Transient Voltage Distribution in Stator Winding of Electrical Machine Fed from a Frequency Converter
ABSTRACT Standard induction motors are exposed to steepfronted, nonsinusoidal voltages when fed from frequency converters. These wave patterns can be destructive to the insulation. The aim of the present work is to develop methods of predicting the magnitude and distribution of fast voltage within the stator winding of an electric machine fed from a frequency converter. Three methods of predicting the magnitude and distribution of fast voltages within form windings commonly used in medium and high voltage machines are described. These methods utilise some aspects of previously published works on the surge propagation studies to achieve simplification of the solution without loss of accuracy. Two of these methods are applied to the voltage calculation in random winding commonly used in low voltage machines. Multiconductor transmission line theory forms the basis of the methods described in this work. Computation of the voltage distribution using either of these methods requires the calculation of the parameters for the slot and the end (overhang) part of the winding. The parallel plate capacitor method, the indirect boundary integral equation method and the finite element method are the three possible methods of calculating the capacitance also described in this work. Duality existing between the magnetic and the electric field has been used for the inductance calculation. Application of these methods to the voltage calculation in the first coil from the lineend of a 6 kV induction motor is shown to be successful. From the computed and measured voltage results it is evident that the improved accuracy for the capacitance values is sufficient to give good agreement between the measured and calculated interturn voltages without the need to infer the presence of a surface impedance effect due to the laminated core. Application of two of these methods for the transient voltage calculation on the first coil from the terminalend of low voltage induction motors with random windings is also shown to be successful. Comparison between the computed and the measured results shows that the turntoground capacitance matrix obtained in overhang part of the coil can be assumed the for the slot part of the coil. With this assumption modelling the first five turns in the lineend coil produce turn and coil voltage that match well with the corresponding measuring result. The methods of voltage computation described in this work should be of great help to engineers and researchers concerned with the turn strength and overvoltage protection in high and low voltage motors. Acta polytechnica Scandinavica. El, Electrical engineering series, ISSN 00016845; 100
 Citations (8)
 Cited In (0)

Article: Computer simulation of first poletoclose multiple prestriking transients in motor systems
[Show abstract] [Hide abstract]
ABSTRACT: Multiple prestriking transients are frequently produced in systems controlled by vacuum switching devices. The authors describe solution methods for evaluating multiple prestriking transients in a source/cable/motor controlled with a vacuum switching device. A solution method based on the Fourier transform is developed. The multiple prestriking condition is simulated by the reiterative use of voltage and current generators, and the piecewise Fourier transform is used to obtain the transforms of nonanalytic functions. A method is developed for modifying the usual piecewise Fourier transform expression so that it may be rapidly evaluated by fast Fourier transform techniquesElectric Power Applications, IEE Proceedings B [see also IEE ProceedingsElectric Power Applications] 10/1989; 
Article: Protecting Machines From Line Surges
[Show abstract] [Hide abstract]
ABSTRACT: Some of the more important technical problems involved in connecting rotating machines directly to overhead electric power transmission lines are discussed in this paper. Methods are developed for protecting the ground and turn insulations Protecting the ground and turn insulations of the armatures of such machines which may be subjected to surge voltages. The ground insulation can be protected by lightning arresters; the turn insulation by sloping off the incoming surge. Methods sloping off the incoming surge. Methods are given for determining the maximum allowable rate of rise of voltage at the machine terminals, and the apparatus needed to limit the rate of rise to that value.Transactions of the American Institute of Electrical Engineers 02/1934; 
Article: Interturn voltages in machine windings evaluated from onsite test results and computer simulation
[Show abstract] [Hide abstract]
ABSTRACT: Interturn voltages produced in the lineend coils of machine windings when steepfronted prestriking transients reach the winding are usually predicted by injecting a simple rampfunction voltage wave into a computer simulation of the winding. In practice, steepfronted prestriking transients have complex waveforms, and it is possible that a simple ramp function does not adequately represent such a wave. The authors examine this uncertainty and also the possibility that the complex waveforms of prestriking transients may cause voltage resonance in lineend coils, and the production of interturn voltages greater than predicted with simple ramp functionsElectric Power Applications, IEE Proceedings B [see also IEE ProceedingsElectric Power Applications] 06/1992;
Page 1
ACTA
POLYTECHNICA
SCANDINAVICA
ELECTRICAL ENGINEERING SERIES NO. 100
Transient Voltage Distribution in Stator Winding of Electrical Machine Fed
from a Frequency Converter
BOLARIN S. OYEGOKE
Helsinki University of Technology
Department of Electrical and Communications Engineering
Laboratory of Electromechanics
P.O Box 3000, FIN02015 HUT, Finland
Dissertation for the degree of Doctor of Technology to be presented with due permission for public
examination and debate in Auditorium S4 at Helsinki University of Technology (Espoo, Finland) on 27 May
2000, at 12 o’ clock noon.
ESPOO 2000
Page 2
2
Oyegoke, B. S.: Transient Voltage Distribution in Stator Winding of Electrical Machine Fed from a
Frequency Converter. Acta Polytechnica Scandinavica, Electrical Engineering Series, No. 100, Espoo,
1999, 74 p. Published by the Finnish Academies of Technology. ISBN 9516665373. ISSN 00016845.
Keywords: electrical machine, stator winding, voltage distribution, frequency converter
ABSTRACT
Standard induction motors are exposed to steepfronted, nonsinusoidal voltages when fed from frequency
converters. These wave patterns can be destructive to the insulation. The aim of the present work is to
develop methods of predicting the magnitude and distribution of fast voltage within the stator winding of an
electric machine fed from a frequency converter.
Three methods of predicting the magnitude and distribution of fast voltages within form windings commonly
used in medium and high voltage machines are described. These methods utilise some aspects of previously
published works on the surge propagation studies to achieve simplification of the solution without loss of
accuracy. Two of these methods are applied to the voltage calculation in random winding commonly used in
low voltage machines.
Multiconductor transmission line theory forms the basis of the methods described in this work. Computation
of the voltage distribution using either of these methods requires the calculation of the parameters for the slot
and the end (overhang) part of the winding. The parallel plate capacitor method, the indirect boundary integral
equation method and the finite element method are the three possible methods of calculating the capacitance
also described in this work. Duality existing between the magnetic and the electric field has been used for the
inductance calculation.
Application of these methods to the voltage calculation in the first coil from the lineend of a 6 kV induction
motor is shown to be successful. From the computed and measured voltage results it is evident that the
improved accuracy for the capacitance values is sufficient to give good agreement between the measured and
calculated interturn voltages without the need to infer the presence of a surface impedance effect due to the
laminated core.
Application of two of these methods for the transient voltage calculation on the first coil from the terminalend
of low voltage induction motors with random windings is also shown to be successful. Comparison between
the computed and the measured results shows that the turntoground capacitance matrix obtained in over
hang part of the coil can be assumed the for the slot part of the coil. With this assumption modelling the first
five turns in the lineend coil produce turn and coil voltage that match well with the corresponding measuring
result.
The methods of voltage computation described in this work should be of great help to engineers and
researchers concerned with the turn strength and overvoltage protection in high and low voltage motors.
All rights reserved. No part of the publication may be reproduced, stored in a retrieval system, or
transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise,
without the prior written permission of the author.
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3
PREFACE
This work was carried out in the Laboratory of Electromechanics, Helsinki University of Technology during
the year 19951999. The work is applied to the transient voltage distribution in the stator winding of electric
machine subjected to a fast rising voltage such as those arising in inverter fed motors, vacuum switches and
lightning.
To my supervisor, Professor Tapani Jokinen, I would like to express my gratitude for the opportunity
given to me to continue my postgraduate studies under his professorship. Your efforts in guiding me through
those hard times are unforgettable. Furthermore, I am very grateful to Associate Professor Ivan Stoyanov
Yatchev and Professor Alexander Krumov Alexandrov of the Department of Electrical Apparatus, Technical
University of Sofia, Bulgaria, for the knowledge inspired in me during my visit to their Laboratory in Sofia.
In addition, I wish to acknowledge the effort of Dr Paavo Paloniemi and Dr Eero Keskinen of ABB
Industry Oy for the useful discussion about this work at a very early stage of its development. Special thanks
and appreciation to Dr Arkkio Antero, Professor Asko Niemenmaa and other members of the Laboratory of
Electromechanics for the time devoted to the editing of my papers technically and otherwise. Their efforts are
quite meritorious. Many thanks to Mr Pertti Saransaari and Mr Osmo Koponen for their support in making the
experimental study possible. Financial support by the Imatran Voima is gratefully acknowledged.
To my family, a word can not express how grateful I am for your patience and continuous support.
Above all infinite gratitude to GOD (ALLAH) the Almighty, the owner of all that is in the heaven and the
earth and all that exists between (seen and unseen) for making this work a reality. If not by His will, this work
would have remained a dream.
Espoo, June 1999
Bolarin S. Oyegoke
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4
CONTENTS
ABSTRACT…………………………………………………………………………………………........... 2
PREFACE………………………………………………………………………………………….............. 3
CONTENTS…………………………………………………………………………………………........... 4
LIST OF SYMBOLS………………………………………………………………………………............. 6
DEDICATION………………………………………………………………………………...................... 8
1 INTRODUCTION……………………………………………………………………………….............. 9
1.1 Background…………………………………………………………………………….............. 9
1.2 Winding failure…………………………………………………………………………............. 9
1.3 Failure modes…………………………………………………………………………............. 10
2 PREVIEW OF PAST WORKS…………………………………………………………….................... 11
2.1 Preview of past works on transient voltage distribution in form winding.....……...............….……....... 11
2.2 Preview of past works on transient voltage distribution in random winding………..........…………....... 14
2.3 Methods for computing voltage transients……………………………………………....………........... 16
2.4 Basic of each method………………………………………………………………….……................ 17
2.4.1 Lumpedparameter method……………………………………………………….…............ 17
2.4.2 Fouriertransform method……………………………………………………….….............. 17
2.4.3 Travellingwave method………………………………………………………….…........…. 17
2.5 Conclusions…………………………………………………………………………………................. 18
2.6 Aim and contents of the present work………………………………………………………................ 18
3 METHODS USED IN THIS WORK……………………………………………………………........... 19
3.1 Coil and its subdivision into parts……………………………………………………….…………........ 19
3.2 Multiconductor transmission line theory……………………………………………….………............ 20
4 COMPUTATION OF WINDING PARAMETERS………………………………………………......... 24
4.1 Parallel plate capacitor approximation…………………………………………………………….….... 25
4.2 Indirect boundary integral equation method……………………………………….……………............ 26
4.3 Finite element method……………………………………………………………………..………....... 27
4.3.1 Finite element solution…………………………………………………..…………............... 27
4.3.2 Piecewise constant approximation…………………………………………………………… 28
4.4 Methods for resistance calculation…............……………………………………………..………....... 29
4.4.1 Proximity effect………………………………………………………..……………............. 29
4.4.2 Correction factor………………………………………………………….…………............ 30
4.5 Limitation of the multiconductor transmission line model of winding………………………..…............ 30
4.6 Conclusions…………………………………………...…………....………………….........……….... 30
5 METHODS FOR INTERTURN VOLTAGE CALCULATION ON FORM WINDING………........… 31
5.1 Why not laddernetwork for voltage calculation in form winding……………………...........………….. 31
5.2 Multiconductor transmission line theory for interturn voltage prediction in form windings…………..... 31
5.2.1 Multiconductor transmission line and scatter matrix concept (MTLSMC)……........…...…... 32
5.2.2 Scatter matrix derivation for junction 1…………………………………………........…….... 32
5.3 Multiconductor transmission line and averaging technique concept (MTLATC)………………….…… 36
5.3.1 Wave propagation………………………….…………………………………….........…….. 36
5.3.2 Wave scattering………………………………………………………………….…............. 36
5.3.3 Wave reflection coefficients…………………………………………………….……........... 37
5.3.4 Voltage calculation…………………………………………………………………….......... 37
5.4 Multiconductor transmission line concept for circuit simulator (MTLCCS)………….........…………... 37
6 EXPERIMENTAL STUDIES OF VOLTAGE DISTRIBUTION IN FORM WINDING……………… 38
Page 5
5
6.1 Measurement of the voltage distribution in the stator winding of a 6 kV induction
motor under a fast rising step input voltage: General arrangement..........................…….…………... 38
6.1.1 Measurement of the coil voltage…………………………………….............…………….... 38
6.1.2 Measurement of the voltage over individual turns…………………................……………... 39
6.2 Effect of different cable lengths………………………………….............................………………... 42
6.3 Conclusions……………………………………………………………………......………………...... 43
7 RESULTS OF VOLTAGE CALCULATION ON FORM WINDINGS………………………............. 44
8 EFFECT OF SOME PARAMETERS ON INTERTURN VOLTAGE………………………………... 46
8.1 Effect of copper resistance on the interturn voltage…………………………..........……………….... 46
8.2 Effect of the overhang capacitance on the interturn voltage………………….………...………........ 47
8.2.1 Computation of the parameters………………………………………......………………..... 48
8.2.2 Capacitance matrices………………………………………………………………………... 48
8.2.3 Computation of the admittance matrix…………………………………………………….… 49
8.2.4 Results………………………………………………………………......………………...... 50
8.2.5 Discussion of the results…………………………………………………………………….. 51
8.2.6 Analysis of other windings…………………………………………………………………... 52
8.2.7 Summary…………………………………………………………………………………….. 53
8.2.8 Conclusions………………………………………………………………………………….. 53
9 METHODS FOR TRANSIENT VOLTAGE CALCULATION ON RANDOM WINDING……..…… 54
9.1 Problem definition..............……………………………………………………..........……………….. 54
9.2 Assumption and estimation of motor parameters…………………………………....………………..... 55
9.3 Computation of the Capacitance Matrix for voltage calculation in random winding.………………….... 55
9.4 Voltage calculation on random winding……………………………………….………………….……. 56
9.5 Measurement arrangements on a random winding machine…………………….…….………….......... 57
9.6 Sensitivity of turn positions…………………………………………………............………………..... 58
9.6.1 Full capacitance matrix of the slot and overhang part of the coil.............………………..... 58
9.6.2 Full capacitance matrix of the slot and turn to ground capacitance for the
overhang part of the coil.............................................................................…………….. 59
9.6.3 Results..........................................................................................................……...…... 59
9.6.4 Turn to ground capacitance of the overhang part is assumed for the slot part........….......... 64
9.6.5 Computed results using the MTLSMC and MTLCCS.............................…………….….... 65
9.7 Further studies on random winding……………………………………………..........………………... 66
10 CONCLUSIONS………………………………………………………………………...…...….......... 68
REFERENCES……………………………………………………………………………...……............. 70
Page 6
6
LIST OF SYMBOLS
( )A w
A w
c
c
( )
C
C
C
(
C
(
i
C
(
v
C
Cintcap
Frequency response of a line
Response of the line to step input
Velocity of light
Capacitance per unit length
Capacitance matrix
Turn to ground capacitance matrix in the overhang region
Turn to ground capacitance
1( )
e
g
)
mod
)
)
Modified capacitance matrix
Current connection matrix
Voltage connection matrix
Capacitance between two adjacent turns
Capacitance of turn 1 to the ground in the slot part
Propagation coefficient of a line
Inverse Fourier transform
Conductance of a line
Junction current column matrix
Cgst1
( )d w
(tF
G
( ) I
( )in
I
( )re
I
K
Kcf
l
( )
L
M
Q
( )
R
R
R
( )
S
s
=
t
u
ug
U
( )
V
( )in
V
( )re
V
( )
Y
( )Y w
( )
Z
( )Z w
Z
Z
Z
)
Incident junction current column matrix
Reflected junction current column matrix
Coefficient of the proximity effect
Proximity effect correction factor
Length of a line
Inductance matrix
..
Mutual inductance
Charge
Resistance matrix
Resistance of a line
Final form of a resistance in a line with skin and proximity effects
Voltage scatter matrix of a junction
Laplace operator
Time
Electric scalar potential
Velocity of propagation
Voltage
Junction voltage column matrix
proximity
12 13
,
M
sm
jw
Incident junction voltage column matrix
Reflected junction voltage column matrix
Admittance matrix
Admittance of a line
Impedance matrix
Characteristic impedance of a line
Impedance of the space between two adjacent turns
Impedance at coil entrance
Impedance seen at the coil exit
sabt
ent
ext
Page 7
7
Zg1
Zglt
Zgnt
0 e
re
µ
rµ
d
r
r
w
Impedance calculated from the first turn of the coil
Impedance calculated from the last turn of the coil in the same slot
Impedance calculated from the first turn of the next coil.
Permittivity of a free space (vacuum)
Relative permittivity of the insulation or dielectric constant
Permeability of a free space (vacuum)
Relative permeability of the insulation
Skin depth
Reflection coefficient at coil entrance
Reflection coefficient at coil exit
Angular frequency
0
1
2
Page 8
8
DEDICATION
This work is dedicated to the glory of God Almighty, beside whom there is none. The Incomprehensible, the
Knowledgeable, the Disposer of affairs, The Guarantor, the Watchful, the Guardian.
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9
INTRODUCTION
1.1 Background
Cage induction motors have been the most popular electric motors in the 20th century. The dynamic progress
made in the field of power electronics and control technology has led to increased application of cage
induction motors in electrical drives. Their rated output power ranges from 70W to 500 kW, with 75% of them
designed with four pole stators.
The squirrel cage induction motor is characterised by its robust and maintenancefree behaviour. Induction
motors operating from a direct on line application with sinusoidal supply voltage have the limitation of
delivering a near constant, unadjustable speed that is defined by the line frequency and the number of poles. In
addition, induction motors fed by direct on line voltage develop only a small starting torque, drawing a large
starting current.
In many applications, adjustable speed drives provide important advantages over constant speed drives.
Adjustable Speed Drives give the possibility for automation and high cost efficiencies in industrial production
processes and for transportation applications. Some applications, for instance electrical vehicles, would not
have been possible without fast and accurate speed control. Because of these needs, adjustable speed drives
have increasingly appeared in use in the recent years. An increasing number of adjustable speed drives are
based on alternating current technology because of the good efficiency of this type of drive and the robustness
of alternate electrical machines.
Adjustable speed drives permit the possibility to overcome the shortcomings of induction motors operating
directly on line voltage, and satisfy most requirements of modern drives. The frequency converter with pulse
width modulation (PWM) and constant direct current voltage has established itself as the standard variable
speed device for low voltage induction motors. With the increased emphasis on energy conversion and lower
cost, the use of higher performance PWM drives has grown at an exponential rate.
For switching on the intermediate circuit voltage in PWM inverter, Silicon Controlled Rectifiers (SCR) at a
frequency of 300 Hz were used before 1980. The SCR gave way to the current Gate Turnoff Thyristors
(GTO). The GTO was commonly used from early 1980 to 1990. From 1990 until the present time, the
insulated Gate Bipolar Transistors (IGBT) have become the new industry standard. The IGBT operates in the
frequency range of about 20 kHz.
Unfortunately, inverters with progressive electronic components, such as IGBT, cause extremely steep and
frequent peaks in the output voltage. These peaks impose large stresses on the winding insulation in a similar
way to transient voltages caused by the fast switching of motors at the mains.
1.2Winding failure
The basic stresses acting on the stator winding can be categorised into the following four groups:
1. Thermal
2. Electrical
3. Ambient
4.Mechanical
All these stresses are impacted by adjustable speed drive voltage waveforms, since the longevity of the
winding is predicted on the basis of the integrity of the whole insulation system.
During the early stages of applying adjustable speed drives to ac motors, the major focus was on the thermal
stress generated by the unwanted drive harmonics passed through to the motor and the associated heating. An
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example is inverters that may use regular thyristors, such as variable voltage sixstep inverters and current
source inverters, which generate a rise time longer than 5 microseconds. More attention is given to rotor
construction (rotor bar shapes) than to the capability of the stator insulation to withstand voltage, since the bar
shape significantly influences the speed torque characteristics of the motor.
With modern PWM drive technology, which utilises much higher switching rates (IGBT), the stator winding
insulation system has become the point of interest. This does not, however, imply that the rotor designs can be
neglected.
1.3Failure modes
Among many factors leading to the failure of ac motors fed by a frequency converter (e.g. PWM inverter)
are the bearing failure and the interturn insulation failure.
Bearing problems account for about 50% of all machine failures (Schoen et al. (1995); Thorsen and Dalva
(1995)). Next to the bearing problems is the failure of the stator winding. In the petrochemical industry, about
22% of the problems in the stator winding are caused by the failure in the interturn insulation (Thorsen and
Dalva (1995)).
The bearing failure is associated with an increase in magnitude of the motor shaft voltage, which in turn is due
to steepfronted voltage such as that arising from the inverters and vacuum switching devices. An increase in
shaft voltage results in current flow through motor bearings and electric discharge current within the bearings.
The electric discharge current within the bearings leads to erosion of the bearing material and an early
mechanical failure.
The interturn insulation failure, a common problem in inverter fed motors, could be a result of a defect
introduced during manufacturing. This could have led to a flaw in the thin insulation between the conductors of
the coil (interturn insulation). Another source of interturn insulation failure is in exploitation when a voltage
that is higher than the nominal turn voltage is applied across a turn.
The problem associated with interturn voltage failure has received increase attention in recent years. This is
due to the availability and use of new and improved materials and devices. The desire to produce cost
effective competitive products has resulted in greater exposure of the motor to high amplitude, repetitively
produced steepfronted transients (Murano et al. (1974a); Murano et al. (1974b); Cornick and Tlesis (1989);
Cornick and Tlesis (1990); Cornick et al. (1992); Gupta et al. (1990)). This can therefore lead to an increase
in the severity of the conditions which interturn insulation has to withstand.
Because of the reliability, compact size, low maintenance needs and long life, the vacuum switching devices
are universally used in conjunction with large motors. In variable speed drive systems, PWM inverters are
widely used. Both the vacuum devices and the inverters, however, have a drawback in that they are capable
of producing high amplitude steepfronted surges during switching operations.
The use of low loss cables between the vacuum interrupter (inverter) and the motor does not lower the
amplitude of the surge or its front. Therefore, this cable cannot be thought of as protection against fast fronted
waves.
Generally speaking, among possible failure modes of a machine fed from a frequency converter lie the
following:
1.Turn to turn failure
2. Coil to coil failure
3.Phase to phase failure
4.Coil to ground failure
5. Open circuit failure
Page 11
11
Of these failure modes, the phase to phase and phase to ground insulation is relatively easy to address and as
a matter of fact is not normally the highest, as it was when operating on sinewave power where the steady
state turn to turn stress was relatively low.
In the light of the facts mentioned above, it has become very important to understand the surge phenomena in
motor windings. The cause of surge phenomena, the system parameters that affect their amplitude and rise
time and the ways in which these surges distribute themselves in winding, all need to be considered.
Knowledge of the surge phenomena will allow quality design of the turn insulation and probably an adequate
design of protective measures against dangerous surge.
2 PREVIEW OF PAST WORK
In this chapter, the situation of the voltage distribution in the stator winding of an induction motor when
confronted by fast rising voltage is reviewed. Steep fronted surges have long been known to subject the turn
insulation of a high voltage motor to voltage much higher than the rated value. The most common source of
fast rise time surge is from the circuit breaker operation. To be precise, when the circuit breaker is close to a
motor, the electrical breakdown across the contacts of the breaker launches a voltage surge down the power
cable, which strikes the motor.
2.1Preview of the past works on transient voltage distribution in form winding
While most of the theoretical investigation of surge phenomena has been concentrated on overhead lines and
transformers, owing to their greater vulnerability, the effects of fast transients, such as switching or lightning
surges on rotating machine insulation have been studied since the 1930’s. Boehne (1930) is one of the first
investigators to study the effect of fast transients on rotating machine insulation.
When a steep fronted surge such as that arising from an inverter or a vacuum switch arrives at the machine
terminal, it propagates through the windings. This surge imposes dielectric stresses on the turn insulation. On
the basis on this fact, Calvert (1934) considers a machine winding to be an inductance having uniformly
distributed capacitance to earth as well as capacitance between the turns. His analysis of impulsevoltage
distribution is concerned only with prediction of the rate of rise of the incoming surge, in order to enable the
interturn voltages of coils to be kept within reasonable limits. However, Calvert, when dealing with machines
of conventional design, did not say anything about the close coupling existing between electrically remote
portions of the winding which are physically close together. An example of such a portion is those parts of the
winding occupying the same slot. The facts mentioned above regarding the work of Calvert have also been
confirmed by Robinson (1953) who proposed the theory of propagation in winding in which twocoil sides are
inside each slot.
Studies performed by Cornick et al. (1989), Wright et al. (1983) and Stone et al. (1984) on the distribution of
steep fronted transients with submicrosecond rise time, show that the steep fronted transient distributions are
quite nonuniform across the coils of the winding and the turns of the coils. In addition, the electrical stress
was found highest across turns in coils near the terminal end of the winding. Thus, fast transients subject the
interturn insulation in coils near the terminal end to very high electrical stress, which can cause breakdown of
the thin insulation between the conductors that make the turn of the winding. This high electrical stress results
in failure of the motor.
Treating the machine winding as a transmission line presents the simplest approach to analysing voltages due
to surges in the stator winding of an electric machine. In this approach, the transmission line equations are
used to calculate the voltages at any point on the winding. The parameters of the transmission line are found
by approximating the coils as the elemental sections of the line, each represented by a series inductance and a
shunt capacitance. This method presents a quick way to evaluate the voltages and has been applied by Knable
(1957).
Page 12
12
Knable’s method has the disadvantage of being incapable of predicting voltage inside the coil. The low pass
filtering properties of the winding are not accounted for by this method and any flattening of the surge front
must be due to losses. However, Mcleay (1982) and Oyegoke (1997b) have pointed it out that a coil acts as a
low pass filter even when losses are not included in the analysis.
The result of an impulse strength test on the turn insulation has been reported by Gupta et al. (1986). Of fifty
three typical coils procured from different manufacturers and tested singly in air, most failures were located at
or very near the bends or the nose (or knuckles) where the conductors (strands/turn) had the least
consolidation and the most severe misalignment. For 100 nanoseconds rise time impulses, the strength of
typical coils varies over a wide range, from about 2 pu to 16 pu. Where one pu is the crest of the rated line to
ground voltage. In other words, one pu is given as
1pu =
2
3
rated line voltage
∗
Weed (1922) showed that the fundamental principle whereby the nonuniformity in voltage distribution and
oscillation can be eliminated from the winding, could be stated as follows:
“If the capacitance that is associated with any inductance is so disposed that the initial distribution of a
suddenly impressed voltage (which is affected by the capacitance) is uniform with respect to inductance, the
growth of current within the inductance will be uniform and the voltage distribution will therefore remain
uniform, each element of capacitance receiving charge at the same rate it loses it.”
On the basis of the importance of the selfcapacitance and the capacitance to the ground, Rudenberg (1940a)
adopted a special method of deriving the differential equations for the transformer winding analysis. In his
attempt to predict the electric stresses between sections of a transformer winding, he began by considering
the behaviour of the network when excited by a single harmonic voltage of an angular frequency w. He then
expressed the applied unit function voltage by a Fourier integral of such harmonics. In 1954, Lewis pointed out
that while Rudebergs’ derivation of the network response to the individual harmonic is correct, his expression
for the response of the voltage is not correct, because of inadequate summation of the frequency components.
In summation of the components, the relative magnitudes and phases were not considered. The same method
was applied to the motor winding by the same author. In Rudebergs’ analysis of a motor winding, the
elemental unit or cell of the winding was a coil. Rudeberg presumed that the winding has a relatively large
number of coils and therefore classified the winding as a system with distributed parameters. Though his
method took into consideration the mutual inductance and the mutual capacitance between two adjacent coils,
the result obtained for voltage distribution may be inaccurate because generally, phase winding of motors
consists of few coils.
The maximum terminal intersection voltage as predicted by Rudeberg (1940b), is incorrect because of the
inadequate summation of various frequency components as mentioned above.
In order to predict the voltage distribution in the motor winding, Lewis (1954) applied a system with lumped
parameters in the form of a ladder network. In his work, a coil is a section of the network. If turns were taken
as a section of the network, there is a tendency to have some value for turn voltage. Whatever the case is,
either a coil or a turn is used as a section of the network. Voltage distribution predicted by this method will not
be accurate enough. This is because the method neglects the mutual coupling between the inductance.
Another fact is that a unit function voltage has been employed throughout and the resistive effect has been
neglected. Therefore, the method cannot be used to analyse the effects of surge rise time that could be of
interest in inverter fed motors. In both Lewis’ and Weed’s work, there is no coil subdivision into slot (iron) and
overhang parts.
Lovass et al. (1963) suggested differential equations of the general alternating ladder network that could take
into consideration mutual coupling between two adjacent sections of the network. In their work, apart from the
fact that losses are neglected, nothing is mentioned about the nonadjacent sections of the network. This
method can be useful if the effect of an arbitrary input voltage is required.
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Adjaye and Cornick (1979) applied a method based on a cascade twoport network to analyse the voltage
distribution of the winding. In their work, the elemental unit of the network is a coil. It was presumed that the
turn voltage is distributed uniformly throughout the coil. This method includes losses, however, if the system is
to be modified in order to represent a coil such that voltage across a turn could be accounted for inaccurate
results will be yielded, since the method neglects the mutual inductance between sections (coil or turn).
While the abovementioned previous investigators have developed techniques to predict coil voltage under
surge conditions, few attempts have been made to compute voltages within the first coil from the terminal.
A classical technique for interturn voltage calculation was developed by Rhudy et al. (1986). In their
approach, a lumped element equivalent circuit represents each turn or coil. Such a technique cannot fully take
into account wave propagation within a coil and consequently some loss of accuracy might occur.
Techniques utilising the travelling wave theory were proposed by Wright et al. (1983a). They made great
contributions in understanding and computing the transient voltage distribution in machine windings, subjected
to steep fronted surges. In their work, the multiconductor transmission line theory is combined with the
scatter matrix theory. The model was used by Wright et al. (1983b) to study the influence of coil and surge
parameters on the transient interturn voltage distribution in the stator winding.
In this research area, Oraee and Mclaren (1985) developed a computational method based on the multi
conductor transmission line theory and the discrete FourierTransform algorithm to construct a frequency
dependent model for the analysis of the voltage distribution in the first line end coil of stator windings.
The results of the measured and computed voltage distributions on a lineend coil embedded in a solid slot core
using Electromagnetic Transient Program (EMTP) were reported by Mclaren and AbdelRahman (1988).
In the papers of Wright et al. (1983a), Oraee and Mclaren (1985), Mclaren and AbdelRahman (1988), the
slot wall was assumed to be a flux barrier at the frequency of interest (110 MHz). However, Tavner and
Jackson (1988) showed that a laminated slot environment does not act as an impenetrable earth screen at
frequencies below (at least a frequency of) 20 MHz.
A computer model for predicting the distribution of steep fronted surges was also developed by Guardado and
Cornick (1989). They combined the multiconductor transmission line model and modal analysis with the
parameter assumption of Wright et al. (1983a). Upon application of the coil admittance concept, Guardado and
Cornick successfully extended the solution of the voltage distribution in a terminal end coil to a full winding
representation.
A report of measurement and analysis of a surge distribution in a motor stator winding was given by Narang
et al. (1989). The authors utilised a simple model that provides insight into the relevant mechanisms and a
detailed model solved by the Electromagnetic Transients Program (EMTP). The influence of various coil
parameters on the interturn and lineend coil voltages is also discussed in that paper. To account for the
influence of motor terminal leads, the coil is represented by its piequivalent circuit.
Following this, Keerthipala and Mclaren (1990) presented the results of experimental recordings. The authors
showed that a solid slot model cannot accurately replace the actual laminated slot environment in the study of
steep fronted surge propagation in machine windings. From their analysis, it became known that maximum
interturn voltages observed for the solid slot model are smaller (by a factor of about 2/3) than those for the
laminated slot environment. They introduced the concept of surface impedance, but it was not described in
their work.
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Subsequent authors Qiong et al. (1995) proposed a method for calculating the surface impedance and
incorporated it in a model for a pulse propagation study in a turbine generator.
A multiconductor transmission line approach for calculating the machine winding electrical parameters for
switching transient studies over a long period of time has recently been proposed by Guardado and Cornick
(1996). The solution technique is based on the solution of onedimensional diffusion equation. The coil
parameters are calculated considering both the magnetic fluxes in the iron and in the air. However, the
maximum interturn voltage due to steep fronted surge in the winding occurs within the first few microseconds
of the first line end coil and therefore does not require a long computation period.
In a publication, Gupta et al. (1987a) reported the results of an extensive programme of surge monitoring.
Gupta et al. (1987b) reported the result of impulse strength on the insulation capability of a large ac motor.
Findings on why some windings have low strength were also reported by Gupta et al. (1987c). So many
papers have been published on surge propagation studies in machine winding that it is very difficult to
acknowledge them all.
2.2Preview of the past works on transient voltage distribution in random winding
With the advent of adjustable speed drives for electrical machines, the problem of nonuniform voltage
distribution within the motor winding due to steep fronted surges has extended to low voltage motors.
Persson (1992) investigated the amplitudes and the rise times of the inverter output voltage with particular
reference to the Pulse Width Modulated (PWM) inverter. Using the basic transmission theory, Persson
carried out simulations regarding voltage reflections for various cable lengths and rise times. The results of
simulations are presented graphically by the same author. Further, his analysis confirms potential problems
associated with the combination of long cables and short rise times. In addition, application precautions are
described.
While only one voltage surge occurs from the circuit breaker when a motor is switched on, the new type of
PWM drives using IGBTs can, however, create thousands of surges per second with rise times as short as
100 nanoseconds. Such drives subject the motor stator winding turn insulation to more surges in a few hours
of operation than the motor would normally be expected to experience in 20 years of conventional operation.
To date there are few scientific papers published that demonstrate that the surges typical of adjustable speed
drives can gradually degrade the turn insulation. The experimental work of Stone et al. (1992) with pure epoxy
has conclusively shown that epoxy insulation can gradually age under the action of repetitive voltage surges,
even in the absence of partial discharge.
Kaufhold et al. (1996) described the failure mechanism of low voltage interturn insulation because of partial
discharges (PDs). The authors showed why and how the insulation design, the temperature and the applied
voltage affect the failure mechanism. These authors made it clear in their analysis that the partial discharge
occurs in the airfilled enamel wires that are touching. The partial discharges erode the insulation and
consequently lead to an interturn insulation breakdown. The authors characterised the pulse from the
converter as oscillating pulses with oscillating frequency ω and damping time constant T. The authors have
successfully shown that in the airfilled gaps between the enamel wires that are touching one another,
repetitive pulses with very steep front, lead to an increased number of partial discharge per time unit for
greater values of ω T.
Bell and Sung (1996) and Kaufhold et al. (1996) concluded that the dielectric failure mechanism due to
repetitive transient does not lead to immediate failure of the insulation, but it happens to be a gradual process
determined by a lower limit imposed by corona inception voltage (CIV) or partial discharge.
As adjustable speed drives become more popular in the higher voltage ranges, we will have to watch carefully
to ensure that insulation problems do not increase. In addressing this problem Oliver and Stone (1995) present
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a broad overview of the types of adjustable speed drive converters. Their paper also covers a brief description
of the effect of steep fronted surges in form winding near the line end.
From the experimental work performed on form windings (used on high and medium voltage motors) to study
the distribution of voltage under surge conditions, Oyegoke (1997b), confirmed the work of the previous
authors in showing that the highest voltage stress occurs on the first terminalend coil. Distribution of voltage
among turns of the first terminalend coil being practically nonuniform for very steep fronted surges is also
reported.
Switching frequencies of 10 to 20 kHz with 0.1 microsecond rise times are common with the current IGBT
technology. In many applications the PWM inverter and the motor must be at separate locations, thus
requiring long motor leads. Von Jouanne et al. (1995) examined the effect of long motor leads on high
frequency PWM inverter fed drives. In their paper, cable transmission theory and cable capacitance analyses
are presented. The voltage reflections were investigated in a similar way to that of Persson (1992), by using
the Bewley lattice diagram technique. The effect of the inverter output pulse rise time and the cable length on
the voltage magnitude at the terminals of the motor is illustrated in their paper. Results of simulation were
experimentally verified.
The area where much confusion still exists in pulse width modulated adjustable speed drives is with the
voltage waveform impact on the motor performance. The reports of Bonnett (1994), (1996) considered the
effects of the maximum voltage, rate of rise, switching frequencies, resonance and harmonics. It is stated in
his work that overvoltage and ringing can occur at both the beginning and end of each pulse from the
inverter. However, it is the repetitions, along with the rise time, that have the most potential for insulation
damage. The fact that as much as 85 % of the peak overvoltage can be dropped across the first turn of the
first coil is mentioned. This is illustrated with a figure showing the range of the voltage drop across the first
turns of the coil as a function of the voltage rise time. Similar studies have been discussed by Melfi et al.
(1997) but with particular attention to the machines powered by the 1990’s preferred drive of choice, (PWM
ASD using IGBT technology) with a rise time in the range 50200 nanoseconds. Mainly through experimental
work, Melfi et al. (1997) have shown that the ASD induced transient voltage pulse at the motor terminals
penetrates into the winding via oscillatory and travelling wave modes. Pulse propagation into the winding via
travelling mode is not linearly distributed. For a rise time of 50 nanoseconds, 80 % of the terminal voltage
appears across the first coil group, for instance in a machine with 6 coil groups per phase. The highest voltage
stress between any two turns of winding which may be in contact was found to exist from the first turns of
the line end coil to the last turns of the coil group.
Factors affecting motor overvoltage are discussed by Saunders et al. (1996) and shown to be as follows:
*
*
*
*
*
*
Motor and cable surge impedance
Motor load
Cable length
Magnitude of drive pulse
Rise time of drive pulse
Spacing of PWM pulses
Kerkman et al. (1996) and Skibinski et al. (1997) have made reports about the importance of cable natural
oscillation frequency. In addition to rise time related excitation frequency in determining the maximum motor
terminal voltage and the cable damping time, the linetoline voltage polarity reversal is described as a new
contributor to motor overvoltage. The fact that the type of modulator establishes the operating regions where
overvoltage is of concern is also discussed. In addition to these, Kerkman et al. (1997) discussed the over
voltage reduction through pulse control, and the overvoltage reduction modification in the modulating signal.
The power supplied to the motor by a PWM inverter has some adverse effects such as increased heating,
high peak voltages and increased audible noise. Lowery et al. (1994), highlighted some of the known possible
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