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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
II
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
Fig.1. 31: Leg voltages and common mode voltage for switching sequence of
(V7, V2, V1, V2, V7) ............................................................................................. 52
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. ...................................................................................... 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
Fig.1. 40: Common mode model for the configuration of a DFIG with
Topology2 ........................................................................................................... 60
Fig.1. 41: Common mode model for the configuration of a DFIG with
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
Fig.5. 13: Leg voltages and common mode voltage for switching sequence of
(V0, V1, V2, V1, V0) ........................................................................................... 162
Fig.5. 14: Leg voltages and common mode voltage for switching sequence of
(V7, V2, V1, V2, V7) ........................................................................................... 163
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. ................................................................................... 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
Fig.6. 5: Leg voltages for a three-level inverter (a) at the centre (b) at the sides
........................................................................................................................... 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)
Vcom = 505 Volts, Vsh = 15.5 Volts 0.0306
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
)
Fig.1. 31: Leg voltages and common mode voltage for switching sequence of (V7, V2, V1, V2, V7)
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)
Fig.1. 34: Leg voltages for a three-level inverter (a) at the centre (b) at the sides
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.
Fig.1. 40: Common mode model for the configuration of a DFIG with Topology2
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.
Fig.1. 41: Common mode model for the configuration of a DFIG with Topology4
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
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68
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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)
By adding two sides of Eq.2-1:
)t(V3)t(V)t(V)t(V)t(V)t(V)t(V nocnbnancoboao (2-2)
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
(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
exist between: the stator winding and rotor (Csr), the stator winding and stator
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)
As shown in this equation, the effective parameters on shaft voltage are d, ρ, g1
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)
Thus, shaft voltage can be simplified as follows:
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)
S,comSR,comRshaft VKVKV (2-15)
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
(2-16)
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.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
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
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:
[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.
[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.
[8] M. M. Swamy, K. Yamada, and T. Kume, "Common mode current
attenuation techniques for use with PWM drives," Power Electronics, IEEE
Transactions on, vol. 16, pp. 248-255, 2001.
[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.
[10] 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
[11] 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
98
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
Box 2434, Brisbane, Australia
** 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)
Vcom,R and Vcom,S are the common mode voltages from the rotor and stator
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
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 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
effective area to calculate capacitive couplings between rotor and stator will
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)
Vcom = 505 Volts, Vsh = 10.5 Volts 0.0207
Test results (without shielded end winding)
Vcom = 505 Volts, Vsh = 15.5 Volts 0.0306
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)
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.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
The authors thank the Australian Research Council (ARC) for the financial
support for this project through the ARC Discovery Grant DP0774497.
3.7 . References
[1] 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.
[2] 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," PESC '03, IEEE 34th Annual, 2003.
[3] 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.
[4] Firuz Zare, “Modelling of Electric Motors for Electromagnetic Compatibility
Analysis”, presented at AUPEC 2006, Melbourne, Australia, Nov 2006.
[5] ABB Technical guide No.5 ‘bearing currents in modern AC Drive systems”,
Helsinki, 1999
119
[6] 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
[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
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
[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
[13] Matthew N.O.Sadiku, “Elements of Electromagnetics” third edition, New
York, Oxford University Press, 2001
[14] ANSYS® Academic Research, Release 11.0, Help System, Electromagnetic
Field Analysis Guide, ANSYS, Inc.
120
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,
*School of Electrical Engineering, Queensland University of Technology, GPO
Box 2434, Brisbane, Australia
** Depts. of ME and ECE, University of Wisconsin-Madison, 1513 University
Avenue, Madison, USA
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
effective area to calculate capacitive couplings between rotor and stator will
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)
As shown in this equation, the effective parameters on shaft voltage are d, ρ, g1
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
The authors thank the Australian Research Council (ARC) for the financial
support for this project through the ARC Discovery Grant DP0774497.
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
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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
School of Electrical Engineering, Queensland University of Technology, GPO
Box 2434, Brisbane, Australia
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)
By adding two sides of Eq.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
)
Fig.5. 13: Leg voltages and common mode voltage for switching sequence of (V0, V1, V2, V1, V0)
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
)
Fig.5. 14: Leg voltages and common mode voltage for switching sequence of (V7, V2, V1, V2, V7)
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
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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,
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characteristics” IEEE Transactions on Industry Applications, vol. 43, no. 5, pp.
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[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
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[9] Qiang Yin, Russel J. Kerkman, Thomas A. Nondahl and Haihui Lu,
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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
[11] Annette Muetze, Andreas Binder, “Calculation of Motor Capacitances for
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
[12] ABB Technical guide No.5 ‘bearing currents in modern AC Drive systems”,
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,
School of Electrical Engineering, Queensland University of Technology, GPO
Box 2434, Brisbane, Australia
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
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). 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)
Thus, shaft voltage can be simplified as follows:
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. 5: Leg voltages for a three-level inverter (a) at the centre (b) at the sides
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
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 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
[1] S.Muller, M.Deicke, R.W.De Doncker, “Doubly fed induction generator
systems for wind turbines”, Industry Appl. Magazine, IEEE, vol. 8, pp. 26 -33,
May. 2002.
[2] 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.
[3] M. M. Swamy, K. Yamada, and T. Kume, "Common mode current
attenuation techniques for use with PWM drives," Power Electronics, IEEE
Transactions on, vol. 16, pp. 248-255, 2001.
[4] M. M. Swamy, K. Yamada, and T. Kume, "Common mode current
attenuation techniques for use with PWM drives," Power Electronics, IEEE
Transactions on, vol. 16, pp. 248-255, 2001.
[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
Doubly Fed Induction Generators” Industry Applications Conference, 2006. 41st
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
182
183
CHAPTER 7
Analysis of Shaft Voltage in a Doubly-fed
Induction Generator
Jafar Adabi*, Firuz Zare*, Arindam Ghosh*, Robert D. Lorenz**
*School of Electrical Engineering, Queensland University of Technology, GPO
Box 2434, Brisbane, Australia
** Depts. of ME and ECE, University of Wisconsin-Madison, 1513 University
Avenue, Madison, USA
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
common mode voltage.
(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:
)t(V3)t(V)t(V)t(V)t(V)t(V)t(V nocnbnancoboao (7-2)
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)
S,comSR,comRshaft VKVKV (7-9)
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)
By considering srbrfwr C C CC , the shaft voltage is determined by Cwr
(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
common mode voltage.
Table.7. 2: Different switching states and resultant common mode voltage [9]
Rotor side converter
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
Rotor side converter
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
The authors thank the Australian Research Council (ARC) for the financial
support for this project through the ARC Discovery Grant DP0774497.
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.
[2] 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.
[3] 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.
[4] 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.
[5] Firuz Zare, “Modelling of Electric Motors for Electromagnetic Compatibility
Analysis”, presented at AUPEC 2006, Melbourne, Australia, Nov 2006.
[6] M. M. Swamy, K. Yamada, and T. Kume, "Common mode current
attenuation techniques for use with PWM drives," Power Electronics, IEEE
Transactions on, vol. 16, pp. 248-255, 2001.
[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.
[8] 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
[9] 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
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**
*School of Electrical Engineering, Queensland University of Technology, GPO
Box 2434, Brisbane, Australia
** Depts. of ME and ECE, University of Wisconsin-Madison, 1513 University
Avenue, Madison, USA
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
The authors thank the Australian Research Council (ARC) for the financial
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.
[4] ABB Technical guide No.5 ‘bearing currents in modern AC Drive systems”,
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.
[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," 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.
206
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
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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
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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.
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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.
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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
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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.