# Transient Voltage Distribution in Stator Winding of Electrical Machine Fed from a Frequency Converter

**ABSTRACT** Standard induction motors are exposed to steep-fronted, non-sinusoidal 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. Multi-conductor 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 (over-hang) 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 line-end 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 inter-turn 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 terminal-end 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 turn-to-ground 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 line-end 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 over-voltage protection in high and low voltage motors. Acta polytechnica Scandinavica. El, Electrical engineering series, ISSN 0001-6845; 100

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**ABSTRACT:**20 kV distribution networks with all its components, such as transformers, switches, cables etc., have existed and been operating safely for many decades. From an economic point of view, it would be convenient to replace the transformer-motor combination by just a single 20 kV asynchronous motor, even if the motor itself were more expensive. The cost of a transformer, facilities and maintenance gained in this way would easily cover the extra costs of a motor. Efficiency considerations also make elimination of the step-down transformer desirable. Furthermore, modern technological advances make the production of 20 kV asynchronous motors possible, which is proved by the existence of 32 kV generators. The main problem lies in overcoming the differences between the construction of the aforementioned network equipment and the high-voltage asynchronous motor. This paper analyzes the weak points in the insulation system of an asynchronous motor, and proposes improvements allowing motor supply voltage to be increased to 20 kV.IEEE Transactions on Dielectrics and Electrical Insulation 03/2009; · 1.23 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The application of inverter-fed drives provides additional electrical stresses in induction motors' insulation system. This is due to steep-fronted voltage pulses responsible for high overvoltages at the motor's input terminals and to an uneven voltage distribution along the windings. This article presents a model for the analysis and characterization of the internal voltage distribution and complex impedance in random wound coils. Experimental and theoretical results are presented using frequency response analysis (FRA) and model effectiveness using different approximations is studied. Finally, the frequency domain characterization will allow a time domain analysis, by means of inverse fast Fourier transform (iFFT).Electric Power Components and Systems 03/2007; · 0.62 Impact Factor

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, FIN-02015 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

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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 951-666-537-3. ISSN 0001-6845.

Keywords: electrical machine, stator winding, voltage distribution, frequency converter

ABSTRACT

Standard induction motors are exposed to steep-fronted, non-sinusoidal 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.

Multi-conductor 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 (over-hang) 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 line-end 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 inter-turn 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 terminal-end

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 turn-to-ground 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 line-end 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 over-voltage 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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PREFACE

This work was carried out in the Laboratory of Electromechanics, Helsinki University of Technology during

the year 1995-1999. 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 post-graduate 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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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 Lumped-parameter method……………………………………………………….…............ 17

2.4.2 Fourier-transform method……………………………………………………….….............. 17

2.4.3 Travelling-wave 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 Multi-conductor 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 multi-conductor transmission line model of winding………………………..…............ 30

4.6 Conclusions…………………………………………...…………....………………….........……….... 30

5 METHODS FOR INTERTURN VOLTAGE CALCULATION ON FORM WINDING………........… 31

5.1 Why not ladder-network for voltage calculation in form winding……………………...........………….. 31

5.2 Multi-conductor transmission line theory for inter-turn voltage prediction in form windings…………..... 31

5.2.1 Multi-conductor transmission line and scatter matrix concept (MTLSMC)……........…...…... 32

5.2.2 Scatter matrix derivation for junction 1…………………………………………........…….... 32

5.3 Multi-conductor 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 Multi-conductor transmission line concept for circuit simulator (MTLCCS)………….........…………... 37

6 EXPERIMENTAL STUDIES OF VOLTAGE DISTRIBUTION IN FORM WINDING……………… 38

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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 INTER-TURN VOLTAGE………………………………... 46

8.1 Effect of copper resistance on the inter-turn voltage…………………………..........……………….... 46

8.2 Effect of the over-hang capacitance on the inter-turn 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 over-hang part of the coil.............………………..... 58

9.6.2 Full capacitance matrix of the slot and turn to ground capacitance for the

over-hang part of the coil.............................................................................…………….. 59

9.6.3 Results..........................................................................................................……...…... 59

9.6.4 Turn to ground capacitance of the over-hang 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

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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 over-hang 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

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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

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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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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 maintenance-free 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 Turn-off 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 six-step 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 inter-turn 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 inter-turn 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 steep-fronted 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 inter-turn 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 (inter-turn insulation). Another source of inter-turn 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 inter-turn 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 steep-fronted 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 inter-turn 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 steep-fronted 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

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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 sine-wave 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 impulse-voltage

distribution is concerned only with prediction of the rate of rise of the incoming surge, in order to enable the

inter-turn 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 two-coil 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 sub-microsecond rise time, show that the steep fronted transient distributions are

quite non-uniform 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

inter-turn 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).

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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 non-uniformity 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 self-capacitance 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 inter-section 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

over-hang 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 non-adjacent 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 two-port 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 above-mentioned 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 inter-turn 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 multi-conductor 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 inter-turn 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 Fourier-Transform 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 line-end coil embedded in a solid slot core

using Electromagnetic Transient Program (EMTP) were reported by Mclaren and Abdel-Rahman (1988).

In the papers of Wright et al. (1983a), Oraee and Mclaren (1985), Mclaren and Abdel-Rahman (1988), the

slot wall was assumed to be a flux barrier at the frequency of interest (1-10 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 multi-conductor 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 inter-turn and line-end coil voltages is also discussed in that paper. To account for the

influence of motor terminal leads, the coil is represented by its pi-equivalent 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

inter-turn 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 multi-conductor 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 one-dimensional diffusion equation. The coil

parameters are calculated considering both the magnetic fluxes in the iron and in the air. However, the

maximum inter-turn 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 non-uniform 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 inter-turn 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 air-filled enamel wires that are touching. The partial discharges erode the insulation and

consequently lead to an inter-turn 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 air-filled 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 terminal-end coil. Distribution of voltage

among turns of the first terminal-end coil being practically non-uniform 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 over-voltage 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 over-voltage 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 50-200 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 over-voltage 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 line-to-line voltage polarity reversal is described as a new

contributor to motor over-voltage. The fact that the type of modulator establishes the operating regions where

over-voltage is of concern is also discussed. In addition to these, Kerkman et al. (1997) discussed the over-

voltage reduction through pulse control, and the over-voltage 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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