AN ABSTRACT OF THE THESIS OF Fahad H. AL-Ghubari for the degree of Master of Science in Electrical and Computer Engineering presented on May 21, 1999. Title: Voltage Analysis ofPWM Inverter Fed Induction Motors.
Redacted for Privacy
Abstract approved:
Wallace, Alan K.
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Abstract approved:
---­
Von Jouanne, Annette R.
Adjustable Speed Drive (ASD) systems are widely used in industry to
effectively improve process efficiency and control. Typically, an ASD system consists
of a motor with its speed controlled by a power electronics converter via varying the
amplitude and frequency of the input voltage. However, several abnormal insulation
failures of random wound motors in ASD applications have been reported. These
failures were related to voltage transients caused by inverters employing fast Insulated
Gate Bipolar Transistors (IGBTs) combined with long cables that connect motors to
inverters.
This thesis further analyzes the distribution of voltage waveforms generated by a
pulse-width modulated (PWM) inverter at the motor terminals and windings.
Experimental work was performed at the Motor Systems and Resource Facility (MSRF)
at Oregon State University on a specially made 5hp induction motor with taps from the
first and second coil and from the first four and last two turns in every phase. Tests were
performed with long and short cables and results are compared. A simple simulation
model was created in PSpice and used to predict maximum voltage transients across
coils and turns. The validation of the model is demonstrated by its capability to predict
most ofthe experimental results.
"Copyright by Fahad H. AL-Ghubari
21st May 1999 All Rights Reserved VOLTAGE ANALYSIS ofPWM INVERTER FED INDUCTION MOTORS
by Fahad H. AL-Ghubari A THESIS submitted to Oregon State University in partial fulfilment of
the requirements for the
degree of .
Master of Science
Presented May 21, 1999 Commencement June 2000 Master of Science thesis ofFahad H. AL-Ghubari presented on May 21. 1999.
APPROVED:
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Co-Major ProYessor, representing Electrical and Computer Engineering
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Co-Major Professor, ~presenting Electrical and Computer Engineering
Redacted for Privacy
Head ofthe n¥artment of Electrical and Computer Engineering
Redacted for Privacy
I understand that my thesis will become part of the permanent collection of Oregon State
University libraries. My signature below authorises release of my thesis to any reader
upon request.
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Fahad H. AL-Ghubari, Author
Acknowledgments
I would like to express my gratitude to my country, the Kingdom of Saudi
Arabia and my company, Saudi Arabian Oil Company (Saudi Aramco), for· sponsoring
my M.S. program. Special thanks are due to those individuals in my department,
Mechanical Services Shops Department (MSSD), who supported me in my pursuit of
this degree hoping that I would meet or exceed their expectations.
I gratefully wish to thank my Co-Major professors, Alan K. Wallace and
Annette von Jouanne, for their precious guidance and priceless support throughout this
program. My thanks are also due to professor Mario E. Magafia, for his valuable
counseling in control systems and for reviewing this thesis.
I also thank Toshiba International Industrial Division, Houston, TX, for
generously providing the tapped motor and the inverter as well as the necessary design
and control data.
I aiso extend my thanks to Richard B. Jeffryes, the manager of the Motor
Systems Resource Facility (MSRF) at OSU, for his professional help in making things
work in the laboratory combined with a beautiful spirit in spite ofhis busy schedule.
Finally, I gratefully thank both the family I left behind, for their consideration
and support when school took me away from their needs, and my wife and kids, who
accompanied me in this journey of learning, for their patience when the entropy was
high and their support when the energy was low. Your love and devotion have fueled
my spirit and kept me sane. I, God willing, promise you better days to come.
Table of Contents
1. Introduction ........................................................................................................... 1 2. Tests to Determine Equivalent Circuit Parameters ................................................ .4 2.1 Phase Resistance Test ....................................................................................4 2.2 No-Load Test .................................................................................................4 2.3 Blocked-Rotor Test ........................................................................................ 5 2.4 Synchronous Test ..........................................................................................6 2.5 Complete Circuit and Sample Performance Calculations ................................ 7 3. Analysis ofPWM Inverter Waveforms ................................................................ 10 3.1 Nature ofPWM Inverter Waveform ............................................................. IO 3.2 Magnitude and Frequency Control ofPWM Inverter Waveform .................. 12 4. Analysis of Motor Terminal Voltages .................................................................. 15 4.1 Experimental Analysis of Motor Terminal Voltages ..................................... 15 4.2 Voltage Reflection at Motor Terminals ........................................................ 17 4.3 Simulation of Motor Terminal Voltages ....................................................... 20 4.4 Comparison ofMeasured and Simulated Terminal Voltages ........................21 4.5 Effects ofHigh Terminal Voltages ...............................................................23 5. Motor Winding Voltage Analysis ........................................................................24 5.1 Windings Description and Layout.. .............................................................. 24 5.2 Experimental Analysis ofWinding Voltages with Short Cables ...................26 5.3 Experimental Analysis ofWinding Voltages with Long Cables .................... 30 6. Simulation ofWinding Voltages .......................................................................... 35 6.1 Measurement of Parameters ......................................................................... 35 6.1.1 Influence of Frequency on Winding Parameters ................................. 36 Table of Contents (Continued)
6.1.2 Calculations of Winding Mutual Inductances .................................... .41 6.1.3 Measurements of Winding Capacitances ........................................... .42 6.2 Model Development ..................................................................................... 43 6.3 Model Limitations....................................................................................... .47 6.4 Simulated Winding Voltages with Short Cables .......................................... .47 6.5 Simulated Winding Voltages with Long Cables .......................................... .48 6.6 Comparison of Simulation and Experimental Results ................................... 50 7. Conclusions ......................................................................................................... 52 Bibliography.............................................................................................................. 54 List of Figures
Figure
1.1 A PWM Inverter based Adjustable Speed Drive System ....................................... 1 2.1 Reduced Equivalent Circuit at NO-Load ............................................................... 5 2.2 Induction Motor's Per-Phase Equivalent Circuit .................................................... 7 3.1 Motor Terminal Voltage Waveforms with Short Cables ...................................... tO 3.2 A Sample PWM Waveform and One Phase Gating Signals.................................. 11 3.3 Normalized
~.I-l,rms Vs
ma with m1 = 15 for a three-phase Inverter ................... 12 3.4 Harmonic Spectrum of a Simulated PWM Inverter Waveform ............................ 13 3. 5 Harmonic Spectrum of a Measured PWM Inverter Waveform ............................ 14 4.1 Measured Motor line-to-line Voltage with Long Cables ...................................... 15 4.2 Enlarged Time-Scale View of Measured Voltage Spikes at Motor Terminals ...... 16 4.3 Motor Surge Impedance Vs Horsepower Rating ................................................. 18 4.4 Rise Time and
Vdc
Magnitude at PWM Inverter Terminals ................................. 19 4.5 Representation of 100' of#12 AWG Cable in PSpice ......................................... 20 4.6 Sub-circuit Representation of an ASD System with 300' Cable in PSpice ........... 21 4.7 Simulated Line-to-Line Voltages with Long Cables ............................................ 22 4.8 Enlarged Time-Scale View of Measured Voltage Spikes at Motor Terminals with Long Cables ............................................................................................... 22 5.1 Coil Connection in a Phase Group ...................................................................... 24 5.2 Taps Schematic Diagram ofPhase A. ................................................................. 25 5.3 Spatial Positions of the Coils/Turns ofPhase A and their Taps ............................ 25 5.4 Winding Voltage Waveforms with Sinusoidal Voltage Input .............................. 26 5.5 Voltage across Coil 01 with PWM Voltage Input ................................................ 27 List of Figures (Continued)
Figure
Page
5.6 Zoomed-in View ofthe Voltage Spike in Fig. 5.5 ............................................... 27 5.7 Voltage across Turn 01 with PWM Voltage Input ............................................... 28 5.8 Zoomed-in View ofthe Voltage Spike in Fig. 5.7 ............................................... 28 5.9
Voltage aeross Turns 2-4, 219, 220 & Coil 02 with PWM Voltage Input ........... 29 5.10 Voltage across Coil 01 with a 300', # 12 AWG Cable between ASD & Motor ... 31 5.11 Voltage across Coil 02 with a 300', # 12 AWG Cable between ASD & Motor ... 31 5.12 Voltage across Tum l(a) & tum 2(b) with long Cables ...................................... 32 5.13 (a-d) Voltage across Turns 3, 4, 219, & 220 with long Cables ............................ 33 6.1 Winding Parameters for High Frequency Simulation .......................................... 36 6.2 Variation of Tum 01 Resistance with Frequency ................................................. 3 7 6.3 Variation of Mutual Inductances with Frequency ................................................ 38 6.4 A Schematic Diagram of Two Coupled Turns/Coils Showing Polarity Dots ....... 38 6.5 Cumulative and Differential Series Coil Connections .......................................... 39 6.6 Equivalent Circuit for Two Mutually Coupled Turns or Coils ............................. 44 6.7 Dependent Sources Representation ofFig. 6.6 in PSpice ..................................... 44 6.8 Complete High Frequency Equivalent Circuit Representing Phase a in PSpice.... 45 6.9
Motor Measured Voltages with PWM Inverter input .......................................... 46 6.10 Simulated Voltage Transients with Short Cables ................................................ 47 6.11 Simulated Turns Voltage Transients with Short Cables ...................................... 48 6.12 Measured Line-to-Ground Voltage with Long Cable .......................................... 49 6.13 Simulated Voltage Transients with Long Cables ......... ~ ...................................... 49 6.14 Measured Turn Voltages with Long & Short Cables .......................................... 51 List of Tables
4.1 Motor Surge Impedance versus Horsepower Ratings ............................................ 17 5.1 Measured Voltage Spike Magnitudes at Full Load with PWM Voltage lnput ........30 5.2 Measured Winding Voltage Spike Magnitudes......................................................34 6.1 Measured Parameters at 5MHz (coill•=coil 1 - 4 turns) ........................................40 6.2 Summary of Simulated and Experimental Results .................................................50 Dedication
To my dear brother Ali I dedicate this work.
VOLTAGE ANALYSIS OF PWM INVERTER FED INDUCTION MOTORS 1. Introduction
The power electronics controllers with pulse-width modulated (PWM) inverters
'
are widely used in industry to control the speed of induction and synchronous motors.
The input voltage magnitude and frequency are simultaneously varied, mostly with a
constant ratio, to modify the motor's speed-torque characteristics to meet diverse load
requirements, which greatly improve the process efficiency. The increasing energy
conservation constraints and the desire to improve process control are the main driving
forces behind favoring these controllers over old flow control techniques such as de
motors, dampers and recycling valves. Fig. 1.1 shows the major components of a typical
Adjustable Speed Drive (ASD) system [1].
Rectifier
3 f2J input
DC link
Inverter
3 f2J Ind.
Motor
Fig. 1.1 A PWM Inverter based Adjustable Speed Drive System
However, motors in ASD applications, especially those connected via long
cables, started to experience frequent insulation failures, which were mainly attributed
to elevated insulation stresses caused by PWM inverters having high voltage rises dvldt
[2-5, 6, 7, & 8]. Unlike the slow rise and fall times of sinusoidal voltages, modem
2
PWM waveforms would rise from zero to the DC bus voltage in a very short time,
which is in the range of 0.1-0.2 microsecond with new Insulated Gate Bipolar
Transistors (IGBTs) used for the inverter switches. These voltage transients are even
worse when remote locations necessitate using long cables between motors and
inverters [3, 8]. Voltage reflection at motor terminals increases the voltage magnitudes
to values higher than 2 per unit which causes insulation failures and unplanned motor
outages.
The subject is widely covered in the literature. However, this thesis will shed
more light on the motor terminals and winding voltage stress created by PWM inverters,
to achieve two main objectives:
I. To investigate ifthe voltage transients propagate beyond the first turns of the
first coil, which is claimed to absorb most of the stress. If they do propagate,
by what magnitudes compared to the first coil. The state-of-the-art electrical
machine and drive testing facility, the Motor Systems Resource Facility
(MSRF) at Oregon State University, enthusiastically encouraged the author
to proceed with this subject.
2. To get familiar with ASDs, especially the inverter and its control
mechanisms, as the author's sponsor, Saudi Arabian Oil Company (S.
Aramco), has started to adopt these systems and would benefit from gaining
such experience. Understanding the features of the drive components is
believed to be the key to properly analyzing their effects on motor terminals
and windings and is very essential before adopting any mitigation technique
proposed by several researchers.
A 5hp induction motor was specially manufactured for this study with
measurement taps from several places in the winding available at the junction box. A
5.5 kVA Toshiba Transistor Inverter drives the motor. A 15 hp DC shunt generator with
a resistor load bank was used to represent the motor's load. First, the motor's equivalent
circuit parameters were determined through measurements since the ones supplied by
the manufacturer were obtained for the low voltage (230 V) connection and it was more
pertinent to perform the analysis at 460 V. Then, a brief description of the PWM
inverter waveforms and its magnitude and frequency control will be provided to better
3
understand what we are dealing with. After that, the motor terminal voltages will be
examined experimentally and through computer simulation using short and then long
cables. The analysis will then be extended to explore the winding voltages inside this
mush, or random, wound machine. The distribution of PWM inverter waveforms across
the first and second coils will be examined through oscilloscope measurements in
addition to those ofthe first four and last two turns.
The rise time of voltage transients generated by the subject IGBT based PWM
inverter was 0.2 microsecond, which corresponds to a fundamental frequency
component of 5 MHz. So, all the circuit parameters of the proposed circuit model have
to be measured or calculated at this frequency to give a true representation of winding
response to such waveforms. However, the mutual coupling among turns and coils at
such a high frequency is different from that of low frequencies and capacitive effects
become more significant especially among coils.
An attempt to simulate the response of the randomly wound stator windings to
PWM inverter waveforms, using simple measured and calculated parameters, will be
presented. Although more advanced simulation using the Finite Element Analysis
(FEA) technique has been done in [7, 9], users have to spare long simulation time aside
from· having to acquire proficiency in using the software. But, the proposed model will
use PSpice with its simple but rather powerful graphical interface for simulating
voltages at the several taps including the machine terminals. Simulation time is
extremely short. The current-controlled voltage source models available in PSpice [14],
were utilized to represent the mutually induced voltages among turns.
The validation of the proposed model is demonstrated by the fact that it can
reproduce most of the experimental results especially for coil voltages. The simulated
tum voltages were higher in magnitude than the experimentally captured ones. This
result would be acceptable if we realized that the model is simulating the maximum
voltage peaks that turns might see in such applications which is of importance if we
need to protect the winding from such destructive surges.
4
2. Tests to Determine Equivalent Circuit Parameters
The per-phase equivalent circuit model shown in Fig. 2.2 is very useful in
calculating the performance of induction machines assuming constant ac terminal
voltage and frequency. The parameters received from the manufacturer were based on a
230 V connection and did not include the core Joss resistance rc. Therefore, it was
necessary to perform the four tests shown in the following sections to obtain parameters
for 460 V. Sample performance calculations are also provided.
2.1 Phase Resistance Test:
The resistance of two phases was measured using a Digital Microhmeter-03700
after running the motor at its rated load for one hour to take . into account the
temperature effects on winding resistance. The measured resistance of the stator,
r1 ,
is
I. 72 0 per phase.
2.2 No-Load Test:
This test measures friction and windage losses in addition to core losses. It is
similar to the open-circuit test on a transformer. Fig. 2.1 shows the reduced equivalent
circuit with zero mechanical load [15]. Since the slip (s) is very small, the term
representing mechanical losses in the machine, r 2 (1- s) Is is large compared to rotor
reactance x , and rotor resistance
lr
r2 .
Therefore, almost all no-load current goes
through the magnetizing reactance xm in parallel with Rfwc. The measured no-load
input power Pnt was 117.46 W.
5
P,., =PJWc + SCL,.,
where SCLnl is the stator copper losses.
(2·1)
Rfwc
Fig. 2.1 Reduced Equivalent Circuit at No-load
A line-to-line voltage of 456.86 V was applied and the measured no-load current
I n1, was 2.09
A. From the above information, the no-load input impedance may be
calculated as
SCLn1 = 3 *Inl
2
*r 1
(2· 2)
SCLn, =3 *(2.09) 2 *1.72=22.54W,
hence,
pfwc =117.46- 22.54 = 94.92
IZn/1
w
=Vnlllnl = 263.77/2.09=126.27 n =xu +xm
(2·3) where xu is the stator leakage reactance and resistive components are negligible by
comparison.
2.3 Blocked-Rotor Test:
The motor shaft was mechanically blocked and the input voltage
vbr,
was
gradually increased using an auto-transformer, until the input current 1br reached the
full- load value, 6.4 A. The measurements in this test are taken at rated current instead
6
ofrated voltage to avoid excessive currents, as the motor is similar to a transformer with
a short-circuited secondary. The measured input three-phase power
Consequently, the blocked rotor impedance
zbr
Pbr,
and resistance
was 440 W
rbr
are calculated
as
(2·4)
2
2
'
rbr =Pb,/3*/br =440/3*6.43 =3.55il=r1 +r2
(2·5)
from (2 · 5) and measured r1 in 2.1,
r2' =3.55 -1.72=1.83il
from(2 · 3)&(2 · 5),
I..----­
2
(xLr +x ,') =v9.07
-3.55 2 =8.34il
1
(2·6)
(2·7)
then, applying a ratio of 2 : 1in (2. 7),
(2xLr =x1r') =>x1,' =5.56il => xLr =2.78il
(2·8)
from(2·3),
Xm =126.27 -2.78=123.48il
(2·9)
2.4 Synchronous Test:
This test separates the friction and windage losses from the core losses. The
motor was driven at its synchronous speed of 1800 rpm while energized, using a de
motor. The input torque was measured to be 0.21 Nm. This torque compensates for
friction and windage losses only. The three-phase input power was 73.0 W. So, core
losses may be calculated as
1800
2
pfw =0.21 * * 1Z' *
= 39.58 w
60
(2·10)
7
from(2·2),
core /osse~P,J=13.0-SC4,1 =50.45W
{2·11)
hence,
rc =V2 /(P,; /3) ::::)~ =266.02 *3/50.454=4.2 kn
(2·12)
This test is more accurate than using the no-load test data in order to obtain a
value of the resistance, which truly reflects the core losses in the machine.
2.5 Complete Circuit and Sample Performance Calculations:
Fig. 2.2 shows the motor's complete equivalent circuit with values in ohms.
XIs
265.58
v
Rc
4.2 k
Xlr'
r2'/s
1.83/s
Fig. 2.2 Induction Motor's Per-Phase Equivalent Circuit
8
The input power, losses in the machine, output torque, and percentage efficiency
may be calculated using the equivalent circuit as
w8 - w
r
w8
The rated s/ip(s)
1800 -1725
1800
0.04
(2.13)
Z1 =(r + jxlr )II (rc II jxm)
s
= (43.84 + j5.56)11(3.63 + j123.48)
= 35.75+ j17.25 = 39.7L25.76°
n
(2.14)
Z;n =Zf +(lj + jxls)
=39.7L25.76o + (1.72 + j2.781)= 42.49L28.12o n
I8 =
4601
J3
42.49L28.123
6.25L-28.12o A
power factor(pf)=cos(28.12)=0.88 lagging
(2.15)
(2.16)
(2.17)
InputPower,~nput=J3 *fl* I 1 * pJ=.fi *460*6.25* .88
=4382.08
w
(2.18)
AirGapPower,P8 =3 *I/ *r1 = 3*(6.25)2 *35.75
= 4189.45W
(2.19)
9
Dev.Mech.Power ,DMP=(l- s) * Pg =(1- .04) * 4.19Kw
=4014.75W
(2.20)
Output Power ,Pout =DMP-P,otational = 4.01Kw- 94.90w
=3919.85W
%Efficiency,q =
~ut
* 100=89.45%
(2.21)
(2.22)
J:nput
OutputMech.Torque,Tm =
3919.85*60
2n*1725
21.70Nm.
(2.23)
The rated (nameplate) % efficiency, power factor and full-load current are 89.86 %,
0.88 and 6.3 A respectively. Hence, the calculated performance values, based on
measured parameters, compare well with the manufacturer's data. This gives confidence
in the validity of the parameteres.
10
3. Analysis ofPWM Inverter Waveforms
A brief explanation of the nature of the PWM inverter waveforms and its control
schemes will be presented. Experimental and simulated waveforms will be provided to
explain how they differ from the regular sinusoidal waveforms.
3.1 Nature ofPWM Inverter Wayeform:
A 10-ft long, #12 AWG cable was connected between the motor and the drive
and the line-to-line voltage at motor terminals was observed and is shown in Fig.3-l . It
has a total rms value of 488 V and a peak value of 660 V. A closer look into the PWM
inverter output waveform and its control is presented in this section. The drive used for
this study has a three-phase uncontrolled rectifier and a thee-phase sinusoidal PWM
hp
stoppecJ
.
.
.
.
....• . •• . • ••• •• •• • 0. 0. 0.
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.
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.
Vp-p
v ec rms
current
. . . . . .
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( t ) 2 . 62500 v
( t) 994.913mV
•••
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2.60938
. . . . . . . . . .
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597. 11911'W
500 mV/dh
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f .000 • 1
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poa •
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. . .. . . . . .. . •
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1 .04538
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••
reeltl.a Trigger Node•
average
Edge
v
2.64007
976.191111Y
1
s
250 .0 ~
Fig. 3-1 Motor Terminal Voltage Waveforms with Short Cables
11
inverter.The objective of the latter is to control the magnitude and the frequency of the
three-phase output voltages with a constant input,
vde, from the rectifier [10]. The
gating signal, which controls a, or the duty cycle of the switches in every phase, is
produced by comparing a triangular signal VITt of high frequency /, , with three
sinusoidal signals Vcontrol 120° apart. The frequency of vcontrol is simply the desired
output frequency and / , is the switching frequency. Fig 3-2 shows a sample PWM
waveform and the control signal of one phase.
1 II T
- - - - - - - - - - - - - · - - - - - - - - - - - - • • • • - • - · - - - - - - - - - - - - - - - - - - - - - - - - - - - • • .,
I
I
1
Wco ntro l
1
I
I
I
I
I
0
0
-1
1
Vtr i
1
u .... ___ ______ _--------- - --- ----- -- -- - - ------ --------- ------- --- -- ___,
1.8KUT·--------------------------------------------------------------.,
I
I
I
I
••
.•
0
I
I
I
I
I
- 1 . 0KU+ --- ---- -- -- - --·r·----- - --------T·--------------~---------- - ---- ~
ItS
sItS
1 IIIIIs
15as
2 a­
u.­
Fig. 3-2 A sample PWM Waveform and One Phase Gating Signals
The amplitude modulation ratio m0 and the frequency modulation ratio m1 , are
defined as
m = v control
Q
v.tn
/,
mr=lr
(3. 1)
(3.2)
12
3.2 Magnitude and Freauency Control ofPWM Inverter Waveform;
The fundamental line-to-line voltage is related to
vde
in the linear modulation
region (ma sl.O) by (3.3) and in the square-wave region (ma >3.24) by (3.4) while the
relationship is non-linear in the over modulation region as shown in Fig. 3.3.
v.ll-1 rml
· ·
=
Vi z-z rm1 =
· ·
J3r;;ma vdc =0.612ma vdc
(3.3)
/34
J6
r;;-Vdc = - Vdc:: 0.18Vdc
(3.4)
2v2
2v2
1f
1f
The amplitude of the output signal is controlled through adjusting main (3.3). The over­
modulation region is used when higher output voltage magnitudes are needed where the
peak of vcontrol is allowed to exceed that of vtri to make ma higher than 1.0.
VLL1,nns Vdc square-wave
.78
••
.
.
I
I
I
I
I
I
I
.612
high
output
voltage
t-­
•••••••••
1+1-.E.......i~-----.;~ +--
square-wave I
,overmodulation :
0
I
I
I
:
1
3.24
Fig 3.3 Normalized Vi.z-z,rms Vs ma with m 1
rna
=15 for a three-phase Inverter
13
For large values of ma, the PWM output degenerates into a square-wave
inverter waveform as shown in Fig. 3.3 [10]. The term .!in (3.4), which governs the
1r
inverter's behavior in the square-wave region, is simply the magnitude factor of the
fundamental sinusoidal component of a square wave. Selecting m1 to be odd and a
multiple of three, eliminates the even harmonics from the line-to-line output voltages
including harmonics at m1 and its odd multiples (co-phasal harmonics). Keeping m1 as
an integer, suppresses significant sub-harmonics of the fundamental (0-60 Hz). An FFT
of a simulated PWM wave with ma of 0.9 (i.e. in the linear region) and m1 of 33, is
shown in Fig. 3.4, where harmonics are shown as sidebands around m1 and its
multiples One of the main advantages for the sinusoidal PWM switching schemes, is
-DDUT·----------·-----------------------------------------------------~
:
FFT of Line-to-Line VoltDge
:
I
:I
I
362.6 V,rms
:
I
I
I
I
2DDU
. 107.7 V, rms .
53.3 V,rms
DU+~------~~------~~._
1Hz
2.1KHz
4.DKHz
____
-JIJ~L------u~~~~
6.11CHz
I.IKHz
Fig. 3.4 Harmonic Spectrum of a simulated PWM Inverter Waveform
that harmonics are pushed further to high frequencies where they are easily filtered with
smaller and hence cheaper filtering components.
14
Fig. 3.5 shows the measured frequency spectrum of the PWM inverter output
voltage waveform of Fig. 3.1. It is shown that the higher order harmonics in Fig 3.5 do
not have as large an amplitude as with ma s:I.O (Fig. 3.4).
TekiiJIIm lO.OkS.I's
279 Acqs
E--·------·-·-----·-··-·----J
.
.
•
•
•
•
•
•
0
•
•
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0
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f-· . . . : . . . . : . . . . : . . . . : . . . .
... : .... : .... : ....
~0 V~s
. . . . .. . . . . .. . . .. . .. . . . .
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.< :
•
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•
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uumv
soo Hz
Fig. 3.5 Harmonic Spectrum of a Measured PWM Inverter Waveform
The line-to-line fundamental rms voltage of 440 V is an indication that the
inverter is in the over-modulation mode because the maximum vde that can be obtained
from an ideal three-phase rectifier, with balanced voltage inputs, is
Vdc
=.fi Vl-l,(input)
(3.5)
hence, applying(3.3)with m 0 = 1,&(3.5),
VJ.,l-l,rml(maxfmum)
=0.612* {1.0) *
.[2 * 460=410.0V
(3.6)
Therefore, ma should be greater than 1.0 for a 460 V input to obtain higher fundamental
output voltage. It is not in the square-wave region since
VJ.,l-l,rms
is less than 0. 78*( vde).
15
4. Analysis of Motor Terminal Voltages
The experimental and simulated results of the voltage stress analysis work on
the terminals of the subject 5hp ASD-driven induction motor, are the focuses of the
following sections.
4.1 Exoerimental Analysis of Motor Terminal Voltages;
A 300-ft long,# 12 AWG wire was connected between the PWM inverter and
the motor. High voltage spikes were observed at the motor terminals, which are also
confirmed by many researchers, but with different cable lengths, [1-5, 7, 8, 11]. Fig. 4.1
shows a measured terminal voltage with the motor running at its rated load. Destructive
over-voltage transients of magnitudes higher than 1.2 KV are observed.
.-----------"""!'-------""----,
stopped
hp
1
I .00 V/dl
o .ooo •
pos•
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Vp-p
v ec
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.
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< t)
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current
4.31250 V
968.5111mV
10.0 ms/dlv
minimum
1.7812, v
319 .072mV
.
•
50.000 IH
meKimUIR
4.607'0 v
1.05620 V
realtime Trigger Mode•
average
Eelge
3.5~35
v
846.593mY
1
.r o.ooo
Fig. 4.1 Measured Motor line-to-line Voltage with Long Cables
•
16
A zoomed-in view on a leading edge, is shown in Fig. 4.2 which also shows
some damped high-frequency oscillations at the motor terminals.
stopped
hp
: : : : t : : : :
1 1.00 V/diY
pos•
0.000 V
1.000•1 I~ de
:::::::::::.::;::::;::::f.:: i:::: i:::: i:::: ~ .... .
0
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( 1) 692.212mY
.
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.
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.
•••••••••••••••••
16.000 us
minimum
0
••••••••••••••••••••
•
0
..
0
2.31250 y
401.139mY
0
•••
I 16.000 us
20.0 us/diY
current
Vp-p
0
0
-84.000 us
v ec rms
•
moxtmum
4.06250 y
694.16SmY
realtime Trigger node•
oYerege
Edge
3.05114 v
569.801mY
1
.f-250.0 mY
Fig. 4.2 Enlarged Time-Scale View ofMeasured Voltage Spikes at Motor Terminals
Higher magnitudes were also observed on the oscilloscope. However, the voltage
limitation on the differential probe (+/- 1000V) did not allow capturing them and the
use of current transformers resulted in the loss of a considerable portion of the
oscillating transients.
The main factors contributing to these voltage transients with high magnitudes
are [5, 8, & 11]:
1. High de bus voltage
Vdc .
2. Small PWM inverter rise time tr;88 •
3. Long cables.
4. Cable to motor surge impedance mismatching.
More details about impedance matching are provided in the following section.
17
4.2 Voltage Reflection at Motor Terminals:
The voltage reflection at the terminals of a PWM inverter fed induction motor is
mainly governed by the relative surge impedances of both the feeder cables, Z 0 , and the
motor,
zm'
[6, 8, 12]. The surge impedance is a function of the per unit length
impedance (Z) and per unit length admittance (Y) and is defined as
rz
z = =iR+JOJL
lJy G+JOJC
o
(4.1)
For high frequency applications, R & Gin (4.1) may be ignored and hence, Z 0 would
become a pure resistive element as
Z=["i:n
0
vc
(4.2)
Table 4.1 shows measured motor surge impedance Zm for several horsepower
ratings starting from 25 hp [6]. The data was extrapolated in MATLAB [16] to generate
the plot of Fig. 4.3, which covers smaller horsepower ratings. Consequently, the Shp
motor has an approximate
zm of2,555.0 n.
Table 4.1 Motor Surge Impedance versus Horsepower Ratings
MotorHP
Sur2e Impedance
25
1500
50
750
100
375
200
188
400
94
18
I
I
I
2500
I
1·
I
I
I
I
I
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I
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2000
---~---~-I
I
CD
u
c:
.g
1500
CD
.§
& 1000
....
::I
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en
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---,---~----~---~---r
I
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---~---~---+---+---~---~---~-I
I
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---+---~---~---~----~---~---~
I
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500
I
---r---r--- ---,--­
Q.
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I
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--L---1---l ___ J ___
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~0"'
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25
30
---~---~
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---r---r---r---,---,---,---~----r---r---r
I
I
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I
5
I
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I
20
Motor hp
Fig 4.3 Motor Surge Impedance Vs Horsepower Rating
The surge impedance Z0 of the #12 AWG cable was calculated based on its
measured per unit length parameters for a piece of three-bundled conductors as
L0 =0.29uH I ft
(4.3)
Co =15.43 pF Ift
R =l.9mfJI ft
hence, for lossless line,
(4.4)
Zo=
~=
vc::
(4.5)
0.29u = 137.0{}
15.43p
(4.6)
A precision LCR (hp 4284A) meter was used for the measurements.
The load reflection coefficient
r.m =Zm -Z
0
Zm +Z0
rm at the motor terminals may now be calculated:
2555.0-137.0
2555.0+ 137
0.90
(4.7)
19
Typical values of rm for motors below 25 hp are between 0.8 and 0.9 [5 & 6].
The magnitude and rise time of the PWM inverter output line-to-line voltage
was measured and shown in Fig. 4.4. A positive peak of 670 V with a rise time of
0.24f,1sec was observed.
hp
stopped
•
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••••••••••••••••••••••••••
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. . . . . . .
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:.
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s
500 mV/dl\
poe•
o.ooo \
1.000•1 IMSli de
0.
····i····l····~····~····!····~····~····~····)····
-3.5000 us
-1.0000 us
ns/dlv
minimum
maximum
500
current
Vp-p
v ec: rms
C3) 1 .35938 V
c 3) 596.662mV
1.31250 v
576.993mV
1.35938 v
59B.755mV
1.5000 us
reeltlme Trigger node•
average
Edge
I .33789 V
S8B.549mV
S S
750.0 m\
Fig. 4.4 Rise Time and Vdc Magnitude at PWM Inverter Terminals
The magnitude is simply the de link capacitor voltage Vdc . A voltage wave of
approximately double this magnitude will appear at the motor terminals, as in (4.8).
VL-L,momcmtary =Vdc + rm vdc =610+ 0. 9*670=1.27 kV
(4.8)
The inverter freewheeling diodes pass the reflected waves to the de link capacitor,
which acts as a short circuit to voltage transients, making
r;nv unity. This helps slightly
in reducing the transients at the motor terminals since the negatively reflected waves
from the inverter subtract from that of the motor terminals.
20
4.3 Simulation of Motor Terminal Voltages:
An equivalent RLC model was built in PSpice for the cable using its measured
parameters and connecting three equal sections in series and using the sub-circuit
technique to represent all components of the ASD system. Each cable section represents
100' of the total length as shown in Fig. 4.5 with the parameters calculated for 100'
length.
R1
L1
~·----------~.19
29uH
R2
L2
~·------~r----~-
.19
R3
29uH
L3
.19
29u~1
l
~·~--~----+--
C2_._
C3 _._
1.5nT,__1_.5"""~~1r--1_.5n~T
0
Fig. 4.5 Representation of 100' of#12 AWG Cable in Pspice
It is adequate to represent the 5hp induction motor with its surge impedance [6]
to properly show the high frequency oscillations at its terminals.
21
The complete ASD system is represented using sub-circuits in PSpice as shown
in Figure 4.6.
Rect111er
Inverter
three Une segments
5hp
motor
Fig. 4.6 Sub-circuit Representation of an ASD System with 300' Cable in PSpice
The simulation results of the line-to-line voltage at the inverter terminals and the
motor terminals are shown in Fig. 4.7. The high voltage magnitudes combined with
high frequency oscillations are zoomed-in and shown in Fig. 4.8. The highest peak
observed has a magnitude of 1.3kV which is almost double what the motor terminals
are expecting to receive from a balanced three-phase sinusoidal source with a peak
value of 650.5 V ( .fi• 460 ).
4.4 Comparison of Measured and Simulated Terminal Voltages:
A close agreement between the simulated and experimental results is observed
in the above analysis. The measured motor terminal magnitude of Fig. 4.2 is slightly
lower than the simulated (Fig. 4.8) due to increased damping, but the waveforms and
their high frequency oscillations are almost identical.
22
1 DKUT------------------------------------------------------------·
at inverter termin~ls
•
1
I
I
I
I
I
I
I
-1.1KU~------------------------------------------------------------2.1KUT-------------------------------~----------------------------·
at motor terminal
I
I
I
I
I
-2.DKU+------------------,-------------------r------------------,--­
Os
1Dats
20.S
38Jas
T .. _
Fig 4.7 Simulated Line-to-Line Voltages with Long Cables
2.UKUT-------------------------------------------------------------­
I
I
I
I
!
1. 309 KV
I
I
I
I
1. &ICU-'
074.03
v
BUT---­
I
I
I
I
I
I
I
I
-1.0KU+---------------r---------------,---------------,-------------­
lls
SUus
1111us
15Uus
2118
Tble
Fig. 4.8 Enlarged Time-Scale View of Simulated Line-to-Line Voltages with Long Cables 23
4.5 Effects of High Terminal Voltages
As shown in the previous sections, motor terminals are experiencing abnormal
voltage transients when fed by PWM inverters through long cables. With today' s faster
switches and higher dv I dt , more stress is added to motor terminals. Furthermore, these
high peak voltages are repeated several thousand time per second, as shown in Fig. 4.7,
while the peak transient overvoltage capability of the motor's dielectric insulation
system has remained almost unchanged over the years at 1200 V peak [8]. The ultimate
result is a destructive insulation failure at the motor terminals.
The following section will explore if these elevated voltage levels will have any
effect on internal voltage distribution among the windings.
24
5. Motor Winding Voltage Analysis
It has been reported in several articles that voltages with high rates of change
( dv I dt ) tend to be distributed unevenly among motor windings in ASD applications [ 1,
7, 9, 11, & 12]. The experimental and simulated results of the voltage distribution
analysis work on the windings of the subject 5hp ASD-driven induction motor will be
discussed in the following sections. Winding details will be presented first to clarify the
position of the measurement taps and to help understand effects of position on winding
parameters.
5.1 Windings Description and Layout:
The 5hp, 4-pole motor has 36 stator slots and 18 single-layer coils, one coil-side
per slot. Coils are grouped into 6 groups of 3 coils per group. Each coil group has two
small coils of36 turns each and a larger coil of38 turns as shown in Fig. 5.1. Each of
the three phases has 6 coils connected in series for 460 V line-to-line voltage.
---------------------,
coil group
I
38 t
coils
36
turns
input
Y-point
Fig. 5.1 Coil Connection in a Phase Group
25
The small coils span 7 slots (2-9) while the larger coils span 9 slots (1-10). Fig.
5.2 shows a schematic diagram for the coils in phase A and the taps which where
brought out from the marked positions to the junction box for the corresponding voltage
measurements. Fig. 5.3 shows their spatial positions inside the stator.
-i.. .. .. .. 1..- 1..
N
.,
•
j
j
j
c»
____l____l__________
~
­.. ..
s
N
N
~
j
-i series coils
Fig 5.2 Taps Schematic Diagram ofPhase A
Slot #
C =Coil tap
T
a
lead wire
t :a tum tap
Fig. 5.3 Spatial Positions ofthe Coils/Turns of Phase A and their Taps
26
The total number of series turns in each phase may be calculated as follows:
Total# of turns I phase = 2 *38 + 4 * 36 = 220turns
(5.1)
The taps from first turns, first coil and, last tum were selected because several
studies on the same subject revealed that these turns experienced the highest voltage
stress in ASD applications [1, 7, 9, 11, 12]. Three more taps were brought out of the
second, third, fourth turns and, the one before the last tum, and from the second coil to
have a better picture ofvoltage distribution inside the windings.
5.2 Experimental Analysis of Winding Voltages with Short Cables:
Some measurements were taken with the motor fed by a balanced sinusoidal
voltage supply of 460 V line-to-line to use them as references when comparing to the
situation when the PWM inverter feeds the motor. Such voltages across the first and last
turns, the first and second coil ofphase a, were measured at full load and shown in Fig
hp
stopped
Vtum.O l,peak= 1.67V
Vtum02,peak= l.67V
Vcoil Ol,peak=59.79V
Vcoil 02,peak=l27.6V
Fig 5.4 Winding Voltage Waveforms with Sinusoidal Voltage Input
27
5.4. A de generator feeding a resistor bank represented the motor's load, which was
maintained at the rated value throughout. The even distribution of the phase voltage
among turns and coils of phase a, is obvious in Fig 5.4. However, this is not the case
any more when a PWM inverter provides the input to the motor where the line-to-line
voltage jumps from zero to approximately 670V in less than a quarter of a micro
second, as was shown in Fig 3.8. Fig. 5.5 & 5.6 show the measured PWM voltage
across the first coil and its zoomed-in view respectively. As depicted from both figures,
,.
&tapped
1
· · · 250V!Div·
•
0
•
SOO
IIIV/dt
oa
o
pas •
•25 .oo
1.000•1
IMQ
..•............
•
................................................
..
. ..
..
..
..
..
..
..
•
•
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0
•
0
0
•
•
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•
•
•
•
•
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•
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•
•
0
•
•
•
-25.002 ma
•
•
•
0
•
••••••••
-2.000
s.oo me/dtv
•
0
•
••••••••••••••
us
24.998 ms
rselttms Trigger Mode•
Edga
1
500
IfNI -25. 0000 liN Fig 5.5 Voltage across Coil 01 with PWM Voltage Input
.
.
.
.
.
.
.
.
.
1 300 nW/d
:
:
:
:
:
:
:
:
:
pos•
o .ooo
····:····:····:····:·········:····:····:····:···· 1.ooo11 1n2
.... : .... :.... ~37ov··
: -~ ... : .... : ....
.
.
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................................................
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'!"''',,.), ':,, • • "••!•• •••"" ':
,J.. •• •• '";••'•• '' '' ••~• "' •• ''' '';" '••" '
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I .00 IIR/rll\1
3.0000 us
rAAlllmA TrlnnAr MnnAa
Fig 5.6 Zoomed-:-in View of the Voltage Spike in Fig. 5.5
28
the voltage peak magnitude is approximately 370V. Similarly, the voltage across the
first tum was observed and shown in Fig 5.7 with its magnified view shown in Fig 5.8.
The measured peak magnitude is 27.5 V.
1 200 mV/dl\
pos•
0.000 \
1.000., lt12 dt
•••
. . ... . . . . ... . . . . .. . . . . ... . . . .
.
.
.
.
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o.ooo
ms
current
< t > 29. 7552mV
.
.
..
0
••••
0
••
•••••••••••••••••••
50.000 ms
reolttme Trigger Mode•
overage
Edge
251.683mY
26 .90:22mY 1 I
250 .o mi.
8
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Fig 5.7 Voltage across Turn 01 with PWM Voltage Input
FILE EXISTS• OVERWRITE?
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993.750mY
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411.000 us
realtime Trigger Mode•
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Edge
521.706mV
..:121. 731mV 1 I
375 .o mi.
Fig 5.8 Zoomed-in View of the Voltage Spike in Fig. 5.7
29
Voltage observation is extended through the winding with more emphasis on the
high spikes more than the steady state waveforms. Figs. 5.9a-f, show the captured
voltage peaks across turns 2-4, 219, 220 and coil #2. The peak magnitudes of these
spikes are summarized in Table 5.1.
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Fig 5.9 Voltage across Turns 2-4,219,220 & Coil 02 with PWM Voltage Input
The voltage transients seem to propagate into the internal coils with
considerable magnitudes unlike what many researchers reported that around 85% of the
spikes are absorbed by the first coil [4, 7, & 12]. Fig. 5.9-(f) shows voltage spikes
across the second coil with a peak-to-peak value of 700 V.
30
Table 5.1 Measured Voltage Spike Magnitudes at Full Load
with PWM Voltage Input
turn
01
Peak Voltage 27.5
Location
turn
02
22.5
turn
03
13
turn
04
22.5
turn
219
3.0
turn coil 01 coil
220
02
2.0
370 310
(volts)
The voltage values in Table I are high, compared to the steady state tum and
coil voltages shown in Fig 5.4 where the voltage peaks were 1.67 V, 59.79 V and 127.6
V for turns 1-220, coil 01 and coil 02 respectively. This is significant, especially in
mush or random windings where two turns of high voltage magnitudes might be placed
adjacent to each other, which further stresses the tum-to-tum insulation and might cause
it to fail.
5.3 Experimental Analysis of Winding Voltages with Long Cables:
The long cables between the PWM inverter and the motor were shown to
dramatically increase the line-to-line voltage magnitudes at the motor tenninals in
section 4 to high levels close to 1.3 KV. This section will show how such voltage
transients, with the same 300-ft cable, are distributed among coils and turns based on
measurements at the available taps. Fig 5.10 shows a magnified view of the first coil
voltage. The first coil is subjected to a positive peak with a magnitude of 625V plus
some damped high frequency ringing at about 500kHz and a peak-to-peak voltage of
1.14kV, much higher than what the coil expects in regular 60 Hz applications. The next
series coil in the phase (#2) experienced a peak voltage of 500 V with much less ringing
as shown in Fig. S.ll.The inductive filtering nature of the machine windings has
damped the ringing as the wave propagates further into the motor. Consequently, it can
be said that the first coil absorbs approximately 52% of the line transient and the second
coil absorbs 42% based on the measured trend.
31
1 500 r
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reel time Trigger MO(
Edge
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174.643mV
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Fig 5.10 Voltage across Coil 01 with a 300', # 12 AWG Cable between ASD & Motor
hp
stopped
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Fig 5.11 Voltage across Coil 02 with a 300', # 12 AWG Cable between ASD & Motor
32
As explained previously, coil # 1 is composed of 36 turns. Now, we need to
examine if the coil transient will be distributed evenly among these turns or not. Fig.
5.12 (a & b) shows the captured transient across the first and the second tum in the coil.
.------'!""-~-·-'!""-----~--, 1
'(a.).tum }. :.
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Fig 5.12 Voltage across Tum 1(a) & turn 2(b) with long Cables
From the above Figure, tum # 1 has a voltage peak of 21 V and tum #2 has a
lower peak of 12.5V. So, the trend is the same, higher transients are absorbed by the
ftrst tum but this peak represents only 3.2% of the coil voltage. The high frequency
oscillation is clear at both locations with higher damping in the second tum. The
transients across the remaining phase turns with available taps are shown in Fig 5.13 (a­
d).
33
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Fig 5.13 (a-d) Voltage across Turns 3, 4, 219, & 220 with long Cables
It is obvious that the last two turns in the phase, do not feel any of the voltage
transients. Table 5.2 summarizes the measured voltage magnitudes in all taps with long
and short cables connected.
34
Table 5.2 Measured Winding Voltage Spike Magnitudes
location
turn turn tum turn turn turn
01 02 03 04 219 220
Peak Voltage 27.5 22.5
with short
cables (volts)
Peak Voltage 20 12.5
with long
cables (volts)
13 22.5 3.0
18
17
coil
coil
01 02
2.0 370 310
Lineto-line
670
3.0 2.0 625 500 1.2 K
Comparing values in Tables 5.1 & 5.2, it could be said that the high voltage
magnitudes at the motor terminals when long cables are employed had forced a slightly
more even distribution of transient voltages among turns of the first coil. Furthermore, a
smaller relative voltage magnitude appeared across the first tum when long cables are
connected. The order of relative magnitudes of tum voltages also differs. With short
cables, turn 01 experienced the highest peak voltage, then 2 & 4, and then tum 3 While
the trend with long cables is tum 01, 3 & 4, then 2. This irregular voltage distribution
among turns is mainly due to the random nature of the mush winding used in almost all
low-voltage motors. With long cables employed, the coils absorbed slightly lower
percentage voltages. 52% of the line spike appeared across the first coil and 42% across
the second compared to 55% and 46% across coill & 2 respectively for short cables.
35
6. Simulation ofWinding Voltages
The distribution of voltage transients produced by PWM inverters among coils
and turns of the windings is simulated in this section using the powerful PSpice
software with its built-in electrical models and the handy graphical interface. Then, the
simulation results will be compared with the previously measured results. Before
proceeding, we will first defme some important parameters, look at how to measure
them, in particular the mutual inductances among turns and coils and, lastly, how to
represent this interaction in a simple equivalent circuit.
6.1 Measurement of Parameters
When the machine is excited by 60 Hz voltage, the series inductances divide the
applied voltage magnitude almost equally among series turns [3]. However, this is not
the case with PWM inverters feeding induction motors. As shown previously, the rise
time of the PWM inverter output voltage is 0.2-0.24 J..I.Sec, which corresponds to an
approximate frequency of 5MHz. At such a high frequency, the capacitive coupling
between the grounded core, as there is no insulation between the frame and the core,
and slot windings play a major role in distributing coil voltages. They simply provide a
lower reactance path at high frequencies. The main parameters shown in Fig. 6.1 are
defmed as
1. Tum series resistance, R, .
2. Tum series self-inductance, L,.
3. Mutual inductance between i 1hand
/h turns, M iJ .
4. Turn capacitance to ground, Cg.
Ideally, a model could be developed representing all the turns in a slot in order
to estimate the distribution of the voltage transient. However,
in practice, this is not
possible, especially in random windings, without using sophisticated software to
calculate the self and mutual impedance matrices of all the coils. The concept of the
36
current research is to develop a simple and a relatively accurate model that can be
simulated with available conventional software.
Fig 6.1 Winding Parameters for High Frequency Simulation
All the parameters have to be evaluated through measurement or calculation at a high
frequency range. This is necessary to give a true representation of the winding response
to waveforms with high dv I dt . It has been shown in previous sections that the first few
turns in the line front coil absorb most of the voltage transients. So, it would be
adequate to model these turns explicitly, and to model the rest of the turns in the coil
and remaining of the phase with their lumped
par~eters.
Several researchers [3, 7, &
9] also implemented this technique.
6. 1.1 Influence ofFrequency on Winding Parameters:
The inductive and capacitive reactances are both functions of frequency
although they vary differently, as shown by equations 6.1 & 6.2.
IXtl =27rfL
IXcl =1/21ffC
(6.1) (6.2) 37
where L &C are the inductance and the capacitance respectively. The series resistance
also varies with frequency due to skin and proximity effects. These two factors also
affect the series inductance but have very little effect on capacitance. Figure 6.2 shows
the measured irregular variation of the resistance ofturn #1 with increasing frequency.
a.l
,.....----~----.------.----......------,
a.•
ea.t
..c
0
.
a.5
~ a.l
c
,!! D.,
.!!!
Ill
m
a.~
0::
a.z
a.t
a~---~~--~-----~---~--~
2
3
0
11
tD t
ID
ta
ID
ID
I D.
Frequency, kHz
Fig. 6.2 Variation of Tum 01 Resistance with Frequency
Figure 6.3 also shows the variation of the measured mutual inductance among
various turns and coils with increasing frequency, using the voltage measurement
technique up to 300 kHz. The influence of frequency in these parameters actually
controls the winding response to input voltage transients. Several attempts were made
as part of this study to precisely measure the mutual inductance among the turns and
coils, especially among those with available measurirtg taps. Figure 6.4 presents a
simplified way to represent the induced voltage in one turn due to a current flowing in
an adjacent one with the numbers referring to the two turns or coils under testing and
not necessarily the first or the second tum in the phase.
38
coil1-coil2
1.5
-1
-1.5
~~------~~~--~~~~~~~--~~~._~w
5
2
3
4
1
10
10
10
10
10
Frequency, Hz Fig. 6.3 Variation ofMutual Inductances with Frequency
,
..
V1-----------I~+____G_____ y2------------~~l
Fig. 6.4 A Schematic Diagram of Two Coupled Turns/Coils Showing Polarity Dots
39
Tum voltages may now be expressed as
Jii = (lj +}OJ L.t)il ± j(J)MI2 i2
(6.3)
V2 =(r2 + jm~2)i2 ±j(J)M2t it
but,
(6.4)
il =i2
and,
(6.5)
MI2=M21
(6.6)
hence,
~b = Jii +V2 = {('i +r2)+ j(J)(L.t +~2±2M12)}*/
(6.7)
hence,
Ltotal = L.t + Lz2 ± 2M12
so,
M12 = ±{L,otal- (L.t +Lz2)}/2
•
(a) Series Cumulative Connection
•
(b) Series Differential Connection
Fig 6.5 Cumulative and Differential Series Coil Connections
(6.8)
40
The sign ofM1 2 is positive ifthe two coils are connected in series cumulatively as in Fig
6.5 (a), and negative if connected differentially as in Fig 6.5 (b).
Since taps to several turns are available, it was possible to measure the self and
total inductances for tapped turns and coils. Then, using Equation. 6.8, the mutual
inductances could be calculated. However, we need to consider two different cases in
order to apply Equation. 6. 8 correctly:
1) 1-+ If Lrotal > (L11 + L22 ), then the+ ve sign applies hence, (6.9) M12 = {Lrotal -(Lu +L22)}/2
2)1-+ If Lrotal <(L11 +L22 ),then the-vesignapplies
hence,
M12 ={ (Lu +L22)-Lroral }/2
(6.10)
Table 6.1 shows some measured parameters for all tapped turns and coils at 5
MHz using Hewlett-Packard model 8752 C network analyzer having a 300KHz to 6
GHz frequency range. These measured tum inductances will be used to calculate the
mutual inductances in the next section. The absence of coils' mutual inductances in
table 6.1 will be explained in the next section.
Table 6.1 Measured Parameters at 5 MHz (coil1 '=coill -4 turns)
Location
turn turn turn turn turn turn coi11' coil2 coils
01
02
03
04 219 220
3-6
1.75 1.89 2.12 2.11 1.57 1.55 24.36 23.65 13.55
Resistance,
ohms
1.30 1.21 1.20 1.22 1.24 1.28
Self
Inductance, uH
-
-
-
4I 6. 1. 2 Calculations of Winding Mutua/Inductances:
The various mutual inductances among turns may now be calculated using the
formulas and data presented in the previous section.
The measured Ltotal is I.40 uH for turn I and turn 2. So, substitution for Ltotal and
for self-inductances from Table 6.I in Equation. 6.I 0 yields
Mt2 = {(1.30 + 1.2I) -1.40),u 0.55 pH
2
(6.II)
taking tum 2 & tum 3 together, Ltotall,2 =1.30,uH &{~ +l:J)={l.2I + 1.20)p = 2.4IpH hence, M23 = (2.4I-1.30)p 0.56,uH
2
(6.I2)
taking tum I, 2 & 3 together,
Ltotall, 2,3 = I.32 ,u H (measured)
= Lt +~ +l:J -2(Mt2 +M23 +M13)
= ((3.7I-2(.55 +0.56+M13 )),uH =>M13 = 0.08,uH
taking tum 3 & 4together, Ltotal3,4 =1.36pH (measured) _ ((I.20+ I.22)-I.36)p
H
=> M 342
- 0.53 p (6.13)
(6.I4)
taking tum 2, 3 & 4together,
Ltotal2,3,4 =1.36,uH (measured)
= L2 +L3 +L4 -2(M23 +M34 +M24)
=((3.63-2(.56+0.53+M24 )),uH ::::>M24 =0.04,uH
(6.15)
taking tum I, 2, 3 & 4 together,
Lrorall,l,J,4 =1.58,uH (measured)
= Ll +L2 +L3 +L4 -2(Mt2 +Mn +Mt4 +M23 +M24 +M34)
(6.I6)
42
I.58pH =((4.93- 2(1.77 +M14 )),uH ~ M 14 = O.IOpH
taking the last two tum 219& 220 together, Ltotal219,222o
(6.17) =1.31pH &(L219 + L22o)={l.24 + 1.28)p = 2.52,uH hence, M
_(2.52-1.3l)p 061 H
219,2202
. ,u
(6.18)
At high frequency, most of the flux is leakage flux, which is confined within the
slot [7]. Consequently, the high frequency inductive mutual coupling among coils
occupying different slots is virtually non-existent and can be neglected. Instead, a
capacitive coupling dominates. This was demonstrated through measurements using the
network analyzer. Whenever a coil is involved, whether with another coil or even
another turn, the measured terminal impedance is capacitive with small series
resistance. Therefore, it was concluded that only tum mutual inductances are to be
represented in the equivalent circuit. The remainder of the first coil and the other coils
in the phase will be represented with a lumped series resistance, series inductance, and a
capacitance to ground.
6.1. 3 Measurements of Winding Capacitances:
The capacitance to ground of the turns is small and varies according to the
position of each random tum with respect to the slot wall [3, 7, & 9]. The farther the
tum from the slot wall the smaller the capacitance. However, an average value of this
capacitance C,_g could be obtained by measuring the capacitance of the complete coil to
ground cc-g' then calculating the turns' capacitances as
43
cc-g
c,_g=N
(6.19)
where N is the number of series turns in the coil
for turns I, 2, 3, & 4, C
~g
= 360.77 pF(measured) =I0.02 >F 36
p
(6.20)
for turns 219 & 220where taps C2 and the grounded neutral are used,
C
t-g
= I.I3nF(measured)
(36*3+38)
=7.73
>F
p
(6.21)
ccoi/2-g =1.55nF(measured)
The capacitance of the rest ofcoil # 1 may be calculated as
CcoilCI- 4turns> =I0.02pF* (36- 4) = 320.64pF
(6.22)
6.2 Model Development
With all the necessary parameters in hand, either measured or calculated, we
may proceed to develop the simulation model in PSpice. Figure 6.6 shows a simple
equivalent circuit that represents the conducted and induced voltages in two mutually
coupled turns or coils [13]. It contains two current-dependent voltage sources, which
represent the mutual or induced voltages. Since all turns in our case are in series and
also the 6 phase coils, they have the same current flowing through them which slightly
simplified their representation on the circuit.
44
Fig. 6.6 Equivalent Circuit for Two Mutually Coupled Turns or Coils
It was attempted to represent the mutual coupling using the exact representation
as in Fig. 6.4. However, the high number of transformers used to replace the mutual
inductances did not support the simulation objective due to transformers acting as flux
barriers against waveforms with small rise time and high dv/dt. Instead, the dependent
source models available in PSpice provided an excellent replacement. The circuit of
Fig.6.6 is represented in PSpice environment as shown in Fig 6.7. A gain of(ro*MIJ) has
R1
L11
R2
Current-controlled
voltage source
Fig. 6.7 Dependent Sources Representation of Fig. 6.6 in PSpice
to be entered in the controlled-source attributes window, every time it is used with the
source frequency expressed in Hz or using the term (FREQ) instead.
45
Then, the basic model ofFig. 6.7 is extended with the same connection strategy
to include all components of Phase a, with 6 taped turns represented explicitly and all
other coils represented with their lumped parameters. Such a circuit will appear as in
Fig. 6.8. The two ports a& b shown in the circuit are called bubbles which enable
linking parts or signals without using wires or buses by connecting them to global or
off-page ports and labeling the port with the same name as the signal.
L1
RfZ
Rt3
L2
Rt4
L3
Ht1t32 Hf.Zt32 HOt4
.,..Cg3
b
0
L4
Rc14
Rc2
Rrem
RfZ19
Lt219
Rt220
U220
0
II
o~b----------~J------~r-C_c2~r-C_~_m_________~+-C-g2_1_9______C_~__~r
~
Fig. 6.8 Complete High Frequency Equivalent Circuit Representing Phase a in PSpice
46
After building up the circuit, the transient analysis option, which calculates the behavior
of the circuit over time, is selected using its dialog box. Simulation time and step size
have to be specified. A voltage pulse (VPULSE) is then selected as input with a
magnitude of 622.5 V and a rise time of 0.24 f.1Sec. This magnitude was precisely
measured between one of the motor terminals and ground as shown in Figure 6.9 (b).
The line-to-neutral or phase voltage cannot be used, as the winding neutral point is not
at zero potential any more as shown in Figure 6.9 (a) and it is important to expose the
simulated winding to what it sees in real life. Several markers are available in the
simulation toolbar and may be positioned at any point in the circuit to measure voltage
level or voltage differential.
...,..
etopped
·
:
:
:
·
:
·
·
:
·
:
:
1
:
· · · ·(a) Neutral Voltage: · · · ·. · · · · : · · · · : · · · · : · · · · : · · · ·
•''tie\'el''''
u,•.
~~~· ··.•
,...
..:::
~
·-~ ·
''
500
IIIV/dl•
po••
o.ooo \
'.ooo ·' IMo d•
··>··!·.
+••.. :..
: : : : ): : : : j : : : : : :: : : : : : :•. : :: : j : : :: ~ : :: : j : : : : : . . . .
-so . ooo u•
o.ooo
10.0 us/div
curranl
Vp-p
11c
C 1) 1.50000 Y
c 1 > 270.242mY
v
rm•
lrp
stopped
s
so.ooo u•
rea1tlme Trigger Mode•
overoga
EGge
mawimum
m~n1mum
:J28.125mY
73.6505mv
1.593'75 V
274.3114­
ct47.072mY
191.226mY
I
1
250 • 0 m\
....I....
.... :Voltage
=~>-~~~~~-: ........ :.... :.... :.... :... .
:
:
.
:
:
:
:
... <2SO VIDiV< ... -: .. ' ..... : .... : .... : ... -: ... .
.... ~ .... ~ .... : .... ~·/'.
:
.. ~ .. ..
.
.
.
.
.
.
.
.
: :
,
~-,··•··(··~··•··<-·~··•··~··)'··l··t"··)··~··c··"'··•··(.. !··•··~ ··)··I· ··~··•··(··o)··~··<>·+··•··i:··!··•··<-··)··t··~·..,··•·· +··~.. ~·.,.··•··-co··
... : .
.
·
·
.
.
... : .
.
. .. : .... ; .... : . .
.
:
:
:
C3
....••........•....•... ..•....•... , ...... .
-16.000 us
-43.000 us
Vp-p
V ec rms
curran l
( 3 ) 1 •23438
< 3 >not found
v
5.00 US/diY
minimum
1.23438
0.00000
v
v
3
500
mY /c
pos •
0 .ooo
1 .000•1 1M2
7.000 Ul
maximum
1.23436
0.00000
v
v
realtime Trigger Mode•
average
Delay Qu61 Ed&
1.23438 v
0.00000 V
S
_F I •042
Fig. 6.9 Motor Measured Voltages with PWM Inverter Point
47
6.3 Model Limitations
The proposed model can predict the maximum voltage transients across tapped
turns and coils. However, due to the nature of random winding, with the unpredicted
relative positioning of turns which affects the mutually induced voltages, the model
cannot actually predict the variations in turn voltages.
6.4.Simulated Winding Voltages with Short Cables;
Voltage across the frrst two coils and first turn of phase a, is simulated and
shown in Figure 6.10. It shows the high voltage magnitudes as a result of the PWM
inverter input with its high dvldt and small rise time.
1.1KUT------------------------------------------------­
'
1
:1·
uu
I
622. 5/·
v
Input Pulse -----------------------------------­
-IIUT------------------------------------------------­
1
I
I
/~ Coi 1· 01 Voltage·
.324 \J
.
.
--~ou~-------------------------------------------------
SIIUT------------------------------------------------­
1
~ Coi 1· 02 Vol toge·
I
:
.. I
.433
v
.·
.·
-s11u~------------------------------------------------6UU~-------------------------------------------------
:
II
~/if\\
Turn: 01 Vo 1 tage :
~-'
.'--.---..
..
39 v
-61U+------------r------------y------------~----------
Os
1. Ius
Ti11te
2. Ius
3. Ius
Fig. 6.10 Simulated Voltage Transients with Short Cables
48
The last two turns in the phase did not feel any of the simulated stress as shown
in Fig.6.11.
-DURUT------------------------------------------------­
0.22 ~
i------'
l
.
~Tu~n. 219
.
Vol tDge
--aoNU~-------------------------------------------------
1-DUT------------------------------------------------­
0.8 y
Turn 220 Voltege
-1 .DU Us
+- -----------,...------------.------------.,----------­
1.0us
Tillie 2.Uus
3.Dus
Fig. 6.11 Simulated Turns Voltage Transients with Short Cables
6.5 Simulated Winding Voltages with Long Cables:
The line-to-ground voltage was experimentally measured as shown in Fig. 6.12
with long cables connected and then applied as a simulated input pulse to the model. A
pulse with 812 V peak was used. The voltage across the first two coils and first tum is
examined and shown in Fig. 6.13.
49
'F
slOppe" .----------~--!"""---------=~.---, 1
500
mV/"i v pos•
0.000
V
........................
.
.
.
1.00011
IMQ: "C
.
.
.
. . . . .. . . . . .. . . . . .. . . . . .. . . . .
.
.
.
. . . . .. . . . . ... . . . . ... . . . . ... . . . . ..
.
.
.
#-•)••1••t•·~•·l•·(••·)••l··~•·;••!••of.. ~··~··(•••l-•·l••f..~··l•·(••·)••!"
.
.
.
.
. . . . .. . . . . .. . . . . .. . . . .
..
..
..
····:··. ·: .... : .. ··:. ...
)
I•
(•••1-··~··~··•)••t .. (·•~·•l••.C•••:,O••i••~··)
.
..
..
..
l ..<••
•·!·•(••+••l••f.•
.
.
.,""""'n.J
·:r ... :. ... ·:. .... :. ... : ... .
. . . -: ... -: .... : .... : ... ·f.· ... : ... -: .... : .... : .. ..
-50.000 us
0.000
10.0
current
( 1) :2.031:25 V
Vp-p
v ac rms
us/div
s
minimum
515.625mY
70.95 12mY
( 1 ) 485 . 339mV
50.000 us
realtime Trigger
average
me~lmum
2.78125 V
5tl2 . 144mY
Mode•
E"ge
1.98755 V
400. 862mY
1
_r
250 . 0
Fig. 6.12 Measured Line-to-Ground Voltage with Long Cable
1.0KUT----------------------------------------------­
::
812 .~J:v
_
Input Pulse
ou
:I
---------- --·---------------------­
5 00U T----------- ------------- -·------------ ---------­
l
:
I
~i I 01: Vol tilge
'425
.
:
v
-soou ...L---- -------------------- -·---------------------­
1.0KUT----------------------------------------------­
l
:~il 0~
I
.
:
·550
v
Voltage
.
-1. OKU...L- ---------------- --------·---------------------­
100U T - - - - - - - - - - - - - - - - - - - - - - - - - · - - - - - - - - - - - - - - - - - - - - - ­
1
I
:~n 0~
·53 V
·
Voltage
:
·
-100U+------------r-----------,------------,--------­
Os
1 • ous
TimP
2. Ous
3. Ous
Fig. 6.13 Simulated Voltage Transients with Long Cables
mV
50
6.6 Comparison of Simulation and Experimental Results:
Table 6.2 provides a brief summary for the voltage transient peaks obtained
through simulation and compares them with those obtained through measurements
either with or without the PWM inverter. The simulated turn voltages are higher than
the measured values but as mentioned before, the model is expected to show the
maximum possible voltage peaks across the tapped turns, which may have not been
captured during measurements. The measured voltage peaks across coil 0 I with long
and short cables are always higher than the corresponding simulation but the opposite is
true for coil 02. The high terminal voltages caused by long cables have generated higher
peak voltages across coils. However, it caused more even voltage distribution among
turns compared to short cables, as shown in Fig 6.14 The discrepancies between
simulated and measured voltages are mainly attributed to the nature of random winding.
It is not possible to reflect the true irregular positioning of turns in the slots into a
simulation model especially if the winding is inserted by hand.
Table 6.2 Summary of Simulated and Experimental Results
With PWM Inverter Input
With Short Cables
With Long Cables
Position
Coil 01
Coil 02
Turn 01
Turn 02
Turn 03
Turn 04
Turn 219
Turn 220
Measured
Vpeak
(volts)
370
310
27.5
22.5
13
22.5
3
2
Simulated
Vpeak
(volts)
324
433
39
36
34
33
0.22
0.8
Measured
Vpeak
(volts)
625
500
20
12.5
18
17
3
2
Peak
Voltages with
Sinusoidal
Simulated
460V L-L
Vpeak
(volts)
Input, V
425
550
53
54
50
42
0.6
1.5
59.79
127.6
1.67
1.67
1.67
1.67
1.67
1.67
51
25
j
.20
~ 15
~
10 5
0
2
1
• short cables
Tum# 3
4
•long cables
Fig. 6.14 Measured Tum Voltages with Long & Short Cables
52
7. Conclusions
The effects of PWM inverter generated voltage transients on both the terminals
and the windings of a small induction motor with random mound coils were
investigated and analyzed in this thesis. Understanding such a nonlinear voltage
distribution is believed to be the key for engineers to: I) determine the dielectric
limitations of motors already in service and: 2) specify the requirements of motor
insulation systems in the vastly growing ASD applications.
It was shown experimentally that the voltage transients propagate deeper from
the terminals into the random winding than has been indicated by many researchers who
have reported that the first coil of the phase absorbs most of the strikes. For example, a
high voltage magnitude was observed across the second coil. Furthermore, it was
observed that higher line-to-line voltages caused by reflections at the terminals resulted
in a more even distribution of the spikes among turns. Long cables between the motor
and the inverter cause lower voltage stress on the first few turns compared to short
cables but they increase the stress further inside the motor. These voltage transients
could have destructive effects on the tum insulation in the end turns where wires tend to
cross over wires ofneighboring coils. Hence, coil damage will not be limited to the first
turn of a winding as has been suggested by the previous work. Neither measured nor
simulated voltage transient effects were observed across the last two turns in the phase,
although these coils are raised above ground potential by common mode effects of the
PWM inverter.
PSpice was utilized to simulate a simple model using measured and calculated
winding parameters. The model is capable of predicting the highest voltage transients
that could appear across tapped coils and turns. The ability of the model to simulate
most of the experimental results demonstrates its validity. However, further
development of the model could expand its ability to cover more turns in the first phase.
Furthermore, it would be a great addition if we could generalize the model for
implementation on any random-wound induction motor without having taps from the
examined turns and coils. In such a case, all winding parameters would have to be
53
calculated at high frequency correspondent to the rise time of the PWM inverter's
output voltage.
The use of 11 inverter grade 11 magnet wires in the construction of new motors and
the repair of failed motors appears warranted by this study.
54
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