Remediation Strategies of Shaft and Common mode...

Remediation Strategies of Shaft and Common

mode voltages in Adjustable Speed Drive

Systems

A Thesis by Publication submitted in

Partial Fulfilment of the Requirement for the

Degree of

Doctor of Philosophy

Jafar Adabi Firouzjaee

M.Sc, B.Eng (Electrical Engineering)

Faculty of Built Environment and Engineering

School of Engineering Systems

Queensland University of Technology

Queensland, Australia

August 2010

III

Acknowledgment

I would like to thank many people and organizations for their help and support

during the period of this study. First of all, I would like to express my deepest

sense of gratitude to my supervisor, Dr. Firuz Zare, who truly made a difference

in my academic perspective. With his support, encouragement and brilliant

advice throughout the PhD program, I developed my interests in the area of

power electronics. I also acknowledge the support of my associate supervisors

Prof. Arindam Ghosh and Prof. Gerard Ledwich during my research program. It

is an honor for me to work with such a great and prestigious supervisory team.

I also would like to convey thanks to Queensland University of Technology

(QUT) to provide me a pleasant research area and laboratory facilities. I

gratefully acknowledge Australian Research council for financial assistance of

this project through the ARC Discovery Grant. Computational resources and

services used in this work were provided by the HPC and Research Support

Group, QUT. The assistance of Mr. Mark Barry and Dr. Prasad Gudimetla in the

simulation and Finite Elements modeling stage of this project is much

appreciated. The assistance of Laboratory Technicians and the staff of Research

Portfolio are also appreciated.

I am indebted to many of my colleagues and friends at the Power Engineering

Group for providing a warm research atmosphere, sharing knowledge, and

encouragements. I will never forget the pleasant times I had with my friends

during the soccer matches and other socializing events.

I would also like to thank my family for the support they provided me through

my entire life. I must acknowledge my wife and best friend, Fatemeh, without

her love, encouragement and assistance; I would not have finished this research

program. My brothers are always encouraged me during the hard times and

always be on my side.

During my three-year stay in Australia, I have never forgotten the tears of my

mother at the departure moment and also heartwarming advice of my father.

They are supervisors of my life and I wish all the best from God for them.

IV

Table of Contents

Abstract ........................................................................................................... XIX

Keywords ....................................................................................................... XXII

Contributions ............................................................................................... XXIII

List of Publications ...................................................................................... XXIV

List of Chapters according to Publications and Contributions ............... XXVI

Scholarship and grants .............................................................................. XXVII

Statement of Original Authorship ........................................................... XXVIII

Chapter 1 .............................................................................................................. 1

Introduction ......................................................................................................... 1

1.1. Description of the Research Problem ......................................................... 2

1.2. Literature Review ....................................................................................... 4

1.2.1. Modern AC motor drive systems......................................................... 4

1.2.2. Three-phase voltage source inverters: leg, phase, line and common

mode voltage.................................................................................................. 6

1.2.3. High frequency modelling and parasitic elements .............................. 9

1.2.4. High frequency related issues in ASD system................................... 12

1.2.4.1. Leakage current .......................................................................... 12

1.2.4.2. Shaft voltage and bearing currents ............................................. 13

1.2.4.3. Conducted and radiated EMI emissions ..................................... 15

1.2.5. Remediation strategies of the common mode problems of the ASD

systems......................................................................................................... 16

1.2.5.1. Bearing current reduction methods ............................................. 17

1.2.5.2. Leakage current mitigation techniques ....................................... 18

1.2.6. High frequency elements in induction generators ............................. 20

1.3. Account of Research Progress Linking the Research Papers ................... 21

1.3.1. Ball bearing damage analysis in AC motor drives ............................ 25

1.3.2. Investigation on design parameters of the motors to reduce shaft

voltage in first step of the design process .................................................... 29

1.3.2.1. Calculation of different capacitances ......................................... 29

V

1.3.2. 2. Analysis of shaft voltage without considering end-winding ..... 33

1.3.2.3. Analysis of shaft voltage with considering end-winding ........... 34

1.3.2.4. Verification of the mathematical analysis with test and simulation

................................................................................................................. 39

1.3. 3. Common mode voltage reduction in different power electronics

topologies .................................................................................................... 49

1.3.3. 1. Common Mode Voltage Reduction in three-phase ASD system

supplied with a single-phase diode rectifier ............................................ 49

1.3.3.2. Multi-Level Inverter Topology and reduction of common mode

voltage ..................................................................................................... 54

1.3.4. Shaft voltage in induction generators of wind turbine ...................... 57

1.3.4.1. Shaft voltage analysis in stator fed IG-based wind power

applications ............................................................................................. 57

1.3.4.2. Shaft voltage analysis in DFIG-based wind power applications 57

1.3.4.3. Discussion on shaft voltage elimination strategies for different

topologies of DFIG-based system ........................................................... 63

1.4. References: ............................................................................................... 67

CHAPTER 2 ...................................................................................................... 75

Investigation of Shaft Voltage in Different configurations of Induction

Generators for Wind Power Applications ...................................................... 75

2.1. Introduction .............................................................................................. 76

2.2. Switching states and common mode voltage of a three phase inverter .... 78

2.3. Shaft voltage analysis in stator fed IG-based wind power applications ... 80

2.3.1. IG model, calculation of different capacitive couplings and finite

elements simulation results ......................................................................... 80

2.3.2. Shaft voltage with regards to different design parameters and PWM

pattern .......................................................................................................... 84

2.4. Shaft voltage analysis in DFIG-based wind power applications ............. 85

4.1. Generator structure and different configurations of LC filters in wind

turbine system ............................................................................................. 86

2.4.2. Discussion on shaft voltage elimination strategies for different

topologies of DFIG-based system ............................................................... 93

2.5. Conclusions .............................................................................................. 96

VI

2.6. References: ............................................................................................... 96

CHAPTER 3 ....................................................................................................... 99

Calculations of Capacitive Couplings in Induction Generators to Analyse

Shaft Voltage ...................................................................................................... 99

3.1. Introduction ............................................................................................ 100

3.2. Calculation of shaft voltage and relevant capacitive couplings in a motor

structure ......................................................................................................... 102

3.3. Simulation Results .................................................................................. 108

3.3.1. Effects of the parameters of stator slot on capacitive couplings ..... 108

3.3.2. Analysis of ball bearing capacitances in different conditions ......... 110

3.4. Experimental Results .............................................................................. 112

3.5. Discussion ............................................................................................... 115

3.6. Conclusions ............................................................................................ 118

3.7. References .............................................................................................. 118

CHAPTER 4 ..................................................................................................... 121

Analysis of the Effects of End-Winding Parameters on the Shaft Voltage of

AC Generators ................................................................................................. 121

4.1. Introduction ............................................................................................ 122

4.2. Analysis of shaft voltage without considering end-winding .................. 125

4.3. Analysis of shaft voltage with considering end-winding ....................... 128

4.3.1. Mathematical Analysis .................................................................... 129

4.3.2. Finite Element Analysis .................................................................. 133

4.4. Experimental Results .............................................................................. 141

4.5. Conclusions ............................................................................................ 143

4.6. References .............................................................................................. 143

CHAPTER 5 ..................................................................................................... 147

Effects of PFC on Common Mode Voltage of a Motor Drive System

Supplied With a Single-phase Diode Rectifier .............................................. 147

5.1. Introduction ............................................................................................ 148

5.2. Common mode voltage and shaft voltage in ASD systems .................... 151

VII

5.3. Common Mode Voltage in 3-φ ASD system supplied with a 1-φ diode

rectifier without PFC ..................................................................................... 154

5.3.1. Circuit Description .......................................................................... 154

5.3.2. Simulation Results .......................................................................... 155

5.4. Common Mode Voltage in 3-φ ASD system supplied with a 1-φ diode

rectifier with a PFC ....................................................................................... 159

5.4.1. Circuit Description .......................................................................... 159

5.4.2. Simulation Results .......................................................................... 160

5.5. Conclusions ............................................................................................ 164

5.6. References .............................................................................................. 165

CHAPTER 6 .................................................................................................... 167

Different Approaches to Reduce Shaft Voltage in AC Generators ............ 167

6.1. Introduction ............................................................................................ 168

6.2. Pulse Width Modulated Voltage without Zero Vectors ......................... 170

6.3. Multi-Level Inverter Topology .............................................................. 173

6.4. Better Motor Design to Minimize Capacitive Coupling ........................ 177

6.5. Active Common mode Filter .................................................................. 179

6.6. Reducing DC Link Voltage and Increasing Modulation Index ............. 180

CHAPTER 7 .................................................................................................... 183

Analysis of Shaft Voltage in a Doubly-fed Induction Generator ................ 183

7.1. Introduction ............................................................................................ 184

7.2. High frequency model of DFIG and shaft voltage calculation .............. 187

7.3. Discussion .............................................................................................. 190

7.4. Conclusions ............................................................................................ 193

7.5. References .............................................................................................. 194

CHAPTER 8 .................................................................................................... 195

Bearing Damage Analysis by Calculation of Capacitive Coupling between

Inner and Outer Races of a Ball Bearing ...................................................... 195

8.1. Introduction ............................................................................................ 196

8.2. Discharge current paths by calculation of capacitive couplings ............ 198

8.2.1. Symmetric Case .............................................................................. 199

VIII

8.2.2. Asymmetric case.............................................................................. 200

8.2.2.1. Asymmetric ball positions ........................................................ 200

8.2.2.3. Asymmetric shaft position ........................................................ 201

8.3. Conclusions ............................................................................................ 204

8.4. References .............................................................................................. 204

CHAPTER 9 ..................................................................................................... 207

Conclusions and Further Research ................................................................ 207

9.1. Conclusions ............................................................................................ 208

9.2. Future research ....................................................................................... 212

IX

List of Figures

Chapter 1

Fig.1. 1: An AC motor supplied with single phase or three phased AC source (a)

uncontrolled speed (b) adjustable speed ............................................................... 4

Fig.1. 2: (a) A power electronic motor drive system with capacitive couplings (b)

input AC voltage and its rectified waveform (c) Pulse width modulated voltage

(d) Three-phase filtered voltages .......................................................................... 5

Fig.1. 3: (a) a three- phase inverter with (b) eight switching states ...................... 6

Fig.1.4: Leg voltages and common mode voltage of the switching pattern ......... 8

Fig.1. 5: A power electronic motor drive system with different capacitive

couplings ............................................................................................................... 9

Fig.1. 6: (a) Structure of an AC motor with (b) different parasitic capacitive

couplings ............................................................................................................. 10

Fig.1. 7: Ball bearings: structures, capacitive couplings and simple model ....... 11

Fig.1. 8: (a) a simple common mode model of the AC motor (b) models for shaft

voltage generation and the leakage current ......................................................... 11

Fig.1. 9: A typical example of high dv/dt and resultant leakage current ............ 13

Fig.1. 10: Damages on the bearing (source: ABB technical guide) .................... 14

Fig.1. 11: An active EMI filter ............................................................................ 19

Fig.1. 12: 3-D model of the motor and a view of electrostatic model of a stator

slot ....................................................................................................................... 24

Fig.1. 13: Possible discharge current paths in the symmetric case ..................... 25

Fig.1. 14: (a) Asymmetric ball positions and discharge current paths (b) upper

side ball (c) lower side ball ................................................................................. 27

Fig.1. 15: Capacitive coupling terms between upper and lower balls and races for

an asymmetric shaft position with Probable discharge current path ................... 28

Fig.1. 16: (a) A stator slot with different design parameters and capacitive

couplings in the slot (b) capacitances in area of stator teeth (c) a model for

capacitance calculations ...................................................................................... 29

Fig.1. 17: Two vertical surfaces ......................................................................... 31

Fig.1. 18: Variation of Vsh/Vcom versus variation of d and g2 ............................. 33

X

Fig.1. 19: (a) structure of an IG with (b) a model for calculation of end-winding

capacitances ......................................................................................................... 35

Fig.1.20: (a) structure of an IG with a (b) model for simulation of end-winding

capacitances ......................................................................................................... 37

Fig.1. 21: 2-D and 3-D simulation results for (a) Crf (b) Csr and its calculated

values ................................................................................................................... 40

Fig.1. 22: Calculated and simulated end-winding capacitances versus variation of

end-winding lengths (a) Rrotor=1000 mm, W=150mm (b) Rrotor=1000mm,

W=200mm ........................................................................................................... 41

Fig.1. 23: (a) test set-up for impedance measurement (b) stator slot model and

different parameters (c) impedance and phase in different frequencies .............. 42

Fig.1. 24: Three different tests to measure capacitive couplings ........................ 43

Fig.1. 25: Comparison between test and simulations for (a) Crs and (b) Crf for 6

different set-ups ................................................................................................... 44

Fig.1. 26: (a) view of machine structure with end-winding (b) view of shielded

end winding ......................................................................................................... 46

Fig.1. 27: Experimental results: Common mode and shaft voltage waveforms (a)

without shielded end winding (b) with shielded end winding ............................. 47

Fig.1. 28: (a) a schematic of an ASD system supplied by a single-phase diode

rectifier with PFC in (b) positive half a cycle and (c) negative half a cycle ....... 50

Fig.1. 29: DC link voltage, voltages at positive and negative points of DC link

with respect to the ground and common mode voltage for switching sequence of

(V0, V1, V2, V7, V2, V1, V0) ................................................................................. 51

Fig.1. 30: Leg voltages and common mode voltage for switching sequence of

(V0, V1, V2, V1, V0) ............................................................................................. 52


(V7, V2, V1, V2, V7) ............................................................................................. 52


(V0, V1, V2, V1, V0) for positive half a cycle and sequence of (V7, V2, V1, V2, V7)

for negative half a cycle. ...................................................................................... 53

Fig.1. 33: A three-level diode clamped inverter ................................................. 54

Fig.1. 34: Leg voltages for a three-level inverter (a) at the centre (b) at the sides

............................................................................................................................. 56

XI

Fig.1. 35: Stator-fed IG arrangement for wind power applications .................... 57

Fig.1. 36: Back-to-back DC-AC-DC inverter in a wind energy system ............. 58

Fig.1. 37: A view of DFIG with different capacitive couplings in a doubly fed

induction generator .............................................................................................. 58

Fig.1. 38: Different placements of L-C filters in wind turbine applications in a

DFIG with a back to back converter ................................................................... 59

Fig.1. 39: Common mode model for the configuration of a DFIG with

Topology1 ........................................................................................................... 59


Topology2 ........................................................................................................... 60


Topology4 ........................................................................................................... 61

Fig.1. 42: A common mode and shaft voltage generated by rotor and stator side

converters (fsr=1 kHz, fss=10 kHz) ...................................................................... 62

Fig.1. 43: Space vector operating region for the converters to eliminate the shaft

voltage ................................................................................................................. 65

Fig.1. 44: A new back-to-back inverters topology with a bidirectional buck

converter and a DFIG .......................................................................................... 65

Fig.1. 45: Common mode and shaft voltages in Topology 4 after applying the

presented PWM ................................................................................................... 66

Chapter 2

Fig.2. 1 :(a) A three phase converter (b) 8 possible switching vectors ............... 78

Fig.2. 2: Three leg voltages of a three phase inverter, common mode voltage

(Van) , a phase voltage (Vao) and a line voltage (Vab) .......................................... 79

Fig.2. 3:stator-fed IG arrangement for wind power applications ........................ 80

Fig.2. 4: (a) Structure of a stator fed induction generator with parasitic capacitive

couplings and its (b) common mode model ........................................................ 81

Fig.2. 5: a stator slot and different design parameters ........................................ 81

Fig.2. 6 : (a) A view of ball bearings and shaft (b) ball, outer and inner races and

Asymmetric (c) ball position (d) shaft position .................................................. 83

Fig.2. 7 : Vsh/Vcom versus d and g2 (ρ=5 mm, x=1) ............................................. 84

Fig.2. 8 : A common mode and shaft voltage for stator-fed IG with a 10 kHz

switching frequency ............................................................................................ 85

XII

Fig.2. 9: back-to-back DC-AC-DC inverter in a wind energy system ................ 85

Fig.2. 10: A view of DFIG with different capacitive couplings in a doubly fed

induction generator .............................................................................................. 86

Fig.2. 11: (a) configuration of a DFIG with Topology1 and its (b) common mode

model ................................................................................................................... 87

Fig.2. 12 : A typical rotor side common mode voltage waveform and its resultant

shaft voltage for Topolog1 (fsr=1 kHz) ............................................................... 88

Fig.2. 13 : (a) Configuration of a DFIG with Topology2 and its (b) common

mode model ......................................................................................................... 89

Fig.2. 14: A typical stator side common mode voltage and its resultant shaft

voltage for Topology2 (fss=10 kHz) ................................................................... 90

Fig.2. 15 : (a) Configuration of a DFIG with Topology3 and its (b) common

mode model ......................................................................................................... 90

Fig.2. 16: (a) configuration of a DFIG with Topology4 and its (b) common mode

model ................................................................................................................... 91

Fig.2. 17: a common mode and shaft voltage shaft voltage generated by rotor and

stator side converters (fsr=1 kHz, fss=10 kHz) ..................................................... 92

Fig.2. 18: Space vector operating region for the converters to eliminate the shaft

voltage ................................................................................................................. 94

Fig.2. 19: a new back-to-back inverters topology with a bidirectional buck

converter and a DFIG .......................................................................................... 95

Fig.2. 20: common mode and shaft voltages in Topology 4 after applying the

presented PWM ................................................................................................... 95

Chapter 3

Fig.3. 1:(a) Structure of an IG with different parasitic capacitive couplings (b) A

view of a DFIG with different parasitic capacitive couplings with and high

frequency model of (c) IG (d) DFIG ................................................................. 101

Fig.3. 2: (a) A view stator slot and different design factors (b) ball bearings and

shaft of a motor with a view of ball, outer and inner races and the capacitances

........................................................................................................................... 103

Fig.3. 3: (a) capacitive couplings in a stator slot (b) a complete system model for

calculation of capacitive couplings (c) simplified model with electric fields and

the capacitive couplings (d) two vertical surfaces ............................................. 105

XIII

Fig.3. 4: The error between simulations and calculations of Csr in a complete

system model versus a variations of g1 and g2 (a) ρ=5mm (b) ρ=25mm .......... 107

Fig.3. 5 : Calculated, 2-D, 3-D results in single stator slot for capacitive

couplings (a) Csr (b) Crf(c) Csf ; 3-D simulation results in a 24 slot IG for (d) Csr

(e) Crf and Csf..................................................................................................... 109

Fig.3. 6: Variation of Cws versus: (a) the changes of g2 (b) stator slot tooth and

two different air gaps. variation of Cwr versus: (c) stator slot tooth (d) the

changes of g2 ..................................................................................................... 110

Fig.3. 7: Asymmetric (a) ball positions (b) shaft position ................................ 111

Fig.3. 8: (a) view of machine structure with end-winding (b) view of shielded

end winding ....................................................................................................... 113

Fig.3. 9:Experimental results: Common mode and shaft voltage waveforms (a)

without shielded end winding (b) with shielded end winding .......................... 114

Fig.3. 10: (a) Vsh/Vcom versus d and g2 (ρ=5 mm, x=1) ; (b) KR versus g2 and d

(c) KS versus g2 and d (d) KR versus εr and gin (e) KS versus εr and gin in a

doubly-fed induction generator ......................................................................... 117

Chapter 4

Fig.4. 1: (a) structure of a stator-fed induction generator system (b) common

mode model of the system ................................................................................. 123

Fig.4. 2: View of a stator slot with different design parameters and capacitive

couplings in the slot .......................................................................................... 126

Fig.4. 3: a 3-D model of the motor and a view of electrostatic model of a stator

slot ..................................................................................................................... 127

Fig.4. 4: 2-D and 3-D simulation results for (a) Crf (b) Csr and its calculated

values for a single stator slot ............................................................................. 128

Fig.4. 5: (a) structure of an IG with (b) a model for calculation of end-winding

capacitances ....................................................................................................... 129

Fig.4. 6: Two surfaces with the voltage difference of V0 and the angle of .. 130

Fig.4. 7: calculated and simulated end-winding capacitances versus variation of

end-winding lengths (a) Rrotor=1000 mm, W=150mm (b) Rrotor=1000mm,

W=200mm (c) Rrotor=600mm, W=75mm (d) Rrotor=600mm, W=125mm ........ 132

Fig.4. 8: (a) structure of an IG with a (b) model for calculation of end-winding

capacitances ....................................................................................................... 134

XIV

Fig.4. 9: percentage error of capacitive couplings in 64 design by varing α from 0

to 30 degree ....................................................................................................... 135

Fig.4. 10:a one to one comparison of capacitive couplings in 64 design by

doubling L2 ........................................................................................................ 136

Fig.4. 11: Different capacitive couplings based on range of parameters in

Table.4. 6 ........................................................................................................... 137

Fig.4. 12: The ratio between the capacitances by changing g2 (from 25 to 5 mm)

versus L1 (a) Lring=25mm (b) Lring=50mm ......................................................... 138

Fig.4. 13: different capacitors in the end-winding ............................................. 139

Fig.4. 14:The share of each capacitance on the total end-capacitance CR1 ....... 139

Fig.4. 15: The ratio between the capacitances by changing gring (from 10 to 30

mm)versus L1 (a) Lring=25mm (b) Lring=50mm ................................................. 140

Fig.4. 16: (a) test set-up for impedance measurement (b) stator slot model and

different parameters (c) impedance and phase in different frequencies ............ 141

Fig.4. 17: Three different tests to measure capacitive couplings ...................... 142

Fig.4. 18: Comparison between test and simulation results for (a) Crs and (b) Crf

for six different set-ups ...................................................................................... 144

Chapter 5

Fig.5. 1:(a) Structure of an AC motor with different parasitic capacitive

couplings (b) common mode model .................................................................. 150

Fig.5. 2: (a) A three-phase converter (b) eight possible switching vectors ....... 151

Fig.5. 3: leg and common mode voltages for proposed pulse pattern ............... 153

Fig.5. 4: (a) an ASD system supplied with a single-phase diode rectifier and

circuit behavior in (b) charging and (b) discharging states of the capacitor in

positive and negative half a cycle ...................................................................... 154

Fig.5. 5:DC link voltage, voltages of positive and negative points of DC link

respect to the ground and common mode voltage for switching sequence of (V0,

V1, V2, V7, V2, V1, V0) ....................................................................................... 155

Fig.5. 6: Leg voltages and common mode voltage in two different switching

cycles in positive and negative half a cycle for switching sequence of (V0, V1,

V2, V7, V2, V1, V0) ............................................................................................. 157

Fig.5. 7: Leg voltages and common mode voltage in two different switching

cycles in positive and negative half a cycle for switching sequence of (V0, V1,

XV

V2, V1, V0) in positive half a cycle and (V7, V2, V1, V2, V7) in negative half a

cycle .................................................................................................................. 158

Fig.5. 8: DC link voltage, voltages of positive and negative points of DC link

respect to the ground and common mode voltage for switching sequence of (V0,

V1, V2, V1, V0) in positive half a cycle and (V7, V2, V1, V2, V7) in negative half a

cycle .................................................................................................................. 158

Fig.5. 9: input current of the proposed system .................................................. 159

Fig.5. 10:(a) a schematic of an ASD system supplied by a single-phase diode

rectifier with PFC in (b) positive half a cycle and (c) negative half a cycle ..... 160

Fig.5. 11: Inductor and input currents with a PFC ............................................ 161

Fig.5. 12: DC link voltage, voltages at positive and negative points of DC link

with respect to the ground and common mode voltage for switching sequence of

(V0, V1, V2, V7, V2, V1, V0) ............................................................................... 161


(V0, V1, V2, V1, V0) ........................................................................................... 162


(V7, V2, V1, V2, V7) ........................................................................................... 163


(V0, V1, V2, V1, V0) for positive half a cycle and sequence of (V7, V2, V1, V2, V7)

for negative half a cycle. ................................................................................... 164

Chapter 6

Fig.6. 1: (a) a wind turbine with a DFIG and a back-to-back AC-DC-AC

converter (b) structure of a DFIG with different capacitive couplings (c) its high

frequency model (d) a view of stator and rotor slots and their windings ......... 169

Fig.6. 2: A three-phase inverter (a) topology (c) voltage vectors in a Space

Vector Frame(b) leg, common mode, phase and line voltage waveforms ........ 171

Fig.6. 3: (a) Magnitudes of common mode voltage based on different switching

states (b) A typical pulse pattern for an inductive load ..................................... 172

Fig.6. 4: a three-level diode clamped inverter ................................................... 173


........................................................................................................................... 176

Fig.6. 6: Simulation results: current and voltage waveforms for a three-level

inverter .............................................................................................................. 176

XVI

Fig.6. 7: Simulation results: current and voltage waveforms for a four-level

inverter ............................................................................................................... 177

Fig.6. 8: Vsh/Vcom (a) versus d and g2 versus g2 and d (c) KR versus εr and gin in a

DFIG .................................................................................................................. 178

Chapter 7

Fig.7. 1: a DFIG with a four-quadrant AC-Dc-AC converter connected to the

rotor windings .................................................................................................... 184

Fig.7. 2: (a) three phase converter (b) common mode voltage generation ........ 185

Fig.7. 3: (a) Capacitance coupling in a doubly fed induction machine and (b) a

view of DFIG with different capacitive couplings ............................................ 187

Fig.7. 4: a DFIG with a back to back inverter ................................................... 188

Fig.7. 5: A high frequency model of a doubly fed induction generator ............ 188

Fig.7. 6:(a) a typical common mode voltage waveforms and resultant shaft

voltage (b) shaft voltage generated by each rotor and stator side converters .... 189

Fig.7. 7: equivalent system of a DFIG system [9] ............................................. 190

Fig.7. 8: a typical common mode voltage waveforms and zero shaft voltage .. 192

Fig.7. 9: a new back-to-back inverters topology with a bidirectional buck

converter and a DFIG ........................................................................................ 193

Chapter 8

Fig.8. 1: Capacitance coupling in an induction motor and a view of stator slot 197

Fig.8. 2: High frequency model of an induction motor ..................................... 198

Fig.8. 3: (a) General structure of ball bearings and shaft and outer and inner race

of an AC machine (b) a view of ball, outer and inner races and capacitive

couplings (c) simple model of ball bearing ....................................................... 198

Fig.8. 4: Possible discharge current paths in the symmetric case ...................... 199

Fig.8. 5: Asymmetric (a) ball positions (b) shaft position ................................. 200

Fig.8. 6: (a) Asymmetric ball positions (b) upper side ball (c) lower side ball . 202

Fig.8. 7: Discharge current paths for asymmetric ball positions ....................... 202

Fig.8. 8: Capacitive coupling terms between upper and lower balls and races for

an asymmetric shaft position ............................................................................. 203

Fig.8. 9: Probable discharge current paths for an asymmetric shaft position .... 203

XVII

List of Tables

Chapter 1

Table.1. 1: switching states, output leg voltage of three- phase inverter .............. 7

Table.1. 2: Switching states, common mode voltages .......................................... 8

Table.1. 3: Capacitive coupling terms and electric fields in an asymmetrical ball

position ................................................................................................................ 26

Table.1. 4: Capacitive coupling terms and electric fields in an asymmetric shaft

position ................................................................................................................ 27

Table.1. 5: Different design parameters of an AC motor .................................... 30

Table.1. 6: Different design parameters for proposed IG structure .................... 39

Table.1. 7: design parameters for end-winding simulations ............................... 40

Table.1. 8: Different design parameters for test setups ....................................... 43

Table.1. 9: Simulation results with and without end-winding (pF) .................... 45

Table.1. 10: Comparison between the simulation and test results ...................... 47

Table.1. 11: Switching states for a three-level inverter ...................................... 55

Table.1. 12: Different switching states and shaft voltage of a DFIG .................. 64

Chapter 2

Table.2. 1:switching states, output leg voltage and common mode voltage of

three phase inverter ............................................................................................. 79

Table.2. 2: Different capacitive couplings for r= 1000mm ................................. 82

Table.2. 3:Capacitive coupling terms in different ball position .......................... 83

Table.2. 4: Different switching states and shaft voltage ..................................... 94

Chapter 3

Table.3. 1: different design parameters for proposed IG structure ................... 108

Table.3. 2: Different design parameters of a single slot for .............................. 110

Table.3. 3: Capacitive coupling terms in different ball position ....................... 111

Table.3. 4: Simulation results with and without end-winding (pF) .................. 112

Table.3. 5: Comparison between the simulation and test results ...................... 114

Chapter 4

Table.4. 1: Different design factors and capacitive couplings in a stator slot .. 125

Table.4. 2: Different design parameters for proposed IG structure .................. 127

Table.4. 3: design parameters for end-winding simulations ............................. 131

XVIII

Table.4. 4: Design factors for a Range of Parameters in end-winding analysis 134

Table.4. 5: A range of design parameters to analyse capacitive couplings ....... 135

Table.4. 6: Different simulation parameters in Fig.4.11 ................................... 136

Table.4. 7: Different simulation parameters in Fig.4.13 ................................... 139

Table.4. 8: Different design parameters for test setups ..................................... 143

Chapter 5

Table.5. 1: switching states, output leg voltage of three-phase inverter ........... 153

Chapter 6

Table.6. 1: Switching states, leg and common mode voltages .......................... 171

Table.6. 2: switching states for a three-level inverter ........................................ 174

Chapter 7

Table.7. 1: Switching states, output leg voltage and common mode voltage of

three phase inverter ............................................................................................ 186

Table.7. 2: Different switching states and resultant common mode voltage [9] 191

Table.7. 3: Different switching states and shaft voltage .................................... 192

Chapter 8

Table.8. 1: Capacitive coupling terms, voltage and electric fields in the

symmetric case .................................................................................................. 199

Table.8. 2: Capacitive coupling terms and electric fields in an asymmetrical ball

position .............................................................................................................. 201

Table.8. 3: Capacitive coupling terms and electric fields in oil thickness of 0.001

mm ..................................................................................................................... 201

Table.8. 4: Capacitive coupling terms and electric fields in an asymmetric shaft

position .............................................................................................................. 202

XIX

Abstract

AC motors are largely used in a wide range of modern systems, from household

appliances to automated industry applications such as: ventilations systems, fans,

pumps, conveyors and machine tool drives. Inverters are widely used in

industrial and commercial applications due to the growing need for speed control

in ASD systems. Fast switching transients and the common mode voltage, in

interaction with parasitic capacitive couplings, may cause many unwanted

problems in the ASD applications. These include shaft voltage and leakage

currents.

One of the inherent characteristics of Pulse Width Modulation (PWM)

techniques is the generation of the common mode voltage, which is defined as

the voltage between the electrical neutral of the inverter output and the ground.

Shaft voltage can cause bearing currents when it exceeds the amount of

breakdown voltage level of the thin lubricant film between the inner and outer

rings of the bearing. This phenomenon is the main reason for early bearing

failures.

A rapid development in power switches technology has lead to a drastic

decrement of switching rise and fall times. Because there is considerable

capacitance between the stator windings and the frame, there can be a significant

capacitive current (ground current escaping to earth through stray capacitors

inside a motor) if the common mode voltage has high frequency components.

This current leads to noises and Electromagnetic Interferences (EMI) issues in

motor drive systems.

These problems have been dealt with using a variety of methods which have

been reported in the literature. However, cost and maintenance issues have

prevented these methods from being widely accepted. Extra cost or rating of the

inverter switches is usually the price to pay for such approaches. Thus, the

XX

determination of cost-effective techniques for shaft and common mode voltage

reduction in ASD systems, with the focus on the first step of the design process,

is the targeted scope of this thesis. An introduction to this research – including a

description of the research problem, the literature review and an account of the

research progress linking the research papers – is presented in Chapter 1.

Electrical power generation from renewable energy sources, such as wind energy

systems, has become a crucial issue because of environmental problems and a

predicted future shortage of traditional energy sources. Thus, Chapter 2 focuses

on the shaft voltage analysis of stator-fed induction generators (IG) and Doubly

Fed Induction Generators DFIGs in wind turbine applications. This shaft voltage

analysis includes: topologies, high frequency modelling, calculation and

mitigation techniques. A back-to-back AC-DC-AC converter is investigated in

terms of shaft voltage generation in a DFIG. Different topologies of LC filter

placement are analysed in an effort to eliminate the shaft voltage.

Different capacitive couplings exist in the motor/generator structure and any

change in design parameters affects the capacitive couplings. Thus, an

appropriate design for AC motors should lead to the smallest possible shaft

voltage. Calculation of the shaft voltage based on different capacitive couplings,

and an investigation of the effects of different design parameters are discussed in

Chapter 3. This is achieved through 2-D and 3-D finite element simulation and

experimental analysis.

End-winding parameters of the motor are also effective factors in the calculation

of the shaft voltage and have not been taken into account in previous reported

studies. Calculation of the end-winding capacitances is rather complex because

of the diversity of end winding shapes and the complexity of their geometry. A

comprehensive analysis of these capacitances has been carried out with 3-D

finite element simulations and experimental studies to determine their effective

XXI

design parameters. These are documented in Chapter 4. Results of this analysis

show that, by choosing appropriate design parameters, it is possible to decrease

the shaft voltage and resultant bearing current in the primary stage of

generator/motor design without using any additional active and passive filter-

based techniques.

The common mode voltage is defined by a switching pattern and, by using the

appropriate pattern; the common mode voltage level can be controlled.

Therefore, any PWM pattern which eliminates or minimizes the common mode

voltage will be an effective shaft voltage reduction technique. Thus, common

mode voltage reduction of a three-phase AC motor supplied with a single-phase

diode rectifier is the focus of Chapter 5. The proposed strategy is mainly based

on proper utilization of the zero vectors.

Multilevel inverters are also used in ASD systems which have more voltage

levels and switching states, and can provide more possibilities to reduce common

mode voltage. A description of common mode voltage of multilevel inverters is

investigated in Chapter 6.

Chapter 7 investigates the elimination techniques of the shaft voltage in a DFIG

based on the methods presented in the literature by the use of simulation results.

However, it could be shown that every solution to reduce the shaft voltage in

DFIG systems has its own characteristics, and these have to be taken into

account in determining the most effective strategy.

Calculation of the capacitive coupling and electric fields between the outer and

inner races and the balls at different motor speeds in symmetrical and

asymmetrical shaft and balls positions is discussed in Chapter 8. The analysis is

carried out using finite element simulations to determine the conditions which

will increase the probability of high rates of bearing failure due to current

discharges through the balls and races.

XXII

Keywords

AC generators

AC motors

Adjustable speed drives (ASD)

Back-to-back inverters

Ball bearing

Bearing currents

Bearing failure

Capacitive couplings

Common mode voltage

Design parameters

Diode rectifiers

Discharge current

Doubly fed induction generator (DFIG)

Electromagnetic interferences (EMI)

End-winding

High Frequency modelling

Filters

Finite element simulations

Induction generators (IG)

Insulation

Leakage current

Multi-level converter

Power factor correction (PFC)

Pulse width modulation (PWM)

Rotor

Shaft voltage

Space vector modulation

Stator slot

Voltage source inverter (VSI)

Winding

Wind turbine generators

XXIII

Contributions

Ball bearing failure analysis

Effective Design Parameters on the Shaft Voltage of AC Drive

Systems

Investigation on design parameters of the motors to reduce shaft

voltage in first step of the design process

Investigation on the effects of the end-winding parameters on the

shaft voltage and precise calculation of the shaft voltage

High frequency modelling of the AC motors

Common mode voltage reduction techniques with proper

PWM strategies

Common mode voltage reduction in three-phase ASD system

supplied with a single-phase diode rectifier

Multi-level inverter topology and reduction of common mode voltage

Shaft voltage studies in induction generators used in wind

turbine systems

High frequency modelling of a doubly fed induction generator

Analysis of the LC filter placements in a wind turbine system with

the back-to-back inverter topology

A PWM technique to reduce the common mode voltage with a back-

to-back inverter and a bidirectional buck converter

XXIV

List of Publications

The Queensland University of Technology (QUT) allows the presentation of a

thesis for the Degree of Doctor of Philosophy in the format of published or

submitted papers, where such papers have been published, accepted or submitted

during the period of candidature. This thesis is composed of eleven

published/submitted papers, of which eight have been published and three are

under review. Note that due to overlap of the paper contents, seven papers have

been selected for the thesis as seven chapters.

Published Peer Reviewed Journal:

1. Jafar Adabi, Firuz Zare, Arindam Ghosh, Robert D. Lorenz,

“Calculations of Capacitive Couplings in Induction Generators to

Analyze Shaft Voltage”, accepted for publication, IET Transaction on

Power Electronics, 2009

2. Jafar Adabi, Firuz Zare, “Investigation of Shaft Voltage in with

Induction Generators” IEEJ Transactions on Electrical and Electronic

Engineering, IA, Vol.129, No.11, 2009

Peer Reviewed Journal under Review:

3. Jafar Adabi, Firuz Zare, Arindam Ghosh, Robert D. Lorenz, “Analysis

of the Effects of End-Winding Parameters on the Shaft Voltage of AC

Generators”, Submitted to IEEE Transaction on Power Electronics, 2009.

4. Firuz Zare, Jafar Adabi, Alireza Nami, Arindam Ghosh, “Effects of PFC

on Common Mode Voltage of a Motor Drive System Supplied With a

Single-phase Diode Rectifier” Submitted to IEEJ Transactions on

Electrical and Electronic Engineering, 2010

XXV

Published Peer Reviewed International Conference Papers

5. Jafar Adabi, Firuz Zare, Arindam Ghosh, Robert D. Lorenz, “Analysis

of shaft voltage in a doubly-fed induction generator”, Renewable energy

and power quality journal, No.7, April 2009 (This paper has been

presented at ICREPQ’09, Valencia, Spain, April 2009 and selected

papers published in the RE&PQ online journal available at:

http://www.icrepq.com/rev-papers-09.htm )

6. Jafar Adabi, Firuz Zare “Analysis, calculation and reduction of shaft

voltage in induction generators”, Renewable energy and power quality

journal, No.7, April 2009 (This paper has been presented at ICREPQ’09,

Valencia, Spain, April 2009 and selected papers published in the RE&PQ

online journal available at: http://www.icrepq.com/rev-papers-09.htm )

7. Jafar Adabi, Firuz Zare , Arindam Ghosh, Arindam Ghosh, “End-

winding Effect on Shaft Voltage in AC Generators ” EPE’09, Barcelona,

Spain, September 2009

8. Jafar Adabi, Firuz Zare , Arindam Ghosh, “Different Approaches to

Reduce Shaft Voltage in AC Generators” EPE’09, Barcelona, Spain,

September 2009

9. Jafar Adabi, Firuz Zare, Gerard Ledwich, Arindam Ghosh, Robert D.

Lorenz, “Bearing Damage Analysis by Calculation of Capacitive

Couplings between Inner and Outer Races and Balls Bearing”, EPE-

PEMC 2008, Poznan, Poland

10. Jafar Adabi, Firuz Zare, Gerard Ledwich, Arindam Ghosh, “Leakage

Current and Common Mode Voltage Issues in Modern AC Drive

Systems”, AUPEC 2007, Perth, Dec 2007

11. Firuz Zare, Jafar Adabi, Alireza Nami, Arindam Ghosh, “Shaft Voltage

Analysis of a Motor Drive System Supplied With a Single-phase Diode

Rectifier” Submitted to IEEE EPE-PEMC 2010

XXVI

List of chapters according to publications and contributions

Remediation Strategies of Shaft and Common-mode voltages in Adjustable Speed Drive Systems

Literature Review“Stage two, confirmation and final thesis”

Ball bearing failure analysis

Research Problem #1 Shaft voltage attenuation in the early stage of the motor design

Research Problem #2 Common mode voltage attenuation with a PWM strategy

shaft voltage reduction in first step of the motor design process

“Calculations of Capacitive Couplings in Induction Generators to Analyze Shaft Voltage”

IET Trans. on Power Electronics, 2009, In Press

Investigation of end-winding effects on shaft voltage

“Analysis of the Effects of End-Winding Parameters on the Shaft Voltage of AC Generators”Submitted at IEEE Trans. on Power

Electronics, 2010

“Bearing Damage Analysis by Calculation of Capacitive Couplings between Inner and Outer Races and Balls Bearing”EPE-PEMC September 2008

Shaft voltage in wind generators

“Analysis of shaft voltage in a doubly-fed induction generator”,REPQ journal, No.7, April 2009

Modelling of DFIG and a PWM technique to reduce the shaft voltage

“Investigation of Shaft Voltage in with Induction Generators”IEEJ Transactions on Electrical and Electronic Engineering, IA, Vol.129, No.11, 2009

Common mode voltage reduction in multi-level inverter topology

“Analysis of shaft voltage in a doubly-fed induction generator”,REPQ journal, No.7, April 2009

Shaft voltage reduction of a three-phase motor with a single phase PFC

“Effects of PFC on Common Mode Voltage of a Motor Drive System Supplied With a Single-phase Diode Rectifier” Submitted to IEEJ Transactions on Electrical and Electronic Eng. 2010

Chapter 8:Chapter 3:

Chapter 4:Chapter 2: Chapter 5:

Chapter 6:Chapter 7:

XXVII

Scholarship and grants

Fee waiver and living allowances scholarship award of an ARC

Discovery award Funded by the Australian Research Council at

Queensland University of Technology for PhD degree for 3 years 2007-

2010

Travel grant from Australian Universities Power Engineering Conference

for attendance at the AUPEC 2007, Perth, WA

QUT grant –in-aid for attendance AUPEC07 conference in Perth, 2007

QUT grant –in-aid for attendance ICREPQ09 conference in Valencia,

Spain, 2009

XXVIII

Statement of Original Authorship

“The work contained in this thesis has not been previously submitted to meet

requirements for an award at this or any other higher education institution. To

the best of my knowledge and belief, the thesis contains no material previously

published or written by another person except where due reference is made.”

Signature Date

1

Chapter 1

Introduction

2

1.1 . Descr ipt ion of the Research Problem

Many industrial applications – such as large paper machines, pumps, fans,

compressors and robots – need adjustable speed capability. ASD systems are

utilized to adjust the speed of the AC motors used in these applications. The

main concept of these systems is the employment of power electronics and

control modules to achieve an AC variable frequency voltage. To adjust the

frequency and the voltage for speed control purposes, PWM inverters have been

used in ASD systems. A DC-AC converter turns the DC-link voltage on and off

with a PWM control strategy to supply an AC motor. The magnitude and

frequency of generated pulse shape voltage can be adjusted to attain the variable

speed.

As an inherent characteristic of a PWM strategy, a voltage between neutral point

and the ground is generated, and is known as ‘a common mode voltage’. This

voltage is a very important factor in the high frequency modelling of a motor and

is a potential origin of the problems in high switching frequencies. Its reduction

techniques play a main role in attenuation of high frequency related problems

with the AC motor drive systems.

There are different parasitic capacitive couplings between the objects of the ASD

system and the motor structure. These capacitances are very small and can be

neglected in the low frequency analysis of motor drive systems. However, as the

switching frequency of a converter is increased due to device improvements, the

parasitic capacitive coupling becomes a dominant side effect. In higher switching

frequencies, these parasitic elements are a proper path for the high frequency

currents to flow. The common mode voltage is also a major cause of the shaft

voltage in interaction with the common mode voltage.

The development of strategies for the reduction of the shaft voltage and leakage

currents is the general aim of this thesis. Major research objectives in this

development include: exploration of the capacitances between different objects

of the motor and the common mode voltage reduction. These considerations lead

to two specific research problems:

Problem #1: Shaft voltage attenuation in the early stage of the motor design

Shaft voltage on an AC motor is known to be influenced by the capacitive

couplings in motor structure. This issue is related to design parameters. Any

3

change in the design factors of the machine which is effective in changing the

parasitic capacitances is an effective solution to reduction of the shaft voltage at

the first stage of the design process. To investigate this issue, the effects of

different design parameters of an AC motor have been considered in terms of

finite element simulations and experimental results. A mathematical approach to

calculating the shaft voltage based on different design parameter is proposed.

Problem #2: Common mode voltage attenuation with a PWM strategy

Another solution to reduce the shaft voltage and leakage current is reduction of

the common mode voltage with an appropriate PWM strategy. As later analysis

shows, the zero voltage vectors in a switching pattern create the maximum

common mode voltage level. Removing zero vectors requires adding another

active vector in order to have a constant switching frequency, and this leads to

increment of the load current harmonics. In the inverter system connected to a

single-phase diode rectifier, there are some choices which make it possible to

minimize the common mode voltage, while keeping the zero vectors in the

switching sequences. The other topology of concern used in ASD systems is the

multilevel inverters which have more choices in switching states to remove the

common mode voltage. Any PWM pattern or pulse position technique which

leads to reduction of the common mode voltage is a low-cost attenuation strategy

for the high frequency related issues in motor drive applications.

As mentioned above, solutions to reduce shaft voltage and leakage current

problems are targeted in this research which is based on an exploration of both

the design parameters of the motors and the switching strategies of the

converters. Targeted solutions do not need any additional devices (active or

passive filters) and their implementation is not complex.

Induction generators in wind energy applications also experience shaft voltage

and leakage problems. Doubly fed induction generators are common in wind

turbine applications and the amount of shaft voltage in these types of generators

is greater than in the stator fed induction generators. For this reason, a high

frequency common mode model of these generators was needed and an analysis

based on this model has been carried out. Besides changing the design

parameters of the DFIGs, a PWM technique with a bidirectional buck converter

is proposed in the topology of the back-to-back converters to minimize the shaft

voltage in these types of generators.

4

1.2 . Li terature Review

1.2.1. Modern AC motor drive systems

Since the mid-1980s, reliable electric adjustable speed control has been available

for medium-voltage, high-horsepower, induction motors. The comparative

simplicity of an induction rotor allowed lower cost solutions. This, in turn, made

electric drivers practical over a much wider range of sizes and speeds [1].

Insulated Gate Bipolar Transistors (IGBTs) have been applied in variable speed

drives since the early 1990s. These devices changed the characteristics of wave

forms applied to the motors due to the speeds at which they cycle on and off.

Because of the increasing need for speed control, PWM inverters are used in ASD

systems [2]. The concept in the ASD systems is the use of a power electronics

module to convert a constant (50 or 60 Hz) AC voltage source to an AC variable

frequency waveform to achieve an adjustable speed.

A typical power conversion is shown in Fig.1.1.a where a three-phase or single-

phase AC voltage source is connected to a motor. In this case, the AC motor has a

fixed, uncontrolled speed. To adjust the speed, a power electronics circuit changes

the constant frequency AC voltage to an AC variable frequency which is needed

for speed controllability.

Fig.1. 1: An AC motor supplied with single phase or three phased AC source (a) uncontrolled

speed (b) adjustable speed

As shown in Fig.1. 2.a, an AC-DC converter (typically, diode rectifiers) converts

the constant frequency sinusoidal voltage to a variable DC voltage. This voltage

will be filtered via a DC-link capacitor which is normally used as a source for a

DC-AC voltage source inverter. The AC voltage and its rectified waveform are

shown in Fig.1. 2.b. To adjust the frequency and the voltage for speed control

5

purposes, PWM inverters have been used in ASD systems. In a DC-AC

converter, the power switches turn the DC-link voltage on and off with a PWM

control technique to generate a pulse width modulated voltage waveform to

supply an AC motor (see Fig.1. 2.c). Basically, an AC motor acts as a filter

which eliminates the high order harmonics; however, in some cases (especially

in motors with long cables), an LC filter is used to generate a sine-wave voltage

at the motor terminal. This is shown in Fig.1. 2.d.

Fig.1. 2: (a) A power electronic motor drive system with capacitive couplings (b) input AC voltage and its rectified waveform (c) Pulse width modulated voltage (d) Three-phase filtered

voltages

As shown in the above figure, the input voltages of the motor are in PWM pulse

shape (in a system without filter). The main concerns with the modulated voltage

for the motor are the dv/dt and the harmonics of the voltage waveform. The dv/dt

is related to the rise and fall time of a switch and may lead to a stress on the

motor terminal. Based on signal processing techniques, pulse patterns are

generated in such a way that the first fundamental component has a desired

magnitude and frequency. In fact, the DC voltage is alternated between different

levels according to the pulse pattern so as to generate the desired fundamental

voltage component [3]. Note that there are other types of converters and

topologies used in ASD systems, such as multilevel inverters and back-to back

converters which have been investigated in section 1.3.3.

6

1.2.2. Three-phase voltage source inverters: leg, phase, line and

common mode voltage

Fig.1. 3.a shows a DC-AC converter connected to an AC motor. Basically, a

three-phase inverter consists of a dc-link and three pairs of switching

components. Different switches turn on and off to generate an AC voltage in

output. Three upper and lower devices will be switched complementary [4]. The

six-switch combination of this inverter has eight (=23) permitted switching

vectors, as shown in Fig.1. 3.b.

(a)

(b)

Fig.1. 3: (a) a three- phase inverter with (b) eight switching states

7

In a three- phase system, (Vao, Vbo, Vco) and (Van, Vbn, Vcn) are the leg voltages

and phase voltages of a three- phase converter, respectively. Vno is the voltage

between neutral point and the ground which is known as ‘common mode

voltage’. Table.1. 1 shows the leg voltages of a three- phase inverter for different

switching vectors based on the configurations of Fig.1. 3.b.

Table.1. 1: switching states, output leg voltage of three- phase inverter

vector S1 S3 S5 Vao Vbo Vco

V1 1 0 0 2

Vdc 2

Vdc 2

Vdc

V2 1 1 0 2

Vdc 2

Vdc 2

Vdc

V3 0 1 0 2

Vdc 2

Vdc 2

Vdc

V4 0 1 1 2

Vdc 2

Vdc 2

Vdc

V5 0 0 1 2

Vdc 2

Vdc 2

Vdc

V6 1 0 1 2

Vdc 2

Vdc 2

Vdc

V7 1 1 1 2

Vdc 2

Vdc 2

Vdc

V0 0 0 0 2

Vdc 2

Vdc 2

Vdc

According to Fig.1. 3, three leg voltages of the converter can be calculated as

follow:

)t(V)t(V)t(V

)t(V)t(V)t(V

)t(V)t(V)t(V

nocnco

nobnbo

noanao

(1-1)

By adding two sides of Eq.1-1:

)t(V3)t(V)t(V)t(V)t(V)t(V)t(V nocnbnancoboao (1-2)

It is obvious that the sum of three- phase voltages is equal to zero

( 0)t(V)t(V)t(V cnbnan ). Therefore, the common mode voltage can be

calculated as:

3

)t(V)t(V)t(V)t(V coboao

no

(1-3)

Switching states of the proposed converter, leg voltages and the resultant

common mode voltage are shown in Table.1. 2.

8

Table.1. 2: Switching states, common mode voltages

Vectors Switching Vcom

V1 100 -Vdc/6

V2 110 +Vdc/6

V3 010 -Vdc/6

V4 011 +Vdc/6

V5 001 -Vdc/6

V6 101 +Vdc/6

V7 111 +Vdc/2

V0 000 -Vdc/2

Suppose that vectors (V0, V1, V2, V7, V2, V1, V0) are employed for the switching

sequence in sector I, according to switching states in Table.1. 1 and the proposed

switching sequence, three leg voltage of the inverter can be shown in Fig.1.4.

Also, common mode voltage is defined by Eq.1-3 and Table.1. 2.

Fig.1.4: Leg voltages and common mode voltage of the switching pattern

It is obvious that the common mode voltage is defined by a switching pattern,

and that by using the appropriate switching pattern, the common mode voltage

level can be controlled. From the above analysis, it is clear that maximum

common mode voltage levels are generated in zero vector switching. These

vectors should be eliminated in switching sequences to reduce the common mode

voltage significantly; however, elimination of the zero switching vector leads to

a variable switching frequency or more current ripple [5-6].

9

1.2.3. High frequency modelling and parasitic elements

As shown in Fig.1. 5, modern power electronic drives consist of a filter, a

rectifier, a dc link capacitor, an inverter and an AC motor. However, as the

switching speeds increased to allow higher carrier frequencies, new concerns

arose over phenomena previously seen only in wave transmission devices such

as antenna and broadcast signal equipment [7-8]. The effects of the high

frequency voltage components introduced by the PWM technique are usually

neglected when the electromechanical performance of the motor is analysed.

Many small capacitive couplings exist in the motor drive systems (which are

related to motor design considerations) and these may be neglected in low

frequency analysis; however, the conditions are completely different in high

frequencies. In higher switching frequencies, a low impedance path is created for

current to flow through these capacitors. On the other hand, the high dv/dt

applied to the motor introduces a non-negligible amount of high frequency

leakage currents which flow through the stray distributed capacitance between

the stator winding and the motor frame. Since the motor frame is usually

connected to the ground by means of the ground circuit, the high frequency

leakage currents are present in the power mains and can cause electromagnetic

interference [9].

Fig.1. 5: A power electronic motor drive system with different capacitive couplings

Assuming no parasitic coupling, an induction motor will only experience the

differential mode voltages and will behave as an ordinary three phase sinusoidal

AC supply, although some differential mode switching harmonic current will

also exist. However, as the switching speeds of a converter are increased due to

device improvements, the parasitic capacitive coupling becomes a dominant side

effect. Two major parasitic coupling paths are found: the stator windings to the

10

stator iron and the stator windings to the rotor iron. It is readily determined that

(roughly) a capacitance of 5-10 nF exists between a stator phase winding to the

stator case in a typical 1-50 kW motor over a frequency range from 1-500 kHz

[5-6][10]. Fig.1. 6 shows the structure of an AC motor where the parasitic

capacitive couplings exist between: the stator winding and rotor (Csr), the stator

winding and stator frame (Csf), the rotor and stator frames (Crf) and the ball

bearing capacitance (Cb).

Fig.1. 6: (a) Structure of an AC motor with (b) different parasitic capacitive couplings

As shown in Fig.1. 7, there are some balls between outer and inner races with

lubricated grease between the balls and the races. The bearing model depends on

the geometrical configuration of the bearing, load, speed, temperature, and

characteristics of the lubricant [11]. Fig.1. 7 shows a general structure of a ball

bearing and shaft in an AC machine. There are capacitive couplings between the

outer and inner races. During operation, the distances between the balls and races

may be changed and will vary the capacitance values and resultant electric field

between the races and balls. Due to this fact, this capacitance has a nonlinear

value. Lubricated grease in the ball bearing cannot withstand a high voltage and

a short circuit through the lubricated grease may occur; thus, this phenomenon

can be modelled as a switch.

11

Fig.1. 7: Ball bearings: structures, capacitive couplings and simple model

As mentioned in previous sections, interaction of the AC motor characteristics

and the power electronics converters creates various unwanted issues such as

bearing currents and leakage currents. A classical model of an electric motor is

used for steady state and dynamic analysis at fundamental frequency (up to few

hundred hertz); however, it cannot be used for shaft voltage and EMI analysis (in

kHz or MHz range) due to the existence of stray capacitances between windings,

rotor and stator. A simple single line capacitive model of the AC motor which is

used for different common mode analysis is shown in Fig.1. 8.a. Note that this

model is only valid for the motors with short cable connections. For the motors

with long cables, the cable model needs to be analysed as well.

(a)

Csr

Rotor

Stator frame

winding

Vcom

+

Vshaft

-

Crf

(b)

Fig.1. 8: (a) a simple common mode model of the AC motor (b) models for shaft voltage

generation and the leakage current

Based on Fig.1. 8.b, a fraction of the common mode voltage is induced on the

shaft (rotor) through the capacitance between winding and the rotor. Also, a

leakage current flows through the capacitive couplings between the rotor and

stator frame [12-13].

12

1.2.4. High frequency related issues in ASD system

The common mode voltage and fast switching transients (high dv/dt), in

interaction with parasitic capacitive couplings, may cause shaft voltage (which

leads to bearing currents) and leakage currents (which lead to noises and EMI) in

an AC motor system. As shown in Fig.1. 8.b, the common mode voltage is

divided on the capacitive couplings between winding, rotor and stator and a

voltage is induced across the shaft and the ground. Also, the capacitive coupling

between winding and stator frame is an effective path for the leakage current.

Therefore, the leakage current is created by a high voltage stress during

switching time and capacitive coupling in an AC motor.

Parasitic capacitances in the motor also provide low-impedance paths for high-

frequency common mode currents to flow. When an AC motor is driven by a

PWM inverter, the output voltage potential of the inverter changes at a very high

frequency according to the turning on and off of power switching devices

(transistors, FETs, IGBTs, etc). The high rates of rise and fall of the line-line

voltage pulses in the range of a few hundred nanoseconds give rise to ground

currents due to cable capacitance to ground and motor winding capacitance to

ground.

It can be concluded that high dv/dt and common mode voltage generated by a

PWM inverter in high frequency applications can cause some unwanted

problems [14-31] such as:

Grounding current escaping to earth through stray capacitors inside a motor

Shaft voltage and resultant bearing currents

Conductive and radiated noises

Motor terminal over voltages.

1.2.4.1. Leakage current

As shown in Fig.1. 9, there is considerable capacitance between the stator

windings and the frame, and because of this, there can be a significant capacitive

current (ground current escaping to earth through stray capacitors inside a motor)

if the common mode voltage has high frequency components. This current leads

to noises and EMI issues in motor systems because of the spikes in the currents.

The leakage current usually consists of spike pulses and if the iron core of the

motor is not grounded, it might give electrical shocks on contact. Also, if not

13

properly mitigated, high frequency ground currents can also interfere with the

power system ground and affect other components of the power system [14-17].

Fig.1. 9 shows a simple example of effects of high dv/dt and resultant leakage

current. The leakage current is created by a high voltage stress during switching

time via a capacitive coupling between winding and stator.

Fig.1. 9: A typical example of high dv/dt and resultant leakage current

1.2.4.2. Shaft voltage and bearing currents

Common mode voltage creates shaft voltage through electrostatic couplings

between a rotor and stator windings (Crs), and the rotor and a frame (Crf). Based

on a simple high frequency model of the motor shown in Fig.1. 8, the common

mode voltage is divided between two mentioned capacitive couplings and, by a

simple voltage divider calculation, the voltage on the shaft can be calculated as:

comrfrsb

rsshaft V

CCC

CV

(1-4)

Shaft voltage on an AC motor is known to be influenced by various factors such

as: design of the motor, the capacitive couplings in motor structure, the

configuration of the main supply, voltage transient on the motor terminal and

PWM pattern. The effectiveness of different design parameters will be

investigated in the following sections.

Shaft voltage can cause bearing currents when the shaft voltage exceeds a

breakdown voltage level of the bearing grease. Fig.1. 10 shows damage on the

bearing. Shaft currents can cause damage in rotating machinery such as: frosting,

spark tracks at the surface of balls and races, pitting, and welding [18].

14

Fig.1. 10: Damages on the bearing (source: ABB technical guide)

The bearing current is related to a capacitive shaft voltage resulting from a

common mode voltage between parasitic capacitances in the motor. If capacitive

shaft voltage exceeds a critical bearing threshold voltage required to break down

the insulating grease thin film, the charge accumulated in a rotor assembly is

then unloaded through the bearing in the form of a discharging current. Different

types of bearing currents are discussed in the literature, and these can be

classified as follows:

Small capacitive currents: Here, the high dv/dt interacts with the

capacitances between stator laminations, windings, rotor and the bearings to

generate a capacitive current flow in the range of 5–200 mA .These currents

are so small that they are usually considered to be harmless [19-20].

Capacitive discharge current: This is related to a capacitive shaft voltage

resulting from a high frequency common mode voltage between parasitic

capacitances in the motor. If capacitive shaft voltage exceeds a critical

bearing threshold voltage required to break down the insulating grease thin

film, the charge accumulated in a rotor assembly is then unloaded through

the bearing in the form of a discharging current. This current is also known

as electrostatic discharge machining (EDM) current [19-20].

The following (two) types of bearing currents are related to the interaction of

common mode voltage with high dv/dt and the capacitance between stator

winding and motor frame.

Shaft grounding current: The common mode voltage can also cause an

increase in the stator frame voltage if the grounding is not satisfactory. The

increase in motor frame voltage is seen from the bearings. If this voltage

exceeds the breakdown voltage of thin oil film, part of the current may flow

through bearings [19-23].

15

High frequency circulating bearing currents: High frequency common

mode currents form a circular time varying magnetic flux around the motor

shaft. This flux is caused by a net asymmetry of capacitive current leaking

from the winding into the stator frame along the stator circumference. This

flux induces a voltage which circulates the stator, rotor, and bearings. If the

proposed voltage exceeds the breakdown voltage of thin oil film, a circular

high frequency current will be formed in the motor bearings. This kind of

shaft voltage occurs in large motors [19-23].

Based on the above issues, all motors have some level of shaft voltage and

resulting bearing current. Two key elements are: Which voltage conditions will

break down the insulating grease film, and how will the resulting current

densities affect bearing life? The mechanisms that cause these voltages and the

ability of bearings to withstand the resulting currents are mentioned in [24-26].

As demonstrated in [27-31] , small inverter-fed AC motors (up to a typical 20

kW at 1500/min) are likely to suffer from discharge bearing currents, while

larger motors are likely to be subject to high-frequency circulating bearing

currents. When comparing motors operated at the same voltage level, the

resulting bearing current density is high for very small and very large motors.

Smaller values occur in-between these two extremes, with medium size motors

in the range (10... 100) kW. Therefore, electric bearing insulation is useful for

larger motors to interrupt the HF circulating bearing current path. Small motors,

on the other hand, need either rotor shielding, common mode voltage filters, or

hybrid bearings.

1.2.4.3. Conducted and radiated EMI emissions

Conducted and radiated Electromagnetic interference emissions is a major

problem with recent motor drives that produces undesirable effects on electronic

devices such as AM radio receivers, medical equipments, communication

systems and cause malfunctions and non-operations in control systems. A review

on noise sources in electric machines and their mitigation techniques has

proposed in [32]. [33] Provides a common understanding of the EMI issues such

as generation of EMI, EMI modelling, mitigation of EMI, EMI coupling

techniques and EMI standards and test method.

16

A comparison between EMI sources of a sinusoidal PWM hard and soft

switching techniques were carried out in [34]. [35] Focuses on the review of

conducted EMI modelling and filter design methods for inverter fed motor drive

systems. Time domain and frequency domain models of differential and common

mode conducted electromagnetic emission prediction for an induction motor

drive system are presented in [36-37]. A comparative analysis between the

standard PWM and a chaos-based PWM for DC/AC converters for electric

drives is investigated in [38]. [39] Proposed a procedure to diagnosis the

induction motor to predict the EMI. It is based on determining the resonance

peaks of high frequency measurements. It can also, a filtering scheme slowing

the removal of EMI from the data when the high frequency data affected by

environmental EMI. In [40-41] inverter switching related noises and switching

characterization of the power switch and its body diode reverse recovery

characterization are evaluated for circuit modelling through simulation and

measurements. The parasitic components and common mode path are identified

and measured with the time-domain reflectometry method. A frequency domain

approach to the prediction of differential mode (DM) conducted electromagnetic

interference for a three-phase inverter is described in [42]. A mathematical

model for the prediction of conducted EMI based on analytical disturbance-

sources and propagation paths to estimate the common mode and differential

mode is pointed out in [43].

1.2.5. Remediation strategies of the common mode problems of the

ASD systems

There are plenty of techniques which have been presented to eliminate the shaft

voltage (and its resultant bearing current) and the common mode currents (to

reduce the reliability and electromagnetic interferences). The following listed

techniques are based on the PWM techniques (to remove the common mode

voltages) or the use of filters and also applying additional devices to remove the

problematic issues in the ASD system. Note that each technique has its own

advantages and disadvantages which are not in the focus of

this literature review.

17

1.2.5.1. Bearing current reduction methods

Following methods are suggested in literature to mitigate bearing currents and

shaft voltage:

Improve high frequency grounding connection from the motor to the drive

and from the motor to the driven equipment [44]

Install a grounded metallic foil tape to cover the stator slot and the end turns

of the winding [18] [20] [43-44]

Using a conductive grease to provide a lower impedance path through the

bearing lubricant preventing excessive voltage build-up on the shaft [13] [18-

20][43-45]

Insulate the both motor and load bearing [13] [18-20][43-45]

Establishing a low resistance current path to ground bypassing the bearings

[13] [18-20][43-45]

Adding a common mode filter [20] [31][43-44]

Changing the cable to the proper installation type [20] [31] [43-44]

Use a potential transformer or coupling L-C filter [13] [20][43-44]

Inserting a Faraday shield in to the air gap of a motor using a conductive

copper surface to collect and attenuate the electrostatically coupled voltage to

ground [13] [20][43-45].

Using R-L-C output filters or output line reactors [20][43-45]

Reduce drive input voltages [18-20][43-45]

Hybrid ceramic bearing [20][43-45]

Bearing insulation sleeve [20][43-45]

Using shielded cable [20][43-44]

Common mode chokes between the PWM inverter and the induction motor

[43-44]

Lowering of PWM frequency [13] [18] [26][45-46]

Use of an embedded circular comb-like coil in the stator slots to provide

capacitance between the stator winding and the grounded coil and at the

same time capacitance between the rotor shaft and the grounded coil . It

18

provides a low impedance path for the high frequency common mode noise.

Then, the peak voltage over the bearing capacitance will be reduced [47].

Eliminate or reduce motor neutral voltage by redesigning common mode

circuitry [48] 1.2.5.2. Leakage current mitigation techniques

1.2.5.2.1. PWM-based

Common mode currents must be eliminated in order to increase reliability and

electromagnetic compatibility of electric drives. Several methods to mitigate

common mode current are suggested in literature based on using active and

passive circuit in inverter output. Several papers are presented PWM strategies to

attenuate common mode voltage generating by zero switching vectors. By using

of a suitable switching scheme, it is possible to control the fluctuation of

common mode voltage in order to reduce the common mode current.

Space vector PWM strategy without zero vectors (states) is used in [49-51]

which allows open loop voltage control and mitigation of common mode voltage

by PWM modulation when the load is capacitively coupled to ground. Random

PWM technique distributes the spectrum contents of load current without

affecting the fundamental component and it may reduce the acoustic noise and

mechanical vibration and electromagnetic interference of an inverter-fed

induction motor drive when the amplitude of harmonics around side bands is

decreased. [51] Involves switching patterns of random SVM techniques for

common mode voltage mitigation.

Approaches to eliminate common mode voltages of multilevel inverters are

presented in [52-55]. Two sinusoidal and space vector PWM techniques are

discussed and applied to a three-level inverter.

1.2.5.2.2. Active and Passive EMI Filters

Active EMI filters based on current injection is a proper solution to cancel the

common mode high frequency currents. Fig.1. 11 shows a block diagram of an

active EMI filter and common mode transducer. A survey of output filter

topologies to minimize impact of PWM inverter fed induction motor is proposed

in [56]. An active common mode noise canceller is presented in [57-58].

Proposed method is composed of an emitter follower using complementary

transistors and a common mode transformer. An improved inverter output filter

19

configuration to reduce both differential mode and common mode dv/dt at motor

terminals with one filter topology is suggested in [59] which consist of a three-

phase RLC network. The filter star point is electrically connected to the dc-link

midpoint. A passive common mode current attenuation technique for use with

PWM drives is presented in [60].

Fig.1. 11: An active EMI filter

A novel passive filter installed at PWM inverter output terminals is proposed in

[61-62] with an objective of eliminating the common mode and differential-

mode voltage generated by PWM inverter simultaneously. The proposed filter

consists of three inductors, three capacitors, one resistor and a common mode

transformer. [63] Introduce a new passive filter consists of a common mode

transformer and a conventional RLC filter.

An active filter technique is presented in [64] to mitigate adverse effects of

PWM inverter fed AC drives and reduce the size of EMI filter. Proposed

common mode noise canceller is composed of a push-pull type emitter follower

circuit using two complementary transistors, a common mode transformer, three

impedances for common mode voltage detection, and two dc voltage sources,

three capacitors, inductor, and resistor. Also, passive EMI filter for proposed

drive system tested and designed in [65-68]. Design and analysis of a current

injection type active EMI filter for switching noise of high frequency inverters is

described in [69]. It consists of two complementary transistors as active elements

and a common mode current transformer. In [70] filter designing techniques are

presented and compared with conventional LPF in order to analyse their effect

on reducing EMI emissions.

20

1.2.6. High frequency elements in induction generators

Electrical power generation from renewable energy sources, such as wind energy

systems, has become a crucial point because of environmental problems and a

shortage of traditional energy sources in the near future. Recently, DFIGs have

played a significant role in converting wind energy to electricity [71]. The main

types of wind turbines are presented at [72] which are: (a) a fixed speed wind

turbine with an asynchronous squirrel cage IG directly connected to the grid via

a transformer (b) a variable speed wind turbine with a DFIG and blade pitch

control (c) a variable speed wind turbine using a permanent magnet synchronous

generator that is connected to the grid through a full-scale frequency converter.

A comparison between the characteristics of the above mentioned wind turbines

and their mathematical models have been investigated in [73]. To achieve a

variable speed constant frequency system, an IG is considered attractive due to

its flexible rotor speed characteristics with respect to the constant stator

frequency. One solution to expand the speed range and reduce the slip

power losses is to doubly excite the stator and rotor windings. The power

converters in the rotor circuit regenerate the majority of the slip power [74]. In a

DFIG, the stator is directly connected to the AC mains, while the wound rotor is

fed from a back-to-back converter via slip rings to allow the DIFG to operate at a

variety of speeds in order to accommodate changing wind speeds. The slip power

can flow in both directions to the rotor from the supply and from the supply to

the rotor and hence the speed of the machine can be controlled from either the

rotor-side or stator-side converter in both super and sub-synchronous speed

ranges [75].

The main issues regarding the operation of power converters used in IG and

DFIG structures are high dv/dt (fast switching transients) and common mode

voltage generated by a PWM strategy which can lead to a shaft voltage and

resultant bearing currents, grounding current escaping to earth through stray

capacitors inside a motor, conducted and radiated noises. The analysis are as the

same as mentioned for the motor drive systems. Recently, some techniques are

presented to mitigate shaft voltage and bearing currents in DFIGs. An approach

is used in [76] to constrain the inverter PWM strategy to reduce overall common

mode voltages across the rectifier/inverter system, and thus significantly reduce

bearing discharge currents. A general common mode model of a doubly fed

induction generators is mentioned in [77] to calculate bearing current.

21

1.3 . Account of Research Progress Linking the

Research Papers

This project began with a comprehensive literature review of high frequency

modelling of ASD systems and of the reported problems of AC motors in drive

applications. Based on these studies, it is determined that the main issues affecting

the motor drive systems in high frequency performances are the shaft voltage and

the leakage current. Therefore, the first step in the research process was a revision

of existing remediation strategies for these phenomena, and of their effects on

motor drive applications.

A survey of these strategies and solutions is published as a conference paper

entitled “Leakage Current and Common Mode Voltage Issues in Modern AC

Drive Systems” at AUPEC 2007, Perth, Australia.

Based on the gaps found as a result of this survey, specific research aims were

then targeted. The most significant of these is the necessity of introducing cost-

effective techniques to reduce the shaft voltage and common mode voltage in

modern AC drives. As mentioned in previous sections, the two main concerns in

the generation of the shaft voltage and leakage currents are the common mode

voltage and design factors in AC motors. Design parameters change the capacitive

couplings between the objects of a motor which create a path for the current to

flow. Common mode voltage is known to be a potential origin of both the shaft

voltage and the leakage current. Therefore, the research was focused on the

investigation of these phenomena and on finding appropriate remedial solutions.

Specifically, the following concerns arose out of the preliminary survey of the

research problems.

Bearing damage in modern inverter-fed AC drive systems is more common

than in motors working with 50 or 60 Hz power supply. Analyses are needed

to determine the conditions which will increase the probability of high rates of

bearing failure due to current discharges through the balls and races. The

results can be used as significant knowledge for design engineers to employ

better quality material in the certain positions of the races.

The effectiveness of the design parameters of the AC motor should be

investigated in order to reduce the shaft voltage. Changing different design

parameters can change the capacitive couplings and, consequently, vary the

22

shaft voltage. This analysis necessitates different mathematical calculations

and simulations in a wide range of designs to formulate a principle that

explains the effects of these parameters on the shaft voltage. This formulation

will lead to a cost effective technique for shaft voltage reduction in the early

stage of the design. These considerations and analyses should be undertaken

with respect to the other electromechanical issues involved in machine design.

Any effective PWM technique which can reduce the common mode voltage

will lead to a cost effective solution in shaft voltage reduction. The side effects

of PWM modification (such as current ripple or variable switching frequency)

on the system should also be addressed. Many of these strategies have been

presented in the literature. However, there is still a need for different power

converter topologies in ASD systems such as multilevel inverters and for three

phase motors supplied with a single phase AC source. Solutions to reduce the

common mode voltage in these structures are targeted in this research.

Induction generators (stator fed or doubly fed) in the wind energy conversion

system have been widely utilized. Basically, in these systems, power

converters are used to convert the generated energy to a constant voltage and

frequency which is acceptable for the utility system. Therefore, the same

scenario regarding motor drive systems applies to induction generators. The

lack of analysis of the shaft voltage in doubly-fed induction generators in the

existing literature spawned the idea of investigating the shaft voltage in

different aspects of this application. These concerns are included in the design

consideration, the modelling of these generators, the placement of the LC

filters, and in the PWM techniques for the back-to-back inverter topology.

The research was developed on the basis of these concerns and the results have

been published or submitted in the form of several journal and conference papers.

The following sections discuss the importance of the research and establish the

links between its different components. The significance of the analysis and the

proposed techniques has been validated by 2-D and 3-D Finite Element (FE)

methods by ANSYS [78], circuit simulations by MATLAB and PLECS [79] and

experimental results.

23

Basically, following procedures are needed in an FE study with ANSYS to

achieve a capacitance matrix for a multi-conductor system.

Step1: Starting the analysis, definition of the analysis parameters,

specification of the element type and material properties

At first step of any FE simulation, the type of the simulation with its main

parameters should be mentioned. In ANSYS, different types of simulation studies

with different modelling procedures are defined as elements. The right element

choice is very important in FE modelling of the proposed system. In electrostatic

analysis, all conductors are considered as nodes in the surface but for the other

components such as insulation, air gaps and etc, the material properties should be

defined.

Step 2: Create a solid model

A Computer-Aided Design (CAD) model is needed in the simulation analysis. The

models can be drawn either in the ANSYS environment or other CAD tools. In

this study, 2-D and 3-D models have been made with AutoCAD and SolidWorks

respectively.

Step 3: Mesh the model and create a FE model component

FE analysis uses a complex system of points called nodes which make a grid

called a mesh. Mesh is programmed to define how the system will react to certain

loading conditions. The meshing procedure is related to the complexity of the

CAD model, the desired accuracy of the analysis, element types and lots more.

Details about the meshing styles can be accessed in [80]. In this stage the

conductors are defined by nodes in their surfaces.

Step 4: Defining a Trefftz domain

In combination with the infinite elements for modelling the open domain of a field

problem, Trefftz method may be chosen that utilizes a hybrid finite element. It

allows treatment of complex surface geometry and offers an accurate method for

handling open boundary domains in electrostatics. Different procedures of

applying this method after building a FE model and enclosing it with the air

(Fig.1.12.a) is as follows:

1) Apply Infinite surface flag to exterior surface of FE region (Fig.1.12.b) as an

infinite surface.

24

2) Create Trefftz source nodes between the parts and the air domain exterior. The

conductors are surrounded by Trefftz-domain (or Trefftz-nodes) to obtain the

capacitance matrix of a multi-conductor system (See Fig.1.12.c). Note that the

these nodes have to be created on the surfaces which satisfies the conditions of

2b

a and 1

c

b .

3) Create the Trefftz substructure, superelements and constraint equations

Fig.1.12.d shows a 3-D model of the motor and a view of electrostatic model of a

stator slot with different nodes.

Step 4: Defining a Trefftz domain

In the ANSYS static analysis, there is an option which gives the capacitance

matrix for the multi-conductor system surrounded by Trefftz nodes.

(a) (b)

(c)

(d)

Fig.1. 12: (a) enclosing an FE model with air (b) Flag the exterior faces (c) Trefftz nodes (d) 3-D model of the motor and a view of electrostatic model of a stator slot

25

1.3.1. Ball bearing damage analysis in AC motor drives

Parasitic capacitive coupling creates a path to discharge current in rotors and

bearings. In order to analyse bearing current discharges and their effect on

bearing damage under different conditions, calculation of the capacitive coupling

between the outer and inner races is needed. As shown in Fig.1. 7, there are balls

between outer and inner races with lubricating grease between balls and the

races. During motor operation, the distances between the balls and races may

change the capacitance values between the outer and inner races. Due to

changing of the thickness and spatial distribution of the lubricating grease, this

capacitance does not have a constant value and is known to change with speed

and load. Thus, the resultant electric field between the races and balls varies

with motor speed. The lubricating grease in the ball bearing cannot withstand

high voltages and a short circuit through the lubricated grease can occur.

The objective is to calculate the capacitive coupling and electric fields between

the outer and inner races and the balls at different motor speeds. The analysis is

carried out using finite element simulations to determine the conditions which

will increase the probability of high rates of bearing failure due to current

discharges through the balls and races.

At high speed, balls and shaft positions are considered symmetric and the

distances between the inner race and balls (dBI) and between outer races and balls

(dBO) are assumed to be equal. Also the shaft position is not changed and the

shaft and outer race are concentric. As depicted in Fig.1. 13, if a short circuit

(breakdown) occurs, then a discharge current will be divided into several paths

and the probability of bearing damage is decreased.

Fig.1. 13: Possible discharge current paths in the symmetric case

26

At low speeds, because of gravity, balls and shaft may shift down and the system

(ball positions and shaft) will be asymmetric. In this study, two different

asymmetric cases (asymmetric ball position, asymmetric shaft position) are

analysed and the results are compared with the symmetric case.

A typical case of 15 balls with the diameter of 20 mm, shaft diameter is 80 mm

and three ranges of 1mm, 0.1mm, 0.01mm oil thickness were considered for the

simulation analysis with a 100 volts voltage across the races. The electric fields

between the outer race and balls (dBO) and between the inner race and balls (dBI)

at different motor speeds would be calculated.

As shown in Table.1. 3, several distances are simulated to compare the

capacitive couplings (CBO, CBI) and electric fields (EBO, EBI) for oil thicknesses

of 0.01mm. As shown in Fig.1. 14.a, in the asymmetrical balls case, balls come

down and the region between the upper ball and shaft (see Fig.1. 14.b) and the

lower ball and shaft (see Fig.1. 14.c) are more important than other areas.

Table.1. 3: Capacitive coupling terms and electric fields in an asymmetrical ball position

Oil

Thickness

(mm)

dBO

(mm)

dBI

(mm)

CBO

(nF)

CBI

(nF)

EBO

(V/mm)

EBI

(V/mm)

0.01 0.001 0.009 26.200 6.890 20821.87 8797.57

0.01 0.003 0.007 13.100 7.800 12443.87 8952.63

0.01 0.005 0.005 11.300 9.020 8881.72 11118.28

0.01 0.007 0.003 9.140 11.800 8048.07 14554.51

0.01 0.009 0.001 8.150 18.700 7736.50 30371.47

From the results in Table.1. 3, the electric field is increased when dBI or dBo are

decreased but the electric field between the inner race and upper ball (E) is more

than the electric field between the outer race and lower ball (E') for the same rate

of change in distances (see the bold numbers of Table.1. 3). The capacitive

coupling terms and resultant electric fields for dBI1=dBO2=0.001 mm &

dBI2=dBO1=0.009 mm are shown in Table.1. 3. However dBO2 & dBI1 are equal,

because of different positions of balls and races (which is shown in Fig.1.

14.b&c), capacitive coupling terms and electric fields are different (EBI1 is 50%

more than EBO2).

27

(a) (b) (c)

Fig.1. 14: (a) Asymmetric ball positions and discharge current paths (b) upper side ball (c) lower side ball

Thus, increasing the electric field between inner race and balls at upper side will

create a path to discharge current. In other words, if a short circuit (breakdown)

occurs at these balls, the probability of dividing the discharge current into other

paths will decrease and the upper ball near the inner race (ball 1 in Fig.1. 14.a) is

the highest probability candidate to create a path for discharging current. If the

voltage breakdown occurs, a bearing damage problem could occur at this area

(position A in Fig.1. 14.a). If the damage occurs at this position, the same

problem will happen at the distance between ball and outer race (position A' in

Fig.1. 14.a).

An asymmetry in the shaft position is analysed via simulations. The simulations

are carried out to find the capacitive coupling terms and electric field in the

separation ranges of 0.001mm. In this case, shaft position is shifted down

corresponding to 20%, 40% and 60% grease thickness. Table.1. 4 shows the

capacitive coupling terms, voltage and electric fields with respect to different

variables associated with the balls position assuming the inner and outer

distances in each side are equal.

Table.1. 4: Capacitive coupling terms and electric fields in an asymmetric shaft position

Shift in

Shaft center (mm)

dBO

(mm)

dBI

(mm)

CBO

(nF)

CBI

(nF)

EBO

(V/mm)

EBI

(V/mm)

0.002 0.004 0.004 13.20 9.960 10767.64 14232.36

0.004 0.003 0.003 17.90 10.200 12121.21 21212.12

0.006 0.002 0.002 24.10 11.600 16308.64 33691.36

According to simulation results, electric field between the lower ball (ball 2 in

Fig.1. 15) and the inner race is more than other separations.

28

Fig.1. 15: Capacitances between upper and lower balls and races for an asymmetric shaft

position with probable discharge current path

In other words, if a breakdown occurs in this area, the probability of division of

the discharge current into other paths will decrease and ball 2 is the highest

probability candidate to create a path for the discharge current. In this case, the

distance between ball 1 and the races is more than the distance between ball 2

and races. Thus, capacitance and the resultant electric field in the upper side is

less than in the lower side (E1<E2 as shown in Fig.1. 15). In the lower side,

because of different positions of ball 2 and the races, the electric field is different

while the distance between ball and races are the same (for instance, at

dBI2=dBO2=.002 mm, EBI2 is 40% more than EBO2). As shown in Fig.1. 15, if the

breakdown voltage is exceeded, a bearing damage problem may occur at this

area (position C in Fig.1. 15). If the damage happens at this position, the same

problem will happen at the distance between ball and outer race (position C' in

Fig.1. 15). This may cause multiple bearing damage sites.

The above mentioned analysis has been mentioned in a conference paper at EPE-

PEMC 2008 entitled “Bearing Damage Analysis by Calculation of Capacitive

Couplings between Inner and Outer Races and Balls Bearing” at Poznan,

Poland.

Note that more design parameters have been considered at that paper and the

analysis has been done based on different parameters in chapter 8. As a result of

this research work, the areas of the inner and outer races and also the ball

bearings which are the first candidate of the damage in case of any breakdown in

the shaft and ball asymmetry system have been determined. This analysis should

be mentioned in the design process of the ball bearing and the races. The quality

of the materials for the mentioned areas also would be mentioned.

29

1.3.2. Investigation on design parameters of the motors to reduce shaft

voltage in first step of the design process

In a motor structure, the parasitic capacitive couplings exist between: winding

and rotor (Crs), stator frame and rotor (Crf), stator winding and frame (Csf) and

the ball bearing capacitances. Refer to the previous section; the stator frame and

the rotor form a capacitor (Crf), which results in a divider network such that a

portion of the common mode voltage appears as the shaft voltage (see Fig.1. 8)

on the rotor with respect to the stator frame (or ground).

The calculation of the shaft voltage (Eq.1-4) confirms that the capacitances are

effective in the generation of the voltage on the shaft. The main goal of this

work-which is to find the effect of machine parameters on the shaft voltage-,

uses a model to analyse of this effect. This is based on the lumped capacitances

because the originality of the shaft voltage is based on the electrostatic

phenomena. In this research, a mathematical equation has been developed to

calculate the shaft voltage in induction generators with respect to many design

parameters.

1.3.2.1. Calculation of different capacitances

Fig.1. 16 shows a view of a single stator slot with the main design parameters

mentioned in Table.1. 5.

g1

d-ρ

ρ

Stator Winding

g1

g2

g2

d

ρ/2ρ/2

Rotor

f1 f2Cf2r

Cf2sCf1s

Cf1r

Csr

Fig.1. 16: (a) A stator slot with different design parameters and capacitive couplings in the slot (b) capacitances in area of stator teeth (c) a model for capacitance calculations

30

It is needed to calculate each capacitive coupling in order to estimate the shaft

voltage based on different design parameters. In this case, different capacitances

have been mentioned with and without end-winding effects.

Table.1. 5: Different design parameters of an AC motor

Air gap between rotor and stator g1

Gap between winding and stator g2

Thickness of the winding insulation gin

Length of slot tooth d

Height of the stator slot ρ

Rotor radius r

Rotor length Lr

Permittivity of free space ε0

Permittivity of the insulation εr

Number of slots n

Width of the winding at the top W

Width of the winding at the bottom W′

length of the stator winding hW

Following capacitive couplings can be calculated in the structure of the AC

motors.

The capacitive coupling between rotor and stator (Crs)

By considering the air gap (g1) to be much smaller than the outer diameter of the

rotor, a capacitive coupling between rotor and stator frame in a single stator slot

can be calculated as follows:

1

r0rs g

L)dn

r2(

C

(1-5)

Where r is the rotor radius and g1 is the air gap, Lr is the rotor length. This

capacitance can be multiplied by the number of slots (n) to calculate the total

capacitance.

The capacitive coupling between stator and winding (Csf)

In this case, there are four surfaces which surround the winding. So, Csf can be

calculated as:

top

in

rWr0sf C

g

Lh2WC

(1-6)

Ctop is the capacitance between the upper side of winding and the stator slot

tooth. This capacitance consists of insulation capacitance (Cin,top) and slot wedge

capacitance (Cwedge). Where:

31

2

r2r0wedge

in

r1r0top,in g

LdWC,

g

LdWC

(1-7)

Therefore, Ctop can be calculated as:

2rin1r2

r2r1r0

wedgetop,in

wedgetop,intop gg

LdW

CC

CCC

(1-8)

Based on these calculations, the capacitance between winding and stator frame

is:

r

2rin1r2

2r1r0

in

Wr0sf L

gg

dW

g

h2WC

(1-9)

Where ε0 is the permittivity of free space and εr1, εr2 are the permittivity of the

insulation and the slot wedge material.

The ball bearing capacitances

Calculation of ball bearing capacitances is not an easy task because the

geometrical structure is rather complex. The ball bearing capacitance analysis

has been presented at previous section and further information about the ball

bearing capacitances is available at chapter 3 and chapter 8.

The capacitive coupling between rotor and winding (Csr)

As shown in Fig.1. 16.b, existing capacitive couplings are: the capacitive

coupling between rotor and winding (Csr), the capacitive coupling between rotor

and stator in left and right sides of the slot tooth (Cf1r, Cf2r), and capacitive

coupling between winding and stator in left and right sides of the slot tooth (Cf1s,

Cf2s). Fig.1. 16.c shows a model to calculate the capacitive couplings. In fact, the

electric fields between stator slot teeth on both sides influence the total electric

field between the rotor and stator. Fig.1. 16.c shows a typical electric field in the

proposed system (the voltages applied to upper, lower and besides objects are 50,

100 and 0 volts respectively).

Fig.1. 17: Two vertical surfaces

32

To calculate the side capacitances (Cf1r, Cf2r, Cf1s, Cf2s), the structure of two

surfaces with the voltage difference of V0 and the angle of (here 090 )

needs to be considered. As shown in Fig.1. 17, the small gap between two

surfaces is ρ1 and the length of the surface is ρ2. The capacitance can be

calculated as:

V

dS.E

V

QC 0

(1-10)

Based on [13], the electric field between two surfaces can be calculated by:

a

Va

d

dV1VE

0

0 (1-11)

Considering adzdds in cylindrical coordinates, the capacitive coupling

between two surfaces is:

1

120

0

0

1

12

0

00

0

0

d

0 0

00

Lnt

V

LntV

V

adzdV

C

2

1 (1-12)

Because of a small gap between the two surfaces, the system model can be

simplified as in Fig.1. 16.c. Thus, the electric field between half of f1 and the

rotor can create a capacitive coupling Cf1r and another half of f1 can create the

capacitive coupling with stator winding (Cf1s). The same is also found in the

other side of the stator slot tooth (f2) and resultant capacitive couplings (Cf2r,

Cf2s). According to Eq.1-12, these capacitances are:

2

20s2fs1f

1

10r2fr1f

g

g2Ln

2CC

g

g2Ln

2CC

(1-13)

Considering the electric field between sides of the slot tooth (S1, S2), the

effective area to calculate capacitive couplings between rotor and stator will

decrease and Csr is:

210sr gg

dC

(1-14)

33

1.3.2. 2. Analysis of shaft voltage without considering end-winding

Based on the simulation results and the analysis in [7-8], in a variety of design

parameters changes, the ratio between Csr and Crf is between 0.05 and 0.1. Also,

the ratio between Cb and Csr (α) is almost equal to 1. In this section, the effective

parameters of the end-winding have not been calculated. Therefore β is defined

as the ratio between end-winding Csr and without end-winding Csr. So, Csr-total is

(1+β) times of Csr without end-winding which is calculated in Eq.1-14. By

substituting equations (1-7) & (1-14) in Eq.1-4, the ratio between shaft voltage

and common mode voltage can be written as:

d,

)dn

r2)(gg()d)(1)(1(g

)d)(1(g

V

V

211

1

com

sh (1-15)

As shown in this equation, the effective parameters on shaft voltage are d, ρ, g1

and g2 and β. It is clear that g1 cannot be changed for a large range of variation

and cannot be an effective parameter in shaft voltage reduction. Fig.1. 18 shows

the variation of Vsh/Vcom versus d and g2 stator slot height of ρ=5 mm.

Fig.1. 18: Variation of Vsh/Vcom versus variation of d and g2

This graph shows the effect of two main design parameters on shaft voltage.

According to simulation results in different parameters:

Csr is an important capacitance in case of shaft voltage generation in an IG

because it can be changed by variation of the design parameters while other

capacitances have not such a freedom to change.

An increment of stator slot tooth increases the shaft voltage while increasing

the gap between the slot tooth and winding decreasing the shaft voltage (see

Fig.1. 18).

34

1.3.2.3. Analysis of shaft voltage with considering end-winding

According to the analysis presented above, Csr is an important parameter in case

of shaft voltage generation because it can change due to the variation of the

design parameters while the other capacitances cannot change. Also, end-

winding parameters affect this parasitic capacitance. Therefore, precise

calculation of this capacitance is crucial (note the fact that this capacitance is

much lower than Crf). Calculation of the end-winding capacitances is rather

complex because of the diversity of end winding shapes and complexity of its

geometry. A typical shape of the stator end-winding is considered in this section

to calculate the capacitances (see Fig.1.18.a). This model is very simple and just

to address the effectiveness of some parameters on the capacitances. Also, a

practical end-winding model (see Fig.1.19) has been used to verify the

capacitance via FEM simulation.

1.3.2.3.1. Mathematical analysis

A model of end-winding and the rotor for a single slot is shown in

Fig.1. 19.b in which the winding comes out of the slot by length of L1 and is bent

with the length of L2 to go to another slot. There are two capacitors in this

system between: shaft and end-winding (Csh-end), rotor frame and end-winding

(Cr-end). For capacitance calculation purposes, the end-winding of a single slot

can be approximately modelled with three surfaces (2 surfaces with width of

W/2 and length of L1, a plate with width of W1 and length of L2). W is the width

of winding at the slot and W1 is the width of winding at the end winding. To

calculate the capacitance between these surfaces, based on [81], the capacitance

can be calculated as:

1

120 Lnt

C (1-16)

For the simplicity of the equation and the simulation is considered as π/2. End-

winding capacitances can be calculated based on Eq.1-16 as:

gL

gLLLn

W2C

g

gLLn

W2C

1

21102end

101end

(1-17)

35

Therefore, the capacitor between rotor and the end-winding of a single slot can

be calculated as:

gL

gLLLn

W2

g

gLLn

W2CCC

1

2110102end1endendr (1-18)

Where g is ( in21 ggg ) and W1 can be defined as ngR2 rotor . By

substitution of W1=k×W in Eq.1-18, one can have:

1k

1

k210

endrgLg

gLLLn

W2C (1-19)

(a)

(b)

Fig.1. 19: (a) structure of an IG with (b) a model for calculation of end-winding capacitances

A shaft to end-winding capacitance is also exists which is equal to:

g

gRLn

)Lk

L(

2Crotor

21

0endsh (1-20)

36

End-winding capacitance for an IG (Csr-end) is the sum of Eq.1-19 and Eq.1-20.

The calculated capacitors should multiply by 2n (n is the number of slots) as the

calculations are for a single slot and one side of the end-winding. Therefore,

capacitive couplings between rotor and stator winding for an n slot generator

structure can be calculated as:

1k1

k21

rotor

21

r21

0totalsr

gLg

gLLLn

W4

g

gRLn

)Lk

L(4

Lgg

d

nC (1-21)

Based on the above mentioned analysis, substituting equations (1-5) and (1-21)

in Eq.1-4, a shaft voltage for a complete generator model can be approximately

calculated:

com

1k1

k21

r

rotorr

21

21

012

shaft V

gLg

gLLLn

L

W4

g

gRLnkL

)LkL(4

gg

d

ndr2

gnV

(1-22)

1.3.2.3.1. Finite element analysis

A typical shape of the end-winding is considered to study the capacitances is

shown in Fig1.19. The parameters required for the investigation of the end-

winding capacitance are as follows:

End-winding parameters: the winding comes out of the slot with the length

of L1 and is bent with an angle of α and with a length of L2. This winding

will be bent again to go to another slot.

Slot parameters: as discussed in previous section (see Fig.1. 16.a), the gap

between rotor and winding surface (ρ+g1+g2) has been considered as g. Also,

stator slot tooth, denoted by d, has not have any effect on end-wind

capacitance and hence is not considered.

Rotor ring parameters: two rings are placed, one on each side of the rotor, to

connect the bars inside rotor (Fig.1.19). The length of the ring is denoted by

Lring, while its thickness is denoted by Dring (Fig.1.19.b). This distance of the

ring from the end of the rotor is gring.

37

Fig.1.20: (a) structure of an IG with a (b) model for simulation of end-winding capacitances

Simulations have been conducted to analyse the effects of the generator end-

parameters on the end-winding parasitic capacitive couplings. A range of design

factors has been considered in the simulation studies. Two values, one large and

one small, are considered for some of the parameters to investigate the effects of

these parameters on the end-winding capacitance. Different design factors have

been investigated in different simulation studies as follows.

Effects of end-winding angle (α): To analyse the effects of angle of end-

winding on capacitance, two different angles (0 and 30) have been tested.

Since the difference is not significant (8% or less) and one of the angles is 0,

it can be concluded that the angle of the end winding does not have a big

impact on the total capacitive coupling.

38

Effects of end-winding length L2: A comparison (in terms of percentage

difference) of the end-winding capacitances between a particular value of L2

and twice that value has been done for different design parameters. The

results are approximately the same for two different end-winding angles (all

the differences are less than 3.5%).

We can therefore conclude that both L2 and α do not have any significant effect

on the end-capacitive coupling. Therefore these two parameters are not further

considered in the investigations.

Effects of end-winding length (L1), ring length (Lring) and ring thickness

(Dring) : In this case, α and L2 are kept constant while L1 has been considered

as multiple of Lring to see the effects of these two parameters together. The

main point that can be observed from these figures is that by increasing the

end-winding length (L1) as multiples of Lring, the value of end-capacitive

couplings will not increase beyond 2×Lring. This implies that the capacitances

reach an approximate constant value even when the end winding length

increases. Therefore, L1 and Lring can be considered as single parameters

which are related together. Based on different simulation results, it is evident

that for a ten times of variation in Dring, the difference between capacitive

couplings is not significant. In fact the calculated percentage difference lies

between 4 to 8 percent. It means that Dring does not affect the total

capacitance.

Effects of g2 and gring: Capacitive couplings in different sets of g2 and gring

have been compared in order to determine the effects of these parameters.

The ratios between capacitances with changes of g2 with two different gring

have been compared. The interesting point to be noted here is when gring

increases; the rate of changes in these capacitances is approximately equal to

the expected ratio. Also, by changing gring, the capacitances did not increase

with the ratio of gap between end-winding and rotor ring and the rage of

variation is very small. In summary, the decrement in the value of the

capacitance by increasing of g (gring+g1+ρ+ g2) is not proportional to the rate

of changes in the ring distance or the other gaps (particularly in lower values

of gring). The main reason is the complexity of the generator structure.

39

1.3.2.4. Verification of the mathematical analysis with test and simulation

1.3.2.4.1. Simulation results:

Simulations have been conducted for a single slot for 12 design structures of

Table.1. 6.

Table.1. 6: Different design parameters for proposed IG structure

Design number

ρ (mm)

g2 (mm)

d (mm)

1 3 5

50

2 5 3 3

15 4 5 5 3

25 6 5 7 3

5

150

8 5 9 3

15 10 5 11 3

25 12 5

The thickness of insulation (gin) is considered as 2.5 mm and r is taken as 2.25

and the rotor radius as 1000 mm. 3-D FEM simulation for Csr and Crf has been

carried out and the results are compared with the calculated values (using 3 and

4). The two results are compared and are shown in Fig.1. 21. In the figure, ‘cal’

indicates the calculated values and ‘3D’ indicates what have been obtained by

FEM simulation. It can be seen that they almost overlap, verifying the accuracy

of the mathematical model.

(a)

40

(b)

Fig.1. 21: 2-D and 3-D simulation results for (a) Crf (b) Csr and its calculated values

In this section, only end winding capacitances has been simulated with the

changes of L1, L2, and W to validate the calculations. Table.1. 7 shows a variety

of design parameters for end-winding simulations and calculation. Fig.1. 22.a&b

show the calculated and simulated end-winding versus variation of L1 and L2 for

rotor radius of 1000 mm with different winding widths (W). The results show

that the equations are valid for a broad range of the design parameters.

Table.1. 7: design parameters for end-winding simulations

Figure #

Rrotor (mm)

Dshaft (mm)

W (mm)

L1 (mm)

L2 (mm)

g (mm)

1.22.a 1000 200 150 variable variable 21 1.22.b 1000 200 200 variable variable 21

(a)

41

(b)

Fig.1. 22: Calculated and simulated end-winding capacitances versus variation of end-winding

lengths (a) Rrotor=1000 mm, W=150mm (b) Rrotor=1000mm, W=200mm

1.3.2.4.2. Test results:

Case A: Flexible stator slots

As it is not possible to change different parameters of a machine, we need a

flexible slot to do the measurements. As shown in Fig.1. 23.a, a single stator slot

with winding and rotor has been designed to measure the capacitive couplings in

a variety of design parameters. Fig.1. 23.b shows the model of the designed slot

and different parameters which have been changed. Test results can be compared

with simulation and calculated values.

Different set-ups have been tested with a vector network analyser to measure the

impedance and phase in a range of frequencies. As it can be seen from Fig.1.

23.c, while the phase angle is -90 degrees, the impedance is pure capacitive.

(a)

42

(b)

(c)

Fig.1. 23: (a) test set-up for impedance measurement (b) stator slot model and different parameters (c) impedance and phase in different frequencies

Therefore, parasitic capacitive couplings can be obtained from the measured

impedance. Impedance is changed after a certain amount of frequency (here

around 16 MHz) from capacitive to inductive. That is because of existence of

very small parasitic inductors which their impedance will be dominant in higher

frequencies. The range of frequency which has been studied in this work is under

10 MHz and the analysis of behaviour of the system in higher frequencies is not

in the focus of this paper. Three tests are needed to find all capacitive couplings

in the set-up which are as follow:

Test1: impedance measurement between winding and the rotor. Ctest1=Csr+

(Csf×Crf)/ (Csf+Crf)

Test2: impedance measurement between winding and the stator frame with

removing rotor. Ctest2= Csf

43

Test3: impedance measurement between stator frame and the rotor with

removing winding. Ctest3= Crf

Consequently, Csr can be calculated as Ctest1-(Ctest2×Ctest3)/ (Ctest2+Ctest3).

Fig.1. 24: Three different tests to measure capacitive couplings

Six set-ups have been tested based on the design factors of Table.1. 8 and the

results for Crs and Crf are shown in Fig.1. 25. The results show that the

capacitances obtained by FEM simulations are approximately the same as test

results. In the cases which the capacitance values are very low, test results are a

little bit far from simulation results because of the measurement error. Also, the

dimensions in practical set-ups are heterogeneous which cause a slight difference

between simulation and test results.

Table.1. 8: Different design parameters for test setups

Test set-up

g1 (mm)

ρ (mm)

d (mm)

A (mm)

B (mm)

d1 (mm)

1 1 12 180

250 200 10

2 2 3 1

33 176 4 2 5 1

13 80 150 100 6 2

44

(a)

(b)

Fig.1. 25: Comparison between test and simulations for (a) Crs and (b) Crf for 6 different set-ups

Case B: shaft voltage measurement with and without end-winding effects

To verify the analysis and simulation results, several tests have been performed

to measure common mode and shaft voltages and compare them with the

simulation results. It is very important to consider practical issues when we

compare test and simulation results. Thus, simulations have been performed for a

5 kW 3-phase induction machine with 36 slots considering practical issues. In a

real machine, in each slot a distance between a winding and the rotor surface

45

(referring to Fig.1. 16.a, the length of g1++g2) is changed along the rotor axis

and in different slots. Based on our measurement, this distance varies between

(3.5 mm and 4.5 mm). Several simulations have been carried out to extract the

capacitive couplings for three different distances (g1++g2), 3.5mm, 4mm and

4.5mm and the results are given in Table.1. 9.

Table.1. 9: Simulation results with and without end-winding (pF)

Another practical issue is the effect the insulator property (εr) on Csr, which has

been analysed and addressed in Eq.1-23. Considering three different εr (2, 2.5

and 3) and the capacitive coupling between the winding and the rotor can be

defined as follows:

air_srin_srair_sr

in_srair_srC

CC

CC

(1-23)

In fact two capacitors, Csr _air and Csr_in are in series and because the thickness of

the insulator is much less than (g1++g2), thus Csr_air<< Csr_in and the capacitive

coupling between the winding and the rotor approximately equals to Csr_air. This

analysis shows that the simulations to extract the capacitive coupling between

the winding and the rotor are not affected by the insulator property (εr). The

simulation results for different εr (2, 2.5 and 3) are given in Table.1. 9.

According to the above discussion and based on the simulation results, the effect

εr on Csr is negligible while the effect of (g1++g2) on Csr is significant. The last

practical issue is the effect of end winding on the shaft voltage. As shown in

Fig.1. 26.a due to a capacitive coupling between the end winding and the rotor

side, Csr_end, the total capacitive coupling between the windings and the rotor,

Csr_total is increased. In a real machine, the length of the end winding and also its

configuration at both sides are not uniform. To analyse this issue, each end

winding has been modelled as a cylinder connected to each side of the winding

Design

Parameters

g

(mm)

Csr

(εr =2)

Csr

(εr =2.5)

Csr

(εr =3)

Csr

(εr ={2-3})

Crf

Vsh/Vcom

without

end

winding

4.5 7.1 7.2 7.2 7.2 545 0.013

4 10.01 10.05 10.08 10.05 545 0.018

3.5 13.22 13.32 13.35 13.29 545 0.024

with

end

winding

4.5 15.71 15.72 15.72 15.72 545 0.028

4 18.62 18.66 18.69 18.66 545 0.033

3.5 21.83 21.93 21.96 21.90 545 0.038

46

as shown in Fig.1. 26. In this induction machine, the length of the end winding

varies between 30mm and 40mm and simulation results show that Csr_end are 8.20

pF and 9.03 pF, respectively. Thus we have considered 8.61 pF an average of the

capacitive coupling between the end windings and the rotor. According to the

simulation results and based on Eq.1-15, Vsh/Vcom ratios have been calculated for

different cases and the results are given in Table.1. 9. Eq.1-24 shows that the

voltage ratio, Vsh/Vcom approximately equals to Csr/Crf. Thus measuring the

common mode and shaft voltages can give Csr/Crf ratio for the given induction

machine.

rf

sr

rfsr

sr

rfsrb

sr

com

sh

C

C

CC

C

CCC

C

V

V

(1-24)

(a)

(b)

Fig.1. 26: (a) view of machine structure with end-winding (b) view of shielded end winding

We have performed two main tests for the induction machine; in the first test, all

capacitive coupling have been considered without shielding any part of the end

winding and the results can be compared with the simulation result (with end

winding). In the second test, we have shielded the end windings to compare the

test result with the simulation result (without end winding). The common mode

and shaft voltage waveforms with and without shielded end windings are shown

47

in Fig.1. 27. Vsh/Vcom ratios have been calculated based on the measurement

results which are given in Table.1. 10.

(a) (b)

Fig.1. 27: Experimental results: Common mode and shaft voltage waveforms (a) without shielded

end winding (b) with shielded end winding

Table.1. 10: Comparison between the simulation and test results

Simulation and test results for with and without end-winding Vsh/Vcom

Simulation, without end winding (g1+ +g2 = 4 mm) 0.018

Simulation, with end winding (g1+ +g2 = 4 mm) 0.033

Test results (with shielded end winding)

Vcom = 505 Volts, Vsh = 10.5 Volts 0.0207

Test results (without shielded end winding)


Considering an average of 4mm for the distance between the windings and the

rotor (g1+ +g2), the difference between the simulation result without end

winding (0.018) and the test result with shielded end winding (0.0207) is around

13%. According to Eq.1-15, Vsh/Vcom significantly depends on Csr and Crf. Thus,

the difference between the simulation and test results are due to the variation of

(g1+ +g2) values which affects Csr. In the other test, we have considered the end

winding effect and the difference between the simulation result with end winding

(0.033) and the test result without shielded end winding (0.0306) is around 8%.

This difference can also be addressed to capacitive couplings between the rotor

and the shielded surfaces which have been grounded on both sides of the rotor

(8.61 pF) and also due to a capacitive coupling between the rotor shaft and the

motor frame which has not been considered in this analysis. Thus, the small

difference between the test and simulation results shows that this analysis and

finite element simulation approach can be used as a good design tool for

Induction Machine Design to analyse and reduce shaft voltage.

48

Out of these simulations, calculation, tests and analyses, a journal paper has been

accepted at IET Power Electronics entitled “Calculations of Capacitive

Couplings in Induction Generators to Analyse Shaft Voltage”. This paper was

mainly based on the effective design parameters of the AC motors/generators on

the shaft voltage and presented in Chapter 3. A conference paper entitled “End-

winding Effect on Shaft Voltage in AC Generators” has been presented at 13th

European Power Electronics conference focusing on the calculation and

simulation of the end-winding capacitance in an AC motor. A detailed analysis

of the shaft voltage with considering end-winding effects, calculation and tests of

the flexible stator slots has been submitted to IEEE Transaction on the Power

Electronics. This paper with the title of “Analysis of the Effects of End-Winding

Parameters on the Shaft Voltage of AC Generators” is presented at Chapter 4.

49

1.3. 3. Common mode voltage reduction in different power electronics

topologies

Different types of the inverter fed motor drive systems have been considered in

this research to reduce the common mode voltage via proper PWM strategies.

These configurations have been classified in following sections.

1.3.3. 1. Common mode voltage reduction in three-phase ASD system

supplied with a single-phase diode rectifier

Fig.1. 28.a shows an ASD supplied by a three-phase inverter system and its

behaviour in different intervals. DC link voltage of the inverter is regulated by a

single phase diode rectifier connected an AC supply. As the input current of the

rectifier is highly distorted, a Power Factor Correction (PFC) unit with boost

converter technique is used to improve the current quality of the AC source.

Current control technique benefits power electronic converters. Hysteresis

current control is a simple current control with fast dynamic response [82].

Therefore, in this topology the inductor current will be compared to a reference

current and forced to be kept inside the upper and lower hysteresis bands. This

results in a sinusoidal current waveform at the input side. Also, a space vector

modulation strategy is employed for the inverter switching control. Fig.1. 28.b

shows the behaviour of the proposed system in positive half a cycle of the input

voltage. When the input voltage is positive, the neutral line is connected to the

negative DC link line for the half a cycle. The positive DC link line has the

maximum potential with respect to the neutral which has a significant impact on

the common mode voltage. Also, Fig.1. 28.c shows the behaviour of the system

in negative half a cycle where the neutral point is connected to the inductor.

In the ASD system with single-phase rectifier topology, the common mode

voltage generated by the inverter is influenced by the AC-DC diode rectifier

because the placement of the neutral point is changing in different rectifier

circuit states. Zero switching vectors are the most important vectors in terms of

common mode voltage generations. Regarding to different placements of the

neutral point, proper switching states will be applied in the PWM pulse pattern to

decrease the common mode voltage. Simulations have been carried out for the

circuit topology shown in Fig.1. 28 in which a hysteresis current control is used

50

to control the PFC switch. A space vector modulation with the switching

frequency of 5 kHz is used to control the three-phase inverter. Different PWM

patterns will be investigated to analyse their effects on the common mode

voltage.

Three Phase DC-AC Inverter

Single Phase AC-DC

diode rectifier

ba

c

p

n

Single PhaseAC Source AC Motor

o

g

S1 S3 S5

S2 S4 S6

D1 D3

D2 D4

L

S

D

Hysteresis current controlΣ

Space Vector Modulation

Reference current

Inductor current

S1-S6

(a)

(b)

Inve

rter

an

d t

he

mo

tor

p

n

g

D1 D3

D2 D4

L

S

Dg

Vs Cdc-link

+ vL -

(c)

Fig.1. 28: (a) a schematic of an ASD system supplied by a single-phase diode rectifier with PFC in (b) positive half a cycle and (c) negative half a cycle

51

A. Using two zero switching vectors in PWM pattern

A typical pulse pattern of (V0, V1, V2, V7, V2, V1, V0) has been employed for the

inverter. Fig.1. 29 shows the DC link voltage and the voltages of positive and

negative points of the DC link with respect to the ground (Vpg and Vng). As

mentioned in section 1.2.2 and Table 1.2, applying V0 and V7 to the pulse pattern

leads to maximum common mode voltage which is changing between voltages

Vpg and Vng.

-300

-200

-100

0

100

200

300

(Vpg &

Vng)

D

C lin

k(V

dc)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

-300

-200

-100

0

100

200

300

Tim e(s )

Com

mon m

ode (

Vcom

)

Fig.1. 29: DC link voltage, voltages at positive and negative points of DC link with respect to the ground and common mode voltage for switching sequence of (V0, V1, V2, V7, V2, V1, V0)

B. Removing V7 from PWM pattern

As mentioned in previous section, by using one of the zero switching vectors, the

benefit of changing neutral point location can be used. A switching sequence of

(V0, V1, V2, V1, V0) is employed to minimize the common mode voltage. Fig.1.

30 shows the leg voltages and common mode voltage with proposed switching

sequence. As shown in Fig.1. 28.b, in the positive half a cycle, neutral point is

connected to the negative point of the DC link capacitor. The difference between

with and without PFC is that the neutral point in a system without PFC is

connected to the negative point only in charging state of capacitor in the positive

half a cycle. However, in a system with PFC, the neutral point is connected to

the negative point in whole duration of positive half a cycle. Therefore applying

V0 leads to decrement of the common mode voltage by one-third in positive half

52

a cycle. This strategy will not help to remove the maximum level of common

mode voltage (-300 volts) in negative half a cycle.

0

100

200

300

Le

g a

(Va)

0

200

Le

g b

(Vb)

0

200

Le

g c

(Vc)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

-300

-200

-100

0

100

200

300

Tim e(s )

Co

mm

on

mo

de

(Vc

om

)

Fig.1. 30: Leg voltages and common mode voltage for switching sequence of (V0, V1, V2, V1, V0)

C. Removing V0 from PWM pattern

A switching sequence of (V7, V2, V1, V2, V7) has also been tested which gives

different leg and common mode voltages as shown in Fig.1. 31.

0

100

200

300

Le

g a

(Va)

0

200

Le

g b

(Vb)

0

100

200

300

Le

g c

(Vc)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008-300

-200

-100

0

100

200

300

Tim e(s )

Co

mm

on

mo

de

(Vc

om

)


According to Fig.1. 28.c, in the negative half a cycle, the neutral point is

connected to the inductor. Based on Fig.1. 31, the maximum common mode

53

voltage level in the negative half a cycle occurred when the voltage of the

positive point to the ground is in its minimum value (around zero). Therefore

applying V7 minimizes the common mode voltage in negative half a cycle by one

third. The maximum common mode voltage value still exists in the positive half

a cycle.

D. Applying V0 in positive half a cycle and applying V7 in negative half a cycle

As mentioned in the previous section, a solution to reduce the shaft voltage is to

use only V0 voltage vector in the positive half a cycle in which it has the lowest

potential with respect to the neutral. V7 will be applied in the negative half a

cycle where the neutral line is connected to PFC inductor and negative DC link

is connected to the source voltage. Therefore, it is better to apply V7 as a zero

vector in negative half a cycle to create the lowest possible common mode

voltage without distortion of the load current. Fig.1. 32 shows the leg voltages

and the common mode voltage of the system with the proposed PWM strategy.

0

100

200

300

Le

g a

(Va)

0

100

200

300

Le

g b

(Vb)

0

100

200

300

Le

g c

(Vc)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

-300

-200

-100

0

100

200

300

Tim e(s )

Co

mm

on

mo

de

(Vc

om

)

Fig.1. 32: Leg voltages and common mode voltage for switching sequence of (V0, V1, V2, V1, V0) for positive half a cycle and sequence of (V7, V2, V1, V2, V7) for negative half a cycle.

Comparison of the common mode voltage achieved in this figures with the other

waveforms show the effectiveness of proposed switching strategy on the

common mode voltage. This method is a cost effective technique which leads to

a lower possible shaft voltage in ASD system supplied with a single-phase diode

rectifier.

54

1.3.3.2. Multi-level inverter topology and reduction of common mode

voltage

In multilevel converters (diode clamped topology is more practical), there are

more voltage levels and switching states which can provide possibilities to

reduce common mode voltage. In this topology, each leg has three voltage

levels: (+Vdc/2, 0, -Vdc/2).

Fig.1. 33: A three-level diode clamped inverter

In a three phase converter with three legs, there are 27 different switching

combinations in a diode clamped topology. All switching states and output

voltages of a three-level inverter are given in Table.1. 11.

Number ‘2’ means that the top switches in a leg are turned on.

Number ‘1’ means that one of the top switches in a leg is turned on.

Number ‘0’ means that the top switches in a leg are turned off.

The common mode voltage magnitudes for this converter are: (+Vdc/2, +Vdc/3,

+Vdc/6, 0, -Vdc/6, -Vdc/3, -Vdc/2)

1: Vectors V0, V13 and V26 are zero voltage vectors in a d-q frame. V0 and V26

create maximum common mode voltage of +/- Vdc/2 while V13 generates no

common mode voltage (zero voltage). Thus, using this topology, it is possible to

reduce common mode voltage without affecting load current quality. In fact

instead of V0, V26 voltage vectors, we can use V13 to generate PWM waveforms.

2: Vectors V1, V3, V9, V17, V23 and V25 are active vectors and they generate +/-

Vdc/3. In these switching vectors, two legs of the converter have +Vdc/2 or -

55

Vdc/2 voltage level and the other one have zero voltage. Using pulse position

method we are able to shift leg voltages in such a way to remove or reduce these

switching states but it may affect the quality of the load current as shown in

Fig.1. 34.a.

Table.1. 11: Switching states for a three-level inverter

Vectors Switching states Vao Vbo Vco Vcom

V0 000 -Vdc/2 -Vdc/2 -Vdc/2 -Vdc/2

V1 100 0 -Vdc/2 - Vdc/2 -Vdc/3

V2 200 Vdc/2 - Vdc/2 - Vdc/2 -Vdc/6

V3 010 - Vdc/2 0 -Vdc/2 -Vdc/3

V4 110 0 0 -Vdc/2 - Vdc/6

V5 210 Vdc/2 0 - Vdc/2 0

V6 020 - Vdc/2 Vdc/2 - Vdc/2 -Vdc/6

V7 120 0 Vdc/2 - Vdc/2 0

V8 220 Vdc/2 Vdc/2 - Vdc/2 Vdc/6

V9 001 - Vdc/2 - Vdc/2 0 - Vdc/3

V10 101 0 -Vdc/2 0 -Vdc/6

V11 201 Vdc/2 - Vdc/2 0 0

V12 011 - Vdc/2 0 0 - Vdc/6

V13 111 0 0 0 0

V14 211 Vdc/2 0 0 Vdc/6

V15 021 - Vdc/2 Vdc/2 0 0

V16 121 0 Vdc/2 0 Vdc/6

V17 221 Vdc/2 Vdc/2 0 Vdc/3

V18 002 - Vdc/2 - Vdc/2 Vdc/2 - Vdc/6

V19 102 0 - Vdc/2 Vdc/2 0

V20 202 Vdc/2 - Vdc/2 Vdc/2 Vdc/6

V21 012 - Vdc/2 0 Vdc/2 0

V22 112 0 0 Vdc/2 Vdc/6

V23 212 Vdc/2 0 Vdc/2 Vdc/3

V24 022 - Vdc/2 Vdc/2 Vdc/2 Vdc/6

V25 122 0 Vdc/2 Vdc/2 Vdc/3

V26 222 Vdc/2 Vdc/2 Vdc/2 Vdc/2

Fig.1. 34.b shows a new pulse pattern as the pulse position in leg ‘a’ is shifted to

left side and the one in leg ‘b’ to the right side of the switching cycle in order to

remove common mode voltage levels of +/-Vdc/3. We can see that other

56

common mode voltage levels (+/-Vdc/3) have been removed but this modulation

method affects the load current ripple and effective switching frequency.

(a)

(b)


Out of these analyses, a paper has been presented at 13th European Power

Electronics Conference with the title of “Different Approaches to Reduce Shaft

Voltage in AC Generators” with focus on common mode voltage reduction in

multilevel inverter topology.

57

1.3.4. Shaft voltage in induction generators of wind turbine

This research also presents the analysis of shaft voltage in different

configurations of an induction generator and a doubly fed induction generator

with a back-to-back inverter in wind turbine applications. Detailed high

frequency model of the proposed systems have been developed based on existing

capacitive couplings in IG & DFIG structures and common mode voltage

sources. Several arrangements of DFIG based wind energy conversion systems

are investigated in case of shaft voltage calculation and its mitigation techniques.

Placements of an LC line filter in different locations and its effects on shaft

voltage elimination are studied via mathematical analysis and simulations. A

PWM technique and a back-to-back inverter with a bidirectional buck converter

have been

1.3.4.1. Shaft voltage analysis in stator fed IG-based wind power

applications

Fig.1. 35 shows an induction generator wind turbine structure in which a power

converter is connected between the generator and the grid. In this case, the

voltage stress is from the stator winding. Common mode voltage creates the shaft

voltage through electrostatic couplings between the rotor and the stator windings

and between the rotor and the frame.

Fig.1. 35: Stator-fed IG arrangement for wind power applications

Shaft voltage analysis in this configuration is the same as the mentioned studies

about the AC motors in the previous sections.

1.3.4.2. Shaft voltage analysis in DFIG-based wind power applications

A. Generator structure and common mode voltage

Fig.1. 36 shows the arrangement of a back-to-back DC-AC-DC inverter. In this

structure, the common mode voltages of the both sides are given as:

58

3

VVVV,

3

VVVV zoyoxo

S,comcoboao

R,com

(1-25)

Where coboao V,V,V & zoyoxo V,V,V are the leg voltages from converter1 and

converter2 converters respectively.

Fig.1. 36: Back-to-back DC-AC-DC inverter in a wind energy system

Fig.1. 37 shows the structures of a DFIG where the parasitic capacitive couplings

exist between: the stator winding and rotor (Csr), the stator winding and stator

frame (Csf), between the rotor and stator frames (Crf), stator winding and rotor

winding (Cws), the rotor winding and rotor (Cwr), rotor winding and stator frame

(Cwf) and ball bearing and outer and inner races (Cb1, Cb2).

Shaft

Stator winding

Rotor

Stator frame

Rotor winding

Cwr

Cwr

Crf

Crf

Cws

Cwf

Cb1

Cb2

Cws

Csf

Csr

Fig.1. 37: A view of DFIG with different capacitive couplings in a doubly fed induction generator

59

In a wind turbine application, stator and rotor windings of a DFIG connect to

both side converters and both sides common mode voltages will be an effective

factor in shaft voltage generation. In this section, different topologies of a DFIG

with a four-quadrant AC-DC-AC converter connected and different placements

of LC filters in both rotor and stator sides, and a line filter (As shown in Fig.1.

38) has been investigated. In general, only the line side current is required to be

sinusoidal to satisfy IEEE standards [76].

Fig.1. 38: Different placements of L-C filters in wind turbine applications in a DFIG with a back

to back converter

B. Shaft voltage analysis with different configurations of LC filters

Topology1: The network side converter is connected to the grid through a line

LC filter which is used to damp the low order harmonics generated by the

switching of semiconductors. This filter is used as a tool to provide reactive

power in order to enable power factor correction on the network within a desired

range [77]. The LC filter which connects the net-side converter and grid reduces

the harmonics and the voltage from stator side is not in a PWM waveform

anymore. Therefore it is not a common mode voltage source from stator side

converter in this configuration. An arrangement of capacitive couplings of a

doubly fed induction generator with an LC filter on the network side converter is

shown in Fig.1. 39.

Fig.1. 39: Common mode model for the configuration of a DFIG with Topology1

60

In this case, the only common mode voltage source is from rotor winding and

this voltage stress creates some shaft voltage which can be easily calculated by a

KCL analysis as:

R,com2

srwssrsfsrbrfwr

srwswssrsfwrshaft V

CCCCCCCC

CCCCCCV

(1-26)

By considering srC as a small value and wrsr CC , it can be concluded that:

0C

CCCCCC

2sr

wssrsfwrwssr (1-27)

Thus, shaft voltage can be simplified as follows:

R,comsrbrfwr

wrshaft V

CCCC

CV

(1-28)

Vcom,R is the common mode voltage from the rotor side converter. The capacitive

coupling between the rotor winding and rotor frame has a significant value

compared with other capacitances. The major part of the common mode voltage

will be placed across the shaft.

Topopolgy2: A filter is placed in the rotor side converter and the voltage from

the rotor side has fewer harmonic and no common mode voltage sources. An

arrangement of capacitive couplings in the proposed structure is shown in Fig.1.

40.


The only common mode voltage source is from the stator winding. By a KCL

analysis in this configuration, the shaft voltage can be derived as:

S,com2

wrwfwrwssrbrfwr

wrwswswfwrsrshaft V

CCCCCCCC

CCCCCCV

(1-29)

wsC & wfC are very small values in compare with other capacitances and can be

neglected in calculations. Eq.1-29 can be rewritten as:

61

S,com2wrsrbrfwr

2wr

wrsr

S,com2wrsrbrfwrwr

wrsrshaft

VCCCCCC

CC

VCCCCCC

CCV

(1-30)

Based on this calculation, shaft voltage is as follow:

S,comsrbrf

srshaft V

CCC

CV

(1-31)

Topology3: Two LC filters in the both rotor and stator sides are used to damp

the higher order harmonics. In this case, there is not any common mode voltage

from both sides. Hence, the possibility of the shaft voltage generation has been

reduced.

Topology4: There is no LC filter in both converters sides. Fig.1. 41 shows the

high frequency model of a doubly fed induction machine without filters.


In this structure, neutral to ground zero sequence voltage of both stator and rotor

winding act as common mode voltage sources. The shaft voltage can be easily

calculated by using KCL in the high frequency model of the doubly fed

generator. According to Fig.1. 41, the shaft voltage is:

S,comsrbrfwr

srR,com

srbrfwr

wrshaft V

C C CC

CV

C C CC

CV

(1-32)

S,comSR,comRshaft VKVKV (1-33)

Vcom,R and Vcom,S are the common mode voltages from the rotor and stator

windings, respectively. KR and KS are defined as capacitance factors which are

effective in total shaft voltage calculation.

srbrfwr

srS

srbrfwr

wrR C C CC

CKand

C C CC

CK

(1-34)

62

By considering srbrfwr C C CC , the shaft voltage is determined by Cwr

(KR is near 1 and KS is a very small value). Fig.1. 42 shows the simulation

results for total shaft voltage and the share of each converter in shaft voltage

generation. The typical values of Cwr=3nF, Crf=1 nF, Csr=0.2nF, Csf=6nF,

Cws=.05 nF, Cwf=0.2nF for a single stator slot and the bearing capacitance of

Cb=0.2nF for a ball bearing are employed for capacitive couplings investigations.

A modulation with switching frequency of 1 kHz from rotor side converter and

10 kHz from stator side converter has been considered.

Fig.1. 42: A common mode and shaft voltage generated by rotor and stator side converters (fsr=1

kHz, fss=10 kHz)

63

A major portion of the rotor side common mode voltage transformed to the shaft

voltage (in this case, 68% of rotor side common mode voltage and only 4.5% of

stator side common mode voltage transformed to shaft voltage). Based on this

analysis, the stator common mode voltage does not have a key effect on shaft

voltage because the capacitive coupling between the stator winding and shaft is

too small in comparison with capacitive coupling between the rotor winding and

shaft.

1.3.4.3. Discussion on shaft voltage elimination strategies for different

topologies of DFIG-based system

Different topologies have been simulated in the previous part in case of shaft

voltage generation. The effects of PWM techniques and filtering are investigated

in each configuration. Choosing one of these options depends on the cost of

filtering, changing the PWM pattern and increasing switching frequency or

employing additional circuits to reduce the rotor side voltage.

The system configuration in Topology 1 can not remove the shaft voltage

because the common mode voltage from the rotor still exists. This voltage has a

major impact on the shaft voltage. In this case by removing stator side common

mode voltage, a small part of shaft voltage will be removed. Removing zero

switching vectors in this case can reduce rotor side common mode voltage and as

a result a reduced shaft voltage can be achieved. As mentioned in the previous

section, removing the rotor side common mode voltage (Topology2) by filtering

the rotor side converter will remove major part of the shaft voltage but there is a

considerable amount of shaft voltage from the stator side. Removing zero

switching vectors from stator side converter can reduce the common mode

voltage and as a result a reduced shaft voltage can be achieved.

In these two topologies (1&2), the price for filtering is paid but there is still a

considerable amount of shaft voltage. Furthermore, it is obvious that the

configuration of Topology3, because of filtering in both sides, will remove both

sides’ common mode voltages and will not generate shaft voltage significantly.

In Topology4, according to Eq.1-33 and Fig.1.42, it is clear that by choosing the

rotor common mode voltage as follow, zero shaft voltage can be achieved.

S,comwr

srR,com V

C

CV (1-35)

Table.1. 12 shows the resultant shaft voltage by different switching states

64

generated by a back-to-back converter applied to the both rotor and stator sides.

Note that, rotor side common mode voltage has been decreased

to S,comwr

sr VCC by a buck converter and shaft voltage is calculated based on

Eq.1-33.

Table.1. 12: Different switching states and shaft voltage of a DFIG

Rotor side converter

Vectors

1,3,5

Vectors

2,4,6

Vector

7

Vector

0

Net

wor

k si

de c

onve

rter

Vectors

1,3,5 3VK dcS 0 3

VK dcS3

VK2 dcS

Vectors

2,4,6 0 3

VK dcS3

VK2 dcS3

VK dcS

Vector

7 3VK dcS 3

VK2 dcS dcSVK 0

Vector

0 3VK2 dcS

3VK dcS 0 dcSVK

To eliminate the shaft voltage, we need to generate common mode voltage on the

rotor side based on Eq.1-35 and Table.12. To meet these requirements, it is

needed to apply odd switching vectors (1, 3, and 5) to one converter and even

switching vectors (2, 4, and 6) to another converter. Also, switching vector V0

from one side and vector V7 from other side is conducted to a zero shaft voltage.

As mentioned in [77], to fully eliminate the common mode it is, in principle,

necessary to coordinate the zero states such that they occur synchronously.

However, since the line side rectifier operates at line voltage and the inverter

requires only a small fraction of the line voltage as it operates at slip frequency

and at a different switching frequency, such a synchronous operation is generally

impractical.

Based on this analysis, a paper has published at ICREPQ 09 to discuses the

presented technique at [77]. It seems that some of the capacitive couplings have

not been mentioned in the model. The problem can be eliminated by simply

avoiding the use of the zero states. Therefore, the odd switching vectors from

one side and the even switching vectors from other side converter is the only

solution (see Fig.1. 43). It can be noted that the penalty for this strategy is an

increase in the switching frequency and losses. However, this is of little

65

consequence for a wind turbine application, and produces only a very small

amount of additional losses.

Fig.1. 43: Space vector operating region for the converters to eliminate the shaft voltage

To achieve the conditions of Eq.1-35, a bidirectional buck converter has been

used to decrease the dc link voltage of C1 (VC1) to VC2. The duty cycle for

proposed converter should be chosen at S,comwr

sr VCC . Fig.1. 45 shows

common mode voltages from rotor and stator side and resultant shaft voltage

after using the PWM technique in Fig.1. 43 and the circuit configuration of

Fig.1. 44. Note that switching frequency of the converters is different but by

using the suitable vectors the common mode voltages are in constant levels.

Fig.1. 44: A new back-to-back inverters topology with a bidirectional buck converter and a DFIG

66

Fig.1. 45: Common mode and shaft voltages in Topology 4 after applying the presented PWM

This research shows that for same conditions induction generators, shaft voltage

in the DFIG is much more than the stator fed IG and presenting a proper

technique is vital. In this analysis, shaft voltage reduction strategies for the

induction generators in wind applications have been investigated. Presented

PWM strategy can eliminate the shaft voltage but the dynamic response of the

system with the alternative power electronic topology should be studied.

Based on the mentioned analysis in this section, a journal paper has been

published at IEEJ Transactions on Electrical and Electronic Engineering with

the title “Investigation of Shaft Voltage in with Induction Generators” with the

focus on the topologies of LC filter, high frequency modelling and application of

a PWM strategy for the shaft voltage reduction. These analyses can be found in

Chapter 2. Also, two conference papers have been presented at International

Conference on Reliable energy and Power Quality, 2009. The presented papers

have been published in the Renewable energy and power quality (RE&PQ)

journal, No.7 online journal available at: http://www.icrepq.com/rev-papers-

09.htm.

67

1.4 . References:

[1] J.C. Rama, A. Gieseche, “High-speed electric drives: technology and

opportunity”, IEEE Industry Applications Magazine, Vol. 3, Issue: 50 pp: 48-55

[2] Rockwell Automation, “Inverter-Driven Induction Motors Shaft and Bearing

Current Solutions,” Industrial White Paper, 11 March 2002.

[3] F. Zare, “Power Electronics Education E-Book (PEEEB)”, available at:

www.peeeb.com, ISBN: 978-0-646-49442-5.

[4] N. Mohan, T. Underland and W. Robins, Power Electronics: Converters,

Applications and Design, 2nd edition, John Wiley and Sons, New York, 1995

[5] Sanmin Wei, N. Zargari, Bin Wu and S. Rizzo, “Comparison and mitigation

of common mode voltage in power converter topologies”, IEEE Industry

Applications Conference, 2004, Volume: 3, on page(s): 1852- 1857

[6] Qiang Yin, Russel J. Kerkman, Thomas A. Nondahl and Haihui Lu,

“Analytical Investigation of the Switching Frequency Harmonic Characteristic

for Common Mode Reduction Modulator”, Industry Applications Conference,

2005, Volume 2, 2-6 Oct. 2005 Page(s):1398 – 1405

[7] Thomas F. Lowery, “Design Considerations for Motors and Variable Speed

Drives” ASHRAE Journal, February 1999

[8] Russel J. Kerkman, Senior Member, “Twenty Years of PWM AC Drives:

When Secondary Issues Become Primary Concerns”, 22nd IEEE IECON

International Conference, Volume 1, on page(s): LVII-LXIII, 1996

[9] A. Boglietti, E. Carpaneto, “Induction motor high frequency model” Industry

Applications Conference, 1999, IEEE, Vol.3, 3-7 Oct. 1999 Page(s):1551 - 1558

[10] Satoshi Ogasawara, Hirofumi Akagi, “Modeling and damping of high-

frequency leakage currents in PWM inverter-fed AC motor drive systems”,

Industry Applications, IEEE Transactions on, Volume 32, Issue 5, Sept.-Oct.

1996 Page(s):1105 - 1114

[11] Doyle Busse, Jay Erdman, Russel J. Kerkman, Dave Schlegel, Gary

Skibinski, “System Electrical Parameters and Their Effects on Bearing

Currents” Industry Applications, IEEE Transactions on, Volume 33, Issue 2,

March-April 1997 Page(s):577 – 584

68

[12] Shaotang Chen; Lipo, T.A. , “Bearing currents and shaft voltages of an

induction motor under hard- and soft-switching inverter excitation” , Industry

Applications, IEEE Transactions on, Volume 34, Issue 5, Sept.-Oct. 1998

Page(s):1042 – 1048

[13] S. Chen, T. A. Lipo, and D. Fitzgerald, "Modelling of motor bearing

currents in PWM inverter drives,” 13th IAS Annual Meeting, IAS '95.,

Conference Record of the 1995 IEEE, 1995.

[14] Yoshihiro Murai, Takehiko Kubota, Yoshihiro Kawase, “Leakage Current

Reduction for a High-Frequency Carrier Inverter Feeding an Induction Motor”

IEEE Transactions on industry applications , Vol. 28, NO. 4, July / August 1992

[15] Masayuki Morimoto, “Reduction of High Frequency Leakage Current from

PWM inverter- motor system at the Integrated Grounding System”, APEC'06,

Twenty-First Annual IEEE, 19-23 March 2006

[16] K. R. M. N. Ratnayake and Y. Murai, “Study of Leakage Current Reduction

Techniques and Their Suitability for Three Level High Power Inverter

Applications”, PESC 98 Record, 29th Annual IEEE,Vol.2, 17-22 May 1998,

Page(s):1456 - 1462

[17] Hirofumi Akagi, Takafumi Doumoto, “An Approach to Eliminating High-

Frequency Shaft Voltage and Ground Leakage Current from an Inverter-Driven

Motor”, IEEE Transactions on Industry Applications, Vol. 40, Issue 4, July-Aug.

2004 Page(s):1162 – 1169

[18] M. J. Costello, "Shaft voltages and rotating machinery," Industry

Applications, IEEE Transactions on, vol. 29, pp. 419-426, 1993

[19] A. Muetze, A.Binder, “Don't lose your bearings”, Industry Applications

Magazine, IEEE, Volume 12, Issue 4, July-Aug. 2006 Page(s):22 – 31

[20] Annette Muetze, Andreas Binder, “Practical Rules for Assessment of

Inverter-Induced Bearing Currents in Inverter-Fed AC Motors up to 500 kW”,

Industrial Electronics, IEEE Transactions on, VOL. 54, NO. 3, JUNE 2007

[21] ABB Technical guide No.5 ‘bearing currents in modern AC Drive systems”,

Helsinki, 1999

[22] Shaotang Chen, Lipo, T.A., “Circulating type motor bearing current in

inverter drives” Industry Applications Magazine, IEEE Volume 4, Issue 1, Jan.-

Feb. 1998 Page(s):32 – 38

69

[23] A. Muetze, A. Binder, H. Vogel, J. Hering, “What Can Bearings Bear?”

IEEE Industry Applications Magazine, Nov-Dec 2006

[24] J.M. Erdman, R.J. Kerkman, D.W. Schlegel, G.L. Skibinski, “Effect of

PWM inverters on AC motor bearing currents and shaft voltages”, Industry

Applications, IEEE Transactions on, Volume 32, Issue 2, March-April 1996

Page(s):250 – 259

[25] D. F. Busse, J. M. Erdman, R. J. Kerkman, D. W. Schlegel, and G. L.

Skibinski, "The effects of PWM voltage source inverters on the mechanical

performance of rolling bearings", IEEE Transactions on Industry Applications,

vol. 33, pp. 567-576, 1997

[26] Busse, D.; Erdman, J.; Kerkman, R.J.; Schlegel, D.; Skibinski, G., “Bearing

currents and their relationship to PWM drives”, IEEE Transactions on Power

Electronics, Volume 12, Issue 2, March 1997 Page(s): 243 – 252

[27] A.Binder, A.Muetze, “Scaling Effects of Inverter-Induced Bearing Currents

in AC Machines” Electric Machines & Drives Conference, EMDC 07, IEEE

International Vol. 2, 3-5 May 2007 Page(s):1477 – 1483

[28] Annette Muetze, Andreas Binder, “Calculation of Motor Capacitances for

Prediction of the Voltage across the Bearings in Machines of Inverter-Based

Drive Systems”, IEEE Transactions on Industry Applications, Vol. 43, No. 3,

May/June 2007

[29] Annette Muetze, Andreas Binder, “Techniques for Measurement of

Parameters Related to Inverter-Induced Bearing Currents”, IEEE Transactions on

Industry Applications, Vol.43, No.5, September/October 2007

[30] Annette Muetze, Andreas Binder, “Calculation of Influence of Insulated

Bearings and Insulated Inner Bearing Seats on Circulating Bearing Currents in

Machines of Inverter-Based Drive Systems”, Industry Applications, IEEE

Transactions on, Vol.42, No.4, JULY/AUGUST 2006

[31] Annette Muetze, Andreas Binder, “Calculation of Circulating Bearing

Currents in Machines of Inverter-Based Drive Systems”, IEEE Transactions on

Industrial Electronics, Vol.54, No.2, APRIL 2007

[32] P. Vijayraghavan and R. Krishnan, "Noise in electric machines: a review,"

Industry Applications, IEEE Transactions on, vol. 35, pp. 1007-1013, 1999

70

[33] G. L. Skibinski, R. J. Kerkman, and D. Schlegel, "EMI emissions of modern

PWM AC drives," Industry Applications Magazine, IEEE, vol.5, pp. 47-80, 1999

[34] Y. Tang, H. Zhu, B. Song, J. S. Lai, and C. Chen, "EMI experimental

comparison of PWM inverters between hard- and soft-switching techniques,"

presented at Power Electronics in Transportation, 1998

[35] Q. Liu, W. Shen, F. Wang, D. Borojevich, and V. Stefanovic, "On

discussion of motor drive conducted EMI issues," IPEMC 2004 The 4th

International, 2004

[36] L. Ran, S. Gokani, J. Clare, K. J. Bradley, and C. Christopoulos,

"Conducted electromagnetic emissions in induction motor drive systems. I. Time

domain analysis and identification of dominant modes,", IEEE Trans on Power

Electron, vol. 13, pp. 757-767, 1998

[37] L. Ran, S. Gokani, J. Clare, K. J. Bradley, and C. Christopoulos,

"Conducted electromagnetic emissions in induction motor drive systems. II.

Frequency domain models," Power Electronics, IEEE Transactions on, vol. 13,

pp. 768-776, 1998

[38] A. Bellini, G. Franceschini, R. Rovatti, G. Setti, and C. Tassoni,

"Generation of low-EMI PWM patterns for induction motor drives with chaotic

maps," 27th IEEE,.IECON '01. 2001

[39] J. Llaquet, D. Gonzalez, E. Aldabas, and L. Romeral, "Improvements in

high frequency modelling of induction motors for diagnostics and EMI

prediction," 28th IES,IEEE, 2002

[40] J.-S. Lai, X. Huang, S. Chen, and T. W. Nehl, "EMI characterization and

simulation with parasitic models for a low-voltage high-current AC motor drive,"

Industry Applications, IEEE Transactions on, 178-185, 2004

[41] J.-S. Lai, X. Huang, and S. Chen, "EMI characterization and simulation with

parasitic models for a low-voltage high-current AC motor drive systems,"

Industry Applications, IEEE Transactions on, vol. 40, pp. 178-185, 2004

[42] X. Huang, E. Pepa, J. S. Lai, S. Chen, and T. W. Nehl, "Three-phase

inverter differential mode EMI modeling and prediction in frequency domain,"

38th IAS Annual Meeting. Conference Record of the, 2003

71

[43] B. Revol, J. Roudet, J. L. Schanen, and P. Loizelet, "Fast EMI prediction

method for three-phase inverter based on Laplace transforms," PESC '03. 2003

IEEE 34th Annual, 2003

[44] R. F. Schiferl and M. J. Melfi, "Bearing current remediation options,"

Industry Applications Magazine, IEEE, 2004

[45] S. Bell, T. J. Cookson, S. A. Cope, R. A. Epperly, A. Fischer, D. W.

Schlegel, and G. L. Skibinski, "Experience with variable-frequency drives and

motor bearing reliability," Industry Applications, IEEE Transactions on, vol. 37,

pp. 1438-1446, 2001.

[46] P. J. Link, "Minimizing electric bearing currents in ASD systems," Industry

Applications Magazine, IEEE, vol. 5, pp. 55-66, 1999.

[47] J.Kim; K.Nam; "A method of lowering bearing current with embedded

circular comb-like coil", IEEE Industry Applications Conference, 2000, vol.3,

Page(s): 1670 - 1674

[48] Fei Wang, “Motor shaft voltages and bearing currents and their reduction in

multilevel medium-voltage PWM voltage-source-inverter drive applications"

IEEE Transactions on Industry Applications, Volume: 36, Issue: 5, Page(s): 1336

-1341, 2000

[49] M. Cacciato, A. Consoli, G. Scarcella, and A. Testa, "Reduction of common

mode currents in PWM inverter motor drives," Industry Applications, IEEE

Transactions on, vol. 35, pp. 469-476, 1999.

[50] G. Oriti, L. Julian, and T. A. Lipo, "An inverter/motor drive with common

mode voltage elimination," Thirty-Second IAS Annual Meeting, IAS '97.,

Conference Record of the 1997 IEEE,

[51] Y. S. Lai, "New random inverter control technique for common mode

voltage mitigation of motor drives," Electric Power Applications, IEE

Proceedings -, vol. 146, pp. 289-296, 1999

[52] A. Videt, P. Le Moigne, N. Idir, P. Baudesson, and J. Ecrabey, "A New

Carrier-Based PWM for the Reduction of Common Mode Currents Applied to

Neutral-Point-Clamped Inverters," APEC 2007 - Twenty Second Annual IEEE,

2007

72

[53] H. Zhang, A. V.Jouanne, S. Dai, A. K. Wallace, "Multilevel inverter

modulation schemes to eliminate common mode voltages," Industry

Applications, IEEE Trans, vol. 36, pp. 1645-1653, 2000

[54] P. N. Tekwani, R. S. Kanchan, K. Gopakumar, and A. Vezzini, "A five-

level inverter topology with common mode voltage elimination for induction

motor drives," presented at Power Electronics and Applications, 2005 European

Conference on, 2005.

[55] R. S. Kanchan, P. N. Tekwani, and K. Gopakumar, "Three-Level Inverter

Scheme With Common Mode Voltage Elimination and DC Link Capacitor

Voltage Balancing for an Open-End Winding Induction Motor Drive," Power

Electronics, IEEE Trans on, vol. 21, pp. 1676-1683, 2006.

[56] C. Choochuan, "A survey of output filter topologies to minimize the impact

of PWM inverter waveforms on three-phase AC induction motors," IPEC 2005.

The 7th International, 2005

[57] S. Ogasawara, H. Ayano, and H. Akagi, "An active circuit for cancellation

of common mode voltage generated by a PWM inverter," Power Electronics,

IEEE Trans, vol. 13, pp. 835-841, 1998

[58] S. Ogasawara and H. Akagi, "Suppression of common mode voltage in a

PWM rectifier/inverter system," Thirty-Sixth IAS Annual Meeting, Conference

Record of the 2001 IEEE, 2001

[59] M. Hongfei, X. Dianguo, C. Xiyou, and C. Bo, "A new common mode

sinusoidal inverter output filter," PESC2002, 2002 IEEE 33rd Annual, 2002

[60] M. M. Swamy, K. Yamada, and T. Kume, "Common mode current

attenuation techniques for use with PWM drives," Power Electronics, IEEE


[61] G. Qiang and X. Dianguo, "A New Approach to Mitigate CM and DM

Voltage dv/dt Value in PWM Inverter Drive Motor Systems," APEC 2007 -

Twenty Second Annual IEEE, 2007

[62] X. Dianguo, G. Qiang, and W. Wei, "Design of a Passive Filter to Reduce

Common mode and Differential-Mode Voltage Generated by Voltage-Source

PWM Inverter," IECON 2006 - 32nd Annual Conference on, 2006

[63] X. Chen, D. Xu, F. Liu, and J. Zhang, "A Novel Inverter-Output Passive

Filter for Reducing Both Differential- and Common mode dv/dt at the Motor

73

Terminals in PWM Drive Systems," Industrial Electronics, IEEE Transactions

on, vol. 54, pp. 419-426, 2007

[64] A. Esmaeli, Y. Sun, and L. Sun, "Mitigation of the adverse effects of PWM

inverter through active filter technique," ISSCAA 2006, 1st International

Symposium on, 2006

[65] A. Esmaeli, K. Zhao, L. Sun, and Q. Wu, "Investigation and Suppression of

the Adverse Effects of PWM Inverter through Passive Filter Technique," 1ST

IEEE Conference on, 2006

[66] Y. Sun, A. Esmaeli, and L. Sun, "A New Method to Mitigate the Adverse

Effects of PWM Inverter," presented at Industrial Electronics and Applications,

2006 1ST IEEE Conference on, 2006.

[67] Y. Sun, A. Esmaeli, L. Sun, and E. Kang, "Investigation and Suppression of

Conducted EMI and Shaft Voltage in Induction Motor Drive System," WCICA

2006. The Sixth World Congress on,

[68] H. Akagi and S. Tamura, "A Passive EMI Filter for Eliminating Both

Bearing Current and Ground Leakage Current From an Inverter-Driven Motor,"

Power Electronics, IEEE Transactions on, vol. 21, pp. 1459-1469, 2006.

[69] I. Takahashi, A. Ogata, H. Kanazawa, and A. Hiruma, "Active EMI filter for

switching noise of high frequency inverters," Power Conversion Conference -

Nagoya 1997

[70] L. H. Kim, H.-K. Yun, C. Y. Won, Y. R. Kim, and G.-S. Choi, "Output

filters design for conducted EMI reduction of PWM inverter-fed induction motor

system," presented at Power Electronics and Drive Systems, 2001. Proceedings,

2001 4th IEEE International Conference on, 2001

[71] S.Muller, M.Deicke, R.W.De Doncker, “Doubly fed induction generator

systems for wind turbines”, Industry Applications Magazine, IEEE, vol. 8, pp. 26

-33, May. 2002.

[72] P.B. Eriksen, T. Ackermann, and etc. “System Operation with High Wind

Penetration”, IEEE Power & Energy Magazine, pp.65-74, Nov/Dec, 2005

[73] Yi Zhang, Sadrul Ula, “Comparison and evaluation of three main types of

wind turbines”, Transmission and Distribution Conference and Exposition, 2008,

T&D. IEEE/PES, pp.1-6, 21-24 April 2008

74

[74] Hans overseth Rostoen, Tore M. Undeland ,Terje Gjengedal, “Doubly Fed

Induction Generator in a Wind Turbine” 3rd International Workshop on Hydro

Scheduling in Competitive Electricity Market ,Oslo, Norway, June 2008

[75] S. K Salman and Babak Badrzadeh, “New Approach for modelling Doubly-

Fed Induction Generator (DFIG) for grid-connection studies” European wind

energy conference an exhibition, London, November 2004

[76] Johann Zitzelsberger, Wilfried Hofmann, Andreas Wiese, “Bearing Currents

in Doubly-Fed Induction Generators”, Power Electronics and Applications, 2005

European Conference on, 11-14 Sept. 2005

[77] A.M.Garcia, D.G. Holmes, T.A. Lipo, “Reduction of Bearing Currents in

Doubly Fed Induction Generators” Industry Applications Conference, 2006. 41st

IAS Annual Meeting, Conference Record of the 2006 IEEE, Volume 1, on

page(s): 84-89

[78] ANSYS® Academic Research, Release 11.0, Help System, Electromagnetic

Field Analysis Guide, ANSYS, Inc.

[79] PLECS, http://www.plexim.com

[80] ANSYS® Academic Research, Release 11.0, Help System, Modeling and

Meshing Guide, ANSYS, Inc.

[81] Matthew N.O.Sadiku, “Elements of Electromagnetics” third edition, New

York, Oxford University Press, 2001

[82] Alireza Nami, Firuz Zare, “A New Random Current Control Technique for

a Single-Phase Inverter with Bipolar and Unipolar Modulations”, IEEJ

Transactions on Industry Applications, vol. 128-D, No.4, 2008

75

CHAPTER 2

Investigation of Shaft Voltage in Different

configurations of Induction Generators for

Wind Power Applications

Jafar Adabi, Firuz Zare,

School of Electrical Engineering, Queensland University of Technology, GPO

Box 2434, Brisbane, Australia

Published at: IEEJ Transactions on Electrical and Electronic Engineering, IA,

Vol.129, No.11, 2009

76

Abstract- This paper presents the analysis of shaft voltage in different

configurations of a doubly fed induction generator (DFIG) and an induction

generator (IG) with a back-to-back inverter in wind turbine applications.

Detailed high frequency model of the proposed systems have been developed

based on existing capacitive couplings in IG & DFIG structures and common

mode voltage sources. In this research work, several arrangements of DFIG

based wind energy conversion systems are investigated in case of shaft voltage

calculation and its mitigation techniques. Placements of an LC line filter in

different locations and its effects on shaft voltage elimination are studied via

Mathematical analysis and simulations. A pulse width modulation (PWM)

technique and a back-to-back inverter with a bidirectional buck converter have

been presented to eliminate the shaft voltage in a DFIG wind turbine.

2 .1 . Introduct ion

Nowadays, electrical power generation from renewable energy sources, such as

wind energy systems (WES), has become a crucial point because of

environmental problems and a shortage of traditional energy sources in the near

future. Recently, DFIGs have played a significant role in converting wind energy

to electricity [1]. The main types of wind turbines are presented at [2] which are:

(a) a fixed speed wind turbine with an asynchronous squirrel cage IG directly

connected to the grid via a transformer (b) a variable speed wind turbine with a

DFIG and blade pitch control (c) a variable speed wind turbine using a

permanent magnet synchronous generator that is connected to the grid through a

full-scale frequency converter. A comparison between the characteristics of the

above mentioned wind turbines and their mathematical models have been

investigated in [3]. To achieve a variable speed constant frequency system, an IG

is considered attractive due to its flexible rotor speed characteristics with respect

to the constant stator frequency. One solution to expand the speed range and

reduce the slip power losses is to doubly excite the stator and rotor windings.

The power converters in the rotor circuit regenerate the majority of the slip

power [4]. In a DFIG, the stator is directly connected to the AC mains, while the

wound rotor is fed from a back-to-back converter via slip rings to allow the

DIFG to operate at a variety of speeds in order to accommodate changing wind

speeds. The slip power can flow in both directions to the rotor from the supply

77

and from the supply to the rotor and hence the speed of the machine can be

controlled from either the rotor- or stator-side converter in both super and sub-

synchronous speed ranges [5].

The main issues regarding the operation of power converters used in IG and

DFIG structures are high dv/dt (fast switching transients) and common mode

voltage generated by a pulse width modulation (PWM) strategy which can lead

to a shaft voltage and resultant bearing currents, grounding current escaping to

earth through stray capacitors inside a motor, conducted and radiated noises [6-

7]. Shaft voltage is influenced by various factors such as: the design of the

generator, capacitive couplings between different parts of the machine structure,

the configuration of the main supply, voltage transient on the machine terminals,

and switching states in PWM pattern. Common mode voltage is a very important

factor in the high frequency modelling of a generator and is seen as a potential

origin of shaft voltage in high switching frequencies [7]. Its reduction techniques

[8] play a main role in attenuation of high frequency related problems of the AC

motor drive systems. The capacitive coupling between different parts of

generator structure is another issue in high frequency analysis [9]. Recently,

some techniques are presented to mitigate shaft voltage and bearing currents in

DFIGs. An approach is used in [10] to constrain the inverter PWM strategy to

reduce the overall common mode voltages across the rectifier/inverter system,

and thus significantly reduce bearing discharge currents. A general common

mode model of DFIGs is mentioned in [11] to calculate bearing current.

This paper focuses on the shaft voltage analysis (topologies, high frequency

model, calculation, mitigation techniques) of IG and DFIGs in wind turbine

applications. A back-to-back AC-DC-AC converter will be investigated in terms

of shaft voltage generation in a DFIG. Different topologies of LC filter

placement will be analysed to eliminate the shaft voltage. An accurate high

frequency model of the grid-connected wind generators based on different

topologies of doubly fed induction generators and back-to-back inverters have

been presented in the following sections. Shaft voltage mitigation techniques

have been presented based on pulse width modulation techniques and a

bidirectional buck converter topology. However, it could be shown that every

solution to reduce the shaft voltage in doubly-fed wind generator systems has its

78

special characteristics which have to be taken into account to get the most

effective strategy.

2.2 . Switching s tates and common mode vol tage of a

three phase inverter

Fig.2. 1.a shows a three phase inverter where (Vao, Vbo, Vco ) and (Van, Vbn, Vcn)

are the leg voltages and phase voltages of a three phase converter, respectively.

Vno is the voltage between neutral point and the ground (common mode voltage).

The six-switch combination of this inverter has eight permitted switching vectors

which have been shown at Fig.2. 1.b.

(a) (b)

Fig.2. 1 :(a) A three phase converter (b) 8 possible switching vectors

According to Fig.2. 1, three leg voltages of the converter can be calculated as

follow:

)t(V)t(V)t(V

)t(V)t(V)t(V

)t(V)t(V)t(V

nocnco

nobnbo

noanao

(2-1)



It is obvious that the sum of three phase voltages is equal to zero

( 0)t(V)t(V)t(V cnbnan ). Therefore, the common mode voltage can be

calculated as:

3

)t(V)t(V)t(V)t(V coboao

no

(2-3)

This equation shows that the common mode voltage is defined by a switching

pattern. By using the appropriate switching pattern, the common mode voltage

79

level can be controlled [9]. Switching states of the proposed converter, leg

voltages and the resultant common mode voltage are shown in Table.2. 1.

Table.2. 1:switching states, output leg voltage and common mode voltage of three phase inverter

vector S1 S3 S5 Vao Vbo Vco Vno

V1 1 0 0 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V2 1 1 0 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V3 0 1 0 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V4 0 1 1 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V5 0 0 1 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V6 1 0 1 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V7 1 1 1 2

Vdc 2

Vdc 2

Vdc 2

Vdc

V0 0 0 0 2

Vdc 2

Vdc 2

Vdc 2

Vdc

Fig.2. 2: Three leg voltages of a three phase inverter, common mode voltage (Van) , a phase voltage (Vao) and a line voltage (Vab)

80

Three leg voltages, common mode voltage (Van), a phase voltage (Vao) and a line

voltage (Vab) for a three phase inverter have been shown in Fig.2. 2 with a

typical pulse width modulation (PWM) switching pattern.

2.3 . Shaft vol tage analys is in s tator fed IG-based

wind power appl icat ions

Fig.2. 3 shows an induction generator wind turbine structure in which a power

converter is connected between the generator and the grid. In this case, the

voltage stress is from the stator winding. Common mode voltage creates the shaft

voltage through electrostatic couplings between the rotor and the stator windings

and between the rotor and the frame.

Fig.2. 3:stator-fed IG arrangement for wind power applications

2.3.1. IG model, calculation of different capacitive couplings and finite

elements simulation results

Fig.2. 4.a shows the structures of an IG where the parasitic capacitive couplings


frame (Csf), between the rotor and stator frames (Crf), and ball bearing and outer

and inner races (Cb1, Cb2). A simple high frequency model of a motor drive is

shown in Fig.2. 4.b and shaft voltage can be calculated as:

comsrrfb

srshaft V

CCC

CV

(2-4)

Fig.2. 5 shows a view of a stator slot, a rotor and winding where g1 is the air gap

between rotor and stator, g2 is the gap between winding and stator and gin is the

thickness of the winding insulation. d is the length of slot tooth and ρ is the

81

height of the stator slot. W and W′ are the width of winding at the top and

bottom respectively. hW is the length of the stator winding at right and the left

side of winding.

Crf

Win

din

g

(a)

(b)

Fig.2. 4: (a) Structure of a stator fed induction generator with parasitic capacitive couplings and its (b) common mode model

Fig.2. 5: a stator slot and different design parameters

82

Different capacitive couplings in a single stator slot can be approximately

calculated by Eq.2-5. These calculations are for without considering end-winding

capacitances. The effect of end-winding will be considered by a factor in the

equations.

210sr

r2rin1r2

2r1r0

in

Wr0sf

1

r0

rf

gg

dC

Lgg

dW

g

h2WC

g

L)dn

r2(

C

(2-5)

Where r is the rotor radius and g1 is the air gap, Lr is the rotor length. ε0 is the

permittivity of free space and εr1, εr2 are the permittivity of the insulation and the

slot wedge materials. Table.2. 2 shows the simulation results for the rotor radius

of 1000 mm and a range of mentioned design parameters. Thickness of

insulation (gin) is considered as 2.5 mm and εr is 2.25. The air gap thickness is

1.5 mm

Table.2. 2: Different capacitive couplings for r= 1000mm

ρ

(mm)

g2

(mm)

d

(mm)

Csr

(pF)

Csf

(nF)

Crf

(nF)

3 5 50 40.3 8.47 1.86

5 5 50 33.8 8.36 1.87

3 15 50 17.1 7.00 1.88

5 15 50 14.6 6.90 1.90

3 25 50 7.95 6.72 1.90

5 25 50 7.45 6.75 1.93

3 5 150 162 7.05 1.03

5 5 150 131 6.98 1.04

3 15 150 70.1 6.89 1.06

5 15 150 61.1 6.83 1.06

3 25 150 41.1 6.74 1.07

5 25 150 38.0 6.67 1.07

Fig.2. 6.a&b show the sketch of the ball bearing in the AC motor and the

schematic of two capacitances of a ball bearing. During operation, the distances

between the balls and races may change and vary the capacitance. At high speed,

balls and shaft positions are considered symmetric and the distances between the

83

inner race and balls (dBI) and between outer races and balls (dBO) are assumed to

be equal. At low speeds, because of gravity, balls (Fig.2. 6.c) and shaft (Fig.2.

6.d) may shift down and the system (balls position and shaft) will be

asymmetrical. In this simulation, there are 22 balls with a diameter of 30 mm, a

shaft diameter of 200 mm and the range of 0.1mm oil thickness was simulated.

Table.2. 3 shows the capacitive coupling terms (CBO, CBI) with respect to

different variables associated with the balls position assuming the equal inner

and outer distances.

shaft

inner raceball

Outer race

(a) (b)

(c) (d)

Fig.2. 6 : (a) A view of ball bearings and shaft (b) ball, outer and inner races and Asymmetric (c) ball position (d) shaft position

Table.2. 3:Capacitive coupling terms in different ball position

Oil Thickness

(mm)

dBO

(mm) dBI

(mm) CBO

(pF) CBI

(pF)

CB

(pF)

0. 1 0.01 0.09 363 78.393 64.47 0. 1 0.03 0.07 173.91 88.01 58.43 0. 1 0.05 0.05 130.07 104.44 57.927 0. 1 0.07 0.03 108.09 132.93 59.614 0. 1 0.09 0.01 94.275 216.14 65.64

Shaft centre shift down

(mm)

dBO

(mm) dBI

(mm) CBO

(pF) CBI

(pF) CB

(pF)

0.02 0.04 0.04 145.84 116.17 64.662 0.04 0.03 0.03 172.07 132.92 74.991 0.06 0.02 0.02 220.54 159.95 92.710

84

2.3.2. Shaft voltage with regards to different design parameters and

PWM pattern

In a variety of design, the ratio between Cb and Csr (α) is almost equal to 1. To

simplify the calculations, β is defined as the ratio between end-winding Csr and

without end-winding Csr. So, Csr-total is (1+β) times of Csr without end-winding.

By substituting of Eq.2-5 in Eq.2-4, the ratio between shaft voltage and common

mode voltage can be written as:

)dn

r2)(gg()d)(1)(1(g

)d)(1(g

V

V

211

1

com

sh

(2-6)


and g2 and β. It is clear that g1 can not be changed for a large range of variation

and can not be an effective parameter in shaft voltage reduction. Fig.2. 7shows

the variation of Vsh/Vcom versus variation of d and g2 stator slot height of ρ=5

mm.

Fig.2. 7 : Vsh/Vcom versus d and g2 (ρ=5 mm, x=1)

According to simulation results in different parameters, Csr is an important

capacitance in case of shaft voltage generation because it can be changed by

variation of the design parameters while other capacitances have not such a

freedom to change. An increment of stator slot tooth increases the shaft voltage

while increasing the gap between the slot tooth and winding decreasing the shaft

voltage (see Fig.2. 7).

85

Fig.2. 8 shows a simulation result for a typical PWM with a 10 kHz switching

frequency where the upper waveform is the common mode voltage and lower

one is resultant shaft voltage. The typical values of Crf=1.5 nF, Csr=0.2nF,

Csf=6nF for a single stator slot and the bearing capacitance of Cb=0.2nF for a ball

bearing are employed for capacitive couplings investigations.

Fig.2. 8 : A common mode and shaft voltage for stator-fed IG with a 10 kHz switching frequency

2.4 . Shaft voltage analys is in DFIG-based wind

power appl icat ions

Fig.2. 9 shows the arrangement of a back-to-back DC-AC-DC inverter. In this

structure, the common mode voltages of the both sides are given as:

3

VVVV,

3

VVVV zoyoxo

S,comcoboao

R,com

(2-7)

Where coboao V,V,V & zoyoxo V,V,V are the leg voltages from converter1 and

converter2 converters respectively.

Fig.2. 9: back-to-back DC-AC-DC inverter in a wind energy system

86

2.4.1. Generator structure and different configurations of LC filters in

wind turbine system

Fig.2. 10 shows the structures of a DFIG where parasitic capacitive couplings

exist in this structure between: the stator winding and rotor (Csr), the stator

winding and stator frame (Csf), between the rotor and stator frames (Crf), stator

winding and rotor winding (Cws), the rotor winding and rotor (Cwr), rotor

winding and stator frame (Cwf) and ball bearing and outer and inner races (Cb1,

Cb2).

Shaft

Stator winding

Rotor

Stator frame

Rotor winding

Cwr

Cwr

Crf

Crf

Cws

Cwf

Cb1

Cb2

Cws

Csf

Csr

Fig.2. 10: A view of DFIG with different capacitive couplings in a doubly fed induction generator

In a wind turbine application, stator and rotor windings of a DFIG connect to

both side converters and both sides common mode voltages will be an effective

factor in shaft voltage generation. In this section, different topologies of a DFIG

with a four-quadrant AC-DC-AC converter connected and different placements

of LC filters in both rotor and stator sides, and a line filter has been investigated.

In general, only the line side current is required to be sinusoidal to satisfy IEEE

standards [10]. The typical values of Cwr=3nF, Crf=1 nF, Csr=0.2nF, Csf=6nF,

Cws=.05 nF, Cwf=0.2nF for a single stator slot and the bearing capacitance of

Cb=0.2nF for a ball bearing are employed for capacitive couplings investigations.

In this research, the focus is not to investigate the dynamic analysis of the

87

system. This work wants to present the possibility of shaft voltage mitigation

techniques with LC filters and PWM pulse pattern. Analysis is not restricted to a

certain amount of frequency or slip of DFIG; however, different switching

frequencies have been presented to show the validity of the analysis. In this

paper, a modulation with switching frequency of 1 kHz from rotor side converter

and 10 kHz from stator side converter has been considered.

Topology1: As shown in Fig.2. 11.a, the network side converter is connected to

the grid through a line LC filter which is used to damp the low order harmonics

generated by the switching of semiconductors. This filter is used as a tool to

provide reactive power in order to enable power factor correction on the network

within a desired range [11]. The LC filter which connects the net-side converter

and grid reduces the harmonics and the voltage from stator side is not in a PWM

waveform anymore. Therefore it is not a common mode voltage source from

stator side converter in this configuration. An arrangement of capacitive

couplings of a doubly fed induction generator with an LC filter on the network

side converter is shown in Fig.11.b.

(a)

(b)

Fig.2. 11: (a) configuration of a DFIG with Topology1 and its (b) common mode model

88

In this case, the only common mode voltage source is from rotor winding and

this voltage stress creates some shaft voltage which can be easily calculated by a

KCL analysis as:

R,com2

srwssrsfsrbrfwr

srwswssrsfwrshaft V

CCCCCCCC

CCCCCCV

(2-8)

By considering srC as a small value and wrsr CC , it can be concluded that:

0C

CCCCCC

2sr

wssrsfwrwssr (2-9)


R,comsrbrfwr

wrshaft V

CCCC

CV

(2-10)

Vcom,R is the common mode voltage from the rotor side converter. The capacitive

coupling between the rotor winding and rotor frame has a significant value

compared with other capacitances. The major part of the common mode voltage

will be placed across the shaft. Fig.2. 12 shows a simulation result where the

upper waveform is the common mode voltage from rotor side and lower one is

resultant shaft voltage. Switching frequency for rotor side converter (fsr) is 1

kHz.

Fig.2. 12 : A typical rotor side common mode voltage waveform and its resultant shaft voltage for Topolog1 (fsr=1 kHz)

Topopolgy2: A filter is placed in the rotor side converter and the voltage from

the rotor side has fewer harmonic and no common mode voltage source (see

89

Fig.2. 13.a). An arrangement of capacitive couplings in the proposed structure is

shown in Fig.2. 13.b.

(a)

(b)

Fig.2. 13 : (a) Configuration of a DFIG with Topology2 and its (b) common mode model

The only common mode voltage source is from the stator winding. By a KCL

analysis in this configuration, the shaft voltage can be derived as:

S,com2wrwfwrwssrbrfwr

wrwswswfwrsrshaft V

CCCCCCCC

CCCCCCV

(2-11)

wsC & wfC are very small values in compare with other capacitances and can be

neglected in calculations. Eq.2-11 can be rewritten as:

S,com2wrsrbrfwr

2wr

wrsr

S,com2wrsrbrfwrwr

wrsrshaft

VCCCCCC

CC

VCCCCCC

CCV

(2-12)

Based on this calculation, shaft voltage is as follow:

S,comsrbrf

srshaft V

CCC

CV

(2-13)

Fig.2. 14 shows a simulation result where the upper waveform is the common

mode voltage from stator side and lower one is the resultant shaft voltage. In this

90

case, 14% of the stator side common mode voltage converts to shaft voltage.

Switching frequency for rotor side converter (fss) is 10 kHz.

Fig.2. 14: A typical stator side common mode voltage and its resultant shaft voltage for Topology2 (fss=10 kHz)

Topology3: Two LC filters in the both rotor and stator sides are used to damp

the higher order harmonics. In this case, there is not any common mode voltage

from both sides (see Fig.2. 15.a). Hence, the possibility of the shaft voltage

generation has been reduced.

(a)

(b)

Fig.2. 15 : (a) Configuration of a DFIG with Topology3 and its (b) common mode model

91

Topology4: As shown in Fig.2. 16.a, there is no LC filter in both converters

sides. Fig.2. 16.b shows the high frequency model of a doubly fed induction

machine without filters.

(a)

(b)

Fig.2. 16: (a) configuration of a DFIG with Topology4 and its (b) common mode model

In this structure, neutral to ground zero sequence voltage of both stator and rotor

winding act as common mode voltage sources. The shaft voltage can be easily

calculated by using KCL in the high frequency model of the doubly fed

generator. According to Fig.2. 16.b, the shaft voltage is:

S,comsrbrfwr

srR,com

srbrfwr

wrshaft V

C C CC

CV

C C CC

CV

(2-14)



windings, respectively. KR and KS are defined as capacitance factors which are

effective in total shaft voltage calculation.

srbrfwr

srS

srbrfwr

wrR

C C CC

CKand

C C CC

CK

(2-16)


(KR is near 1 and KS is a very small value). Fig.2. 17 shows the simulation

92

results for total shaft voltage and the share of each converter in shaft voltage

generation.

Fig.2. 17: a common mode and shaft voltage shaft voltage generated by rotor and stator side converters (fsr=1 kHz, fss=10 kHz)

A major portion of the rotor side common mode voltage transformed to the shaft

voltage (in this case, 68% of rotor side common mode voltage and only 4.5% of

stator side common mode voltage transformed to shaft voltage). Based on this

analysis, the stator common mode voltage does not have a key effect on shaft

voltage because the capacitive coupling between the stator winding and shaft is

too small in comparison with capacitive coupling between the rotor winding and

shaft.

93

2.4.2. Discussion on shaft voltage elimination strategies for different

topologies of DFIG-based system

Different topologies have been simulated in the previous part in case of shaft

voltage generation. The effects of PWM techniques and filtering are investigated

in each configuration. Choosing one of these options depends on the cost of

filtering, changing the PWM pattern and increasing switching frequency or

employing additional circuits to reduce the rotor side voltage.

The system configuration in Topology 1 can not remove the shaft voltage

because the common mode voltage from the rotor still exists. This voltage has a

major impact on the shaft voltage. In this case by removing stator side common

mode voltage, a small part of shaft voltage will be removed. Removing zero

switching vectors in this case can reduce rotor side common mode voltage and as

a result a reduced shaft voltage can be achieved. As mentioned in the previous

section, removing the rotor side common mode voltage (Topology2) by filtering

the rotor side converter will remove major part of the shaft voltage but there is a

considerable amount of shaft voltage from the stator side. Removing zero

switching vectors from stator side converter can reduce the common mode

voltage and as a result a reduced shaft voltage can be achieved.

In these two topologies (1&2), the price for filtering is paid but there is still a

considerable amount of shaft voltage. Furthermore, it is obvious that the

configuration of Topology3, because of filtering in both sides, will remove both

sides’ common mode voltages and will not generate shaft voltage significantly.

In Topology4, according to Eq.2-15 and Fig.2. 16.b, it is clear that by choosing

the rotor common mode voltage as follow, zero shaft voltage can be achieved.

S,comwr

srR,com V

C

CV (2-17)

Table.2. 4 shows the resultant shaft voltage by different switching states

generated by a back-to-back converter applied to the both rotor and stator sides.

Note that, rotor side common mode voltage has been decreased

to S,comwr

sr VCC by a buck converter and shaft voltage is calculated based on

Eq.2-15 and Table.2. 4. To eliminate the shaft voltage, we need to generate

common mode voltage on the rotor side based on Eq.2-17. To meet these

94

requirements, it is needed to apply odd switching vectors (1, 3, and 5) to one

converter and even switching vectors (2, 4, and 6) to another converter. Also,

switching vector V0 from one side and vector V7 from other side is conducted to

a zero shaft voltage. As mentioned in [11], to fully eliminate the common mode

it is, in principle, necessary to coordinate the zero states such that they occur

synchronously.

Table.2. 4: Different switching states and shaft voltage


Vectors

1,3,5

Vectors

2,4,6

Vector

7

Vector

0

Net

wor

k si

de c

onve

rter

Vectors

1,3,5 3VK dcS 0 3

VK dcS3

VK2 dcS

Vectors

2,4,6 0 3

VK dcS3

VK2 dcS3

VK dcS

Vector

7 3VK dcS 3

VK2 dcS dcSVK 0

Vector

0 3VK2 dcS

3VK dcS 0 dcSVK

However, since the line side rectifier operates at line voltage and the inverter

requires only a small fraction of the line voltage as it operates at slip frequency

and at a different switching frequency, such a synchronous operation is generally

impractical. The problem can be eliminated by simply avoiding the use of the

zero states. Therefore, the odd switching vectors from one side and the even

switching vectors from other side converter is the only solution (see Fig.2. 18). It

can be noted that the penalty for this strategy is an increase in the switching

frequency and losses. However, this is of little consequence for a wind turbine

application, and produces only a very small amount of additional losses.

Fig.2. 18: Space vector operating region for the converters to eliminate the shaft voltage

95

To achieve the conditions of Eq.2-17, a bidirectional buck converter has been

used to decrease the dc link voltage of C1 (VC1) to Vc2. the duty cycle for

proposed converter should be chosen at S,comwr

sr VCC . Fig.2. 20 shows common

mode voltages from rotor and stator side and resultant shaft voltage after using

the PWM technique in Fig.2. 18 and the circuit configuration of Fig.2. 19. Note

that switching frequency of the converters is different but by using the suitable

vectors the common mode voltages are in constant levels.

Fig.2. 19: a new back-to-back inverters topology with a bidirectional buck converter and a DFIG

Fig.2. 20: common mode and shaft voltages in Topology 4 after applying the presented PWM

96

2.5 . Conclus ions

Different configurations of IG and DFIGs are analysed in terms of shaft voltage

generation. Filtering in different converters side, PWM techniques and a circuit

topology have been presented in order to reduce the shaft voltage. According to

analyses, filtering in the rotor or stator side can not help to fully mitigate shaft

voltage, and using PWM techniques can not eliminate the shaft voltage

(removing zero states can help to reduce the shaft voltage.). A zero shaft voltage

can be achieved by filtering at both sides converter because both sides’ common

mode voltage sources forced to be zero. To fully eliminate the common mode it

is, in principle, necessary to coordinate the zero states such that they occur

synchronously. However, since the line side rectifier operates at line voltage and

the inverter requires only a small fraction of the line voltage as it operates at slip

frequency and at a different switching frequency, such a synchronous operation

is generally impractical. The problem can be eliminated by simply avoiding the

use of the zero states. Therefore, the odd switching vectors from one side and the

even switching vectors from other side converter is the only solution. A

bidirectional buck converter has been employed to reduce the dc link capacitor

voltage and as a result reduce the rotor side common mode voltage.

Mathematical analysis and simulation results have been presented to verify the

investigations.

Acknowledgment

The authors thank the Australian Research Council (ARC) for the financial

support for this project through the ARC Discovery Grant DP0774497.

2.6 . References:


systems for wind turbines”, Industry Applications Magazine, IEEE, vol. 8, pp. 26

-33, May. 2002.

[2] P.B. Eriksen, T. Ackermann, and etc. “System Operation with High Wind

Penetration”, IEEE Power & Energy Magazine, pp.65-74, Nov/Dec, 2005

[3] Yi Zhang , Sadrul Ula, “ Comparison and evaluation of three main types of

wind turbines”, Transmission and Distribution Conference and Exposition, 2008.

T&D. IEEE/PES, pp.1-6, 21-24 April 2008

97

[4] Hans overseth Rostoen, Tore M. Undeland ,Terje Gjengedal, “Doubly Fed

Induction Generator in a Wind Turbine” 3rd International Workshop on Hydro

Scheduling in Competitive Electricity Market ,Oslo, Norway, June 2008

[5] S. K Salman and Babak Badrzadeh, “New Approach for modelling Doubly-

Fed Induction Generator (DFIG) for grid-connection studies” European wind

energy conference an exhibition, London, November 2004

[6] J. M. Erdman, R. J. Kerkman, D. W. Schlegel, and G. L. Skibinski, "Effect of

PWM inverters on AC motor bearing currents and shaft voltages," Industry

Applications, IEEE Transactions on, vol. 32, pp. 250-259, 1996.

[7] C. Mei, J. C. Balda, W. P. Waite, and K. Carr, "Minimization and

cancellation of common mode currents, shaft voltages and bearing currents for

induction motor drives," presented at Power Electronics Specialist Conference,

2003. PESC '03, IEEE 34th Annual, 2003.




[9] Jafar Adabi, Firuz Zare, Gerard Ledwich, Arindam Ghosh, “Leakage Current

and Common Mode Voltage Issues in Modern AC Drive Systems”, presented at

AUPEC 2007, Perth, Australia, Dec 2007.


in Doubly-Fed Induction Generators”, Power Electronics and Applications, 2005

European Conference on, 11-14 Sept. 2005

[11] A.M.Garcia, D.G. Holmes, T.A. Lipo, , “Reduction of Bearing Currents in



page(s): 84-89

99

CHAPTER 3

Calculations of Capacitive Couplings in

Induction Generators to Analyse Shaft Voltage

*Jafar Adabi, * Firuz Zare, * Arindam Ghosh, ** Robert D. Lorenz

*School of Electrical Engineering, Queensland University of Technology, GPO


** Depts. of ME and ECE, University of Wisconsin-Madison, 1513 University

Avenue, Madison, USA

Accepted for Publication: IET Transaction on Power Electronics

100

Abstract- This paper deals with an analysis of the parameters which are

effective in shaft voltage generation of induction generators. It focuses on

different parasitic capacitive couplings by mathematical equations, Finite

element simulations and experiments. The effects of different design parameters

have been studied on proposed capacitances and resultant shaft voltage. Some

parameters can change proposed capacitive coupling such as: stator slot tooth,

the gap between slot tooth and winding, and the height of the slot tooth, as well

as the air gap between the rotor and the stator. This analysis can be used in a

primary stage of a generator design to reduce motor shaft voltage and avoid

additional costs for resultant bearing current mitigation.

3 .1 . Introduct ion

Pulse width modulated inverters are widely used in industrial and commercial

applications due to the growing need of speed control in adjustable speed motor

drive systems. This voltage generated by an inverter is a major cause of motor

bearing failures in a motor drive system. All inverters generate a common mode

voltage relative to the ground, which makes a shaft voltage due to parasitic

capacitances in the motor. This occurrence can cause many unwanted problems

in the interaction with parasitic capacitive couplings in an AC motor [1-3].

Common mode voltage generated by a PWM inverter in AC motor drive systems

can cause shaft voltage and resultant bearing currents due to capacitive coupling

between winding, stator and rotor [4-5].

Different approaches and techniques have been analysed in [4, 8] in order to

calculate capacitive coupling in AC motors and to extract high frequency

parameters of an AC motor for EMI analysis. In [6-7] different types of

techniques to measure shaft voltage and bearing current in motor drive systems

have been discussed. As zero voltage vectors in a three-phase inverter generate

significant common mode voltage, thus using only active voltage vectors in a

three-phase inverter can reduce common mode voltage significantly. Active EMI

filter using an extra leg in an inverter to cancel zero voltage vectors have been

proposed in [9]. Common mode voltage and shaft voltage in a doubly fed

induction generator (DFIG) and their reduction techniques have been discussed

in [10-12]. In these papers the effect of PWM voltage from both stator and rotor

101

sides have been considered and methods for shaft voltage reduction have been

investigated.

This paper focuses on the design parameters of a stator slot which are effective

in high frequency analysis. A detailed mathematical analysis will be carried out

to determine the effects of these parameters on motor shaft voltage. Fig.3. 1.a&b

show the structures of an stator-fed induction generator (IG) and a DFIG where

the parasitic capacitive couplings exist between: the stator winding and rotor

(Csr), the stator winding and stator frame (Csf), the rotor and stator frames (Crf),

stator winding and rotor winding (Cws), the rotor winding and rotor (Cwr), rotor

winding and stator frame (Cwf) and ball bearing and outer and inner races (CBO,

CBI).

(a)

(b)

(c)

(d)

Fig.3. 1:(a) Structure of an IG with different parasitic capacitive couplings (b) A view of a DFIG with different parasitic capacitive couplings with and high frequency model of (c) IG (d)

DFIG

Common mode voltage creates the shaft voltage through electrostatic couplings.

A simple high frequency model of IG is shown in Fig.3. 1.c and shaft voltage

can be calculated as:

comsrrfb

srshaft V

CCC

CV

(3-1)

102

The main issues regarding the operation of power converters used in DFIG

structures are common mode voltage from both rotor and stator side converters.

According to Fig.3. 1.d, the shaft voltage in a DFIG can be calculated as:

S,comSR,comR

S,comsrbrfwr

srR,com

srbrfwr

wrshaft

VKVK

VC C CC

CV

C C CC

CV

(3-2)


windings, respectively. KR and KS are defined as rotor and stator side

capacitance factors which are effective in total shaft voltage generation.

The main goal of this work-which is to find the effect of machine parameters on

the shaft voltage-, uses a model to analyse of this effect. This is based on the

lumped capacitances because the originality of the shaft voltage is based on the

electrostatic phenomena. In this research, a mathematical equation has been

developed to calculate the shaft voltage in induction generators with respect to

many design parameters.

3 .2 . Calculat ion of shaft vol tage and re levant

capaci t ive coupl ings in a generator s tructure

Fig.3. 2.a shows a view of a stator slot, a rotor and winding where g1 is the air

gap between rotor and stator, g2 is the gap between winding and stator and gin is

the thickness of the winding insulation. d is the length of slot tooth and ρ is the


bottom respectively. hW is the length of the stator winding at both the right and

the left side of winding. Following capacitive couplings can be calculated in the

structure of induction generators.

3.2.1. The capacitive coupling between rotor and stator frame (Crf)

By considering the air gap (g1) to be much smaller than the outer diameter of the

rotor, a capacitive coupling between rotor and stator frame in a single stator slot

can be calculated as follows:

1

r0

rf g

L)dn

r2(

C

(3-3)

103

Where r is the rotor radius and g1 is the air gap, Lr is the rotor length. This

capacitance can be multiplied by the number of slots (n) to calculate the total

capacitance.

(a)

(b)

Fig.3. 2: (a) A view stator slot and different design factors (b) ball bearings and shaft of a motor with a view of ball, outer and inner races and the capacitances

3.2.2. The capacitive coupling between frame and stator winding (Csf)

In this case, there are four surfaces which surround the winding. So, Csf can be

calculated as:

top

in

rWr0sf C

g

Lh2WC

(3-4)

Ctop is the capacitance between the upper side of winding and the stator slot

tooth. This capacitance consists of insulation capacitance (Cin,top) and slot wedge

capacitance (Cwedge). Where:

2

r2r0wedge

in

r1r0top,in g

LdWC,

g

LdWC

(3-5)

104

Therefore, Ctop can be calculated as:

2rin1r2

r2r1r0

wedgetop,in

wedgetop,intop gg

LdW

CC

CCC

(3-6)

Based on these calculations, the capacitance between winding and stator frame

is:

r

2rin1r2

2r1r0

in

Wr0sf L

gg

dW

g

h2WC

(3-7)

Where ε0 is the permittivity of free space and εr1, εr2 are the permittivity of the

insulation and the slot wedge material.

3.2.3. The capacitive coupling between ball bearings and inner and outer

races

Fig.3. 2.b shows the sketch of the ball bearing in the AC generator and the

schematic of two capacitances of a ball bearing. Calculation of ball bearing

capacitances is not an easy task because the geometrical structure is rather

complex [1]. Therefore some references [6-8] have different approaches to

calculate these capacitive couplings. As shown in this figure, there are balls

between the outer and the inner races with lubricating grease between the balls

and the races. There are capacitive couplings between ball bearings and the outer

and inner races (CBO and CBI). The ball bearing capacitance is calculated by:

BOBI

B

C

1

C

11

C

(3-8)

3.2.4. The capacitive coupling between rotor and stator winding (Csr)

As shown in Fig.3. 3.a, existing capacitive couplings are: the capacitive coupling

between rotor and winding (Csr), the capacitive coupling between rotor and stator

in left and right sides of the slot tooth (Cf1r, Cf2r), and capacitive coupling

between winding and stator in left and right sides of the slot tooth (Cf1s, Cf2s).

Fig.3. 3.b shows a model to calculate the capacitive couplings. In fact, the

electric fields between stator slot teeth on both sides influence the total electric

field between the rotor and stator. Fig.3. 3.c shows a typical electric field in the

proposed system (the voltages applied to upper, lower and besides objects are 50,

100 and 0 volts respectively).

105

(a)

(b)

(c)

(d)

Fig.3. 3: (a) capacitive couplings in a stator slot (b) a complete system model for calculation of capacitive couplings (c) simplified model with

electric fields and the capacitive couplings (d) two vertical surfaces

106

To calculate the side capacitances (Cf1r, Cf2r, Cf1s, Cf2s), the structure of two

surfaces with the voltage difference of V0 and the angle of (here 090 ) needs

to be considered. As shown in Fig.3. 3.d, the small gap between two surfaces is

ρ1 and the length of the surface is ρ2. The capacitance can be calculated as:

V

dS.E

V

QC 0

(3-9)

Based on [13], the electric field between two surfaces can be calculated by:

a

Va

d

dV1VE

0

0 (3-10)

Considering adzdds in cylindrical coordinates, the capacitive coupling

between two surfaces is:

1

120

0

0

1

12

0

00

0

0

d

0 0

00

Lnt

V

LntV

V

adzdV

C

2

1 (3-11)

Because of a small gap between the two surfaces, the system model in Fig.3. 3.b

can be simplified as in Fig.3. 3.c. Thus, the electric field between half of f1 and

the rotor can create a capacitive coupling Cf1r and another half of f1 can create

the capacitive coupling with stator winding (Cf1s). The same is also found in the

other side of the stator slot tooth (f2) and resultant capacitive couplings (Cf2r,

Cf2s). According to Eq.3-10, these capacitances are:

2

20s2fs1f

1

10r2fr1f

g

g2Ln

2CC

g

g2Ln

2CC

(3-12)

Considering the electric field between sides of the slot tooth (S1, S2), the


decrease and Csr is:

210sr gg

dC

(3-13)

Fig.3. 4 shows the difference between simulations and calculations of Csr in a

complete system model versus a variation of g2 (ρ=5, 25 mm and g1=1, 2 mm)

over a wide rage of stator slot tooth (d).

107

(a)

(b)

Fig.3. 4: The difference between simulations and calculations of Csr in a complete system model versus a variations of g1 and g2

(a) ρ=5mm (b) ρ=25mm

108

3.3 . S imulat ion resul ts

Capacitance matrixes of multi-conductor systems in different 3-D model designs

of the motor have been extracted by simulation [14] and compared with the 2-D

simulation analysis and the calculation results. Also, a simulation study for ball

bearing capacitances was carried out for different conditions.

3.3.1. Effects of the parameters of stator slot on capacitive couplings

Rotor radius=1000mm

In this section, simulations were conducted for a single slot for 12 design

structures of Table.3. 1. The thickness of insulation (gin) is considered as 2.5 mm

and r is 2.25. Fig.3. 5.a, b and c show the calculated, 2-D, 3-D results in single

stator slot for Csr, Crf, Csf respectively. In a 3-D analysis, fringing effects at the

both sides of the stator have been considered while in 2-D analysis, it is not

possible to consider that effects. A complete generator system (number of

slots=24) has been simulated based on the first six designs of Table.3. 1 (see

Fig.3. 5.d & e) using 3-D analysis.

Table.3. 1: different design parameters for proposed IG structure

Design

number

ρ

(mm)

g2

(mm)

d

(mm)

w

(mm)

hw

(mm)

1 3 5 50 200 289

2 5 5 50 200 287

3 3 15 50 201 278

4 5 15 50 201 276

5 3 25 50 203 268

6 5 25 50 205 266

7 3 5 150 200 289

8 5 5 150 200 287

9 3 15 150 201 278

10 5 15 150 201 276

11 3 25 150 203 268

12 5 25 150 205 266

109

Capacitive coupling between rotor and stator winding

0

20

40

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8 9 10 11 12Design number

Csr

(p

F)

Csr-cal Csr-2D Csr-3D

(a)

Capacitive coupling between rotor and stator frame (Crf)

0.85

1.05

1.25

1.45

1.65

1.85

1 2 3 4 5 6 7 8 9 10 11 12

Design number

Crf

(n

F)

Crf-cal Crf-2D Crf-3D

Capacitive coupling between stator winding and the frame(Csf)

6.1

6.3

6.5

6.7

6.9

7.1

7.3

1 2 3 4 5 6 7 8 9 10 11 12Design number

Csf

(n

F)

Csf-cal Csf-2D Csf-3D

(b) (c)

Csr for a 24 slot structure

200

300

400

500

600

700

800

1 2 3 4 5 6Design nember

Cs

r (p

F)

Crf and Csf for a 24 slot structure

35

45

55

65

75

85

95

1 2 3 4 5 6Design number

Crf

(n

F),

Cs

f (n

F)

Csf Crf

(d) (e)

Fig.3. 5 : Calculated, 2-D, 3-D results in single stator slot for capacitive couplings (a) Csr (b) Crf(c) Csf ; 3-D simulation results in a 24 slot IG for (d) Csr (e) Crf and Csf

Rotor radius=600mm: A simulation study has been carried out for a single

stator slot with the design parameters of Table.3. 2. Fig.3. 6.a shows the variation

of Csf versus the changes of g2 where g1=1mm, d=8, ρ=4mm. It shows that by

changing g2 from 5 to 50 mm, Csf changes between 4.88nF and 4.04 nF which is

not a big variation. Fig.3. 6.b shows the variation of Csf versus stator slot tooth

and two different air gaps. Thus, the effects of the stator slot tooth on Csf are

very low. Fig.3. 6.c shows the changes of Csr versus stator slot tooth at two

different air gaps. It shows slot tooth variation has a great effect on this

110

capacitance while the air gap is not an effective factor. As shown in Fig.3. 6.d,

the capacitance decreases with increments of the stator slot tooth.

Capacitive couplings between winding and stator

4

4.1

4.24.3

4.4

4.5

4.6

4.74.8

4.9

5

5 10 15 20 25 30 35 40 45 50

gap between slot tooth and winding (mm)

Csf

(n

F)

Capacitive coupling between winding and stator

4.8

4.81

4.82

4.83

4.84

4.85

4.86

4.87

4.88

4.89

8 16 24 32 40

stator slot tooth (mm)

Csf

(n

F)

g=1 mm g=1.5 mm

(a) (b)

Capacitive coupling between rotor and w inding

0

5

10

15

20

25

30

35

8 16 24 32 40stator slot tooth (mm)

csr

(pF

)

g=1 mm g=1.5 mm

Capacitive coupling betw een rotor and winding

0

2

4

6

8

10

12

14

5 10 15 20 25 30 35 40 45 50gap betw een slot tooth and winding (mm)

Csr

(p

F)

g=1 mm g=1.5mm

(c) (d)

Fig.3. 6: Variation of Cws versus: (a) the changes of g2 (b) stator slot tooth and two different air gaps. variation of Cwr versus: (c) stator slot tooth (d) the changes of g2

Table.3. 2: Different design parameters of a single slot for

3.3.2. Analysis of ball bearing capacitances in different conditions

During operation, the distances between the balls and races may change and vary

the capacitance. At high speed, balls and shaft positions are considered

symmetric and the distances between the inner race and balls (dBI) and between

outer races and balls (dBO) are assumed to be equal. Also the shaft position is not

changed and the shaft and outer race is concentric (see Fig.3. 2). At low speeds,

Rotor radius 600 mm

Stator Slot tooth(d) 8, 16,24,32,40 mm

Air gap (g1) 1, 1.5 mm

Gap between slot tooth

and winding (g2) 5,10,15,…,50 mm

Height of slot tooth (ρ) 4,8,12 mm

111

because of gravity, balls and shaft may shift down and the system (balls position

and shaft) will be asymmetrical.

(a) (b)

Fig.3. 7: Asymmetric (a) ball positions (b) shaft position

As shown in Fig.3. 7.a, in this asymmetric case, the upper and lower side balls

are shifted down because of gravity but the separations between the inner and

outer races with other is approximately symmetrical. As shown as in Fig.3. 7.b,

at lower speeds, an asymmetric shaft position may occur, which is more common

than other cases. In this simulation, there are 22 balls with a diameter of 30 mm,

a shaft diameter of 200 mm and the range of 0.1mm oil thickness was simulated.

In this case, shaft position is shifted down corresponding to 20%, 40% and 60%

grease thickness. Table.3. 3 shows the capacitive coupling terms (CBO, CBI) with

respect to different variables associated with the balls position assuming the

equal inner and outer distances.

Table.3. 3: Capacitive coupling terms in different ball position

Oil

Thickness (mm)

dBO

(mm)

dBI

(mm)

CBO

(pF)

CBI

(pF)

CB

(pF)

0. 1 0.01 0.09 363 78.393 64.47

0. 1 0.03 0.07 173.91 88.01 58.43

0. 1 0.05 0.05 130.07 104.44 57.927

0. 1 0.07 0.03 108.09 132.93 59.614

0. 1 0.09 0.01 94.275 216.14 65.64

Shaft centre shift

down (mm)

dBO

(mm)

dBI

(mm)

CBO

(pF)

CBI

(pF)

CB

(pF)

0.02 0.04 0.04 145.84 116.17 64.662

0.04 0.03 0.03 172.07 132.92 74.991

0.06 0.02 0.02 220.54 159.95 92.710

112

According to Fig.3. 1.d, in the high frequency model of the system, Cb is in

parallel with the Crf. Crf is a big capacitance compared with bearing capacitances.

Therefore, it has less effect than other capacitances. That means the value of the

capacitance cannot change the shaft voltage significantly. Crf +Cb approximately

equals to Crf.

3.4 . Experimental resul ts

To verify the analysis and simulation results, several tests have been performed

to measure common mode and shaft voltages and compare them with the

simulation results. It is very important to consider practical issues when we

compare test and simulation results. Thus, simulations have been performed for a

5 kW 3-phase induction machine with 36 slots considering practical issues. In a

real machine, in each slot a distance between a winding and the rotor surface

(referring to Fig.3. 2.a, the length of g1++g2) is changed along the rotor axis and

in different slots. Based on our measurement, this distance varies between (3.5

mm and 4.5 mm). Several simulations have been carried out to extract the

capacitive couplings for three different distances (g1++g2), 3.5mm, 4mm and

4.5mm and the results are given in Table.3. 4.

Table.3. 4: Simulation results with and without end-winding (pF)

Another practical issue is the effect the insulator property (εr) on Csr, which has

been analysed and addressed in Eq.3-14. Considering three different εr (2, 2.5

and 3) and also based on Fig.3. 3.a, the capacitive coupling between the winding

and the rotor can be defined as follows:

air_srin_srair_sr

in_srair_srC

CC

CC

(3-14)

g

(mm)

Csr

(εr =2)

Csr

(εr =2.5)

Csr

(εr =3)

Csr

(εr ={2-3})

Crf

Vsh/Vcom

without

end

winding

4.5 7.1 7.2 7.2 7.2 545 0.013

4 10.01 10.05 10.08 10.05 545 0.018

3.5 13.22 13.32 13.35 13.29 545 0.024

with

end

winding

4.5 15.71 15.72 15.72 15.72 545 0.028

4 18.62 18.66 18.69 18.66 545 0.033

3.5 21.83 21.93 21.96 21.90 545 0.038

113

In fact two capacitors, Csr _air and Csr_in are in series and because the thickness of

the insulator is much less than (g1++g2), thus Csr_air<< Csr_in and the capacitive

coupling between the winding and the rotor approximately equals to Csr_air. This

analysis shows that the simulations to extract the capacitive coupling between

the winding and the rotor are not affected by the insulator property (εr). The

simulation results for different εr (2, 2.5 and 3) are given in Table.3. 4.

According to the above discussion and based on the simulation results, the effect

εr on Csr is negligible while the effect of (g1++g2) on Csr is significant. The last

practical issue is the effect of end winding on the shaft voltage. As shown in

Fig.3.8.a due to a capacitive coupling between the end winding and the rotor

side, Csr_end, the total capacitive coupling between the windings and the rotor,

Csr_total is increased. In a real machine, the length of the end winding and also its

configuration at both sides are not uniform. To analyse this issue, each end

winding has been modelled as a cylinder connected to each side of the winding

as shown in Fig.3.8.b.

(a) (b)

Fig.3. 8: (a) view of machine structure with end-winding (b) view of shielded end winding

In this induction machine, the length of the end winding varies between 30mm

and 40mm and simulation results show that Csr_end are 8.20 pF and 9.03 pF,

respectively. Thus we have considered 8.61 pF an average of the capacitive

coupling between the end windings and the rotor. According to the simulation

results and based on Eq.3-15, Vsh/Vcom ratios have been calculated for different

cases and the results are given in Table.3. 4. Eq.3-15 shows that the voltage ratio,

Vsh/Vcom approximately equals to Csr/Crf. Thus measuring the common mode and

shaft voltages can give Csr/Crf ratio for the given induction machine.

114

rf

sr

rfsr

sr

rfsrb

sr

com

sh

C

C

CC

C

CCC

C

V

V

(3-15)

(a) (b)

Fig.3. 9:Experimental results: Common mode and shaft voltage waveforms (a) without shielded end winding (b) with shielded end winding

We have performed two main tests for the induction machine; in the first test, all

capacitive coupling have been considered without shielding any part of the end

winding and the results can be compared with the simulation result (with end

winding). In the second test, we have shielded the end windings to compare the

test result with the simulation result (without end winding). The common mode

and shaft voltage waveforms with and without shielded end windings are shown

in Fig.3. 9. Vsh/Vcom ratios have been calculated based on the measurement

results which are given in Table.3. 5.

Table.3. 5: Comparison between the simulation and test results

Simulation and test results with and without

end winding Vsh/Vcom

Simulation, without end winding

g1+ +g2 = 4 mm 0.018

Simulation, with end winding

g1+ +g2 = 4 mm 0.033

Test results (with shielded end winding)


Test results (without shielded end winding)


Considering an average of 4mm for the distance between the windings and the

rotor (g1+ +g2), the difference between the simulation result without end

winding (0.018) and the test result with shielded end winding (0.0207) is around

13%. According to Eq.3-15, Vsh/Vcom significantly depends on Csr and Crf. Thus,

115

the difference between the simulation and test results are due to the variation of

(g1+ +g2) values which affects Csr. In the other test, we have considered the end

winding effect and the difference between the simulation result with end winding

(0.033) and the test result without shielded end winding (0.0306) is around 8%.

This difference can also be addressed to capacitive couplings between the rotor

and the shielded surfaces which have been grounded on both sides of the rotor

(8.61 pF) and also due to a capacitive coupling between the rotor shaft and the

motor frame which has not been considered in this analysis. Thus, the small error

between the test and simulation results shows that this analysis and finite

element simulation approach can be used as a good design tool for Induction

Machine Design to analyse and reduce shaft voltage.

3.5 . Discuss ion

Stator-fed induction generator: Based on the simulation results and the

analysis in [7-8], in a variety of design parameters changes, the ratio between Csr

and Crf is between 0.05 and 0.1. Also, the ratio between Cb and Csr (α) is almost

equal to 1. β is defined as the ratio between end-winding Csr and without end-

winding Csr. So, Csr-total is (1+β) times of Csr without end-winding which is

calculated in Eq.3-13. By substituting equations (3-3) & (3-13) in Eq.3-1, the

ratio between shaft voltage and common mode voltage can be written as:

d,

)dn

r2)(gg()d)(1)(1(g

)d)(1(g

V

V

211

1

com

sh (3-16)


and g2 and β. It is clear that g1 cannot be changed for a large range of variation

and cannot be an effective parameter in shaft voltage reduction. Fig.3. 10.a

shows the variation of Vsh/Vcom versus variation of d and g2 stator slot height of

ρ=5 mm. This graph shows the effect of two main design parameters on shaft

voltage. According to simulation results in different parameters:

Csr is an important capacitance in case of shaft voltage generation in an IG

because it can be changed by variation of the design parameters (see Fig.3.

5and 6) while other capacitances has not such a freedom to change.

An increment of stator slot tooth increases the shaft voltage while increasing

the gap between the slot tooth and winding decreasing the shaft voltage (see

116

Fig.3. 10.a). This information can be taken into account in the design

procedure of the motor structure and the motor designer can choose design

parameters which are a trade off between shaft voltage issue and other

electromechanical considerations.

Doubly-fed induction generator: If the rotor slot shape in a DFIG is

considered same as the stator slot in Fig.3. 2, the shaft voltage in DFIG is

calculated based on Eq.3-2 as S,comSR,comRshaft VKVKV , where KR and

KS are:

)d)(1(gdn

r2g)1(Agg

g)d(K

)d)(1(gdn

r2g)1(Agg

)1(AggK

11

1S

11

1R

(3-17)

λ is the ratio between end-winding Cwr and without end-winding Cwr which is

usually less than 0.05. g and A are:

21

2rin1r2in

2r1r0inW2rin1r21rwr

ggg

)gg(g

dWg)h2W()gg(CA

(3-18)

Therefore, shaft voltage in DFIG is a function of different parameters such as:

W, d, hw, gin, εr, ρ, g1, g2. Fig.3. 10.b and c show the KR and KS versus variations

of g2 and d (λ=0.05, ρ=5mm, g1=1mm, w′=150, W=120 mm, hW=230 mm,

gin=2mm, εr=2.25). Fig.3. 10.d and e show the KR and KS versus variations of εr

and gin (λ=0.05, ρ=5mm, g1=1mm, w′=150mm, W=120mm, hW=230 mm,

d=50mm, g2=10mm).

According to the analysis:

Majority of rotor side common mode voltage converts to shaft voltage (by

factor of KR which is near 1) while the stator side common mode voltage has

not a big effect on the shaft voltage. This fact should be mentioned as a key

factor in shaft voltage mitigation techniques. The capacitive coupling

between the rotor winding and rotor frame has a significant value compared

with other capacitances. The major part of the common mode voltage will be

placed across the shaft.

117

With a variation of gap between winding and stator (g2) and length of slot

tooth (d), it is possible to control the shaft voltage but as it can be seen from

Fig.3. 10.b and c, the effects of these factors are not so high. As shown in

Fig.3. 10.d and e, the effects of the permittivity and thickness of the insulator

in the rotor slots are very effective in shaft voltage reduction. In fact the

permittivity and thickness of the insulator in the stator slots has less effect in

reducing shaft voltage (Fig.3. 10.a).

(a)

(b) (c)

(d) (e)

Fig.3. 10: (a) Vsh/Vcom versus d and g2 (ρ=5 mm, x=1) ; (b) KR versus g2 and d (c) KS versus g2 and d (d) KR versus εr and gin (e) KS versus εr and gin in a doubly-fed induction generator

118

3.6 . Conclus ions

The capacitive coupling between rotor and stator winding is a key factor in shaft

voltage generation for a stator-fed IG. Some parameters can change proposed

capacitance such as: stator slot tooth, the gap between slot tooth and winding,

and the height of slot tooth, as well as the air gap between rotor and stator. In a

DFIG, the capacitive coupling between the rotor winding and rotor frame has a

significant value compared with other capacitances. The effects of the insulation

parameters such as permittivity and the thickness of the insulation are very

effective in shaft voltage reduction (see Fig.3. 10). Theses parameters can be

changed to achieve the lowest possible shaft voltage but the range of variation

have to meet the electromechanical and thermal considerations of the generator

design. To reduce the shaft voltage, this analysis needs to be considered in the

design procedure for the induction generator structures.

Acknowledgment



3.7 . References





cancellation of common mode currents, shaft voltages and bearing currents for

induction motor drives," PESC '03, IEEE 34th Annual, 2003.


and Common Mode Voltage Issues in Modern AC Drive Systems”, presented at

AUPEC 2007, Perth, Australia, Dec 2007.

[4] Firuz Zare, “Modelling of Electric Motors for Electromagnetic Compatibility

Analysis”, presented at AUPEC 2006, Melbourne, Australia, Nov 2006.


Helsinki, 1999

119



Industry Applications, Vol. 43, No. 5, September/October 2007

[7] Annette Muetze, Andreas Binder, “Calculation of Influence of Insulated

Bearings and Insulated Inner Bearing Seats on Circulating Bearing Currents in

Machines of Inverter-Based Drive Systems”, Industry Applications, IEEE

Transactions on, Vol. 42, No. 4, July/August 2006

[8] A. Muetze, A. Binder, “Calculation of motor capacitances for prediction of

the voltage across the bearings in machines of inverter-based drive systems” ,

IEEE Transactions on Industry Applications, vol. 43, no. 3, pp. 665-672,

May/June 2007

[9] S. Chen, T. A. Lipo, and D. Fitzgerald, “Source of induction motor bearing

currents caused by PWM inverters” Energy Conversion, IEEE Transaction on,

vol. 11, pp. 25-32, 1996.

[10] A.M.Garcia, D.G. Holmes, T.A. Lipo, “Reduction of Bearing Currents in



page(s): 84-89

[11] Jafar Adabi, Firuz Zare, Arindam Ghosh, Robert D. Lorenz, “Analysis of

Shaft Voltage in a Doubly-fed Induction Generator”, ICREPQ’09, Valencia,

Spain, April 2009

[12] Jafar Adabi, Firuz Zare, “Analysis, Calculation and Reduction of Shaft

Voltage in Induction Generators”, ICREPQ’09, Valencia, Spain, April 2009




Field Analysis Guide, ANSYS, Inc.

121

CHAPTER 4

Analysis of the Effects of End-Winding

Parameters on the Shaft Voltage of AC

Generators

*Jafar Adabi, *Firuz Zare, *Arindam Ghosh, **Robert D. Lorenz,





Accepted for Publication: IET Transaction on Power Electronics

122

Abstract- This paper analyses the effects of end-winding parameters on shaft

voltage in AC generators which have not taken into account by previous reported

studies. Calculation of the end-winding capacitances is rather complex because

of the diversity of end winding shapes and complexity of its geometry. A

comprehensive analysis has been carried out to determine the effective design

parameters with 3-D finite element simulations. Different parameters of end-

winding, stator slot and the rings in each side of the rotor have been considered

in a variety of ranges and effectiveness of each design factors on the parasitic

capacitive couplings have been discussed. Based on achieved information, by

choosing appropriate design parameters, it is possible to decrease the shaft

voltage and resultant bearing current in a primary stage of generator/motor

design without using any other additional active and passive filter-based

techniques. Experimental results have been presented to verify the simulation

and mathematical analysis.

4.1 . Introduct ion

The use of power converters in ac drives systems have changed the approach to

modelling of the ac generators/motors due to an increment in the switching

frequency and short rise times of pulse width modulation (PWM) voltage pulses.

Development of PWM-based drive systems increased the efficiency,

performance, and controllability in induction motor applications, low acoustic

noise and more efficient power conversion. However, high speed switching of

power switches leads to high-frequency ground leakage current, bearing current

and shaft voltage in inverter-fed drive systems [1-3]. One of the inherent

characteristics of PWM techniques is the generation of the common mode

voltage, which is defined as the voltage between the electrical neutral of the

inverter output and the ground [4].

Fig.4. 1.a shows the cross sections of a stator-fed induction generator structure

where the stator windings are capacitively coupled to both the stator frame

(normally grounded) and the rotor. The stator frame and the rotor form a

capacitor (Csr), which results in a divider network such that a portion of the

common mode voltage appears as the shaft voltage (see Fig.4. 1.b) on the rotor

with respect to the stator frame (or ground) [5]. When this voltage exceeds the

breakdown voltage of the thin lubricant film between the inner and outer rings of

123

the bearing, there is a miniature flash over. This causes pitting in the bearings

and is the main reason for early bearing failures [6-7].

Parasitic capacitances in the motor also provide low-impedance paths for high-

frequency common mode currents. The high rates of rise and fall of the line-line

voltage pulses in the range of a few hundreds of nanoseconds give rise to ground

currents due to cable capacitance to ground and motor winding capacitance to

ground. If not properly mitigated, high frequency ground currents can also

interfere with the power system ground and affect other equipments on the

power system [8-9].

(a)

(b)

Fig.4. 1: (a) structure of a stator-fed induction generator system (b) common mode model of the

system

A simple model to predict the common mode ground current from design

parameters is presented at [10] based on the calculation of some of the

capacitances. Different types of inverter-induced bearing currents [11] and a

description of techniques for measuring the different parameters of importance,

such as calculation and measurement of bearing capacitances in different motors,

have been discussed in [12-13]. The influence of different parameters of a

variable speed drive system on the phenomena of inverter-induced bearing

currents has been studied in [14]. A three-phase induction motor model that

124

shows the motor behaviour over a wide range of frequencies from 10 Hz to 10

MHz is presented in [15] where a common mode, differential-mode, and bearing

circuit models are combined into one three-phase universal equivalent circuit

model. Two high-frequency modelling methods of induction motors for

frequency- and time-domain simulation are presented in [16]. Many mitigation

techniques to cancel the common mode voltage and consequently shaft voltage

of inverter-fed drive system and limit other high frequency based phenomena

have been presented in [4],[17].

It has been shown in [18] that the occurrence of discharge bearing currents (also

called “electric discharge machining (EDM) currents”), which can occur in

electric machines of inverter-based drive systems, depends strongly on the value

of the capacitive voltage divider which can be calculated as:

srrfb

sr

com

shaft

CCC

C

V

V

(4-1)

where, the parasitic capacitive couplings exist between: the stator winding and

rotor (Csr), the stator winding and stator frame (Csf), the rotor and stator frames

(Crf), and ball bearing and outer and inner races (CBO, CBI).

A full description of the shaft voltage of induction generators in different

structures and calculation of the capacitive couplings has been proposed in [19],

in which the mathematical analyses have been confirmed by finite element

method (FEM) simulations and experimental studies. However the effects of

end-winding parameters, which have a considerable influence on the shaft

voltage has been ignored. In this paper, the effects end-winding geometric shape

on the shaft voltage is analysed. Based on this analysis, systematic approach to

the choice of design parameters is outlined. The analysis in this paper is based on

both mathematical model and 3-D FEM simulations. The simulations have been

carried out for a 24 slot induction generators under two conditions: 1) removing

end-winding to investigate design factor inside the generator (see Fig.4. 3) and 2)

removing the inside part of the generator and modelling the end-winding

winding (see Figures 4.5 & 4.8). In each section, different variations of design

parameters will be simulated and the results will be compiled to find the most

effective factors on capacitive coupling and resultant shaft voltage. Experiments

have been carried out to verify the mathematical and FEM simulation analysis.

125

4.2 . Analys is of shaft vol tage without considering

end-winding

According to the analysis in [18-19], in a variety of design parameters changes,

Csr and Cb are much lower than Crf. Thus Eq.4-1 can be rewritten as:

rf

sr

com

shaft

C

C

V

V (4-2)

It is clear from the above equation that Csr and Crf are very important in shaft

voltage generation and a precise calculation of values of these capacitances is

crucial. The total capacitance in the generator structure is composed of the

capacitance inside the generator and the capacitance at the end sides of the

generator where the winding comes out of the slot. As mentioned earlier, in all

the previous studies, capacitances were calculated without considering the end-

winding effects. In the present analysis, end-winding parameters have been taken

into account.

Fig.4. 2 shows a view of a stator slot, a rotor and winding with different design

parameters. These are given in Table.4. 1. By considering the air gap (g1) to be

much smaller than the outer diameter of the rotor, a capacitive coupling between

rotor and stator frame in a single stator slot can be calculated as follows:

1

r0

rf g

L)dn

r2(

C

(4-3)

This capacitance can be multiplied by the number of slots (n) to calculate the

total capacitance.

Table.4. 1: Different design factors and capacitive couplings in a stator slot

Air gap between rotor and stator g1

Gap between winding and stator g2

Thickness of the winding insulation gin

Length of slot tooth d

Height of the stator slot ρ

Rotor radius r

Rotor length Lr

Permittivity of free space ε0

Permittivity of the insulation εr

Number of slots n

126

g1

d-ρ

ρ

Stator Winding

g1

g2

g2

d

ρ/2ρ/2

Rotor

f1 f2Cf2r

Cf2sCf1s

Cf1r

Csr

Fig.4. 2: View of a stator slot with different design parameters and capacitive couplings in the slot

As shown in Fig.4. 2, the electric field between rotor and winding is not uniform

and existing capacitive couplings are: the capacitive coupling between rotor and

winding (Csr), the capacitive coupling between rotor and stator in left and right

sides of the slot tooth (Cf1r, Cf2r), and capacitive coupling between winding and

stator in left and right sides of the slot tooth (Cf1s, Cf2s). Calculation of these

capacitances is not in the scope of this paper. However, based on [19], the


decrease from d to d-ρ and Csr can be calculated as:

r21

0sr Lgg

dC

(4-4)

Finally, by substitution of equations (4-2) and (4-3) in Eq.4-1, shaft voltage can

be approximately calculated as:

d,V

)ndr2)(gg(

)d(ngV com

21

1sh (4-5)


and g2. It is clear that g1 cannot be changed for a large range of variations and is

not an effective parameter in shaft voltage reduction. An increment of stator slot

tooth increases the shaft voltage while increasing the gap between the slot tooth

and winding decreasing the shaft voltage.

Fig.4. 3 shows a 3-D model of the motor and a view of electrostatic model of a

stator slot. In an electrostatic analysis, all the conductors are considered as nodes

127

in the surface. These conductors are surrounded by Trefftz-domain (or Trefftz-

nodes) to obtain the capacitance matrix of a multi-conductor system [20].

Fig.4. 3: a 3-D model of the motor and a view of electrostatic model of a stator slot

Simulations have been conducted for a single slot for 12 design structures of

Table.4. 2.

Table.4. 2: Different design parameters for proposed IG structure

Design

number

ρ

(mm)

g2

(mm)

d

(mm)

1 3 5

50

2 5

3 3 15

4 5

5 3 25

6 5

7 3 5

150

8 5

9 3 15

10 5

11 3 25

12 5

128

The thickness of insulation (gin) is considered as 2.5 mm and r is taken as 2.25

and the rotor radius as 1000 mm. 3-D FEM simulation for Csr and Crf has been

carried out and the results are compared with the calculated values (using 3 and

4). The two results are compared and are shown in Fig.4. 4. In the figure, ‘cal’

indicates the calculated values and ‘3D’ indicates what have been obtained by

FEM simulation. It can be seen that they almost overlap, verifying the accuracy

of the mathematical model.

(a) (b)

Fig.4. 4: 2-D and 3-D simulation results for (a) Crf (b) Csr and its calculated values for a single stator slot

4.3 . Analys is of shaft vol tage with considering end-

winding

According to the analysis presented above, Csr is an important parameter in case

of shaft voltage generation because it can change due to the variation of the

design parameters while the other capacitances cannot change. Also, end-

winding parameters affect this parasitic capacitance. Therefore, precise

calculation of this capacitance is crucial (note the fact that this capacitance is

much lower than Crf). Calculation of the end-winding capacitances is rather

complex because of the diversity of end winding shapes and complexity of its

geometry. A typical shape of the stator end-winding is considered in section 3.1

to calculate the capacitances (see Fig.4. 5.a). This model is very simple and just

to address the effectiveness of some parameters on the capacitances. Also, a

practical end-winding model (seeFig.4. 8) has been used to verify the

capacitance via FEM simulation in section 4.3.2.

129

4.3.1. Mathematical analysis

A model of end-winding and the rotor for a single slot is shown in Fig.4. 5.b in

which the winding comes out of the slot by length of L1 and is bent with the

length of L2 to go to another slot. There are two capacitors in this system

between: shaft and end-winding (Csh-end), rotor frame and end-winding (Cr-end).

(a)

(b)

Fig.4. 5: (a) structure of an IG with (b) a model for calculation of end-winding capacitances

130

For capacitance calculation purposes, the end-winding of a single slot can be

approximately modelled with three surfaces (2 surfaces with width of W/2 and

length of L1, a plate with width of W1 and length of L2). W is the width of

winding at the slot and W1 is the width of winding at the end winding. To

calculate the capacitance between these surfaces, structure of two surfaces with

the voltage difference of V0 and the angle of is shown in Fig.4. 6. The small

gap between two surfaces is ρ1 and the length of the surface is ρ2.

Fig.4. 6: Two surfaces with the voltage difference of V0 and the angle of

Based on [21], the capacitance can be calculated as:

1

120 Lnt

C (4-6)

For the simplicity of the equation and the simulation is considered as π/2. End-

winding capacitances can be calculated based on Eq.4-6 as:

gL

gLLLn

W2C

g

gLLn

W2C

1

21102end

101end

(4-7)

Therefore, the capacitor between rotor and the end-winding of a single slot can

be calculated as:

gL

gLLLn

W2

g

gLLn

W2CCC

1

2110102end1endendr (4-8)

Where g is ( in21 ggg ) and W1 can be defined as ngR2 rotor . By

substitution of W1=k×W in Eq.4-8, one can have:

131

1k1

k210

endrgLg

gLLLn

W2C (4-9)

A shaft to end-winding capacitance is also exists which is equal to:

g

gRLn

)Lk

L(

2Crotor

21

0endsh (4-10)

End-winding capacitance for an IG (Csr-end) is the sum of Eq.4-9 and Eq.4-10.

The calculated capacitors should multiply by 2n (n is the number of slots) as the

calculations are for a single slot and one side of the end-winding. Therefore,

capacitive couplings between rotor and stator winding for an n slot generator

structure can be calculated as:

g

gRLn

)Lk

L(4

gLg

gLLLn

W4L

gg

dnC

rotor

21

1k1

k21

r21

0totalsr(4-11)

In this section, only end winding capacitances has been simulated with the

changes of L1, L2, and W to validate the calculations. Table.4. 3 shows a variety

of design parameters for end-winding simulations and calculation. Fig.4. 7 show

the calculated and simulated end-winding capacitances versus variation of L1 and

L2 for two rotor radiuses of 1000 and 600 mm with different winding widths

(W). The results show that the equations are valid for a broad range of the design

parameters.

Table.4. 3: design parameters for end-winding simulations

Figure

#

Rrotor

(mm)

Dshaft

(mm)

W

(mm)

L1

(mm)

L2

(mm)

g

(mm)

4.7.a 1000 200 150 variable variable 21

4.7.b 1000 200 200 variable variable 21

4.7.c 600 150 75 variable variable 14

4.7.d 600 150 125 variable variable 14

132

(a)

(b)

(c)

(d)

Fig.4. 7: calculated and simulated end-winding capacitances versus variation of end-winding lengths (a) Rrotor=1000 mm, W=150mm (b) Rrotor=1000mm, W=200mm (c) Rrotor=600mm,

W=75mm (d) Rrotor=600mm, W=125mm

133

Based on the above mentioned analysis, substituting Equations (4-3) and (4-11)

in Eq.4-2, a shaft voltage for a complete generator model can be approximately

calculated:

com

rotorr

21

1k1

k21

r2101

2

shaft V

g

gRLnkL

)LkL(4

gLg

gLLLn

L

W4

gg

d

ndr2

gnV

(4-12)

4.3.2. Finite element analysis

A typical shape of the end-winding is considered to study the capacitances, as

shown in Fig.4. 8. A comprehensive analysis has been carried out to determine

the effective design parameters with 3-D FEM simulations in a variety of design

parameters. From Fig.4. 8, the parameters required for the investigation of the

end-winding capacitance are as follows:

End-winding parameters: the winding comes out of the slot with the length

of L1 and is bent with an angle of α and with a length of L2. This winding

will be bent again to go to another slot.

Slot parameters: as discussed in previous section (see Fig.4. 2), the gap

between rotor and winding surface (ρ+g1+g2) has been considered as g. Also,

stator slot tooth, denoted by d, has not have any effect on end-wind

capacitance and hence is not considered.

Rotor ring parameters: two rings are placed, one on each side of the rotor,

to hold the bars inside rotor (see Fig.4. 8.b). The length of the ring is denoted

by Lring, while its thickness is denoted by Dring (Fig.4. 8.b). This distance of

the ring from the end of the rotor is gring.

Simulations have been conducted to analyse the effects of the generator end-

parameters on the end-winding parasitic capacitive couplings. Table.4. 4 shows

the range of design factors which has been considered in the simulation studies.

Two values, one large and one small, are considered for some of the parameters

as shown in Table.4. 4 to investigate the effects of these parameters on the end-

winding capacitance. Different design factors have been investigated in different

simulation studies as follows.

134

(a)

(b)

Fig.4. 8: (a) structure of an IG with a (b) model for calculation of end-winding capacitances

Table.4. 4: Design factors for a Range of Parameters in end-winding analysis

Rrotor 1000 mm

Rshaft 200 mm

g1 1 mm

ρ 5 mm

g2 5 mm, 25 mm

g= ρ+g2+g1 11mm, 31 mm

Dring 1% Rrotor and 10% Rrotor

L1 50 mm, 150 mm

L2 L1 and 2L1

gring 5% Rshaft and 15% Rshaft

Lring L1/2 and L1

135

Effects of end-winding angle (α)

In this section, the results of the 64 simulations that have been completed based

on the parameters shown in Table.4. 5 are presented. Two different ranges (big

and small end winding sizes) are considered. To analyse the effects of angle

(Fig.4. 8.b) of end-winding on capacitance, two different angles (0 and 30) have

been tested. Two values of are considered – 0 and 30 degree. For each of these

two angles, thirty-two cases are considered.

Table.4. 5: A range of design parameters to analyse capacitive couplings

End-winding Lring

(mm)

L2

(mm)

L1

(mm)

α

(degree)

gring

(mm)

g2

(mm)

Small size (25,50) (50,100) 50 (0,30) (10,30) (5,25)

Large size (75,100) (150,300) 150 (0,30) (10,30) (5,25)

Fig.4. 9 shows the percentage difference in the end winding capacitance for the

two values of the angle mentioned above.

Fig.4. 9: percentage error of capacitive couplings in 64 design by varying α from 0 to 30 degree

Since the difference is not significant (8% or less) and one of the angles is 0, it

can be concluded that the angle of the end winding does not have a big impact on

the total capacitive coupling.

Effects of end-winding length L2

Fig.4. 10 shows a comparison (in terms of percentage error) of the end-winding

capacitances between a particular value of L2 and twice that value. The design

parameters of Table.4. 5 have been used with both big and small sizes. The

results are approximately the same for two different end-winding angles (all the

errors are less than 3.5%).

136

Fig.4. 10:a one to one comparison of capacitive couplings in 64 design by doubling L2

We can therefore conclude that both L2 and α do not have any significant effect

on the end-capacitive coupling. Therefore these two parameters are not further

considered in the investigations.

Effects of end-winding length (L1), ring length (Lring) and ring thickness

(Dring)

In this case, α and L2 are kept constant while L1 has been considered as multiple

of Lring to see the effects of these two parameters together. Fig.4. 11 shows the

end-capacitive coupling versus L1 based on the parameters of Table.4. 6. The

main point that can be observed from these figures is that by increasing the end-

winding length (L1) as multiples of Lring, the value of end-capacitive couplings

will not increase beyond 2×Lring. This implies that the capacitances reach an

approximate constant value even when the end winding length increases.

Therefore, L1 and Lring can be considered as single parameters which are related

together. In Fig.4. 11, for each case presented, Lring and gring are kept constant.

Furthermore, two values of g2 (5 and 25 mm) and two values of Dring (10 and 100

mm) are considered. It is evident from Fig.4. 11 that for a ten times of variation

in Dring, the difference between capacitive couplings is not significant. In fact the

calculated percentage error lies between 4 to 8 percent. It means that Dring does

not affect the total capacitance.

Table.4. 6: Different simulation parameters in Fig.4. 11

g2

(mm)

gring

(mm)

Lring

(mm)

Dring

(mm)

L2

(mm) α

(5,25) (10,30) (25,50) (10,100) 100 30

137

(a)

(b)

(c)

(d)

Fig.4. 11: Different capacitive couplings based on range of parameters in Table.4. 6

138

Effects of g2

In this section, capacitive couplings in different sets of g2 and gring have been

compared in order to determine the effects of these parameters. The ratios

between capacitances with changes of g2 (from 25 to 5 mm) are shown in Fig.4.

12 with two different gring. This comparison is carried out based on the results in

Fig.4. 11 and design parameters of Table.4. 6(only for Dring=10 mm is considered

in the analysis). As shown in Fig.4. 12, g2 is changed from 25 to 5 mm. In

smaller gring (10mm), the gap between ring and the end-winding (g=

gring+g1+ρ+g2) change from 41 to 21, while the capacitance does not increase by

this ratio (41/21=1.952). For a larger value of gring (30 mm), the gap between

ring and the winding (g) decreases by the ratio of 61:41, which is nearly the

same as this ratio. The interesting point to be noted here is when gring increases;

the rate of changes in these capacitances is approximately equal to the expected

ratio.

(a)

(b)

Fig.4. 12: The ratio between the capacitances by changing g2 (from 25 to 5 mm) versus L1 (a) Lring=25mm (b) Lring=50mm

139

Effects of gring

As it can be seen in Fig.4. 13, the total end-winding capacitance is composed of

different capacitances which are: the radial capacitance between gring and the

winding (CR1), the radial capacitance between Dring and end-winding (CR2), the

parallel capacitance between ring length and winding (CP). To extract CR1 (which

shows the effects of gring), a test can be obtained by removing gring with the

parameters of Table.4. 7.

Table.4. 7: Different simulation parameters in Fig.4. 13

α 30

g2 5, 25 mm

L1 25, 50, 100, 200 mm

Lring 25, 50, 100, 200 mm

gring 10, 30 mm

Dring 10 mm

L2 100mm

Fig.4. 13: different capacitors in the end-winding

Fig.4. 14:The share of each capacitance on the total end-capacitance CR1

140

As shown in Fig.4. 14, the effect of CR1 is around 10% in lower amounts of L1

but when L1 and Lring increase, the share of this capacitance reduces

significantly. It means that gring has less effect on the end-winding capacitance.

The same observation can be made by the ratio between capacitances from the

changes of gring. As shown in the Fig.4. 15, by changing gring, the capacitances

did not increase with the ratio of gap between end-winding and rotor ring and the

rage of variation is very small. For instance, by changing (g2, gring) from (5, 30)

mm to (5, 10) mm in Lring=25 mm, the ratio of the capacitances is below than 1.2

while the gap between ring and winding is increased by the ratio of 41:21

(1.952).

(a)

(b)

Fig.4. 15: The ratio between the capacitances by changing gring (from 10 to 30 mm)versus L1 (a) Lring=25mm (b) Lring=50mm

In summary, the decrement in the value of the capacitance by increasing of g

(gring+g1+ρ+ g2) is not proportional to the rate of changes in the ring distance or

the other gaps (particularly in lower values of gring). The main reason is the

complexity of the generator structure.

141

4.4 . Experimental resul ts

As it is not possible to change different parameters of a machine, we need a

flexible slot to do the measurements. As shown in Fig.4. 16.a, a single stator slot,

winding and rotor have been designed to measure the capacitive couplings in a

variety of design parameters. Fig.4. 16.b shows the model of the designed slot

and different parameters which have been changed. Test results can be compared

with simulation and calculated values.

(a)

(b)

(c)

Fig.4. 16: (a) test set-up for impedance measurement (b) stator slot model and different parameters (c) impedance and phase in different frequencies

142

Different set-ups have been tested with a vector network analyser to measure the

impedance and phase in a range of frequencies. As it can be seen from Fig.4.

16.c, while the phase angle is -90 degrees, the impedance is pure capacitive.

Therefore, parasitic capacitive couplings can be obtained from the measured

impedance. Impedance is changed after a certain amount of frequency (here

around 16 MHz) from capacitive to inductive. That is because of existence of

very small parasitic inductors which their impedance will be dominant in higher

frequencies. The range of frequency which has been studied in this work is under

10 MHz and the analysis of behaviour of the system in higher frequencies is not

in the focus of this paper.

As shown in Fig.4.17, three tests are needed to find all capacitive couplings in

the set-up which are as follow:

Test1: impedance measurement between winding and the rotor.

Ctest1=Csr+ (Csf×Crf)/ (Csf+Crf)

Test2: impedance measurement between winding and the stator frame

with removing rotor. Ctest2= Csf

Test3: impedance measurement between stator frame and the rotor with

removing winding. Ctest3= Crf

Consequently, Csr can be calculated as Ctest1-(Ctest2×Ctest3)/ (Ctest2+Ctest3).

Csf Crf

Csr

Rotor

Frame

Statorwinding

Test 1

Csf

Frame

Stator winding

Test 2 Crf

Rotor

Frame

Test 3

Fig.4. 17: Three different tests to measure capacitive couplings

Six set-ups have been tested based on the design factors of Table.4. 8 and the

results for Crs and Crf are shown in Fig.4. 18. The results show that the

capacitances obtained by FEM simulations are approximately the same as test

results. In the cases which the capacitance values are very low, test results are a

little bit far from simulation results because of the measurement error. Also, the

143

dimensions in practical set-ups are heterogeneous which cause a slight difference

between simulation and test results.

Table.4. 8: Different design parameters for test setups

Test

set-up

g1

(mm)

ρ

(mm)

d

(mm)

A

(mm)

B

(mm)

d1

(mm)

1 1 12 180

250 200

10

2 2

3 1 33 176

4 2

5 1 13 80 150 100

6 2

4.5 . Conclus ions

This paper presented a mathematical analysis and simulation study to calculate

shaft voltage phenomena based on different design parameters. Analysis has

been verified with 3-D FEM simulation results to explore the effective designs in

which a lowest possible shaft voltage can be achieved. Also, the range of

variation has to meet the electromechanical and thermal considerations of the

generator design. The end-winding parameters are the focus in this analysis, in

which a simple geometric model of the end-winding was considered. In this

model, the end-winding length (L1) and rotor ring length (Lring) are most

important factors which are effective in total capacitances. The main conclusion

from these studies is that by increasing the end-winding length (L1) as multiples

of Lring, the value of end-winding capacitive couplings will not increase after

2×Lring. This information can be taken into account in the design procedure of the

motor structure and the motor designer can choose design parameters which are

a trade off between shaft voltage issue and other design considerations.

Acknowledgment



Computational resources and services used in this work were provided by the

HPC and Research Support Group, Queensland University of Technology,

Brisbane, Australia.

144

(a)

(b)

Fig.4. 18: Comparison between test and simulation results for (a) Crs and (b) Crf for six different set-ups

145

4.6 . References

[1] P. Maki-Ontto, J. Luomi, “Induction motor model for the analysis of

capacitive and induced shaft voltages” IEEE International Conference on

Electric Machines and Drives, pp.1653–1660, May 2005

[2] H.Akagi, T.Doumoto, “An approach to eliminating high-frequency shaft

voltage and ground leakage current from an inverter-driven motor” IEEE Trans.

on Industry Applications, Volume 40, Issue 4, pp.1162-69, July-Aug. 2004

[3] D. Macdonald, W. Gray, “PWM drive related bearing failures”, IEEE

Industry Applications Magazine, Vol.5, Issue 4, pp.41-47, July-Aug. 1999



Transactions on, vol. 16, pp. 248-255, 2001

[5] R. Naik,T.A. Nondahl, M.J. Melfi, R. Schiferl, J.S. Wang, “Circuit Model for

Shaft Voltage Prediction in Induction Motors Fed by PWM-Based AC Drives”,

IEEE Trans. on Industry Applications, vol. 39, no. 5, Sep/Oct 2007.

[6] S. Chen, T. A. Lipo, and D. Fitzgerald, “Source of induction motor bearing

currents caused by PWM inverters” Energy Conversion, IEEE Transaction on,

vol. 11, pp. 25-32, 1996

[7] S. Chen, T.A.Lipo, D. Fitzgerald, “Modelling of motor bearing currents in

PWM inverter drives” IEEE Trans. on Industry Applications”, Vol. 32, Issue 6,

pp. 1365-70, Nov.-Dec. 1996

[8] J. M. Erdman, R. J. Kerkman, D. W. Schlegel, and G. L. Skibinski, “Effect of

PWM inverters on AC motor bearing currents and shaft voltages” , Industry

Applications, IEEE Transactions on, vol. 32, pp. 250-259, 1996

[9] D.Busse, J.Erdman, R.J.Kerkman, D.Schlegel, G.Skibinski, “Bearing

currents and their relationship to PWM drives IEEE Transactions on Power

Electronics” ,Volume 12, Issue 2, pp.243 - 252 March 1997

[10] O.Magdun, A. Binder, A. Rocks, O. Henze, “Prediction of common mode

ground current in motors of inverter-based drive systems”, ACEMP '07, pp.

806-811, Sept. 2007



Industry Applications, Vol. 43, No. 5, September/October 2007

146

[12] A. Muetze, A. Binder, “Calculation of Influence of Insulated Bearings and

Insulated Inner Bearing Seats on Circulating Bearing Currents in Machines of

Inverter-Based Drive Systems”, IEEE Trans. on Industry Applications, Vol. 42,

No. 4, July/August 2006.

[13] A. Muetze, A. Binder, “Calculation of motor capacitances for prediction of

the voltage across the bearings in machines of inverter-based drive systems” ,

IEEE Transactions on Industry Applications, vol. 43, no. 3, pp. 665-672,

May/June 2007

[14] Annette Muetze, Andreas Binder, “Practical Rules for Assessment of

Inverter-Induced Bearing Currents in Inverter-Fed AC Motors up to 500 kW”,

IEEE Transactions on Industrial Electronics, vol. 54, No. 3, June 2007

[15] B. Mirafzal, G.L. Skibinski, R.M. Tallam, D.W. Schlegel, R.A.

Lukaszewski, “Universal induction motor model With low-to-high frequency-

response characteristics” IEEE Transactions on Industry Applications, vol. 43,

no. 5, pp. 1233 - 1246, Sep/Oct 2007

[16] N.Idir, Y.Weens, M.Moreau, J.J.Franchaud, “High-Frequency Behaviour

Models of AC Motors” IEEE Transactions on Magnetics, Volume 45, Issue 1,

Part 1, pp.133 - 138, Jan. 2009

[17] M.M. Swamy, K.Yamada, T. Kume, “Common Mode Current Attenuation

Techniques for Use with PWM Drives” IEEE Transactions on Power

Electronics”, Volume 16, No. 2, March 2001


Prediction of the Voltage Across the Bearings in Machines of Inverter-Based

Drive Systems”, IEEE Transactions on Industry Applications, Vol. 43, No. 3,

pp.665-672, May/June 2007

[19] Jafar Adabi, Firuz Zare, Arindam Ghosh, Robert D. Lorenz, “Calculations

of Capacitive Couplings in Induction Generators to Analyze Shaft Voltage”,

accepted for publication, IET Power Electronics, 2009


Field Analysis Guide, ANSYS, Inc



147

CHAPTER 5

Effects of PFC on Common Mode Voltage of a

Motor Drive System Supplied With a Single-

phase Diode Rectif ier

Firuz Zare, Jafar Adabi, Alireza Nami, Arindam Ghosh



Submitted at: IEEJ Transactions on Electrical and Electronic Engineering

148

Abstract- Common mode voltage generated by a power converter in

combination with parasitic capacitive couplings is a potential source of shaft

voltage in an AC motor drive system. In this paper, a three-phase motor drive

system with a single-phase AC-DC diode rectifier is investigated in order to

reduce shaft voltage in a three-phase AC motor drive system. In this topology,

the common mode voltage generated by the inverter is influenced by the AC-DC

diode rectifier because the placement of the neutral point is changing in different

rectifier circuit states. A pulse width modulation technique is presented by a

proper placement of the zero vectors to reduce the common mode voltage level,

which leads to a cost effective shaft voltage reduction technique without load

current distortion, while keeping the switching frequency constant. Analysis and

simulations have been presented to investigate the proposed method.

5.1 . Introduct ion

Adjustable Speed Drive (ASD) systems are largely used in a wide range of

modern systems, from household appliances to automated industry applications.

The concept in the ASD systems is the use of a power electronics module to

convert a constant frequency (50 or 60 Hz) AC voltage source to an AC variable

frequency waveform to achieve an adjustable speed [1-2]. Regarding the

growing requirements of speed control, pulse width modulated (PWM) inverters

are used in ASD systems. The development of PWM-based drive systems

increased the efficiency, performance, and controllability in AC motor

applications, low acoustic noise and more efficient power conversion. However,

as the switching speed of the power switches is increased to allow higher carrier

frequencies, new concerns arose due to the interface of power converters and AC

motor characteristics which was previously seen only in wave transmission

devices like antenna and broadcast signal equipments. The effects of the high

frequency voltage components introduced by the PWM technique are usually

neglected when the electromechanical performance of the motor is analysed.

Many small capacitive couplings exist in the motor drive systems which may be

neglected in low frequency analysis, but the conditions are completely different

in high frequencies [3-6].

As a consequent of PWM patterns in three-phase inverter, a voltage will be

generated between a neutral point and the ground, which is called common mode

149

voltage. This voltage acts as a source for many unwanted problems in motor

drives such as shaft voltage and bearing currents due to the existence of parasitic

capacitances in the motor. It will be shown that the switching state creates the

common mode voltage regardless of the motor impedance [7-8]. An LC filter can

be used to eliminate the low order harmonics and remove the pulse width

modulated signal from the pulse shape generated by an inverter and the common

mode voltage will therefore be eliminated. The main drawback of using the filter

is its bulky size especially in large motor drive systems. Then, a proper PWM

technique is the best possible solution to reduce or eliminate the common mode

voltage.

Assuming no parasitic coupling, an induction motor will only experience

differential mode voltages and will behave as an ordinary three-phase sinusoidal

AC supply [9-10]. However, as the switching speeds of a converter are

increased due to switching device improvements, the parasitic capacitive

coupling becomes a dominant side effect. Two major parasitic coupling paths

what can affect shaft voltage are the stator windings to the stator iron and the

stator windings to the rotor iron [11-12]. The capacitive couplings in the motor

structure and common mode voltage generated by the inverter forms a model for

the ASD system, which leads to a voltage across the rotor and stator frames

called shaft voltage. Fig.5. 1.a shows the structures of an AC motor where the

parasitic capacitive couplings exist between the stator winding and rotor (Cwr),

the winding and stator frame (Cws), the rotor and stator frame (Crs), and outer and

inner races of the ball bearing (CBO, CBI). A simple high frequency model of the

motor is shown in Fig.5. 1.b and shaft voltage can be calculated as:

comwrrsb

wrshaft V

CCC

CV

(5-1)

Shaft voltage is the main cause of the motor bearing current and leads to bearing

damage and decrement of the bearing lifetime. Shaft voltage is influenced by

various factors such as: the design of the generator, capacitive couplings between

different parts of the machine structure, the configuration of the main supply,

voltage transient on the machine terminals, and switching states in PWM pattern.

Generally, the solutions to reduce this phenomenon are based on the motor

design consideration (to decrease the effective capacitive couplings in the first

150

step of the design [13]) and the common mode voltage reduction by proper

PWM techniques which are studied in [14-15] via PWM without zero vectors in

three-phase in inverters, multilevel inverter topology, and reducing DC link

voltage.

(a)

(b)

Fig.5. 1:(a) Structure of an AC motor with different parasitic capacitive couplings (b) common mode model

In this paper, a single-phase diode rectifier is used to supply a three-phase motor

by a single-phase AC voltage source. As the input current of the rectifier is

highly distorted, a Power Factor Correction (PFC) unit with boost converter

technique is used to improve the current quality of the AC source. A survey on

power factor correction of the single-phase rectifiers is presented in [16] and the

design of a single-phase rectifier with improved power factor and low THD

using boost converter technique is investigated in [17]. In the ASD system with

single-phase rectifier topology, the common mode voltage generated by the

inverter is influenced by the AC-DC diode rectifier, because the placement of the

neutral point is changing in different rectifier circuit states. Zero switching

vectors are the most important vectors in terms of common mode voltage

generations. Regarding the different placements of the neutral point, proper

switching states will be applied in the PWM pulse pattern to decrease the

common mode voltage.

151

5.2 . Common mode vol tage and shaft vol tage in ASD

systems

Fig.5. 2 shows a DC-AC converter connected to an AC motor assuming that the

ground (g) is connected to the negative point of the DC link (n). Basically, a

three-phase inverter consists of a DC link and three pairs of switching

components. The switches turn on and off to generate an AC voltage of the

output. The six-switch combination of this inverter has eight permitted switching

vectors which have been shown in Fig.5. 2.b. In a three-phase system, (Vag Vbg

Vcg) are the leg voltages of a three-phase converter, respectively. Vog is the

voltage between the neutral point and the ground (common mode voltage). In

this section, a constant DC voltage is considered as a DC source for the inverter.

(a)

(b)

Fig.5. 2: (a) A three-phase converter (b) eight possible switching vectors

Regardless of the type of modulation technique, in each switching cycle (Ts)

different switching states will be employed. For instance, in a Space Vector

Modulation (SVM) pulse pattern, a control strategy is implemented to treat the

152

sinusoidal voltage as a constant amplitude vector rotating at constant frequency.

The PWM technique approximates the reference voltage (Vref) by a combination

of eight switching patterns (V0 to V7). A three-phase voltage is transformed into

a vector in the stationary dq coordinate frame which represents the three-phase

voltage in abc coordinate. The vectors V1 to V6 divide the plane into six sectors

(each sector: 60 degrees). Vref is generated by two adjacent non-zero vectors (V1

to V6) and two zero vectors (V0 and V7), and the duration of each vectors depend

on the magnitude of reference voltage.

Suppose that the vectors (V0, V1, V2, V7, V2, V1, V0) are employed for the

switching sequence in sector I, according to Fig.5. 2, three leg voltages of the

converter can be calculated as follows:

)t(V)t(V)t(V

)t(V)t(V)t(V

)t(V)t(V)t(V

ogcocg

ogbobg

ogaoag

(5-2)


)t(V3)t(V)t(V)t(V)t(V)t(V)t(V ogcoboaocgbgag (5-3)

It is obvious that the sum of three-phase voltages is equal to zero

( 0)t(V)t(V)t(V coboao ). Therefore, the common mode voltage can be

calculated as:

3

)t(V)t(V)t(V)t(V

cgbgagog

(5-4)

The switching states of the proposed converter, the leg voltages and the resultant

common mode voltage are shown in Table.5. 1. According to the switching

states in this table and the proposed switching sequence, the three leg voltages of

the inverter are shown in Fig.5. 3. It is obvious that the common mode voltage

can be controlled by an appropriate switching pattern. Note that the ground

placement is an important issue in common mode voltage calculation. Suppose

that the ground is connected to the positive point of DC link, V0 is the zero

vector which is generating the maximum negative common mode voltage (all

three lower switches are turned on and all leg voltages will be -Vdc).

Consequently, the common mode voltage will be -Vdc. The same scenario is

valid for the V7 which leads to a common mode voltage Vdc.

153

Fig.5. 3: leg and common mode voltages for proposed pulse pattern

Table.5. 1: switching states, output leg voltage of three-phase inverter

vector S1 S3 S5 Vag Vbg Vcg Vcom

V1 1 0 0 Vdc 0 0 Vdc/3

V2 1 1 0 Vdc Vdc 0 2Vdc/3

V3 0 1 0 0 Vdc 0 Vdc/3

V4 0 1 1 0 Vdc Vdc 2Vdc/3

V5 0 0 1 0 0 Vdc Vdc/3

V6 1 0 1 Vdc 0 Vdc 2Vdc/3

V7 1 1 1 Vdc Vdc Vdc Vdc

V0 0 0 0 0 0 0 0

These zero vectors should be eliminated in switching sequences to reduce the

common mode voltage significantly but elimination of the zero switching vectors

leads to a variable switching frequency or more current ripple. The scenario of

the ground placement changing takes place in the single phase diode rectifier

topology which is used as a voltage source for a three phase inverter system and

will be discussed in detail in the following sections.

154

5.3 . Common mode vol tage in 3-φ ASD system

suppl ied with a 1-φ d iode rect i f ier without PFC

5.3.1. Circuit description

Fig.5. 4.a shows an ASD supplied by a three-phase inverter system. The DC link

voltage of the inverter is regulated by a single phase diode rectifier connected to

an AC supply. As shown in Fig.5. 4.b, while the AC voltage is in positive half a

cycle, the diodes D1D4 are in forward bias to charge the DC link capacitor

(Interval 1 according to Fig.5.4 and 5.5), so that ground is connected to the

bottom of the DC link. In the discharging interval (Interval 2), the diode rectifier

will be disconnected from the DC-link as DC link voltage is greater than the

input voltage. Same charging (Interval 3) and discharging (Interval 4) intervals

occurs in the negative half a cycle; however due to the forward bias across D2D3,

ground is connected to the point “p” of the DC link in the charging period (see

Fig.5. 4.c).

Fig.5. 4: (a) an ASD system supplied with a single-phase diode rectifier and circuit behavior in (b) charging and (b) discharging states of the capacitor in positive and negative half a cycle

155

The DC link voltage waveform in all intervals is demonstrated in Fig.5. 5.

According to the circuit configuration in the different subintervals, the ground is

not fixed in all intervals in contrast with configuration in Fig.5. 2.a, and changed

between the point “n” in the positive half a cycle and the point “p” in the

negative half a cycle. This can affect the common mode voltage by choosing the

switching vectors. This issue will be analysed with simulations in the following

sections.

5.3.2. Simulation results

Simulations have been conducted based on the configuration shown in Fig.5. 4 in

which a 300 volts AC voltage is regulated through a single-phase diode rectifier

connected to a DC link capacitor of 100 µF. Space vector modulation technique

(fs=5 kHz) is implemented in the proposed system to reduce maximum levels of

the common mode voltage.

Voltage waveforms across the DC link and the positive and negative points of

the DC link with respect to the ground are shown in Fig.5. 5. As mentioned in

Table.5. 1 and shown in Fig.5. 3, common mode voltage is changed between

different voltage levels. Note that the voltage levels at this table are based on a

constant DC source which is grounded to the lower point of the DC link.

-300

-200

-100

0

100

200

300

(Vp

g &

Vn

g)

D

C l

ink (

Vd

c)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008-300

-200

-100

0

100

200

300

Tim e(s )

Co

mm

on

mo

de

(V

co

m)

Fig.5. 5:DC link voltage, voltages of positive and negative points of DC link respect to the ground and common mode voltage for switching sequence of (V0, V1, V2, V7, V2, V1, V0)

156

Here, with the single-phase rectifier as a source of inverter, both the positive and

negative point of the DC link has a voltage with respect to the ground. Therefore,

the common mode voltage is changing between maximum positive and

minimum negative DC link voltage. Different space vector switching sequences

have been tested to analyse the effects of the switching pattern on common mode

voltage. In this case, a typical pulse pattern of (V0, V1, V2, V7, V2, V1, V0) has

been employed for the inverter. Fig.5. 5 also shows the common mode voltage

for the proposed system. It shows that by applying V0 and V7, we have the

maximum common mode voltage level in both positive and negative half a

cycles. By applying V0 to an inverter, three lower switches of the inverter are

turned on. If the ground is connected to the positive point of DC link (charging

state of capacitor in negative half a cycle of the rectifier), all three leg voltages

would be Vng and based on the Eq.5-4, common mode voltage would be Vng

which is the maximum negative value of the common mode voltage. The same

scenario is valid for applying V7 especially when the ground is connected to the

negative point of DC link (charging state of capacitor in positive half a cycle of

the rectifier). All three leg voltages would be Vpg, and consequently, the common

mode voltage will be Vpg.

As shown in Fig.5. 5, the worst case of common mode voltage happens on the

maximum voltage of the positive point of DC link (Vpg) and the minimum

voltage of negative point of the DC link while the capacitor is charging and its

value is at its maximum value. It is clear that in the discharging states of the

capacitor, the DC link voltages decreases which leads to a lower common mode

voltage. Fig.5. 6 shows the leg voltage and the common mode voltage in two

different switching cycles in positive and negative half a cycles. It is obvious that

by zero switching vectors V0 and V7, we will have maximum common mode

voltage levels of +300 and -300 volts respectively.

As shown in Fig.5. 5, applying zero vectors lead to maximum common mode

voltage. Using only active voltage vectors (V1-V6) can reduce the common mode

voltage significantly, but a main drawback is the quality of load current.

Removing V0 and V7 requires adding another active vector in order to have a

constant switching frequency. This modulation method increases the load current

harmonics. In the inverter system connected to a single-phase diode rectifier,

157

there are some choices which are possible to minimize the common mode

voltage with keeping the zero vectors in the switching sequences by using the

different ground placement as a benefit.

0

100

200

300

Vo

lta

ge

(V)

Pos i tive ha l f a cycle Leg a

0

100

200

300

Negative ha l f a cycleLeg b

0

100

200

300

Vo

lta

ge

(V)

Leg b

0

100

200

300Leg b

0

100

200

300V

olt

ag

e(V

)Leg c

0

100

200

300Leg c

0 Ts0

100

200

300

Vo

lta

ge

(V)

Com m on m ode

0 Ts-300

-200

-100

0Com m on m ode

Fig.5. 6: Leg voltages and common mode voltage in two different switching cycles in positive and negative half a cycle for switching sequence of (V0, V1, V2, V7, V2, V1, V0)

In a without PFC system, the zero voltage vectors should be applied in the

charging intervals (V0 and V7 should be applied in charging intervals of positive

and negative half a cycles respectively), because the ground is connected to

either positive or negative points of the DC link and applying these vectors leads

to zero leg voltages. In this case, the common mode voltage generated by the

inverter is influenced by the AC-DC diode rectifier. In the positive half a cycle,

ground is connected to the lower point so that V0 is the suitable zero switching

vector. A switching sequence of (V0, V1, V2, V1, V0) is employed for the

proposed system in the positive half a cycle. It can be seen that the maximum

common mode voltage level in the positive half a cycle is decreased by one-third

because the ground during the capacitor’s charging state in this half a cycle is

connected to the negative point of DC link, and applying V0 (in which all three

bottom switches of the inverter are switched on) leads to a zero common mode

voltage instead of achieving maximum positive value.

In the negative half a cycle where the positive point of the DC link is connected

to the ground, V7 is the proper option. Also, a switching sequence of (V7, V2, V1,

V2, V7) is employed for the proposed system. It can be seen that the maximum

common mode voltage level in the negative half a cycle is decreased by one-

third because the ground during the capacitor’s charging state in this half a cycle

is connected to the positive point of DC link and applying V7 (in which all three

158

upper switches of the inverter is switched on) leads to a zero common mode

voltage instead of achieving maximum negative value. Fig.5. 7 shows the leg

voltages and common mode voltage in two different switching cycles in positive

and negative half a cycle for proposed switching sequence.

0

100

200

300

Positive half a cycleLeg a

0

100

200

300Leg b

0

100

200

300Leg c

0 Ts0

100

200

300Com m on m ode

0

100

200

300

Negative hal f a cycleLeg a

0

100

200

300Leg b

0

100

200

300Leg c

0 Ts-300

-200

-100

0Com m on m ode

Fig.5. 7: Leg voltages and common mode voltage in two different switching cycles in positive and negative half a cycle for switching sequence of (V0, V1, V2, V1, V0) in positive half a cycle

and (V7, V2, V1, V2, V7) in negative half a cycle

-300

-200

-100

0

100

200

300

(Vp

g&

Vn

g)

DC

lin

k(V

dc)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008-300

-200

-100

0

100

200

300

Tim e(s )

Co

mm

on

mo

de

(V

co

m)

Fig.5. 8: DC link voltage, voltages of positive and negative points of DC link respect to the ground and common mode voltage for switching sequence of (V0, V1, V2, V1, V0) in positive half

a cycle and (V7, V2, V1, V2, V7) in negative half a cycle

The comparison between the common mode voltages obtained in Fig.5. 5 (with

V0 and V7 in a switching cycle) and Fig.5. 8 (V0 in the first half a cycle and V7 in

the negative half a cycle) shows the influence of the proposed pulse pattern. As

159

shown in Fig.5. 9, the input current is distorted significantly and using a power

factor corrector is necessary to improve the input current quality and the system

power factor. A PFC unit is used to shape the input current to a sinusoidal

waveform in phase with the input voltage which will be discussed in the next

section and common mode voltage analysis will be mentioned.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-60

-40

-20

0

20

40

60

Tim e(s )

Fig.5. 9: input current of the proposed system

5.4 . Common mode vol tage in 3-φ ASD system

suppl ied with a 1-φ d iode rect i f ier with a PFC

5.4.1. Circuit description

Fig.5. 10.a shows the structure of an ASD system with a single phase diode

rectifier and PFC system where the input current is controlled using a boost

converter technique. Current control technique benefits power electronic

converters. Hysteresis current control is a simple current control with fast

dynamic response [18]. Therefore, in this topology the inductor current will be

compared to a reference current and forced to be kept inside the upper and lower

hysteresis bands. This results in a sinusoidal current waveform at the input side

as shown in Fig.5. 11. Also, a space vector modulation strategy is employed for

the inverter switching control. Fig.5. 10.b shows the behavior of the proposed

system in the positive half a cycle of the input voltage. When the input voltage is

positive, the neutral line is connected to the negative DC link line for the half a

cycle. The positive DC link line has maximum potential with respect to the

neutral which has a significant impact on the common mode voltage. Also, Fig.5.

160

10.c shows the behaviour of the system in the negative half a cycle where the

neutral point is connected to the inductor.

(a)

(b)

(c)

Fig.5. 10:(a) a schematic of an ASD system supplied by a single-phase diode rectifier with PFC in (b) positive half a cycle and (c) negative half a cycle

5.4.2. Simulation results

Simulations have been conducted for the circuit topology shown in Fig.5. 10.a,

in which a hysteresis current control is used to control the PFC switch (to

generate an 11A sinusoidal current). A space vector modulation with a switching

frequency of 5 kHz is used to control the three-phase inverter. Other parameters

161

are the same as those in Section 5.3.2. Fig.5. 11 shows the inductor and input

current controlled within the hysteresis bands which generates a sine wave

current. It is clear that the quality of the input current has been improved

significantly with a PFC unit.

-5

0

5

10

15

Cu

rre

nt(

A)

Indcutor current

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008-15

-10

-5

0

5

10

15

Tim e(s )

Curr

en

t(A

)

Input current

Fig.5. 11: Inductor and input currents with a PFC

A typical pulse pattern of (V0, V1, V2, V7, V2, V1, V0) has been employed for the

inverter. Fig.5. 12 shows the DC link voltage and the voltages of the positive and

negative points of the DC link with respect to the ground (Vpg and Vng).

Applying V0 and V7 to the pulse pattern leads to maximum common mode

voltage, which changes between voltages Vpg and Vng.

-300

-200

-100

0

100

200

300

(Vp

g &

Vn

g)

DC

lin

k(V

dc)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

-300

-200

-100

0

100

200

300

Tim e(s )

Co

mm

on

mo

de

(V

co

m)

Fig.5. 12: DC link voltage, voltages at positive and negative points of DC link with respect to the ground and common mode voltage for switching sequence of (V0, V1, V2, V7, V2, V1, V0)

162

As mentioned in the previous section, by using one of the zero switching vectors,

the benefit of changing the neutral point location can be used. A switching

sequence of (V0, V1, V2, V1, V0) is employed to minimize the common mode

voltage. Fig.5. 13 shows the leg voltages and common mode voltage with

proposed switching sequence. As shown in Fig.5. 10.b, in the positive half a

cycle, neutral point is connected to the negative point of the DC link capacitor.

0

100

200

300

Le

g a

(Va)

0

200

Le

g b

(Vb)

0

200

Le

g c

(Vc)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

-300

-200

-100

0

100

200

300

Tim e(s )

Co

mm

on

mo

de

(Vc

om

)


The difference between PFC and not using PFC is that the neutral point in a

system without PFC is connected to the negative point only in capacitor’s

charging state in the positive half a cycle. However, in a system with PFC, the

neutral point is connected to the negative point for the whole duration of positive

half a cycle. Therefore applying V0 leads to decrement of the common mode

voltage by one-third in positive half a cycle. This strategy will not help to

remove the maximum level of common mode voltage (-300 volts) in negative

half a cycle. A switching sequence of (V7, V2, V1, V2, V7) has also been tested

which gives different leg and common mode voltages as shown in Fig.5. 14.

According to Fig.5. 10.c, in the negative half a cycle, the neutral point is

connected to the inductor. Based on Fig.5. 13, the maximum common mode

voltage level in the negative half a cycle occurred when the voltage of the

163

positive point to the ground is in its minimum value (around zero). Therefore

applying V7 minimizes the common mode voltage in negative half a cycle by one

third. The maximum common mode voltage value still exists in the positive half

a cycle.

0

100

200

300L

eg

a(V

a)

0

200

Le

g b

(Vb)

0

100

200

300

Le

g c

(Vc)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008-300

-200

-100

0

100

200

300

Tim e(s )

Co

mm

on

mo

de

(Vc

om

)


As mentioned in the previous section, a solution to reduce the shaft voltage is to

use only V0 voltage vector in the positive half a cycle in which it has the lowest

potential with respect to the neutral. V7 will be applied in the negative half a

cycle where the neutral line is connected to PFC inductor and negative DC link

is connected to the source voltage. Therefore, it is better to apply V7 as a zero

vector in negative half a cycle to create the lowest possible common mode

voltage without distortion of the load current. Fig.5. 15 shows the leg voltages

and the common mode voltage of the system with the proposed PWM strategy.

Comparison of the common mode voltage achieved in Fig.5. 15 with the voltage

shown in Fig.5. 12 show the effectiveness of proposed switching strategy on the

common mode voltage. This method is a cost effective technique which leads to

a lower possible shaft voltage in adjustable speed drives supplied with a single-

phase diode rectifier.

164

0

100

200

300

Leg a

(Va)

0

100

200

300

Leg b

(Vb)

0

100

200

300

Leg c

(Vc)

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

-300

-200

-100

0

100

200

300

Tim e(s )

Com

mon m

ode(V

com

)

Fig.5. 15: Leg voltages and common mode voltage for switching sequence of (V0, V1, V2, V1, V0) for positive half a cycle and sequence of (V7, V2, V1, V2, V7) for negative half a cycle.

5.5 . Conclus ions

A three-phase inverter system supplied by a single-phase diode rectifier with and

without PFC has been studied in terms of common mode generation. Different

placements of the ground in different diode rectifier circuit intervals can

influence the common mode voltage. Therefore, a PWM technique is presented

by a proper placement of the zero vectors to reduce the common mode voltage

level. This method leads to a cost effective shaft voltage reduction technique

without load current distortion and keeping the switching frequency constant.

Analysis and simulations have been presented to verify the proposed method.

165

5.6 . References

[1] J.C. Rama, A. Gieseche, “High-speed electric drives: technology and

opportunity” Industry Applications Magazine, IEEE, Volume 3, Issue: 5On

page(s): 48-55, Sep 1997

[2] T. F. Lowery, “Design Considerations for Motors and Variable Speed

Drives” ASHRAE Journal, February 1999

[3] Russel J. Kerkman, Senior Member, “Twenty Years of PWM AC Drives:

When Secondary Issues Become Primary Concerns”, 22nd IEEE IECON

International Conference, Volume 1, p.p. LVII-LXIII, 1996

[4] A. Boglietti, E. Carpaneto, “Induction motor high frequency model” Industry

Applications Conference, 1999, IEEE, Volume 3, 3-7 Oct. 1999 Page(s):1551 -

1558 vol.3

[5] B. Mirafzal, G.L. Skibinski, R.M. Tallam, D.W. Schlegel, R.A. Lukaszewski,

“Universal induction motor model With low-to-high frequency-response

characteristics” IEEE Transactions on Industry Applications, vol. 43, no. 5, pp.

1233 - 1246, Sep/Oct 2007

[6] N.Idir, Y.Weens, M.Moreau, J.J.Franchaud, “High-Frequency Behaviour

Models of AC Motors” IEEE Transactions on Magnetics, Volume 45, Issue 1,

Part 1, pp.133 - 138, Jan. 2009

[7] M.M. Swamy, K.Yamada, T. Kume, “Common Mode Current Attenuation

Techniques for Use with PWM Drives” IEEE Transactions on Power

Electronics”, Vol.16, No. 2, March 2001

[8] Sanmin Wei, N. Zargari, Bin Wu and S. Rizzo, “Comparison and mitigation

of common mode voltage in power converter topologies”, Industry Applications

Conference, 2004.IEEE, Volume: 3, on page(s): 1852- 1857

[9] Qiang Yin, Russel J. Kerkman, Thomas A. Nondahl and Haihui Lu,

“Analytical Investigation of the Switching Frequency Harmonic Characteristic

for Common Mode Reduction Modulator”, Industry Applications Conference,

Volume 2, 2-6 Oct. 2005 Page(s):1398 – 1405

166

[10] Satoshi Ogasawara, Hirofumi Akagi, “Modelling and damping of high-

frequency leakage currents in PWM inverter-fed AC motor drive systems”,

Industry Applications, IEEE Transactions on, Volume 32, Issue 5, Sept.-Oct.

1996 Page(s):1105 - 1114


Prediction of the Voltage Across the Bearings in Machines of Inverter-Based

Drive Systems”, IEEE Trans. on Industry Applications, Vol. 43, No. 3, pp.665-

672, May/June 2007


Helsinki, 1999

[13] Jafar Adabi, Firuz Zare, Arindam Ghosh, Robert D. Lorenz, “Calculations

of Capacitive Couplings in Induction Generators to Analyse Shaft Voltage”,

accepted for publication, IET Power Electronics, 2009

[14] Firuz Zare, Jafar Adabi, Arindam Ghosh, “Different Approaches to Reduce

Shaft Voltage in AC Generators”, 13th European Conference on Power

Electronics and Applications, 8-10 Sept. 2009 Page(s):1 – 9

[15] H.D.Lee, S.K.Sul, "Common mode voltage reduction method modifying the

distribution of zero-voltage vector in PWM converter/inverter system," IEEE

Transactions on Industry Applications, vol. 37, pp. 1732-1738, 2001

[16] O.García, J.A. Cobos, Roberto Prieto, Pedro Alou, and Javier Uceda,

“Single-phase Power Factor Correction: A Survey”, IEEE Transactions on

Power Electronics, Vol. 18, No. 3, May 2003

[17] Ismail Daut, Rosnazri Ali and Soib Taib, “Design of a Single-Phase

Rectifier with Improved Power Factor and Low THD using Boost Converter

Technique” American Journal of Applied Sciences 3 (7): 1902-1904, 2006

[18] Alireza Nami, Firuz Zare, “A New Random Current Control Technique for

a Single-Phase Inverter with Bipolar and Unipolar Modulations”, IEEJ

Transactions on Industry Applications, vol. 128-D, No.4, 2008

167

CHAPTER 6

Different Approaches to Reduce Shaft Voltage

in AC Generators

Jafar Adabi, Firuz Zare, Arindam Ghosh,



Presented at: EPE 2009, Barcelona, Spain

168

Abstract- This paper presents several shaft voltage reduction techniques for

doubly-fed induction generators in wind turbine applications. These techniques

includes: pulse width modulated voltage without zero vectors, multi-level

inverters with proper PWM strategy, better generator design to minimize

effective capacitive couplings in shaft voltage, active common mode filter,

reducing dc-link voltage and increasing modulation index. These methods have

been verified with mathematical analysis and simulations.

6.1 . Introduct ion

Doubly-fed induction generators (DFIG) are widely used in wind turbine

applications. In a DFIG, the stator is directly connected to the grid, while the

wound rotor is fed from a back-to-back converter via slip rings to allow the

DIFG to operate at a variety of speeds in order to accommodate changing wind

speeds [1]. Due to the inherent behavior of pulse width modulation of a voltage

source inverter in high frequency applications, a common mode voltage will be

generated [2-3]. This occurrence can cause many unwanted problems such as

shaft voltage in the interaction with parasitic capacitive couplings in an induction

generator.

Shaft voltage is influenced by various factors such as: capacitive couplings

between different parts of the machine structure, the configuration of the main

supply, voltage transient on the machine terminals, and switching states in PWM

pattern. Its reduction techniques [4] play a main role in attenuation of high

frequency related problems of the AC drive systems. The common mode voltage

and parasitic capacitances create a high frequency equivalent circuit for

Induction generators to generate shaft voltage [5]. Recently, some techniques are

presented to mitigate shaft voltage and bearing currents in DFIGs. An approach

is used in [6] to constrain the inverter PWM strategy to reduce the overall

common mode voltages across the rectifier/inverter system, and thus

significantly reduce bearing discharge currents. A common mode model of

DFIGs is mentioned in [7-9] to calculate bearing current and a PWM technique

has been presented to eliminate the common mode voltage. Fig.6. 1.a shows the

structure of generator, converters and other components of a wind energy

conversion system. A full description of shaft voltage calculation and analysis

for different topologies has been presented in [8].

169

Win

d T

urb

ine

(a)

(b)

(c)

(d)

Fig.6. 1: (a) a wind turbine with a DFIG and a back-to-back AC-DC-AC converter (b) structure of a DFIG with different capacitive couplings (c) its high frequency model (d) a view of stator

and rotor slots and their windings

Fig.6. 1.b shows the structure of a DFIG where the parasitic capacitive couplings


frame (Csf), the rotor and stator frames (Crf), stator winding and rotor winding

(Cws), the rotor winding and rotor (Cwr), rotor winding and stator frame (Cwf) and

ball bearing and outer and inner races (CBO, CBI). Fig.6. 1.c shows the high

frequency model of the generator with this configuration.

170

As shown in Fig.6. 1.c, the network side converter is connected to the grid

through a line LC filter which is used to damp the higher order harmonics

generated by the switching of semiconductors switches. In this case, the only

common mode voltage source is from the rotor winding and this voltage stress

creates shaft voltage which can be easily calculated by a KCL analysis as:

0CandCCCCCC

and

VCCCCCCCC

CCCCCCV

2srwssrsfwrwssr

R,com2srwssrsfsrbrfwr

srwswssrsfwrshaft

(6-1)


R,comsrbrfwr

wrshaft V

CCCC

CV

(6-2)

Vcom,R is the rotor side common mode voltage. The capacitive coupling between

the rotor winding and rotor frame has a significant value compared with other

capacitances. The major part of the common mode voltage will be placed across

the shaft. Therefore, it can be concluded that shaft voltage in a DFIG is much

greater than stator-fed IG which has been fully investigated in [9]. This paper

focuses on different PWM techniques, power electronic topologies and design

considerations in AC generators.

6.2 . Pulse width modulated vol tage without zero

vectors

Pulse Width Modulated Voltage generated by an inverter is a major cause of

motor bearing failures in a motor drive system. All inverters generate a common

mode voltage relative to the ground, which makes a shaft voltage due to parasitic

capacitances in the motor. According to Fig.6. 2, phase voltages and a common

mode voltage (Vcom) can be derived based on leg voltages of a power converter

(Vao, Vbo, Vco). The leg voltages of the three phase inverter are as follows:

Vao=Van+Vcom

Vbo=Vbn+Vcom (6-3)

Vco=Vcn+Vcom

Sum of the leg voltages is given in Eq.6-4. :

171

Vao+Vbo+Vco=(Van+Vbn+Vcn)+3Vcom (6-4)

It is clear that in a three-phase system:

Van+Vbn+Vcn=0 (6-5)

Thus, the common mode voltage can be calculated as:

Vcom=(Vao+Vbo+Vco)/3 (6-6)

In a three-phase converter, there are eight switching states; the leg voltages and

the common voltage in terms of the DC link voltage are given in Table.6. 1.

Table.6. 1: Switching states, leg and common mode voltages

Vectors Switching Vao Vbo Vco Vcom

V1 100 +Vdc/2 -Vdc/2 -Vdc/2 -Vdc/6

V2 110 +Vdc/2 +Vdc/2 -Vdc/2 +Vdc/6

V3 010 -Vdc/2 +Vdc/2 -Vdc/2 -Vdc/6

V4 011 -Vdc/2 +Vdc/2 +Vdc/2 +Vdc/6

V5 001 -Vdc/2 -Vdc/2 +Vdc/2 -Vdc/6

V6 101 +Vdc/2 -Vdc/2 +Vdc/2 +Vdc/6

V7 111 +Vdc/2 +Vdc/2 +Vdc/2 +Vdc/2

V0 000 -Vdc/2 -Vdc/2 -Vdc/2 -Vdc/2

(a)

(c)

(b)

Fig.6. 2: A three-phase inverter (a) topology (c) voltage vectors in a Space Vector Frame(b) leg, common mode, phase and line voltage waveforms

172

Fig.6. 3.a shows that using only active voltage vectors (V1-V6), the common

mode voltage can be reduced significantly but a main drawback is the quality of

load current. One of the most popular Space Vector switching sequences is V0,

V1, V2, V7. Removing V0 and V7 requires adding another active vector in order

to have a constant switching frequency. This new modulation method increases

the load current harmonics.

(a)

(b)

Fig.6. 3: (a) Magnitudes of common mode voltage based on different switching states (b) A typical pulse pattern for an inductive load

In order to consider the effect of pulse position on an inductive load, two

different PWM voltages with same duty cycle and switching frequency are

173

drawn in Fig.6. 3.b. In the first one, pulses are placed at the centre of each

switching cycle while in the second one they are at the end of the switching

cycle. The inductor current at the beginning of the switching cycle is I0 and at the

end of the switching cycle is ITs. In fact in the both switching pulse patterns, the

inductor currents at the end of the switching cycle are same but a difference is on

the inductor current ripple. The first one has a better current waveform and lower

harmonics compare to the second one. This issue can be addressed based on a

fact that the first modulation creases two pulses per switching cycle while the

second one has one pulse. That means the effective switching frequency for the

first pulse pattern is more that the second one.

6 .3 . Mult i - leve l Inverter topology

In Multilevel Converters (diode clamped topology is more practical), there are

more voltage levels and switching states which can provide possibilities to

reduce common mode voltage. A full description of common mode voltage

control of multilevel Inverters has been investigated in [10]. In this topology,

each leg has three voltage levels: (+Vdc/2, 0 , -Vdc/2).

Fig.6. 4: a three-level diode clamped inverter

In a three phase converter with three legs, there are 27 different switching

combinations in a diode clamped topology. All switching states and output

voltages of a three-level inverter are given in Table.6. 2.

Number ‘2’ means that the top switches in a leg are turned on.

174

Number ‘1’ means that one of the top switches in a leg is turned on.

Number ‘0’ means that the top switches in a leg are turned off.

The common mode voltage magnitudes for this converter are:

(+Vdc/2, +Vdc/3, +Vdc/6, 0, -Vdc/6, -Vdc/3, -Vdc/2)

Table.6. 2: switching states for a three-level inverter

Switching states Vao Vbo Vco Vcom

V0 000 -Vdc/2 -Vdc/2 -Vdc/2 -Vdc/2

V1 100 0 -Vdc/2 - Vdc/2 -Vdc/3

V2 200 Vdc/2 - Vdc/2 - Vdc/2 -Vdc/6

V3 010 - Vdc/2 0 -Vdc/2 -Vdc/3

V4 110 0 0 -Vdc/2 - Vdc/6

V5 210 Vdc/2 0 - Vdc/2 0

V6 020 - Vdc/2 Vdc/2 - Vdc/2 -Vdc/6

V7 120 0 Vdc/2 - Vdc/2 0

V8 220 Vdc/2 Vdc/2 - Vdc/2 Vdc/6

V9 001 - Vdc/2 - Vdc/2 0 - Vdc/3

V10 101 0 -Vdc/2 0 -Vdc/6

V11 201 Vdc/2 - Vdc/2 0 0

V12 011 - Vdc/2 0 0 - Vdc/6

V13 111 0 0 0 0

V14 211 Vdc/2 0 0 Vdc/6

V15 021 - Vdc/2 Vdc/2 0 0

V16 121 0 Vdc/2 0 Vdc/6

V17 221 Vdc/2 Vdc/2 0 Vdc/3

V18 002 - Vdc/2 - Vdc/2 Vdc/2 - Vdc/6

V19 102 0 - Vdc/2 Vdc/2 0

V20 202 Vdc/2 - Vdc/2 Vdc/2 Vdc/6

V21 012 - Vdc/2 0 Vdc/2 0

V22 112 0 0 Vdc/2 Vdc/6

V23 212 Vdc/2 0 Vdc/2 Vdc/3

V24 022 - Vdc/2 Vdc/2 Vdc/2 Vdc/6

V25 122 0 Vdc/2 Vdc/2 Vdc/3

V26 222 Vdc/2 Vdc/2 Vdc/2 Vdc/2

1: Vectors V0, V13 and V26 are zero voltage vectors in a d-q frame. V0 and V26

create maximum common mode voltage of +/- Vdc/2 while V13 generates no

common mode voltage (zero voltage). Thus, using this topology, it is possible to

175

reduce common mode voltage without affecting load current quality. In fact

instead of V0, V26 voltage vectors, we can use V13 to generate PWM waveforms.

2: Vectors V1, V3, V9, V17, V23 and V25 are active vectors and they generate +/-

Vdc/3. In these switching vectors, two legs of the converter have +Vdc/2 or -

Vdc/2 voltage level and the other one have zero voltage. Using pulse position

method we are able to shift leg voltages in such a way to remove or reduce these

switching states but it may affect the quality of the load current as shown in

Fig.6. 5.a. Fig.5.b shows a new pulse pattern as the pulse position in leg ‘a’ is

shifted to left side and the one in leg ‘b’ to the right side of the switching cycle in

order to remove common mode voltage levels of +/_Vdc/3. We can see that other

common mode voltage levels (+/-Vdc/3) have been removed but this modulation

method affects the load current ripple and effective switching frequency. Fig.6. 6

shows simulation results based on these methods. We can see the common mode

voltage is reduced while the load current ripple is increased. Another simulation

result is shown in Fig.6. 7 for a four-level inverter. The benefit of using a multi-

level converter is not only to reduce the common mode voltage.

(a)

176

(b)


Fig.6. 6: Simulation results: current and voltage waveforms for a three-level inverter

177

Fig.6. 7: Simulation results: current and voltage waveforms for a four-level inverter

6.4 . Bet ter generator des ign to minimize capaci t ive

coupl ing

Fig.6. 1.d shows a view of stator and rotor windings where g1 is the air gap

between rotor and stator, g2 is the gap between winding and stator and gin is the

thickness of the winding insulation. d is the length of slot tooth and ρ is the


bottom respectively. hW is the length of the stator winding at both the right and

the left side of winding. r is the rotor radius and g1 is the air gap, Lr is the rotor

length. This capacitance can be multiplied by the number of slots (n) to calculate

the total capacitance. ε0 is the permittivity of free space and εr1, εr2 are the

permittivity of the insulation and the slot wedge material. If the rotor slot shape

in a DFIG is considered same as the stator slot in Fig.6. 1.d, the shaft voltage in

a DFIG can be calculated by calculation of each capacitor versus different

design parameters. Finalized calculation of shaft voltage is:

178

)d)(1(gdn

r2g)1(Agg

)1(Agg

CCCC

C

V

V

11

1

srbrfwr

wr

R,com

shaft

(6-7)

λ is the ratio between end-winding Cwr and without end-winding Cwr which is

usually less than 0.05. g and A are:

21

2rin1r2in

2r1r0inW2rin1r21rwr

ggg

)gg(g

dWg)h2W()gg(CA

(6-8)

Therefore, shaft voltage in DFIG is a function of different parameters such as:

W, d, hw, gin, εr, ρ, g1, g2. Fig.6. 8.a shows the ratio between shaft adn common

mode voltages versus variations of g2 and d (λ=0.05, ρ=5mm, g1=1mm, w′=150,

W=120 mm, hW=230 mm, gin=2mm, εr=2.25). Fig.6. 8.b shows the ratio

between shaft adn common mode voltages versus variations of εr and gin

(λ=0.05, ρ=5mm, g1=1mm, w′=150mm, W=120mm, hW=230 mm, d=50mm,

g2=10mm).

(a)

(a)

Fig.6. 8: Vsh/Vcom (a) versus d and g2 versus g2 and d (c) KR versus εr and gin in a DFIG

179

According to the analysis, with a variation of gap between winding and stator

(g2) and length of slot tooth (d), it is possible to control the shaft voltage but the

effects of these factors are not so high. The effects of the insulation parameters

such as permittivity and the thickness of the insulation are very effective in shaft

voltage reduction. By changing these parameters, shaft voltage can be optimized

while the range of variations should be compromised considering other

electromechanical parameters [9]. High frequency modelling of electric motors

has been presented in [11] based on measurement results.

6.5 . Act ive common mode f i l ter

A main concept of using an active filter to cancel common mode voltage in a

motor drive is based on series compensation method in which a transformer is

connected in series between the inverter and the motor and almost same common

mode voltage is generated by an auxiliary circuit. Thus, the common mode

voltage generated by the inverter and the auxiliary filter cancel each other and

the motor does not have any common mode voltage. In a traditional 2-level

inverter using all voltage vectors, the common mode voltage levels generated by

the PWM voltage are (+Vdc/2, +Vdc/6, -Vdc/6, -Vdc/2) (refer to Table I). To

cancel these voltage levels we need a variable DC voltage while in the motor

drive we can only access to a DC link voltage (Vdc).

There are two concepts to cancel the common mode voltage using an active

filter. The first one [12] is based on emitter follower in which the common mode

voltage is detected and a push-pull transistor connected to the DC voltage can

generate same common mode voltage between the motor drive and the motor

and cancel out the common mode voltage. Some practical problems for this

topology can be:

Cost of push-pull transistors operating at high DC link voltage.

Losses

Conducted emission noise due to leakage current in the motor

The second method is based on switching concept in which an inverter with extra

legs (leg) generates different voltages to cancel out or reduce common mode

voltage. In a four leg inverter, a controller turns on switches in the forth leg to

generate +Vdc/2 or –Vdc/2 voltage in order to reduce the common mode voltage.

180

6.6 . Reducing DC Link vol tage and increas ing

modulat ion index

In this case, the percentage of zero vector used in modulation is decreased which

reduces a pulse width associated with the zero vectors (V0 or V7). Also reducing

the DC link voltage reduces the common mode and shaft voltages. Increasing

modulation index improves the Total Harmonic Distortion.

6.7 . Conclus ions

Different shaft voltage reduction techniques have been addressed for a DFIG in

wind turbine applications. Effects of zero voltage vector elimination in a

tradition 2-level inverter and using a proper PWM strategy with a multilevel

converter topology are two possible solutions to reduce shaft voltage in a

generator system. Changing design parameters of a generator can be an effective

technique in a primary stage of design which can reduce the cost of additional

shaft voltage elimination techniques. Other possible strategies such as different

topologies of active filters and also reducing DC link voltage and increasing

modulation index has been verified in order to eliminate or reduce the shaft

voltage based on the analysis, simulations and a literature review on existing

techniques.

6.8 . References


systems for wind turbines”, Industry Appl. Magazine, IEEE, vol. 8, pp. 26 -33,

May. 2002.










[5] J.Adabi, F.Zare, G.Ledwich, A.Ghosh, “Leakage Current and Common Mode

Voltage Issues in Modern AC Drive Systems”, AUPEC, Perth, Australia, 2007

181

[6] J.Zitzelsberger, W.Hofmann, A.Wiese, “Bearing Currents in Doubly-Fed

Induction Generators”, Power Electronics and Applications, 2005 European

Conference on, 11-14 Sept. 2005

[7] A.M.Garcia, D.G. Holmes, T.A. Lipo, ,” Reduction of Bearing Currents in


IAS Annual Meeting, Volume 1,pp. 84-89

[8] J.Adabi, F.Zare, A.Ghosh, R.D. Lorenz, “Analysis of Shaft Voltage in a

Doubly-fed Induction Generator”, ICREPQ’09, Valencia, Spain, April 2009

[9] Jafar Adabi, Firuz Zare, “Analysis, Calculation and Reduction of Shaft

Voltage in Induction Generators”, ICREPQ’09, Valencia, Spain, April 2009

[10] Hoda Ghoreishy, Firuz Zare, Hamid Hassanpour, “Controlling the Common

mode Voltage in Multilevel Inverters”, The International Journal of Engineering,

Vol. 21, No. 3, September 2008

[11] Firuz Zare, “High frequency model of an electric motor based on

measurement results”, Australian Journal of Electrical & Electronics Engineering

(AJEEE), Vol 4, No 1, 2008, page 17-24.

[12] Satoshi Ogasawara, Hideki Ayano, Hirofumi Akagi, “An Active Circuit for

Cancellation of Common mode Voltage Generated by a PWM Inverter”, IEEE

Transactions on Power Electronics, Vol. 13, No. 5, Sep. 1998

[13] Alexander L. Julian, Giovanna Oriti, Thomas A. Lipo, “Elimination of

Common mode Voltage in Three-Phase Sinusoidal Power Converters”, IEEE

Transactions on Power Electronics, Vol. 14, No. 5, September 1999

[14] Giovanna Briti, Alexander E. Julian, Thomas A.lipo, “A New Space Vector

Modulation Strategy for Common Mode Voltage Reduction”, IEEE PESC’97,

Volume 2, 22-27 June 1997, Page(s):1541 - 1546 vol.2

183

CHAPTER 7

Analysis of Shaft Voltage in a Doubly-fed

Induction Generator

Jafar Adabi*, Firuz Zare*, Arindam Ghosh*, Robert D. Lorenz**





Presented at: ICREPQ 2009, Valencia, Spain

184

Abstract- Fast switching transients and common mode voltage generated by

pulse width modulated voltage in high frequency applications may cause many

unwanted problems such as shaft voltage and resultant bearing currents. The

main objective of this research work is to analyse shaft voltage generation in a

doubly-fed induction generator (DFIG) with a back to back converter. A detailed

high frequency model of the proposed system has been developed based on

capacitive couplings between differfent objects of the machine. The proposed

model can be used for shaft voltage calculations and finding parameters which

have key effect on shaft voltage and resultant bearing currents. A discussion

about the presented technique for shaft voltage elimination in existing literature

is also presented based on mathematical analysis and simulations.

7.1 . Introduct ion

Fig.7. 1 shows a DFIG with a four-quadrant AC-DC-AC converter connected to

the rotor windings which enables decoupled control of active and reactive power

[1].

Fig.7. 1: A DFIG with a four-quadrant AC-DC-AC converter connected to the rotor windings

Power inverters are widely used in wind energy systems to convert AC output

voltage of generators with variable frequency to an adjustable AC voltage for

grid connection. On the contrary, there are many parasitic capacitive couplings

between different parts of electric machine structure which may be neglected in

low frequency analysis but the conditions are completely different in high

frequencies. In fast switching converters, a low impedance path is created for the

current to flow through these capacitors [2-4]. Due to rapid developments of

IGBT technology, switching frequency has dramatically increased. High dv/dt

(fast switching transients) and common mode voltage generated by a power

inverter in high frequency applications can cause unwanted problems such as:

185

shaft voltage and resultant bearing currents, grounding current escaping to earth

through stray capacitors inside a motor, conducted and radiated noises [5-7].

Common mode voltage is known as a potential origin of shaft voltage. Fig.7. 2

shows a three phase inverter and typical waveforms of three leg voltages and the


(a)

(b)

Fig.7. 2: (a) three phase converter (b) common mode voltage generation

According to Fig.7. 2.a, three leg voltages of the converter can be calculated as

follow:

)t(V)t(V)t(V

)t(V)t(V)t(V

)t(V)t(V)t(V

nocnco

nobnbo

noanao

(7-1)

Where (Vao, Vbo, Vco ) and (Van, Vbn, Vcn) are the leg voltages and phase voltages

of a three phase converter, respectively. Vno is the voltage between neutral point

and the ground (common mode voltage). By adding two sides of Eq.1:


It is obvious that the sum of three phase voltages is equal to zero

( 0)t(V)t(V)t(V cnbnan ). Therefore, common mode voltage can be calculated as:

186

comcoboao

no V3

)t(V)t(V)t(V)t(V

(7-3)

This equation shows that the common mode voltage is defined by switching

pattern. By using appropriate switching pattern, the common mode voltage level

can be controlled. Switching states of proposed converter and output voltages

and resultant common mode voltage are shown in Table.7. 1.

Table.7. 1: Switching states, output leg voltage and common mode voltage of three phase inverter

vector S1 S3 S5 Vao Vbo Vco Vcom

V1 1 0 0 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V2 1 1 0 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V3 0 1 0 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V4 0 1 1 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V5 0 0 1 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V6 1 0 1 2

Vdc 2

Vdc 2

Vdc 6

Vdc

V7 1 1 1 2

Vdc 2

Vdc 2

Vdc 2

Vdc

V0 0 0 0 2

Vdc 2

Vdc 2

Vdc 2

Vdc

Recently, some techniques are presented to mitigate shaft voltage and bearing

currents in DFIGs. An approach presented in [8] is to constrain the inverter

PWM strategy to reduce overall common mode voltages across the

rectifier/inverter system, and thus significantly reduce bearing discharge

currents. A general common mode model of DFIGs is mentioned in [9] to

calculate bearing current.

In this paper, mathematical analysis and simulations have been carried out to

find the effective parameters on the shaft voltage of grid-connected induction

generators. This paper also presents analysis with an accurate high frequency

model of the grid-connected wind generators and voltage sources in high

frequencies with simulation results and discussions.

187

7.2 . High frequency model of DFIG and shaft

vol tage calculat ion

Fig.7. 3 shows the capacitive couplings in a DFIG and a view of proposed

machine structure. Following parasitic capacitive couplings are existed in the

proposed machine structure between:

Stator winding and rotor: Csr

Stator winding and stator frame: Csf

Stator winding and rotor winding: Cws

Stator frame and rotor: Crf

Rotor winding and rotor: Cwr

Rotor winding and Stator frame: Cwf

Ball bearing , inner and outer races: Cb1,Cb2

As shown in the DFIG structure, a capacitive coupling between the rotor winding

and stator winding has a variable value because facing areas of two stator and

rotor slots are always changing due to rotor movement.

(a)

(b)

Fig.7. 3: (a) Capacitance coupling in a doubly fed induction machine and (b) a view of DFIG with different capacitive couplings

188

Fig.7. 4 shows the arrangement of a DFIG with a back to back inverter. In this

structure, neutral to ground zero sequence voltage of both stator and rotor

windings act as common mode voltage sources. The common mode voltage of

rotor side and stator side are given as:

3

VVVV coboao

S,com

(7-4)

3

VVVV

zoyoxoR,com

(7-5)

Where coboao V,V,V & zoyoxo V,V,V are the leg voltages of the converters

connected to the stator and rotor, respectively.

Fig.7. 4: a DFIG with a back to back inverter

A high frequency model of the proposed doubly fed induction machine is shown

in Fig.7. 5.

Fig.7. 5: A high frequency model of a doubly fed induction generator

Shaft voltage can be easily calculated by using KCL in the high frequency model

of the doubly fed induction generator. According to Fig.5.7:

0CVV C CVCVV srS,comshaftbrfshaftwrR,comshaft (7-6)

So, shaft voltage is:

srbrfwr

srS,comwrR,comshaft C C CC

CVCVV

(7-7)

189

S,comsrbrfwr

srR,com

srbrfwr

wrshaft V

C C CC

CV

C C CC

CV

(7-8)


Vcom,R and Vcom,S are the common mode voltage generated by the converters

connected to the rotor and the stator windings, respectively. KR and KS are

defined as capacitance factors which are effective in total shaft voltage

calculation.

srbrfwr

srS

srbrfwr

wrR

C C CC

CK

C C CC

CK

(7-10)


(KR is almost near 1 and KS is a very small value). Fig.7. 6.a shows the

simulation results for total shaft voltage. Following values are considered for

capacitive couplings: Cwr=5nF, Crf=0.6nF, Csr=0.3nF, Cb=0.1nF.

(a)

(b)

Fig.7. 6:(a) a typical common mode voltage waveforms and resultant shaft voltage (b) shaft voltage generated by each rotor and stator side converters

190

Fig.7. 6.b shows the share of each converter in shaft voltage generation. Major

portion of the rotor side common mode voltage is transformed to shaft voltage

(in this case, 83% of the rotor side common mode voltage and only 5% of the

stator side common mode voltage). Based on this analysis, the stator common

mode voltage has not a key effect on shaft voltage because the capacitive

coupling between the stator winding and shaft is too small compare with

capacitive coupling between the rotor winding and shaft.

7.3 . Discuss ion

Analysis of shaft voltage reduction in a DFIG with a back to back inverter was

presented in [9] with a pulse width modulation technique to fully remove the

shaft voltage based on an equivalent circuit presented in Fig.7. 7.

Fig.7. 7: equivalent system of a DFIG system [9]

This arrangement identifies key voltage quantities for purposes of analysis. The

capacitance Csg represents the capacitance of the stator windings with respect to

the stator frame which is assumed to be grounded and Crg represents the

capacitance between the rotor windings with respect to the stator frame. It can be

observed that even though the circuit is grounded, if the voltage potentials of

points s and r fluctuate in identical fashion then the current flow in the loop

containing the ground point g is identically zero so that the ground current can be

effectively eliminated if this condition can be reached [9]. Analysis of this circuit

shows that the voltage between the two neutral points is:

3

VVV

3

VVVV csbsasysyrxr

rs

(7-11)

This voltage is called common mode voltage in a DFIG. The presented technique

in [9] suggested equalizing of the common mode voltage from rotor and stator

side to remove the common mode voltage and as a result the shaft voltage can be

considered as zero. Table.7. 2 shows the different switching states of a back to

191

back converter considering switching vectors of each converter and resultant


Table.7. 2: Different switching states and resultant common mode voltage [9]


Vectors 1,3,5

Vectors 2,4,6

Vector 7

Vector 0

Sta

tor

side

con

vert

er Vectors

1,3,5 0

3

Vdc

3

V2 dc 0

Vectors 2,4,6 3

Vdc0

3

Vdc

3

V2 dc

Vector 7 3

V2 dc3

Vdc0 dcV

Vector 0 3

Vdc

3

V2 dcdcV 0

According to this table, if the switching states of machine side converter and line

side converter are both odd, both even or the same zero states from both side

converters, the common mode voltage can be forced to zero. In this case,

switching vectors (1, 3, 5) or (2, 4, 6) are used with and without using zero

states.

The main concern is that this technique does not eliminate the shaft voltage and

still we have the significant amount of voltage across the shaft which is affected

by two sides’ voltage sources (neutral points of stator and rotor winding to the

ground). In other words, the voltage that is forced to be zero in proposed paper

([9]) is not related to the shaft voltage. This voltage is just the voltage between

neutral points of stator winding and rotor winding. Regardless of switching loss,

the PWM technique in this paper can not help to mitigate shaft voltage and

resultant bearing current. It seems that the capacitive coupling between rotor

winding and rotor (Cwr) which has a significant effect was not taken into account

in the analysis.

To achieve a zero shaft voltage or at least reducing shaft voltage to an

appropriate value, both common mode voltage sources should be considered

based on an accurate high frequency model of the system. Based on the Eq.8 and

Fig.7. 5, it is clear that by choosing a proper rotor common mode voltage

(Eq.12), a zero shaft voltage will be achieved.

S,comwr

srR,com V

C

CV (7-12)

Table.7. 3 shows the resultant shaft voltage by different switching states of both

rotor and stator sides converters. Note that, rotor side common mode voltage has

192

been decreased to S,comwr

sr VC

C by a buck converter and shaft voltage is

calculated based on Eq.8 and Table.7. 1.

Table.7. 3: Different switching states and shaft voltage


Vectors 1,3,5

Vectors 2,4,6 Vector

7 Vector

0

Net

wor

k si

de

conv

erte

r

Vectors 1,3,5 3

VK dcS 0

3

VK dcS 3

VK2 dcS

Vectors 2,4,6

0 3

VK dcS 3

VK2 dcS 3

VK dcS

Vector 7 3

VK dcS 3

VK2 dcS dcSVK 0

Vector 0 3

VK2 dcS

3

VK dcS 0 dcSVK

To eliminate the shaft voltage completely, the condition of Eq.12 should be

applied in the analysis. To meet these requirements, it is needed to apply odd

switching vectors (1, 3, and 5) to one converter and even switching vectors (2, 4,

and 6) to another converter. Also, switching V0 from one side and V7 from other

side is conducted to generate zero shaft voltage. As it can be seen from this table,

the results in Table.7.3 are completely different to Table.7. 2. Fig.7. 8 shows a

typical common mode voltage from rotor side, common mode voltage from

stator side and resultant shaft voltage based on proposed switching pattern. In

this case, rotor side voltage is decreased based on the ratio of Cwr and Csr and the

shaft voltage is forced to be zero. From the analysis, it is obvious that rotor side

converter is playing key role in shaft voltage generation of a DFIG structure.

Fig.7. 8: a typical common mode voltage waveforms and zero shaft voltage

The presented PWM pattern can be used as an effective technique to reduce the

shaft voltage. One of the issues regarding to this technique is that, a bidirectional

193

buck converter should be employed to reduce the dc-link voltage (Vc1) by the

ratio of wr

sr

C

C to create a rotor side common mode voltage equal to

S,comwr

sr VC

C (see Fig.7. 9).

Fig.7. 9: a new back-to-back inverters topology with a bidirectional buck converter and a DFIG

In this configuration, the limitation of the duty cycle of the buck converter

should be considered. These conditions may affect the dynamic performance of

the DFIG. Therefore, cancellation of the shaft voltage based on this topology

should be mentioned in terms of practical barriers and dynamic analysis of the

system which is beyond the scope of this paper.

7.4 . Conclus ions

In this paper, an accurate high frequency model of a DFIG has been presented to

analyse mitigation techniques of the shaft voltage. Proposed model is based on

the capacitive couplings between different parts of the generator structure and

the common mode voltage source. Mathematical equations which define the

shaft voltage based on capacitive couplings between rotor and stator frames and

their windings have been presented. According to the analysis, the most

important capacitive coupling in a doubly fed induction generator is the

capacitive coupling between the rotor winding and the rotor frame. A PWM

technique has been presented in literature to remove the overall common mode

voltage in a DFIG but the above mentioned analysis shows that this technique

can not help to eliminate the shaft voltage. Mathematical analysis and simulation

results have been presented to verify the investigations.

194

Acknowledgement



7.5 . References

[1] S.Muller, M.Deicke, R.W.De Doncker, Doubly fed induction generator

systems for wind turbines, Industry Applications Magazine, IEEE, vol. 8, pp.

26 -33, May. 2002.





cancellation of common mode currents, shaft voltages and bearing currents

for induction motor drives," presented at Power Electronics Specialist

Conference, 2003. PESC '03, IEEE 34th Annual, 2003.


and Common Mode Voltage Issues in Modern AC Drive Systems”, presented

at AUPEC 2007, Perth, Australia, Dec 2007.

[5] Firuz Zare, “Modelling of Electric Motors for Electromagnetic Compatibility

Analysis”, presented at AUPEC 2006, Melbourne, Australia, Nov 2006.




[7] S. Chen, T. A. Lipo, and D. Fitzgerald, "Source of induction motor bearing

currents caused by PWM inverters" Energy Conversion, IEEE Transaction

on, vol. 11, pp. 25-32, 1996.


in Doubly-Fed Induction Generators”, Power Electronics and Applications,

2005 European Conference on, 11-14 Sept. 2005

[9] A.M.Garcia, D.G. Holmes, T.A. Lipo, ,” Reduction of Bearing Currents in


IAS Annual Meeting, Conference Record of the 2006 IEEE, Volume 1, on page

195

CHAPTER 8

Bearing Damage Analysis by Calculation of

Capacitive Coupling between Inner and Outer

Races of a Ball Bearing

Jafar Adabi*, Firuz Zare*, Gerard Ledwich*, Arindam Ghosh*, Robert D.Lorenz**





Presented at: EPE-PEMC 2008, Poznan, Poland

196

Abstract- Bearing damage in modern inverter-fed AC drive systems is more

common than in motors working with 50 or 60 Hz power supply. Fast switching

transients and common mode voltage generated by a PWM inverter cause

unwanted shaft voltage and resultant bearing currents. Parasitic capacitive

coupling creates a path to discharge current in rotors and bearings. In order to

analyse bearing current discharges and their effect on bearing damage under

different conditions, calculation of the capacitive coupling between the outer and

inner races is needed. During motor operation, the distances between the balls

and races may change the capacitance values. Due to changing of the thickness

and spatial distribution of the lubricating grease, this capacitance does not have a

constant value and is known to change with speed and load. Thus, the resultant

electric field between the races and balls varies with motor speed. The

lubricating grease in the ball bearing cannot withstand high voltages and a short

circuit through the lubricated grease can occur. At low speeds, because of

gravity, balls and shaft voltage may shift down and the system (ball positions

and shaft) will be asymmetric. In this study, two different asymmetric cases

(asymmetric ball position, asymmetric shaft position) are analysed and the

results are compared with the symmetric case. The objective of this paper is to

calculate the capacitive coupling and electric fields between the outer and inner

races and the balls at different motor speeds in symmetrical and asymmetrical

shaft and balls positions. The analysis is carried out using finite element

simulations to determine the conditions which will increase the probability of

high rates of bearing failure due to current discharges through the balls and

races.

8.1 . Introduct ion

Nowadays, modern AC motor drive systems are widely used in industrial and

commercial applications. Due to rapid developments of IGBT technology,

switching times have decreased to a fraction of a micro second and as a result,

the switching frequency has dramatically increased. Fig.8. 1.a shows the

structure of a modern power electronic drive consisting a filter, a rectifier, a dc

link capacitor, an inverter and an AC motor. It also shows that many parasitic

capacitive couplings exist which may be neglected in low frequency analysis but

the conditions are completely different in high frequencies. In high switching

197

frequencies, a low impedance path is created for the current to flow through

these capacitors [1-2].

Fig.8. 1.b shows the different forms of capacitive coupling in an induction

motor, where CWR is the capacitive coupling between the stator winding and

rotor, CWS is the capacitive coupling between the stator winding and stator, CSR

is the capacitive coupling between the rotor and stator frame. In principle, all

inverters generate common mode voltages relative to the earth ground due to

coupling through the parasitic capacitances [1]. Fig.8. 2 shows a simple

equivalent circuit model of an AC motor which depicts the main high frequency

coupling capacitances [2-3].

(a)

(b)

Fig.8. 1: Capacitance coupling in an induction motor and a view of stator slot

High dv/dt (fast switching transients) and common mode voltage generated by a

PWM inverter can cause unwanted problems such as shaft voltage and resultant

bearing currents [4-7]. Fig.8. 3 shows the general structure of ball bearings and

shaft in an AC machine. As shown in this figure, there are balls between outer

and inner races with lubricating grease between balls and the races. There is a

capacitive coupling between the outer and inner races.

198

Fig.8. 2: High frequency model of an induction motor

During operation, the distances between the balls and races may change and vary

the capacitance and resultant electric field between the races and balls. This

capacitance has a nonlinear relationship with load and speed. Lubricating grease

in the ball bearing cannot withstand high voltages and a short circuit through the

lubricated grease can occur. This breakdown phenomenon can be modelled as a

switch.

(a) (b) (c)

Fig.8. 3: (a) General structure of ball bearings and shaft and outer and inner race of an AC machine (b) a view of ball, outer and inner races and capacitive couplings (c) simple model of

ball bearing

This paper focuses on calculation of capacitive coupling between ball bearing

and inner and outer races using finite element simulations to analyse the

probability of increased bearing failure rates under different conditions.

8.2 . Discharge current paths by calculat ion of

capaci t ive coupl ings

2-D Finite element simulations are carried out based on the proposed structure in

order to calculate capacitive coupling terms between the inner and outer races

and balls in low and high speeds in symmetrical and asymmetrical positions. For

the test case bearing as shown in Fig.8. 3, there are 15 balls with the diameter of

20 mm, shaft diameter is 80 mm and three ranges of 1mm, 0.1mm, 0.01mm oil

199

thickness were simulated. The objective of the simulation is to calculate the

electric fields between the outer race and balls (dBO) and between the inner race

and balls (dBI) at different motor speeds which cause symmetrical and

asymmetrical shaft and ball positions. Analyses are carried out in order to

determine the conditions under which the probability of bearing failure rate due

to discharging current through the balls and races are very high. Several

conditions are simulated based on balls and shaft positions in different speeds.

8.2.1. Symmetric Case

At high speed, balls and shaft positions are considered symmetric and the

distances between the inner race and balls (dBI) and between outer races and balls

(dBO) are assumed to be equal. Also the shaft position is not changed and the

shaft and outer race are concentric. Table.8. 1 shows the capacitive coupling

between the inner and outer races and the ball, the electric field in the area

between the inner race and ball (EBI) and the outer race (EBO) assuming a typical

100 volts voltage across the races.

Table.8. 1: Capacitive coupling terms, voltage and electric fields in the symmetric case

dBO

(mm)

dBI

(mm)

CBO

(nF)

CBI

(nF)

EBO

(V/mm)

EBI

(V/mm)

0.5 0.5 1.010 0.807 88.87 111.13

0.05 0.05 3.540 2.890 899.47 1100.53

0.005 0.005 11.300 9.020 8881.72 11118.28

As depicted in Fig.8. 4, if a short circuit (breakdown) occurs, then a discharge

current will be divided into several paths and the probability of bearing damage

is decreased.

Fig.8. 4: Possible discharge current paths in the symmetric case

200

8.2.2. Asymmetric case

At low speeds, because of gravity, balls and shaft may shift down and the system

(balls position and shaft) will be asymmetrical. In this study, two different cases

(asymmetric ball positions, asymmetric shaft position) are analysed. Fig.8. 5

shows these two types of asymmetries. As shown in Fig.8. 5.a, in this

asymmetric case, the upper and lower side balls are shifted down because of

gravity but the separations between the inner and outer races with other balls can

approximately be considered as symmetric. As shown as in Fig.8. 5.b, at lower

speeds, an asymmetric shaft position may occur, which is more common than

other cases.

(a) (b)

Fig.8. 5: Asymmetric (a) ball positions (b) shaft position

8.2.2.1. Asymmetric ball positions

As shown in Table.8. 2, several distances are simulated to compare the

capacitive couplings (CBO, CBI) and electric fields (EBO, EBI) for each of them.

Simulations are carried out for oil thicknesses of 1mm, 0.1mm, and 0.01mm. As

shown in Fig.8. 6.a, in the asymmetrical balls case, balls come down and the

region between the upper ball and shaft (see Fig.8. 6.b) and the lower ball and

shaft (see Fig.8. 6.c) are more important than other areas.

From the results in Table.8. 2, the electric field is increased when dBI or dBo are

decreased but the electric field between the inner race and upper ball (E) is more

than the electric field between the outer race and lower ball (E') for the same rate

of change in distances. The capacitive coupling terms and resultant electric

fields for dBI1=dBO2=0.001 mm & dBI2=dBO1=0.009 mm as shown in Table.8. 3.

However dBO2 & dBI1 are equal, because of different positions of balls and races

(which is shown in Fig.8. 6.b&c), capacitive coupling terms and electric fields

are different (EBI1 is 50% more than EBO2).

201

Table.8. 2: Capacitive coupling terms and electric fields in an asymmetrical ball position

Oil

Thickness

(mm)

dBO

(mm)

dBI

(mm)

CBO

(nF)

CBI

(nF)

EBO

(V/mm)

EBI

(V/mm)

1 0.1 0.9 2.490 0.616 198.71 89.03

1 0.3 0.7 1.400 0.710 111.97 94.87

1 0.5 0.5 1.010 0.807 88.86 111.13

1 0.7 0.3 0.893 1.130 79.82 147.08

1 0.9 0.1 0.778 2.020 80.21 278.05

0.1 0.01 0.09 7.760 2.130 2155.97 871.56

0.1 0.03 0.07 4.570 2.430 1157.93 932.31

0.1 0.05 0.05 3.540 2.890 899.46 1100.53

0.1 0.07 0.03 2.980 3.750 796.03 1475.91

0.1 0.09 0.01 2.620 6.530 792.73 2865.36

0.01 0.001 0.009 26.200 6.890 20821.87 8797.57

0.01 0.003 0.007 13.100 7.800 12443.87 8952.63

0.01 0.005 0.005 11.300 9.020 8881.72 11118.28

0.01 0.007 0.003 9.140 11.800 8048.07 14554.51

0.01 0.009 0.001 8.150 18.700 7736.50 30371.47

Table.8. 3: Capacitive coupling terms and electric fields in oil thickness of 0.001 mm

ball

Oil

Thickness

(mm)

dBO

(mm)

dBI

(mm)

CBO

(nF)

CBI

(nF)

EBO

(V/mm)

EBI

(V/mm)

1 0.01 0.009 0.001 8.150 18.700 7736.50 30371.47

2 0.01 0.001 0.009 26.20 6.890 20821.87 8797.57

Thus, increasing the electric field between inner race and balls at upper side will

create a path to discharge current. In other words, if a short circuit (breakdown)

occurs at these balls, the probability of dividing the discharge current into other

paths will decrease and the upper ball near the inner race (ball 1 in Fig.8. 6.a) is

the highest probability candidate to create a path for discharging current. If the

voltage breakdown occurs, a bearing damage problem could occur at this area

(position A in Fig.8. 7). If the damage occurs at this position, the same problem

will happen at the distance between ball and outer race (position A' in Fig.8. 7).

8.2.2.3. Asymmetric shaft position

An asymmetry in the shaft position is analysed via simulations. The simulations

are carried out to find the capacitive coupling terms and electric field in three

202

separation ranges: 1mm, 0.1mm, and 0.001mm. In this case, shaft position is

shifted down corresponding to 20%, 40% and 60% grease thickness. Table.8. 4

shows the capacitive coupling terms, voltage and electric fields with respect to

different variables associated with the balls position assuming the inner and outer

distances in each side are equal.

(a) (b) (c)

Fig.8. 6: (a) Asymmetric ball positions (b) upper side ball (c) lower side ball

Table.8. 4: Capacitive coupling terms and electric fields in an asymmetric shaft position

Shift

in Shaft centre (mm)

dBO

(mm)

dBI

(mm)

CBO

(nF)

CBI

(nF)

EBO

(V/mm)

EBI

(V/mm)

0.2 0.4 0.4 1.21 0.967 111.21 138.79

0.4 0.3 0.3 1.41 1.130 148.54 184.79

0.6 0.2 0.2 1.74 1.400 223.22 276.78

0.02 0.04 0.04 4.01 3.240 1117.02 1382.99

0.04 0.03 0.03 4.64 3.750 1489.93 1843.40

0.06 0.02 0.02 5.71 4.610 2233.12 2766.88

0.002 0.004 0.004 13.20 9.960 10767.64 14232.36

0.004 0.003 0.003 17.90 10.200 12121.21 21212.12

0.006 0.002 0.002 24.10 11.600 16308.64 33691.36

Fig.8. 7: Discharge current paths for asymmetric ball positions

203

Fig.8. 8: Capacitive coupling terms between upper and lower balls and races for an asymmetric shaft position

According to simulation results, electric field between the lower ball (ball 2 in

Fig.8. 8) and the inner race is more than other separations. In other words, if a

breakdown occurs in this area, the probability of division of the discharge current

into other paths will decrease and ball 2 is the highest probability candidate to

create a path for the discharge current. In this case, the distance between ball 1

and the races is more than the distance between ball 2 and races. Thus,

capacitance and the resultant electric field in the upper side is less than in the

lower side (E1<E2 as shown in Fig.8. 8). In the lower side, because of different

positions of ball 2 and the races, the electric field is different while the distance

between ball and races are the same (for instance, at dBI2=dBO2=.002 mm, EBI2 is

40% more than EBO2). As shown in Fig.8. 9, if the breakdown voltage is

exceeded, a bearing damage problem may occur at this area (position C in Fig.8.

9). If the damage happens at this position, the same problem will happen at the

distance between ball and outer race (position C' in Fig.8. 9). This may cause

multiple bearing damage sites.

Fig.8. 9: Probable discharge current paths for an asymmetric shaft position

204

8.3 . Conclus ions

Based on the simulation and analysis which are presented in this paper, during

motor operation, the distances between the balls and races may change the

capacitance values. At a high speed, balls and shaft positions are considered

symmetrical and the distances between the inner race and balls (dBI) and between

outer races and balls (dBO) are assumed to be equal. Also the shaft position is not

changed and the centres of the shaft and the outer race are the same (symmetrical

position). In a low speed case, because of gravity, balls and shaft voltage may

shift down and the system (balls position and shaft) will be in an asymmetric

shape. In this study, two different asymmetric cases (asymmetric ball positions,

asymmetric shaft position) are analysed and the results are compared with the

symmetrical case to determine the probability of bearing damage. Several

distances are simulated to compare the capacitive couplings between ball bearing

and inner and outer races (CBO, CBI) and electric fields (EBO, EBI) for each of

them. Simulations are carried out for oil thicknesses of 1mm, 0.1mm, and

0.01mm for both symmetrical and asymmetrical cases to determine the

conditions which will increase the probability of high rates of bearing failure due

to current discharges through the balls and races.

Acknowledgement


support for this project through the ARC Discovery Grant DP0774497

8.4 . References

[1] S. Chen, T. A. Lipo, and D. Fitzgerald, "Modeling of motor bearing currents

in PWM inverter drives," Proc. of the 30th Annual IEEE Industry Applications

Conference, vol.32, issue 6, pp. 1365-1370, 1995.

[2] S. Chen, T. A. Lipo, and D. Fitzgerald, "Source of induction motor bearing

currents caused by PWM inverters" IEEE Transactions on Energy Conversion,

vol. 11, pp. 25-32, 1996.

205

[3] A. Muetze and A. Binder, "Calculation of Circulating Bearing Currents in

Machines of Inverter-Based Drive Systems" IEEE Transactions on Industrial

Electronics, vol. 54, pp. 932-938, 2007.


Helsinki, 1999

[5] A. Muetze and A. Binder, "Practical Rules for Assessment of Inverter-

Induced Bearing Currents in Inverter-Fed AC Motors up to 500 kW," IEEE

Transactions on Industrial Electronics, vol. 54, pp. 1614-1622, 2007.


PWM inverters on AC motor bearing currents and shaft voltages," IEEE

Transactions on Industry Applications, vol. 32, pp. 250-259, 1996.

[7] Michael J. Devaney and Levent Eren, “Detecting motor bearing faults”, IEEE

Instrumentation & Measurement Magazine, Volume 7, Issue 4, pp. 30-50, Dec

2004.

207

CHAPTER 9

Conclusions and Further Research

208

9.1 . Conclus ions

The solutions to reduce or eliminate shaft and common mode voltages of ASD

systems have been investigated in the scope of this thesis. Various investigations

have been undertaken to achieve practical and cost effective strategies which can

be classified as:

The solutions to reduce shaft voltage at motor design stage

The solutions to reduce shaft voltage current AC motors in use

1) Shaft voltage reduction at early stage of motor design

Analyses of the parameters which are effective in shaft voltage generation of AC

motors/generators have been investigated. Investigations focused on different

parasitic capacitive couplings through mathematical equations, finite element

simulations and experiments. The effects of different design parameters on

proposed capacitances and resultant shaft voltage have been studied. Analyses

have been undertaken for normal AC motors (or for stator fed induction

generators in wind turbine applications) and wound rotor AC motors (or for a

DFIG in wind applications). It has been found that:

The capacitive coupling between rotor and stator winding is a key factor in

shaft voltage generation for a normal AC motor. Some parameters can

change proposed capacitance such as: stator slot tooth, the gap between slot

tooth and winding, and the height of slot tooth, as well as the air gap between

rotor and stator.

In a wound rotor motor, the capacitive coupling between the rotor winding

and rotor frame has a significant value compared with other capacitances.

The effects of the insulation parameters – such as permittivity and the

thickness of the insulation – are very effective in shaft voltage reduction.

The end-winding parameters were also the focus of this analysis, in which a

simple geometric model of the end-winding was considered. In this model,

the end-winding length (L1) and rotor ring length (Lring) are most important

factors which are effective in total capacitances. The main conclusion from

these studies is that by increasing the end-winding length (L1) as multiples of

209

Lring, the value of end-winding capacitive couplings will not increase after

2×Lring.

High frequency models are presented and mathematical equations are offered

to calculate the shaft voltage based on different capacitive couplings, and the

common mode voltage in both squirrel cage and wound rotor motor (or

generators). The validity of these equations has been verified via simulation

analysis in a wide range of design parameters and tests.

A ball bearing damage analysis has been done by 2-D simulation. As a result

of this work, the areas of the inner and outer races and ball bearings (which

are the first candidates for damage in case of any breakdown in the shaft and

ball asymmetry system) have been determined. This analysis should be

considered in the design process for the ball bearing and the races. The

quality of the materials for these areas also needs to be considered. At low

speeds, because of gravity, balls and shaft may shift down and the system

(ball positions and shaft) will be asymmetric. Asymmetric cases are

analysed and the results are compared with the symmetric case.

In the stage of motor design, the best option is to use the analysis about the

effective motor parameters at the optimisation software of the motor design to

reduce motor shaft voltage and avoid additional costs for mitigation of the

resultant bearing current. Theses parameters can be changed to achieve the

lowest possible shaft voltage; however, the range of variation has to meet the

electromechanical and thermal considerations of the generator design.

2) Shaft voltage for present ASD systems

For the present motor drive systems, the best option is to reduce the shaft voltage

via reduction of common mode voltage with proper PWM strategy. These types

of motors/generators can be classified as low power, high power and very high

power wind turbine generators. For each case, the proper PWM strategies have

been presented. Different topologies and configurations have been investigated

in the scope of this thesis as explained below:

In the low power AC motors applications, inverter system connected to a

single-phase diode rectifier. There are some choices which can minimize the

210

common mode voltage with keeping the zero vectors in the switching

sequences by using the different ground placement as a benefit. A means of

reducing the shaft voltage is to use only V0 voltage vector in the positive half

cycle in which it has the lowest potential with respect to the neutral. V7 will

be applied in the negative half cycle where the neutral line is connected to

PFC inductor and negative DC link is connected to the source voltage.

Therefore, it is better to apply V7 as a zero vector in negative half cycle to

create the lowest possible common mode voltage without distortion of the

load current.

In high power applications, inverter system connected to a three-phase diode

rectifier. Based on the analyses, the zero vectors in PWM patterns create the

maximum level of common mode voltage, and elimination of the zero states

by using only active voltage vectors (V1-V6) can reduce the common mode

voltage significantly. However, a main drawback is the quality of load

current. Removing V0 and V7 requires adding another active vector in order

to have a constant switching frequency. This modulation method increases

the load current harmonics. In multilevel converters (diode clamped topology

is more practical), there are more voltage levels and switching states which

can provide possibilities to reduce common mode voltage. In this topology,

each leg has three voltage levels: (+Vdc/2, 0, -Vdc/2). Different switching

strategies have been proposed to reduce the common mode voltage in this

topology. With regard to Table.1. 11, Vectors V0, V13 and V26 are zero

voltage vectors in a d-q frame. V0 and V26 create maximum common mode

voltage of +/- Vdc/2, while V13 generates no common mode voltage (zero

voltage). Thus, instead of V0, V26 voltage vectors, we can use V13 to generate

PWM waveforms. Vectors V1, V3, V9, V17, V23 and V25 are active vectors

and they generate +/-Vdc/3. In these switching vectors, two legs of the

converter have +Vdc/2 or - Vdc/2 voltage level and the other have zero

voltage. Using the pulse position method we are able to shift leg voltages in

such a way as to remove or reduce these switching states; however, this may

affect the quality of the load current.

211

In very high power wind turbine applications, different configurations of a

doubly fed induction generator (DFIG) and an induction generator (IG) with

a back-to-back inverter in wind turbine applications have been investigated

in terms of shaft voltage generation. Detailed high frequency models of the

proposed systems have been developed based on existing capacitive

couplings in IG and DFIG structures and common mode voltage sources. In

this research, several arrangements of DFIG based wind energy conversion

systems were investigated with respect to shaft voltage calculation and its

mitigation techniques. Filtering in different converters sides, PWM

techniques and a circuit topology are proposed to reduce the shaft voltage.

According to the analyses, filtering in the rotor or stator side cannot fully

mitigate shaft voltage, and using PWM techniques cannot eliminate the shaft

voltage (Removing zero states can help to reduce the shaft voltage). A zero

shaft voltage can be achieved by filtering at both sides converter because

both sides’ common mode voltage sources are forced to be zero. To fully

eliminate the shaft voltage, we need to generate common mode voltage on

the rotor side, based on Eq.1-35 and Table.1. 12. To meet these requirements,

it is necessary to have opposite switching vectors from each converter side.

For example, odd switching vectors (1, 3, and 5) should be applied to one

converter and even switching vectors (2, 4, and 6) applied to another

converter. Also, switching vector V0 from one side and vector V7 from the

other side achieves a zero shaft voltage. A PWM technique and a back-to-

back inverter with a bidirectional buck converter are proposed to eliminate

the shaft voltage in a DFIG wind turbine to address these issues.

There are also many types of shaft voltage reduction technique which has been

mentioned in literature review. The most important solutions are to shield the

motor windings (to remove the capacitive coupling between rotor and winding)

and use insulated ceramic ball bearing (to avoid the current to flow through

bearings). These techniques are not easy to implement and costly and because of

that, this research investigated on the solutions which are practical, cost effective

and easy to implement.

212

9.2 . Future research

The above analyses have lead to gainful shaft voltage reduction strategies in the

first step of the design process and also to common mode voltage reduction

techniques in motor drive systems and wind turbine applications. Opportunities

for future related research can be classified in the following areas:

Optimisation of motor design considering shaft voltage and leakage current

Dynamic analysis of the proposed PWM technique and circuit topology for

the DFIG-based wind turbine

Utilization of multilevel inverter topology in the DFIG systems

Development of very high frequency converters to reduce LC filter size.

Optimisation of motor design considering shaft voltage and leakage current

In the analysis of the design factors of an AC motor, a wide range of design

parameters are considered in the analysis. Changes in these parameters have

been offered as a strategy in the first step of the design to reduce the shaft

voltage. The range of the acceptable design parameters needs to satisfy other

electro-mechanical issues in the electric motor design. For example, any

decrement in the length of the stator slot tooth or the gap between slot tooth and

the winding can decrease the shaft voltage. On the other hand, dramatic

decrement of these parameters can also affect flux density, magnetization

current, reactance and resistances, electrical losses and efficiency. Therefore,

there should be a balance between these parameters and the shaft voltage.

Further investigations are needed to determine the practicality of such a

technique which adds an additional component to the motor design process.

As already mentioned, the capacitive coupling between the rotor winding and

rotor frame in a wound rotor motor has a significant value compared with other

capacitances. This capacitance is related to the thickness and the permittivity (εr)

of the insulation. Any changes in these two parameters may directly change the

thermal behavior of the system which needs to be measured through coupled-

field (electro-thermal) analysis with finite element simulation tools. A future

circuit-electromagnetic analysis could also provide a better understanding of the

213

real system with respect to the generation of the leakage currents and the shaft

voltage.

Dynamic analysis of the proposed PWM technique and circuit topology for

the DFIG-based wind turbine

As mentioned in the analysis, a PWM strategy has been suggested to reduce the

shaft voltage. Also, a bidirectional buck converter has been added in the back-to-

back inverter topology to reduce the rotor side common mode voltage by a

certain amount. In this research, the focus was not to investigate the dynamic

analysis of the system, but to present the possibility of shaft voltage mitigation

techniques with LC filters and PWM pulse pattern. Analysis was not restricted to

a certain amount of frequency or slip of DFIG, and different switching

frequencies have been presented to show the validity of the analysis. Therefore,

adding a buck converter circuit requires future dynamic study of the system.

Voltage balancing of the DC-link capacitor is also a task that should be

considered in future work.

Utilization of multilevel inverter topology in the DFIG systems

The analysis of the multilevel inverter shows that there are more switching

choices in this type of converter which can reduce the common mode voltage. As

the rotor-side converter is much more important to common mode voltage

generation, this type of converter can help to reduce the rotor side common mode

voltage.

Development of very high frequency converters to reduce LC filter size

Utilising a power converter in higher frequency (e.g.100 kHz) can reduce the

size of the LC filters to eliminate the common mode voltage. This type of

converter needs to be further analysed in terms of high frequency analysis and

shaft voltage reduction in motor drive systems.

Remediation Strategies of Shaft and Common mode...

Documents

Transcript of Remediation Strategies of Shaft and Common mode...