selection through a lookup table [39].

In this chapter a new switching technique for Direct Torque Control (DTC) fault tolerant induction motor drive is presented, if one inverter leg is completely lost due to such abnormal condition, this system modifies the switching table of DTC system using the available stator voltage vectors in two phase mode with Four Switch Three Phase Inverter (FSTPI) topology to track the stator flux reference and directly control the torque and maintain the performance of induction motor as in the Six Switch Three Phase Inverter (SSTPI) mode [41].

5.2 Principle of Direct Torque Control (DTC) method. The developed torque can be expressed in vector form as in Eq.5.1. ̅

̅

( )̅

…….. (5.1) and ̅

Where ̅

, In the complex form, ̅ and ̅

can be expressed as a function of currents as ̅ ̅

̅ ̅

̅

…….. (5.2) ̅

…….. (5.3)

201

Chapter (5)


Eliminating ̅ from Eq.5.2 we get: ̅

̅

̅

. The corresponding expression of ̅ is

Where ̅

̅

̅

…….. (5.4)

Substituting Eq.5.4 in Eq.5.1 and simplifying that yields ̅

( )

̅

̅

…….. (5.5)

So the magnitude of torque can be expressed as ̅ Where

( )

|

||

|

…….. (5.6)

is the angle between the stator and rotor fluxes. Fig.5.1 shows the

vector diagram of Eq.5.6 indicating the vectors of ̅

̅

̅ for positive

developed torque [43],[44],[45]. If the rotor flux remains constant and the stator flux is changed incrementally by stator voltage corresponding change of

angle is

̅ as shown. And the

, the incremental torque

expression

is given as ( )

|

||̅̅̅

̅̅̅|

…….. (5.7)

Fig.5.1 Stator, rotor fluxes and stator current vectors on d s-qs plane 201

Chapter (5)


5.2.1 Torque and Stator Flux Estimation in DTC The stator flux can be estimated from the stator voltage equations in ds-qs as

So,

∫

,

…….. (5.8)

So,

∫

,

…….. (5.9)

̂

√

,

…….. (5.10)

̂

And the torque can be estimated from motor variables as ( ) ( ) (

)

…….. (5.11)

5.2.2 Control Strategy of DTC The block diagram of DTC shown in Fig.5.2 explains the control strategy. The flux command

and the torque command

magnitudes are compared with

the estimated values, and the errors are processed through hysteresis band controllers [46],[47],[48],[49]. The flux loop controller has two levels of digital output according to the following relations: }

…….. (5.12)

201

Chapter (5)


Fig.5.2 Direct Torque control block diagram Where 2HBψ = total hysteresis band width of the flux controller. The circular trajectory of the command flux vector ̅ with the hysteresis band rotates in an anti-clockwise direction as shown In Fig.5.3. The actual stator flux ̅ is constrained within the hysteresis band and it tracks the command flux in a zigzag path. The torque control loop has three levels of digital output, which have the following relations:

}

…….. (5.13)

The feedback flux and torque are calculated from the machine terminals voltages and currents. The flux and torque calculation block also calculates the sector number S(k) in which the flux vector ̅ lies. There are six sectors (each π/3 angle wide), as indicated in Fig.5.3, the voltage vector table block in Fig.5.2 receives the input signals

and S(k) and generates the appropriate 201

Chapter (5)


control voltage vector (switching states) for the inverter by a lookup table, which is shown in table.5.I,the inverter voltage vectors (six active and two zero states) and a typical ̅ are shown in Fig.5.3 neglecting the stator resistance Rs of the machine, we can write. ̅

̅

,

̅

̅

.

Fig.5.3 Stator flux vector trajectory in DTC control Which means that ̅ can be changed incrementally by applying stator voltage vector ̅ for time increment

. The flux increment vector corresponding to

each of the six inverter voltage vector is shown in Fig.5.3. The flux in the machine is initially established at zero frequency (DC) along the radial trajectory OA with the rated flux, the command torque is applied and the ̅ vector starts rotating. Table 5.I applies the selected voltage vector which essentially affects both the torque and flux simultaneously. The flux trajectory segments AB, BC , CD and DE by the respective voltage vectors V 3 , V4 , V3 and V4 are shown in Fig.5.3. The total and incremental torque due to

̅ are explained in Fig.5.3 note that

the stator flux vector changes quickly by ̅ , but ̅ change is very sluggish due 201

Chapter (5)


to large time constant of the rotor Tr . Since ̅ is more filtered, it moves uniformly at frequency ωe , where as ̅ movement is jerky. The jerky variation of stator flux and

angle introduces the torque ripple.

Table.5.I summarizes the flux and torque changes for applying the voltage vectors for the location of ̅ the flux can be increased by the vectors V1,V2,V6 where it can be decreased by the vectors V3 , V4 , V5 . Similarly, torque is increased by the vectors V2, V3, V4, but decreased by the vectors V1 , V5 , V6. The zero vector (V0 , V7) short circuits the machine terminals and keeps the flux and torque unaltered [48]. Table.5.I: Switching table of inverter voltage vectors

1

0

1 0 -1 1 0 -1

S(1) S(2) S(3) S(4) S(5) S(6) V2 V3 V4 V5 V6 V1 V0 V7 V0 V7 V0 V7 V6 V1 V2 V3 V4 V5 V3 V4 V5 V6 V1 V2 V7 V0 V7 V0 V7 V0 V5 V6 V1 V2 V3 V4

5.3 The Proposed Fault Tolerant Control Algorithm. To discuss the proposed fault tolerant control algorithm which can be used with the direct torque controlled induction motor drives, it is recommended to discuss the four switch three phase inverter (FSTPI) topology firstly. Then it will be applied in case of disconnection of phase (a) and (c) respectively. 5.3.1 Four Switch Three Phase Inverter (FSTPI) Topology. When an inverter phase leg is disconnected, the faulty phase terminal should be connected to the mid-point of the DC link in order to operate the machine in

201

Chapter (5)


two phase mode, this topology of the inverter is called Four Switch Three Phase Inverter (FSTPI) and shown in Fig.5.4.

Fig.5.4. Four Switch Three Phase Inverter (FSTPI) with phase (a) is connected to DC link mid-point The transition from six switch three phase inverter (SSTPI) topology to Four switch three phase inverter (FSTPI) can be done with the aid of some switching devices such as TRIACS and fast blown fuses, when the system detects an abnormal condition (for example open IGBT gate drive fault) the system firstly disconnect the faulty phase leg by firing Thyristors (T1 or T4) in series with the phase leg as shown in Fig.5.5 Then Connecting the faulty phase terminal to the mid-point of the DC link by firing TRIACs (TRa or TRb or TRc) to operate the machine as a balanced two phase motor[50]. This algorithm has been applied in two cases

201

Chapter (5)


Fig.5.5. Fault isolation method using TRIACs 5.3.2 Phase (a) is disconnected. When phase (a) is disconnected from the inverter output terminal and reconnected to the mid-point of the dc link, the system operates in (FSTPI) mode. The pole voltages Va0 , Vb0 , Vc0 can be determined as a function of upper switches states as in Eq.5.10.

(

)

(

)

}

…….. (5.10)

Where S3 and S5 are the switching states of the upper switches of healthy phases (b) and (c) respectively. The combinations of switches (Q3,Q5,Q6,Q2) result in four non zero general space vectors V1,V2,V3,V4 as shown in Fig. 6 and there is no zero vectors as in case of Six Switches Three Phase Inverter (SSTPI) [51],[52],[53],[54]. 201

Chapter (5)


The voltage vector (α-β) components can be calculated from stator phase voltages (Van,Vbn,Vcn) by using Clark's transformation as in Eq.5.11.

[ ]

[

√

√

][

]

…….. (5.11)

The available voltage vectors (V1,V2,V3,V4) are listed in table 5.II and shown in Fig.5.6. There are only four sectors (each π/2 angle wide). The stator flux space vector trajectory should be accomplished by the available voltage vectors. TABLE 5.II: Stator space vectors if phase (a) is disconnected ̅

S3

S5

0

0

1

0

̅̅̅

1

1

̅̅̅

0

1

̅

̅

Fig.5.6. Stator voltage space vector if phase (a) is disconnected 220

Chapter (5)


The selection of the optimum inverter switching state which satisfies flux and torque requirement is explained in only one sector, and then the idea can be applied to all sectors. As shown in Fig.5.7-(a), assuming the stator flux vector lies in sector 1, if its magnitude has to be increased, there are two vectors that satisfy this condition: V1,V2. But the two vectors have different effect on the motor torque [55]. The selection of V1 results in a decrease in the angle between stator and rotor flux, thereby the magnitude of the torque will be reduced. Conversely, if V2 is selected to increase the flux magnitude, the angle between stator and rotor flux will increase, consequently the motor torque will be increased [27]. The same discussion can be applied if the stator flux vector magnitude has to be decreased as shown in Fig.5.7-(b).

(a)

(b)

Fig.5.7. Selection of suitable voltage vector (a) increasing s, (b) decreasing s According to the previous discussion, the lookup table in this case can be made as indicated in Table 5.III. And the stator flux space vector trajectory is shown in Fig.5.8. 222

Chapter (5)


TABLE 5.III: DTC Lookup Table S(1) S(2) S(3) S(4)

1

0

1

V2

V3

V4

V1

-1

V1

V2

V3

V4

1

V3

V4

V1

V2

-1

V4

V1

V2

V3

Fig.5.8.Stator flux space vector trajectory if phase (a) is disconnected 5.3.3 Phase (c) is disconnected. When phase (c) is disconnected from the inverter output terminal and reconnected to the mid-point of the dc link, the Phase to common point voltages Va0 , Vb0 , Vc0 can be determined as a function of upper switches states as in Eq.5.12.

221

Chapter (5)


(

)

(

)

}

…….. (5.12)

Where S1 and S3 are the switching states of the upper switches of phases (a) and (b) respectively. The combinations of switches S1,S2,S3,S4 result in four non zero general space vectors V1,V2,V3,V4 as shown in Fig.5.9-(a) and there is no zero vectors as in case of (SSTPI). Table 5.IV shows the switching states and the corresponding voltage space vectors. As discussed before in case of disconnection of phase (a). Table 5.V shows the lookup table with the suitable voltages to control the flux and torque if phase (c) is disconnected. The stator flux vector trajectory is shown in Fig.5.9-(b). TABLE 5.IV: Switching states and the corresponding voltage space vectors S1

S3

̅

0

0

̅

1

0

̅̅̅

1

1

̅̅̅

0

1

̅

TABLE 5.V: DTC lookup table

1 0

1 -1 1 -1

S(1) S(2) S(3) S(4) V3 V4 V1 V2 V2 V3 V4 V1 V4 V1 V2 V3 V1 V2 V3 V4

221

Chapter (5)


(a)

(b)

Fig.5.9. Phase (c) is disconnected: (a) the stator voltage space vector and (b) The stator flux space vector trajectory

5.4 Modeling of the Proposed System Using Matlab-Simulink The proposed system can be simulated in MATLAB- Simulink as shown in Figs.4 to 8.

Fig.5.10. Modeling of DTC induction motor drive system using MatlabSimulink 221

Chapter (5)


2-D L-Up -T1 1 sector 2 depsi

1 vector

V-Select

3 deltaTe 2-D L-Up-T 2

Fig.5.11 Look up tables and vector selection block 1 In 1 (1

0

0)

Constant 1 (1

1

2*u(1)-1

0)

-K -

1 vao

3

Fcn

Constant 2 (0

1

0)

2*u(2)-1

Constant 3 (0

1

2 vbo

1

Fcn1

Scope 4

1) 2*u(3)-1

Constant 4 (0

-K -

0

-K -

Fcn2

1)

3 vc 0

2

Constant 5 (1

0

1)

Constant 6

Multiport Switch

Fig.5.12 Determination of pole voltages according to the suitable voltage vector 1

1

epsids

vsd

2 iqs

2

1

isd

Product 1

isq2

-K -

1

3

Td

3 torqued

epsiqs 4 isds

1

Sum 1

1/s epsiq

4

-KGain 1

Fig.5.14 Estimation of the stator flux

Fig.5.13 Estimation of the developed torque

221

1 epsisd

Gain

3

isq

isd2

1/s epsid

-K-

vsq

Product

Sum

2 epsisq

Chapter (5)


>

1 th

-30

1

R1

AND

g1

thc

1 TH 1

30

1

R4

AND

g3

thc 2

2 1

1

90 thc 5

R5

g5

150

1 THH

1

R8

g7

thc 6 AND 210

1

R9

g9

thc9

AND 270

R12

1 g11

AND

thc 10

6 Sum 4 TH 6