Synchronous Generator Performance Prediction using Finite Element analysis and Arithmetic ...

228 Pages·2012·8.15 MB·English

Advanced Performance Prediction Tools for the Analysis
of Rotating Electrical Machines

Philip Alexander Hargreaves

Thesis Submitted for the degree of Engineering Doctorate

Department of Electrical, Electronic and Computer Engineering
Newcastle University

In collaboration with General Electric Power Conversion

©2012
COMMERCIAL IN CONFIDENCE
Abstract
Abstract
This thesis seeks to advance the design tools for electrical generators. It aims to
undertake an electrical generator’s design, using the Finite Element method within a
defined time frame. The thesis looks at the history of generator design systems and
outlines the parameters a designer must predict. These parameters are then duly
calculated using various finite element methods.

The thesis introduces a Pseudo Rotating Superposition system, which allows large
quantities of data to be found from single static finite element simulations. Initially the
system is used to predict machine saturation curves, and it is later expanded to predict
the transient performance of generators. The full load performance of generators is
found using a novel multivariable clustered optimisation routine. An extension using a
rotating finite element solver, with pseudo rotating superposition, is then demonstrated.
This creates a method which allows voltage harmonics to be quickly, accurately and
validly predicted. Finally a study of iron loss is undertaken and using the above method
it is shown that iron loss can be validly calculated using the quicker Radial/Tangential
reference frame, rather than a slower Major/Minor frame.

A collection of 48 manufactured machines are used throughout as a test group for the
created methods. Results from design calculations are compared to both factory test
results and to the predictions from an existing customised in house design software tool.
The methods within this thesis are shown to be over 35% more accurate in the majority
of cases. The whole suite of methods created can automatically calculate results for any
given machine in less than 1 hour.

The computer macros described in this thesis and the comparison with existing design
methods and test were all made by the Author.
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Acknowledgements
Acknowledgements
Firstly I would like to thank the backers of this research - the Engineering and Physical
Sciences Research Council, my Industrial sponsor GE Energy and The Engineering
Doctorate scheme at Newcastle University. Without them this work would never have
taken place.

I'd like to thank my industrial supervisor Ross Hall. I first met him when he supervised
my 2nd year Lab sessions and now 8 years on he's still supervising albeit as my Boss!
Thank you for head hunting me into the company and for pursuing an industrial purpose
for this work. I'd also like to thank all the employees at GE who I've hassled for
information or have taken the time to help me over the years.

As my academic supervisor Barrie Mecrow deserves the most thanks. Constantly
patient and always tactful in pointing out the flaws in my incoherent babble. Our Friday
phone calls have been the highlight of my work week. Furthermore Barrie deserves a
medal for reading the early drafts of this thesis, as it is safe to say that I am not a literary
scholar. For this and many more things Thank you Barrie.

This work is the culmination of two decades of education and I cannot thank enough the
teachers and mentors who have inspired and encouraged me on this journey. These
include Miss Pretty and Mrs Fuller my maths teachers, Mr Archer and Mr Haworth
from the Physics Department and Mr Collins my technology teacher. Additionally I
cannot imagine myself being at this point without the excellent machines lectures given
by both Barrie Mecrow and Alan Jack.

Finally I'd just like to say "It's about bloody time!"
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Principal List of Abbreviations and Symbols
Principal List of Abbreviations and Symbols
B Magnetic Flux Density
H Magnetic Field Strength
H coercive force
c
μ Permeability
J Current Density
A Vector Potential
E Back EMF or Electric Field Strength
P Permeance
F MMF
V Terminal voltage
I Field current
f
I Armature current
a
X Armature direct axis reactance
ad
X Leakage reactance
l
X End winding leakage reactance
lew
X Field winding reactance
f
X Damper cage reactance
kd
R Field winding resistance
f
R Damper cage resistance
kd
R Armature Resistance
a
W Wieseman Coefficient
L Effective Axial Length
a_eff
T' /τ' / t' Transient D axis reactance
d d d
T'' / τ'' / t'' Subtransient D axis reactance
d d d
T' /τ' / t' Transient D axis time constant
d d d
T'' / τ'' / t'' Subtransient D axis time constant
d d d
PF Power factor
θ Power factor angle
l Axial Length
a
N Number of radial ventilation ducts
d
w Axial width of ventilation ducts
d
v
Principal List of Abbreviations and Symbols
ZPF/ zpf Zero Power Factor (Saturation Curve)
SCC/ scc Short Circuit (Saturation Curve)
OCC/occ Open Circuit (Saturation Curve)
3phaseSS Three phase short circuit from open circuit
FE Finite Element
T.H.D. Total Harmonic Distortion
T.I.F. Telephonic Interference Factor
T.H.F. Telephonic Harmonic Factor
CAD Computer Aided Design
GUI Graphical User Interface
PRS Pseudo Rotating Superposition
RPRS Rotating Pseudo Rotating Superposition

vi
Index
Index
Abstract ........................................................................................................................... iii
Acknowledgements .......................................................................................................... iv
Principal List of Abbreviations and Symbols ................................................................... v
Index .......................................................................................................................... vii
List of Figures .................................................................................................................. xi
Chapter 1. Introduction ............................................................................................... 1
1.1. The Company ......................................................................................................... 1
1.2. Aims and Objectives .............................................................................................. 5
1.3. Contributions to Knowledge .................................................................................. 6
1.4. Chapter Outline ...................................................................................................... 7
1.5. Published work ....................................................................................................... 9
Chapter 2. Overview of Design Systems for Generators .......................................... 10
2.1. Genesis ................................................................................................................. 10
2.2. Trend Sheets ......................................................................................................... 12
2.3. General Electric's Machines ................................................................................. 13
2.3.1. Design Variable Parameters........................................................................... 15
2.4. Analytical Design Systems ................................................................................... 18
2.4.1. Electronic Deign System - EDS..................................................................... 18
2.4.2. Speed Lab ...................................................................................................... 21
2.5. Finite Element Method ......................................................................................... 22
2.5.1. History ........................................................................................................... 22
2.5.2. Equations ....................................................................................................... 22
2.5.3. Finite Element Design Systems ..................................................................... 24
2.5.4. Finite Element Systems ................................................................................. 25
2.6. Integrated Design Systems ................................................................................... 27
2.7. Chapter Summary ................................................................................................. 28
Chapter 3. Initial Design Characterisation ................................................................ 30
3.1. Introduction .......................................................................................................... 30
3.2. Methodology ........................................................................................................ 31
3.2.1. Magnetic Coupling ........................................................................................ 31
3.2.2. Pseudo Rotating Superposition ...................................................................... 31
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Index
3.2.3. Open Circuit Curve (OCC) ............................................................................ 33
3.2.4. Sustained Short Circuit curve (SCC) ............................................................. 36
3.2.5. Zero power factor curve (ZPF) ...................................................................... 38
3.3. Further Calculations and Considerations.............................................................. 40
3.3.1. Effective Axial Length................................................................................... 40
3.3.2. B-H curve Dilution ........................................................................................ 44
3.3.3. End winding Leakage .................................................................................... 48
3.3.4. Initial Field Current Calculation using Carters Coefficient ........................... 51
3.3.5. Conductor Placement and Insulation ............................................................. 53
3.3.6. Mesh Size ....................................................................................................... 55
3.3.7. Finite Element Machine Construction ........................................................... 61
3.4. Results and Discussion ......................................................................................... 61
3.4.1. Open Circuit Curve ........................................................................................ 62
3.4.2. Sustained Short Circuit Curve (SCC) ............................................................ 64
3.4.3. Zero Power Factor Saturation Curve (ZPF) ................................................... 65
3.4.4. Leakage Paths ................................................................................................ 66
3.4.5. Calculation Speed .......................................................................................... 67
3.5. Chapter Summary ................................................................................................. 68
Chapter 4. Calculation of Transient Parameters ....................................................... 70
4.1. Introduction .......................................................................................................... 70
4.2. Standstill Frequency Analysis .............................................................................. 70
4.2.1. Analysis System ............................................................................................. 71
4.2.2. Simulation ...................................................................................................... 72
4.2.3. Limitations ..................................................................................................... 85
4.3. Equivalent Circuit ................................................................................................. 86
4.3.1. Leakage reactance - X ................................................................................... 87
l
4.3.2. Field reactance - X ......................................................................................... 88
f
4.3.3. Wieseman Coefficients .................................................................................. 90
4.3.4. Transient Time constant - T'd ........................................................................ 91
4.3.5. Subtransient Parameters ................................................................................. 94
4.3.6. Calculation Speed ........................................................................................ 105
4.4. Results ................................................................................................................ 105
4.5. Chapter Summary ............................................................................................... 109
Chapter 5. Full Load Operating Point Prediction ................................................... 111
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Index
5.1. Introduction ........................................................................................................ 111
5.2. Potier's Method ................................................................................................... 112
5.2.1. Potier Reactance .......................................................................................... 112
5.2.2. Full Load Calculation .................................................................................. 113
5.3. Direct Full Load Calculation Using Finite Element ........................................... 116
5.4. Finite Element Static Analysis Using Multivariable Curve Fitting ................... 116
5.4.1. Surface fitting and Solution Identification................................................... 117
5.4.2. End Winding Inductance ............................................................................. 120
5.4.3. Cluster Analysis vs. Matrix analysis............................................................ 121
5.4.4. Program Flow .............................................................................................. 123
5.5. Results ................................................................................................................ 124
5.6. Chapter Summary ............................................................................................... 128
Chapter 6. Prediction of Waveform Harmonics ..................................................... 130
6.1. Analytical method .............................................................................................. 130
6.1.1. Flux Density Waves Due to Stator and Rotor Permeance Variations ......... 130
6.1.2. Limitations of Analytical Methods .............................................................. 132
6.2. Proposed Method of Predicting The Open Circuit Waveform ........................... 133
6.2.1. Rotating Pseudo Rotating Superposition (RPRS) ........................................ 135
6.2.2. Comparison With Measurement .................................................................. 139
6.3. Influence Of The Field Current Source .............................................................. 142
6.3.1. Effect Of Exciter Harmonics Upon Field Excitation ................................... 143
6.4. Voltage Distortion Parameters ........................................................................... 145
6.5. Comparison Of Total Harmonic Distortion ........................................................ 147
6.6. The Effect of Damper Bars within Synchronous Machines ............................... 149
6.7. Automated Damper Bar Optimisation ................................................................ 152
6.8. Chapter Summary ............................................................................................... 154
Chapter 7. Iron Loss Calculation ............................................................................ 156
7.1. Abstract .............................................................................................................. 156
7.2. Introduction ........................................................................................................ 156
7.3. Continuous time and Discrete time. ................................................................... 157
7.4. Orthogonal Components ..................................................................................... 158
7.5. Alternative Calculations ..................................................................................... 161
7.6. Summary of Methods ......................................................................................... 162
7.7. Use of Pseudo Rotating Superposition (PRS) .................................................... 162
ix
Index
7.8. Determination of Constants ................................................................................ 164
7.9. The metre cube ................................................................................................... 167
7.10. The machine ..................................................................................................... 169
7.11. Comparison To Test Results ............................................................................ 170
7.12. Chapter Summary ............................................................................................. 173
Chapter 8. Conclusions ........................................................................................... 174
8.1. Summary of Errors ............................................................................................. 175
8.2. Contributions to Knowledge .............................................................................. 176
8.3. Limitations .......................................................................................................... 177
8.3.1. Programming Limitations ............................................................................ 177
8.3.2. Fundamental Limitations ............................................................................. 178
8.4. Further work ....................................................................................................... 180
Appendix Index .................................................................................................................. I
A. Open Circuit Voltage Results - 1 pu ................................................................. II
B. Open Circuit Voltage Results - 0.5 pu ............................................................. III
C. Short Circuit Current Results ........................................................................... IV
D. Zero Power Factor Results ................................................................................ V
E. Calculation of the End Winding Length .......................................................... VI
F. Calculation of R2 ........................................................................................... VIII
G. Frequency to Time Domain Transform............................................................ IX
H. Graphical User Interface ................................................................................ XII
I. Transferring Impedances across an Ideal transformer ............................... XVIII
J. T.H.F. and T.I.F. Weighting Factors ............................................................. XIX
References ................................................................................................................. XXIII
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