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Williillilfi'lx‘lllllMilli!

3 1293 00892 9675

This is to certify that the

thesis entitled

Vulnerability of Pulse-Width-Modulated Adjustable
Speed Drives to Utility Capacitor Switching

presented by

Van E. Wagner

has been accepted towards fulfillment
of the requirements for

Jaimie—degree in Jlectrical
Engineering

6% 0,5 G'S‘L’tqu 6%

Major professor

Date Q3 1)? C (fa

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

LIBRARY
Michigan State
University

 

 

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PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.

‘ H DATE DUE DATE DUE 4 DATE DUE

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l MSU Is An Affirmative ActiorVEquel Opportunity Institution
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VULNERABILITY OF PULSE-WIDTH-MODULATED
ADJUSTABLE SPEED DRIVES TO
UTILITY CAPACITOR SWITCHING
by

Van E Wagner

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Electrical Engineering

Fall 1992

ABSTRACT

VULNERABILITY OF PULSE-WIDTH—MODULATED
ADJUSTABLE SPEED DRIVES TO
UTILITY CAPACITOR SWITCHING

by

Van E Wagner

Surges of less than 200% magnitude caused by utility capacitor switching can disrupt
PWM drives. In this thesis, the disruption mechanism of the drive is investigated by
SPICE Simulations and laboratory experimentation. Field tests are analyzed to understand
the generation and propagation of the capacitor switching transient through the power
network. It is Shown that drive dc filter inductor transient saturation is the most significant
mechanism of drive disruption. It is further shown that the power network bandwidth

determines whether the switching transient propagates from the source to the drive.

TABLE OF CONTENTS

LIST OF FIGURES ........................................................................................................ v

LIST OF TABLES .......................................................................................................... vii
1 INTRODUCTION .................................................................................................... l
2 CAPACITOR SWITCHING TRANSIENT ............................................................. 3
2.1 Mathematical Representation ........................................................................ 3
2.2 Transient Source ........................................................................................... 6
2.3 Damping ........................................................................................................ 9

2.4 Transient Modes ............................................................................................ 10

2.5 Transient Propagation ................................................................................... 11

3 PWM DRIVE SUSCEPTIBILITY ........................................................................... 15

3.1 Pulse Width Modulated Drive Description ................................................... 15

3.2 Susceptibility ................................................................................................ 16

3.2.1 Rectifier .......................................................................................... 17

3.2.2 Inverter ........................................................................................... 17

3.2.3 Filter .............................................................................................. 18

4 EXPERIMENTAL RESULTS .................................................................................. 23

4.1 Field Investigation ......................................................................................... 23

4.1.1 Test Description ............................................................................. 24

4.1.2 Network Analysis ........................................................................... 26

4.1.3 Drive Analysis ................................................................................ 32

4.2 Laboratory Tests ........................................................................................... 34

5 SIMULATION RESULTS ....................................................................................... 37

5.1 Circuit Model ................................................................................................ 37

5.2 Simulation Results ........................................................................................ 41

5.2.1 Drive with Linear Inductor ............................................................ 41

5.2.2 Drive with Saturating Inductor ...................................................... 43

5.2.4 Drive with No Inductor .................................................................. 47

5.3 Comparison with Experimental Results ........................................................ 49

5.3.1 Drive with Linear Inductor ............................................................ 49

5.3.2 Drive with Saturating Inductor ...................................................... 50

iii

6 MITIGATION ........................................................................................................... 54

6.1 Utility Switching Options ............................................................................. 54
6.2 Drive Design Options .................................................................................... 57
6.3 Transient Filters ............................................................................................ 57
7 CONCLUSIONS ....................................................................................................... 63
APPENDD( A: SPICE MODEL ..................................................................................... 65
LIST OF REFERENCES ................................................................................................ 70

iv

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LIST OF FIGURES

 

Capacitor switching transient at drive terminals ................................................. 1

Circuit for analysis of the capacitor switching transient ..................................... 4

Effect of damping ratio on peak transient voltage. ............................................. 6

Computed voltage across capacitor ..................................................................... 7

Capacitor voltage response with a damping factor of 0.2 ............. _ -_ 10
Lumped transient propagation model. ................................................................ l2
Diagram of PWM drive ....................................................................................... 16
The LC filter ........................................................................................................ 19
The currents and voltages contributing to inductor flux. .................................... 21
RC integrating network. ...................................................................................... 22
Diagram of utility and plant electrical network. ................................................. 24
Method for measuring drive ac and dc voltage ................................................... 25
Disturbance monitor/utility interface .................................................................. 26
Recorded transient at plant east utility feed ........................................................ 27
Recorded transient at plant west utility feed ....................................................... 27
Computed west utility capacitor response .......................................................... 29
Computed east utility capacitor response ............................................................ 30
Gantry drive u'ansient waveforms ....................................................................... 31
Grinder drive transient waveforms ..................................................................... 32
Inductor saturation test configuration ................................................................. 34
Laboratory simulation of capacitor switching transient ...................................... 35
Laboratory test response of PWM drive ............................................................. 36
SPICE circuit diagram ........................................................................................ 38
Drive ac input voltage ......................................................................................... 39
Circuit model for saturating inductor .................................................................. 40
Filter transient voltage response with linear inductor ......................................... 42
Inductor current with and without transient ........................................................ 42
SPICE inductor B/I-I curve .................................................................................. 44
Filter transient voltage response with inductor saturation .................................. 45
Inductor transient current with saturation ........................................................... 46

V

3 l
32
33
34
35
36
37
38
39

41
42
43

Filter transient voltage response with saturable inductor at light load ............... 47
Filter transient voltage response without an inductor ......................................... 48
Filter transient current without an inductor ......................................................... 49
Operation of pre-insertion resistors ..................................................................... 55
Utility capacitor voltage with synchronous closing ............................................ 56
SPICE model with ac reactors added .................................................................. 58
Three phase transient voltage at drive with ac reactors ...................................... 59
Filter transient voltages with a saturable dc inductor and ac reactor .................. 60
Drive dc current with saturable dc inductor and ac reactor ................................ 61
Drive dc transient voltage with ac reactor and no dc inductor ............................ 61
Drive dc current with ac reactor and no dc inductor ........................................... 62
SPICE PWM drive circuit with node numbers ................................................... 65
SPICE three-phase voltage source GEN3 ........................................................... 67
SPICE nonlinear inductor model CORE ............................................................. 68

vi

\iO‘MhWNt-‘t

LIST OF TABLES

Characteristic transient frequencies and associated circuit elements .................. 11
Computed and measured transient frequencies ................................................... 28
Computed and measured transient peaks ............................................................ 28
Drive ac and dc transient peaks ........................................................................... 33
SPICE PWM drive circuit data ........................................................................... 65
SPICE three-phase voltage source GEN3 data ................................................... 67
SPICE nonlinear inductor model CORE data ..................................................... 68

vii

CHAPTER 1
INTRODUCTION

The proliferation of power electronics has introduced several incompatibilities
between electronic equipment and typical variations of utility electric power. One of the
most common is disruption of operation of pulse-width-modulated (PWM) adjustable
speed drives due to the transient caused by closing utility capacitors (see Figure 1). A
switching transient magnitude of only 1.10 to 1.30 pu can be sufficient to disrupt a drive.
Equipment designers consider high frequency transients (greater than 10 kHz) as more of
a threat to their equipment than low frequency utility capacitor switching transients less
than 1 kHz. As a result, capacitor switching transient disruption of PWM drives is the

second most common power quality complaint received by utilities, after disruption due

 

to voltage sags.
7m .
D
60
:3
'5 I
>
.7“) «I
1

 

o 20
Time (ms)

Figure l. Capacitor switching transient at drive terminals

Historically the study of capacitor switching transients on the power system has

focused on the prevention of over-voltage damage to insulation [1]. However, the
1

2
disruption and damage thresholds for power electronic equipment are much lower than

for the electromagnetic and electromechanical equipment previously addressed. The first
discussion of this problem in the literature appeared in 1990 by Wagner et a1 [2] in the
form of a detailed case study. In 1991 both Hensley et a1 [3] and McGranaghan et al [4]
conducted computer simulations of the problem with the Electromagnetic Transients
Program (EMTP) sponsored by the Electric Power Research Institute (EPRI). Since
EMTP is primarily an electric utility modeling tool, the results provide only limited
information on drive response. Despite the magnitude of the problem, there have been no

further serious analyses of the problem beyond these first three papers.

Because it is a relatively recently discovered problem, industry standards have not
addressed the voltage transient from either the utility or equipment perspective. A
recently published standard [5] does suggest an optional 5 kHz ring wave test for low
voltage equipment intended to simulate a capacitor switching transient. However, a
Standardized procedure has not been developed to define conformance to the ring wave

test.

This thesis explores the generation, propagation, and impact on PWM drives of the
utility capacitor switching transient. The primary focus is determination of the drive
response mechanism by analysis, simulation, and experimentation. Although the thesis
only investigates the impact of the transient on PWM drives, the results also apply to
other types of power electronic equipment. The secondary focus is transient generation
by analysis and field tests. The mechanism of transmission of the transient between the

utility capacitor and the drive is also analyzed.

CHAPTER 2
CAPACITOR SWITCHING TRANSIENT

The generation and propagation of the capacitor switching transient is analytically
developed in this chapter. First an expression for the transient is derived and then the

associated characteristics are examined.
2.1 Mathematical Representation

The capacitor switching transient is the result of connecting a capacitor to a voltage
source through resistance and inductance (see Figure 2). The transient response is found

from

Ecosmt=Lfl+Ri+lIidt (1)
dt Co

where L and R are the equivalent inductance and resistance of the network between the
capacitor and the source voltage, E is the source voltage at frequency (u, and C is the
capacitance of the switched capacitor. Assuming no initial inductor current or initial

capacitor charge, the current, i, is

 

 

. E -;m EcosO E l (usine Ca) cosG .
r=Ecos((ut-0)+e ' - Z costu,t+— —— - " srntuut

and L Z Z
(2)
where the natural frequency, a)", of the circuit is defined as
a, _. 1 (3)
" w/LC

 

 

 

Figure 2. Circuit for analysis of the capacitor switching transient
the damping factor, C, is defined as

_R
2;'2

r
L
and the damped frequency of oscillation, cud, is
a), = a), 1 - C2
The circuit steady state parameters are the phase angle 0

mL-_1_

9=tan-1___QQ
R

and the impedance Z

“tutu-a

 

(4)

(5)

(6)

(7)

5
The equipment affected by the switching transient is in parallel with the capacitor. In this

analysis we'll assume that the current drawn by the drive to be is much less than the
current in the capacitor due to the u'ansient. Hence, the drive does not affect the capacitor
voltage or the initial conditions. The voltage during the transient applied to the drive is

found by substituting the current solution (2) into (1)

7 Ee'cm" [c036
C [(Cmu)2+m42]l- Z
l (1 (Mint) Cmncose

_.._ _..——-——— a) sinm t+(o c080) t
L z Z )(g n n d l )]

 

 

v = EZ sin (cot - 6) + (Ca), cosam - (0,, sin rent)

(8)

The peak transient voltage is determined by the damping factor and can be derived
from the voltage expression (8). However, a simpler approach to derive the same
conclusion is to assume that the system voltage, E, is constant during the transient

resulting in the following differential equation:

di . 1'.
E = LE+ Rt +E£rdt (9)

The voltage across the capacitor from the current solution to the above equation is
1 ' C - .
=— E -e “’"srntu rd: 10
v C! J L ‘ ( )

After integrating and rearranging terms the voltage is

v=E1- e-m.‘ sin[(udt+tan" 1.? (11)
31-? I;

6

The peak voltage occurs at t = 2 seconds and depends entirely on the damping ratio. If
(0n

1; = 0, the peak voltage becomes 2E which is the upper limit for the circuit. Figure 3 is a

graph of the maximum transient voltage verses damping factor from equation (1 l).

 

 

1.6. \
1.4. \
. \

1.2 \\
1 . i I I I I 1 I 1 t X h—
0 0.2 0.4 0.6 0.8 1

DAMPING RATIO

 

 

 

PEAK CAPACITOR VOLTAGE (PU)

 

 

 

 

 

 

 

Figure 3. Effect of damping ratio on peak transient voltage.

2.2 Transient Source

The electric utility is the most common source of capacitor switching on the power
system. Utility capacitors provide leading reactive power to balance the lagging reactive
power generated by utility customers. They switch capacitors near their loads to improve
power factor and stabilize voltage. Capacitors are gradually added and removed either
automatically or manually over the course of the daily load cycle. There are seasonal
trends in voltage and some capacitors, therefore, remain on during high load seasons,

such as the summer, and are switched, as needed, during other parts of the year.

7
Capacitors are operating aids and, as such, are not left on throughout the year. A

capacitor that is needed continuously indicates a system design deficiency.

The transient voltage at the utility bus as a result of the capacitor closing computed
from expression (8) is shown in Figure 4. The data for the equation was from a typical 40
kV station with X = 18.7 % and R = 0.87 % on 100 MVA base closing a 12 MVAR

capacitor.

 

'or to

Ill] lllllllll

—L

 

 

—L

 

.0
or

 

 

 

 

 

 

 

 

 

I It

 

 

 

 

 

 

 

CAPACITOR VOLTAGE (PU)
o

 

 

 

 

 

 

-0.5
.1 = H
I V
.4
4.5 ; W
1 I
-2 d U I U I I U I U U fir U I I
0 0.006 0.012 0.018
TIME (See)

Figure 4. Computed voltage across capacitor

Another source of the capacitor switching transient is the power factor correction
capacitors within facilities. These capacitors are added primarily to prevent utility power
factor penalties for large utility customers. Generally, these capacitors are left on and are
not automatically switched. However, if under light load conditions the capacitors cause

excessively high facility voltage, the capacitors are automatically switched off.

8
Since utility capacitor switching is the most common source of the transient, the

remainder of this analysis focuses on the utility network. Nevertheless, the results may

also be applied to facility capacitors.

In the previous analysis of the voltage transient the capacitor was assumed to be fully
discharged when closed into the circuit. Another mechanism that can generate even
higher transient voltages is restrike of the switching device. During opening or closing of
a capacitor, the arc may be momentarily interrupted. When reestablished the capacitor is
charged, increasing the transient magnitude. Further restrikes can escalate the capacitor
voltage to very large transient magnitudes as each reignition begins with progressively
higher initial voltage across the capacitor. As utility capacitor banks increased in number
form the 1950s and 19605, restriking became more of a problem. Pflanz and Lester [6]

discuss some of the equipment options to reduce resuike.

The peak restrike voltages can be derived from the differential equation (9) by setting

resistance equal to zero and adding an initial capacitor voltage Vc(0).

di 1'
E=L—+— 'dr 12
dt C!‘ ( )

The voltage across the capacitor then becomes

- i' _ £-
v-V,(0)+C I (E Vc(0))J:smm,tdz (13)

01’

v = E+(V,_.(0) - E)coscu,,t (14)

If the capacitor has an initial voltage Vc(0) = -E, the peak transient voltage is 3E.

Air or SF6 insulated capacitor circuit switchers in service today are designed to
reduce the possibility of restrikes. The circuit switcher is a special purpose device
designed for capacitor switching duty. They have no fault duty rating but are more
economical than circuit breakers for frequent switching service. Although these devices
minimize restrikes, they are not universally applied and can still cause restrikes as a result

of malfunction.

2.3 Damping

As shown in Section 2.1, the peak transient voltage depends entirely on the damping
ratio and is most sensitive to resistance. Because losses are minimized in power systems,
damping is not a practical means to control the transient. For example, the damping ratio
for the utility 12 MVAR capacitor closing shown in Figure 4 is 0.0152. There is no
accepted peak voltage limit that would assure the transient would not cause problems. A
damping ratio of 0.2 would limit the peak voltage to 1.5 pu as shown in Figure 5. Yet,
this damping ratio is twice as large as any practical damping ratio for a utility network.
Therefore, the natural damping provided by the utility network is insufficient to reduce

the magnitude of the transient.

10

 

N

.4
01

 

u—l

 

 

.0
or

 

 

.<'>
or

 

‘g_/

 

 

.1.
b. J.

 

CAPACITOR VOLTAGE (PU)
0
Jill llll lllj III] II 1 .11] 111111111

I
N

 

U U I U I U I

 

 

 

 

0.006 0.012 0.018

TIME (Sec)

0

Figure 5. Capacitor voltage response with a damping factor of 0.2

2.4 Transient Modes

It has been assumed in this analysis that the utility capacitor bank and step-down
transformer are the primary circuit elements that determine transient behavior. However,
distinctive oscillation frequencies following closure result from the interaction of
different combinations of network capacitances and inductances. Pflanz and Lester
grouped the equipment and corresponding transient frequencies and the results are shown

in Table l.

l 1
Table 1. Characteristic transient frequencies and associated circuit elements

 

 

 

 

 

Capacitive Inductive System Frequency
- _ __ Element _ __ _ _ g _
Switched Bank Transformer 10
Switched Bank Transformer 102
& Energized Bank
Switched Bank Inter-Bank 103
& Energized Bank Inductance
Cable Cable I 104

 

 

 

 

 

The 104 times mode involves reflections due to line termination impedance mismatch.
Drives are almost exclusively affected by the 10 times frequency mode which
corresponds to a range of approximately 300 Hz to 900 Hz. The reason for the particular

window of vulnerability of drives to this frequency band is discussed later.

Another possible mode not covered by Pflanz and Lester is a result of line switching.
The switched cable or line capacitance would interact with the step-down transformer
inductance to produce a transient. Since a line has approximately 1% to 2% the
capacitance of the capacitor bank, the transient frequency mode is 10. times greater than

the transformer-capacitor bank mode.
2.5 Transient Propagation
The mechanism of propagation of the transient away from the source depends on the

transient frequency and the network. If the length of the network is less than 1/6 the

wavelength of the transient, the network can be considered an extended lumped

 

12
parameter circuit. If the length of the network is greater than ll6 the wavelength of the

transient, the network can be considered a high frequency transmission line. Since 600
Hz is the average transient frequency affecting drives, the corresponding wavelength is
500 km. To use the lumped parameter network model, the circuit must be less than 83

km. Most utility distribution and sub—transmission circuit lengths are under 60 km.

The number of networks between the source and the load equipment is determined by
the decoupling points which are, most commonly, power transformers. If the transformer
and load impedance of the sub-network is much less than the source network, the two
may be treated separately. Vilcheck and Gonzalez suggest the ratio of the irnpedances
between the two subonetworks be greater than 25 [7]. For each of the sub-networks, a
separate lumped RLC (resistor, inductor, and capacitor) circuit can be developed (See
Figure 6). The circuit model is derived from a series inductance and resistance
representing the transformer and conductor with a shunt capacitance representing the
intra-conductor capacitance or capacitor banks. The circuit behaves as a low pass filter.
Power distribution networks typically resonate at between 300 Hz and 500 Hz [4] and,

therefore, will attenuate transients above that frequency.

Rs LS R1 L1 R2 L2

E Q C1 (:2 I Load
°s T

Figure 6. Lumped transient propagation model.

 

13
However, a problem can arise near the resonant frequency. An underdamped circuit

can magnify a transient whose frequency is near the network's resonant frequency.
Zaborszky and Rittenhouse show that the sub-network can multiply the initial transient
by 11.6 times [8]. Schultz et al describe three conditions necessary for magnification of

the capacitor switching transient within a sub-network [9]:

1. To be considered a sub-network, it must be decoupled from the other networks
connected to it, including the source network.

2. The frequency of the transient must be close to the resonant frequency of the sub-
network.

3. The sub-network must be underdamped.

The first issue has already been discussed. For the second issue, the proximity of the
transient and sub-network resonant frequencies can be quantified by the quality factor,

Q), used for filter circuits and defined as

0),,L
Q“ R

 

(15)

.818

where (film is the bandwidth between the two frequencies on either side of the resonant
frequency that are é times the peak magnitude. For the utility network just used, the

bandwidth is 3 Hz. Because the X/R ratio at system frequency of power systems is
typically 5 or greater, the bandwidth will not be more than 12 Hz. Therefore, the
transient frequency must be very close to the resonant frequency of the sub-network for

the transient to be sustained.

The third item is a restatement of the fact that, at resonance, the voltage across the

capacitor for a series RLC circuit can be much greater than the circuit source voltage.

14
For the sub-network in series resonance, the current is determined by the resistance. The

ratio of the magnitude of the output voltage to the input voltage, 11, is

l

ijC 1‘]? 1
= " =— —=— 16
n 15,, R C 2; ( )

 

 

 

 

Since C can vary from zero to one, the transient voltage out of the sub-network can be

vary from NZ the magnitude of the input to infinity.

With the damping ratio typically less than 0.1 for power systems, the neamess of the
transient frequency to the sub-network resonant frequency determines how the capacitor

switching transient is transmitted from the source network.

CHAPTER 3
PWM DRIVE SUSCEPTIBILITY

The pulse-width-modulated (PWM) adjustable Speed drive is the most common
equipment to be affected by the capacitor switching transient and this chapter explores
the possible reasons for the vulnerability. Although the discussion is limited to PWM
drives, the mechanisms can apply to other types of drives and other power converters.

First, the PWM drive is described and then the sub-parts analyzed for vulnerability.

3.1 Pulse Width Modulated Drive Description

The PWM drive varies motor speed by providing power of variable frequency and
voltage to induction or synchronous motors. The essential elements of the drive are
shown in Figure 7. The three phase full-wave rectifier section uses uncontrolled diodes:
hence losses are reduced, power factor is increased, and control circuitry is minimized
compared to thyristor drives. The inductor-capacitor (LC) filter is the dc link between the
rectifier and inverter that filters the ripple and further improves power factor. The
inverter section converts the dc to the required ac frequency and voltage by pulse-width-
modulation at a switching frequency of 10 to 20 times the base frequency. Because of the
required switching speed, the inverter section most frequently uses bipolar transistors,
insulated gate bipolar transistors (IGBT), or field effect transistors (FET). These
semiconductors have simpler gating requirements than thyristors and, hence, require less
complex control circuitry. However, transistors do not have the current handling
capability of slower semiconductors and, consequently, PWM drives are only available

up to several hundred horsepower.

15

16
An advantage of the PWM drive is that it produces a sinusoidal-like voltage

waveform for the motor. With reduced motor voltage harmonics, cogging is prevented
and motor losses are reduced. For constant torque operation from approximately 10% to
110% synchronous speed, the volts per hertz ratio is held constant at the output of the
inverter to maintain a constant stator magnetic field. If voltage is held constant as
frequency is changed, torque will vary inversely with speed and the motor will provide

constant horsepower over approximately a 2 to 1 speed range.

A further advantage is that the PWM drive uses a standard induction motor. The
induction motor is a rugged, simple, inexpensive, and low maintenance device compared

to dc or specialty motors.

RECTIFIER I FILTER INVERTER

(GI :32 (GI

 

 

MOTO '

\I
ll

 

 

 

 

 

 

 

 

-_ ———

Figure 7. Diagram of PWM drive

3.2 Susceptibility

The three major sub-parts of the PWM drive are analyzed for their susceptibility to

the capacitor switching transient. They are the rectifier, filter, and inverter sections.

17
3.2.1 Rectifier

The 60 Hz rectification section consists of a three phase full-wave bridge. The diodes
conduct symmetrically about the peak of the crest of the voltage waveform. The width of
the conduction interval depends on the drive load level with higher load requiring a wider
conduction interval. Since when conducting the diode directly passes the voltage
waveform, a damped oscillatory transient in the range of 300 Hz to 900 Hz readily passes

through the rectification stage.

The rectifier section contains devices to protect the semiconductors from disruptive
and damaging electrical disturbances. Transient voltage surge suppressors are connected
at the ac incoming terminals. However, these devices begin operating at 200% to 300%
of rated voltage. Since the capacitor switching transient can be 100% to 200% greater
than rated voltage, the surge suppressors have no effect. If the surge suppressor is sized
to a lower voltage, it partially conducts during high voltage conditions and will over heat.
Noise filters are also sometimes added to the incoming power lines to protect the drive
against conducted noise. These are ineffective since their cut-off frequencies are
generally at a few kilohertz and are too high to attenuate the transient in question.
Because of the harmonic currents generated by the rectifier, lower cutoff frequencies

could cause excessive insertion loss.

3.2.2 Inverter

The capacitor switching transient can cause excessive voltage at the inverter input.
Due to cost, the inverter transistors may have limited over voltage capability. ’ For
example, 480 V drives use 1200 V transistors where the rectified do can be as much as

690 V. To protect the inverter transistors, an over voltage trip is provided at

18
approximately 760 V for 400 us that shuts down the inverter. Consequently, for nominal

input voltage conditions, the inverter has only a 10% over-voltage margin. For such an
event, the drive controls often provide fault code that will indicate high dc voltage as the
cause. This mechanism is much less likely with 240 V drives since they use 800 to 1000

V u'ansistors and have a 40% or greater over-voltage margin.

Some drive manufacturers have recommended that their dynamic braking option will
decrease susceptibility to the transient. In situations where the mechanical load drives the
motor above synchronous speed, the motor operates as an induction generator and
increases the drive dc voltage. An example would be quickly decreasing the drive
frequency while the motor is operating a high inertia load. The frequency corresponding
to the motor's speed may, momentarily, exceed the inverter output frequency. The brake
is a resistor that is electronically switched across the drive dc bus to lower the dc voltage.
However, in all the cases where this was attempted, the brake did not respond sufficiently

fast to limit the transient voltage.

3.2.3 Filter

Although other factors contribute toward susceptibility to the capacitor switching
transient, the dc filter design is the most important. Since the filter components are
relatively expensive compared to other drive components, filter performance must be
balanced against cost. There are two mechanisms by which the filter can cause
equipment disruption. The first is the filter presents a low impedance to the transient and
causes a corresponding current transient that can either trip over-current devices or
damage the rectifiers. The second is that the filter passes the voltage transient and

inverter dc over-voltage protection is actuated.

19
The filter normally takes the form of an inductor-capacitor (LC) low pass filter (see

Figure 8). Ripple current is shunted through the capacitor and ripple voltage is dropped
across the inductor. The capacitor is sized to shunt most of the ripple current from the
load. If the load is variable, the criterion should be applied at maximum load. If the load
is assumed to be purely resistive and represented by RL, the filter capacitor is sized by

the criterion

(17)

 

RL >>

 

Figure 8. The LC filter.

where nut is the ripple frequency. Setting RL to be 10 times the capacitive reactance, C

becomes

(18)

 

The load ripple voltage can be determined by applying the voltage divider rule across
the inductor and capacitor. If VIN is the rrns value of the ripple voltage into the filter and

V0m' is the ripple voltage out of the filter,

20

 

_Vry_
C V
V - "‘9 _ I” (19)
0'” w,” 1 (anLc—r
nmC

The inductor is then sized to provide the specified voltage ripple reduction from the

expression

V

——0‘” +1

(I: (o) C

In effect, the load impedance determines capacitance and the desired voltage ripple
determines the inductance. Although the amount of ripple depends on the application,
1% or less is considered typical. The resonant frequency of the LC network should be
chosen between the possible harmonic current frequencies of the drive to prevent
resonance. The inductor also affects power factor and the current range over which the
rectifiers continuously conduct. On low power equipment (for example drives under 5

hp), the inductor is frequently omitted to reduce cost.

Since the filter capacitor can be considered a short circuit at the transient frequencies
under discussion, the inductor determines transient current response. If the transient
current magnitude is high enough, the drive may be disrupted or damaged. For
ecjuipment that operates with variable load, the mechanism is more probable at heavy
rather than light load conditions since device thermal margins are narrower. The current
surge could cause the over current protection for the equipment to operate. Or, due to
poor design, the rectifiers may fail before the over-current protection acts. In small motor
drives without an inductor in the filter, fuse blowing is the most common response to

capacitor switching.

21

The other mechanism of disruption is that the voltage transient passes through the
filter to the inverter where over-voltage protection operates. Smaller drives where the
filter inductor has been omitted are very vulnerable to this mechanism. Those filters that
include the inductor would be expected to attenuate the transient Since the transient
frequency is above the ripple frequency. However, there are cases where an inductor is
present and transient passes through the filter with little, if any, attenuation. For this to
occur, the inductor must saturate because of the transient. With the inductance at an
eighth or tenth of its unsaturated value, the filter would let pass transients of frequency
less than 1 kHz.

McLyman describes one approach for inductor design in [10]. The maximum
operating flux for the inductor may be 20% to 30% below saturation and is composed of
flux due to the maximum dc current and flux as a result of the voltage across the inductor
(see Figure 9). Assuming the voltage across the inductor to be sinusoidal, the resulting

current through the inductor creates a flux density Bac

B = V“
“ 4.4400,,ACN-10'8

 

(21)

+ VR -
—9
'dc

Figure 9. The currents and voltages contributing to inductor flux.

where V3 is the ripple voltage, Ac is the core cross sectional area, and N is the number of

turns. The flux density due to the dc current [dc is

22

_ 0.41mi, -10"
l

1

Ba.-

 

(22)

where 18 is the core gap length. The total flux is the sum of the ac and dc components

and is given by

_ 0.4mm, -10" + v,
l 4.44m,A CAI-10"

8

B

 

 

(23)

The ripple voltage for a three phase full wave rectifier is only 6% of the phase
voltage. If the capacitor switching transient is 20% or more of the phase voltage and [dc
is at its rated value, the transient can easily drive the inductor into saturation. It appears

that a heavily loaded drive would be more susceptible to transient saturation.

With the inductor in saturation, the filter behaves like an RC network (see Figure 10)
where R is the equivalent resistance of the filter. The transient voltage integrates across

the capacitor until the over voltage limit is exceeded for the inverter.

 

Figure 10. RC integrating network.

CHAPTER 4
EXPERIMENTAL RESULTS

Two experiments to evaluate the response of PWM drives to the capacitor switching .
transient are described. The first is a field test of the response of the power distribution
network and two drives in an automobile engine factory when utility station capacitors
are switched. The second test is application of a laboratory generated transient to a PWM
drive.

4.1 Field Investigation

The field investigation was at a dual utility fed automotive engine manufacturing
plant. Each 40 kV plant feed is from separate 120 kV to 40 kV utility stations (east and
west) as shown in Figure 11. Plant primary voltage was stepped-down to 13.2 kV to
operate large motors and numerous unit substations that further reduced voltage to 480V.
The plant operates two camshaft grinders from separate primary sources; each grinder
utilizes one 10 hp and one 50 hp PWM drive. The west utility station had one 40 kV 12
MVAR capacitor bank while the east station has two 18 MVAR and two 24 MVAR
banks. When the west station 12 MVAR bank was energized, the 50 hp drive would
frequently trip. Yet the identical drive fed from the east station never tripped when any
of the four station capacitor banks were energized. The camshaft grinders were added
two years prior to the discovery of the problem. During those years, the 12 MVAR bank
was switched infrequently and, therefore, a correlation with the drive trips was difficult to

establish.

23

24

 

WEST UTILITY STATION EAST UTILITY STATION
120 kv T
++
40 kV
12 WAR 2 @ 18 MVAR
+4
I.— ___________________
v 13.2 kV
PLANT
480 V
O ® ® 0 @
GANTRY TRIPPING NON-TRIPPING
LOADER GRINDER GRINDER

® MEASUREMENT LOCATION

Figure 11. Diagram of utility and plant electrical network.
4.1.1 Test Description

The goal of the investigation was to identify the trip mechanism of the 50 hp drive
and to determine how other 480 V buses within the facility would respond to the same
transient. Since an identical 50 hp drive was not available on another 480 V bus fed from
the same primary source, a gantry loader servo positioner was selected. The rectifier and
filter sections of the servo positioner were similar to the PWM drive. When the 50 hp
drive tripped, the diagnostic indication was high dc bus voltage. Therefore, for the test
the dc voltage was recorded as well as the phase voltage for both drives while the 12
MVAR capacitor bank was switched (see Figure 12). The loader and grinder were

operated without work pieces to prevent damage to the machines during drive trips.

25
Drive operating power levels were not measured. The voltages were recorded at separate

locations simultaneously by dual channel digital oscilloscopes connected through voltage

isolators. The isolators were necessary to isolate the oscilloscope chassis from line

 

 

 

 

 

 

potential.
(02 (.2 '32
e
’——9—' ; : MOTO '
O—Q

 

 

 

 

 

 

 

 

 

 

—‘| VOLTAGE
I ISOLATOR
l l

 

 

 

 

DIGITAL OSCILLOSCOPE

Figure 12. Method for measuring drive ac and dc voltage

In separate tests, the transients were measured at the primaries of the plant's two 40
kV transformers with power quality disturbance instruments monitoring at the utility

revenue meter potential transformers (see Figure 13).

26
To Utility Station

40 WI 120 V Utility Revenue Meter
1 Potential Transformers

 

 

  

 

 

 

)
D
)
I 3
Power Quality Disturbance
Monitor
To Plant 40 kV/13.2 kV
Transformer

Figure 13. Disturbance monitor/utility interface

4.1.2 Network Analysis

The measured frequencies of the transient at several points in the network are shown
in Table 2. The frequency of the transient at the plant's two 40 kV transformers for the
table were taken from the measurements Shown in Figures 14 and 15, which were
conducted independently of the 480 V measurements. From the discussion on transient
propagation in Chapter 2, it follows that the sub-network response depends on the how

close the transient frequency is to the sub-network resonant frequency.

The resonant frequency for the 40 kV utility bus is calculated from (5) and utility
data. The computed value for the east Station frequency is identical to the measured
value. However, there is a significant difference between the computed and measured
values for the west station. The only possible explanation for the mismatch is that the
utility data for the west station is less accurate than the data for the east station. Since the
tests were conducted at an operating plant, there was little opportunity for further

investigation.

 

27

 

 

Voltage

 

 

 

 

- 50 V/div 5ms/div

Figure 14. Recorded transient at plant east utility feed

 

 

 

Voltage

 

 

 

 

50 V/div Sms/div

Figure 15. Recorded transient at plant west utility feed

 

28

Table 2. Computed and measured transient frequencies

 

 

 

 

 

 

 

 

Measure? Measured Measured
Station Computed at at at
40 kV Plant 40 kV Grinder 480 Gantry 480
can on V V
cod and
East 667 Hz 660 Hz - -
I West I 525 Hz I 420 Hz I 450 Hz I 400 Hz I

 

The transient was only measured at the 480 V level on buses fed from the west utility
station. Since the identical grinder drive fed from the east utility station was not affected
by capacitor switching, it would be difficult to capture the transient at that grinder. The
transient frequencies at the grinder and gantry 480 V feeds are close to the measured 40
kV frequency. The slight difference among the 40 kV and the 480 V frequencies is likely

due to the error in reading the frequencies directly from the voltage plots.

Table 3. Computed and measured transient peaks

 

Computed Measured Measured
Station at 40 kV at at at
Capacitor Plant 40 kV Grinder 480 Gantry 480
(pu) (pa) V V

 

 

 

 

 

 

 

 

West I 1.9 I 1.2 I

The transient response at the utility capacitor banks were computed from equation (8)
and are shown in Figures 16 and 17. These figures can be compared to the measured
transients shown in Figures 14 and 15 taken at the plant transformer primaries. As shown
in Table 3, the peak transient voltage of both of the plant feeds is approximately 1.2 pu
whereas the computed peaks are 1.9 pu. The plant 40 kV and utility 40 kV bus are all

29
part of the source network: there are no intervening sub-networks between the two

locations to attenuate the transient. Nevertheless, there are two reasons for a lower value
at the plant. First, since the plant is several kilometers from the utility station, part of the
difference may be due to voltage drop on the utility lines. The second is that the
disturbance monitor that recorded the transient was coupled through potential
transformers. The potential transformers may not have sufficient bandwidth to accurately
reproduce the transient. The other measurements for the field investigation were

performed with directly connected monitors and avoid this problem.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2‘
51.53 A
e... 1: II II II
“J :
2 05: I
'3 ' = I
9 o:
s = I I A V
:-0.51 .
1m
“ 5 III V
04.5: V
-2: f! U U ! r U I I 1 ffi U
0 0.006 0.012 0.018
TlME(Sec)

Figure 16. Computed west utility capacitor response

30

N

 

.5
I
.5 01
1111 1111 1111
3D

 

 

 

O
01
b

 

 

 

 

 

 

 

 

 

 

 

CAPACITOR VOLTAGE (PU)
o

 

 

 

 

 

055 {I
-1 :
: V b V V
4.5: I -
-2: I I U T l I U I I f 1 I U
0 0.006 0.012 0.018
TIME (See)

Figure 17. Computed east utility capacitor response

Table 3 shows the peak magnitudes of the transient corresponding to the test points in
Table 2. The per unit magnitude of the transient at the 480 V grinder was equal to the 40
kV magnitude. The per unit magnitude of the ganU'y drive 480 V transient was lower

than at the other two measurement points.

The ac magnitude of the phase voltage transient at the two drive locations showed the
different responses of the two 480 V networks to the same input transient. The
magnitude of the transient at the gantry drive was 1.08 pu of nominal voltage and it was
1.24 pu at the grinder drive terminals. Indeed, it appears the grinder drive would not trip
if it were fed from the same 480 V bus as the gantry drive. The difference in response
may be due to different resonant characteristics. The design and operating characteristics
of the two networks were identical. Each had 60 kVAR of power factor correcting
capacitors, the same nominal transformer impedance, and less than 10% loading during

the test. At the time of the investigation, the 480 V network resonance characteristics

31

 

 

 

 

300 ‘
Drive dc
o q
0
00
g ac Input
§ ”0 '
4
am .
0 20 40 to

Time (ms)

Figure 18. Gantry drive transient waveforms

were not considered an issue and, therefore, were not examined. However, the
maintenance condition of the two networks were thought to be relevant and were
compared. The bus, cables and associated equipment feeding the grinder were inspected
and tested for ground impedance, voltage imbalance, connection integrity, open capacitor
fuses, and harmonics. The results showed the network was in very sound condition and

the cause for the separate responses of the two networks was not investigated further.

 

32

 

 

 

“I ‘ __J-"f
Drive dc
3» o
3.3;
o
> ac Input
m I
‘ ‘
.m a
0 10 40

Time (ms)

Figure 19. Grinder drive transient waveforms
4.1.3 Drive Analysis

The ac and dc responses at the two pieces of equipment are shown in Figures 18 and
19. Due to the scale of the figures, the relative amplitudes of the transients are actually

opposite to what they appear.

The magnitude of the transient response on the dc buses closely followed the
magnitude of the transient on the phase voltage on both of the drives (see Table 4). The
dc transient magnitude was 1.20 pu on the 50 hp grinder drive and 1.06 pu on the gantry
drive. The station capacitor bank was closed three times for the test and in each case the
grinder drive tripped on high dc voltage and the gantry drive did not. The dc trip voltage
for the grinder drive is 760 V while the peak transient voltage shown on the response plot

is 843 V. It was not known where exactly the grinder drive tripped on Figure 19.

. _ __.__ “7‘?

33
Table 4. Drive ac and dc transient peaks

 

  
  

480 V
Transient

Drive dc
Transient

   
 

  

 

. P
Gnnder

Gantry
Loader 1.08 1.06

 

 

The response out of the LC filters of the two drives were very different. There was a
small step change of dc voltage at the gantry loader drive due to the transient. The dc
voltage at the time of the transient at the grinder drive appears from Figure 19 to be the
result of integration of the transient voltage. The LC filter of the 50 hp grinder drive has
a cutoff frequency of 107 Hz and should have attenuated the 450 Hz transient by 22 db.
As discussed in Chapter 3, the mechanism operating in this case may be saturation of the

LC filter inductor.

To determine if the inductor was saturating, the inductors from two drives were
tested. One was from the 50 hp grinder drive and the other was from a 10 hp PWM drive
known not to trip from the capacitor switching transient. The inductors were driven by a
voltage source 2 kW audio amplifier at 450 Hz (see Figure 20). Unlike an actual drive
filter, there was no dc bias current through the inductor. Saturation was indicated by the
cross-over to distorted voltage across the inductor by an oscilloscope. The inductor from
the 10 hp drive saturated at 90 Vrms and the inductor from the 50 hp drive saturated at 14
Vrms. From these results, it is evident that inductor saturation is the most probable cause

of the 50 hp drive trip due to the capacitor switching transient.

34
Inductor Under

 

 

 

 

Test
2 kw , ,
450 Hz , Audio Digital
Oscillator Amplifier Oscilliscope

 

 

 

 

 

 

 

 

 

 

Figure 20. Inductor saturation test configuration
4.2 Laboratory Tests

A laboratory test of the response of a PWM drive to the capacitor switching transient
was performed to gain a broader understanding of the response. The test set-up for the
drive is shown in Figure 21. The 10 hp drive operates from 480 V three phase with a
series notch filter on one of the phases tuned to the frequency of the transient. A 500 Hz
damped transient generated by the function generator drives the 2 kW audio amplifier.
The amplifier is isolated from line voltage by a 4:1 step-up transfonner. The filter's high
impedance at the transient frequency causes the transient current to flow through the ac
lines to the drive. The equivalent utility source impedance is very low at this frequency.
The transient frequency was chosen to be between the drive 8th and 9th current
harmonics to prevent excessive voltage drop across the filter. To evaluate the impact of
the transient at several motor load levels, the motor load is controlled by an eddy current
dynamometer. The voltage is monitored through two voltage isolators that attenuate the
signal and isolate the measured voltage from the oscilloscope ground. Only two
oscilloscope channels were available for the test so that the results show two separate

events.

35

 

 

 

 

, I I Dynamometer

 

 

 

 

 

 

 

 

 

 

 

 

 

480 V __
3 (II PWM 10 hp
500 Hz Notch Drive Motor
Filter __) l_
Isolation UUVU

 

 

Transformer m

2 kW Audio Function
Amplifier Generator

Figure 21. Laboratory simulation of capacitor switching transient

 

 

 

 

 

 

Results of the test are shown in Figure 22 for the ac input, rectifier output, and LC
filter output with an applied transient magnitude of 0.38 pu. In no case did the transient
cause the drive to trip. The transient is clearly present in the rectifier output but almost
entirely absent from the LC filter output. There is a slight step increase of dc voltage
similar to the increase observed in the gantry loader drive (compare to Figure 18).
Although the test results shown in Figure 22 were with the drive lightly loaded, results
were independent of drive load. The test verifies that this drive would not be vulnerable

to the capacitor switching transient.

36

 

 

 

 

 

1000 -
1% #7“ AVJ'W‘ NUT-:71 “'i'Lr' 1'.er ‘J'LTITLE ‘ rw ‘
~ 500 r
E
0 . Filter Output
1000 -
§ W
:5 500 -
o - Rectifier Output
1000 ,
.500 r
S
2 0 r
'6
>
-500 -
-1000 -
ac Input
1 1 r r
8 16 24 32
1.lmetms)

Figure 22. Laboratory test response of PWM drive

CHAPTER 5
SIMULATION RESULTS

To evaluate the effect of the capacitor switching transient on PWM drives, a drive
was modeled with the SPICE electronic simulation program. The simulation provides a
flexible means of exploring circuit behavior without the cost and time required for the
equivalent hardware tests. First, the SPICE model is described and then the results of the
simulations are presented. Finally, the simulation results are compared to the

experimental results from Chapter 4.

5.1 Circuit Model

SPICE was originally developed as simulation program for low power analog circuits.
For power electronic applications, two problems arise. First, the program must readily
handle three phase sources with the flexibility and accuracy of single phase sources.
Second, device models must be available in the current and voltage ratings common for

power electronic applications.

The SPICE program selected for the drive modelling is a Macintosh based version
from Intusoft compatible with Berkeley SPICE 26.6. Intusoft provides a three phase
voltage source, GEN3, that allows control of frequency, phase, amplitude, and balance.
However, the number of high voltage and current semiconductor device models is
limited. Consequently, the simulations were sealed for 240 V from the actual supply
voltage of the field tests of 480 V.

The circuit modelled for the simulation is based on a Vee-Arc 10 hp PWM 480 V

induction motor drive. To scale the drive for 240 V operation without adjusting the

37

38
component current ratings, the motor size was reduced to 5 hp. The Vee-Arc has no field

history or laboratory test evidence of capacitor switching transient susceptibility. The
challenge of the simulation is to perturb a well performing drive so that it behave like a

highly susceptible drive.

The circuit modelled in SPICE is shown in Figure 23 and includes the electrical
source, the drive and the motor. An input listing for the simulation is contained in
Appendix A. GEN3 creates a balanced three phase 240 V rrns source for the circuit with
the neutral resistor added to terminate the neutral node from the source. The source
impedance is represented by the RS and LS phase elements and is identical to the source
impedance for the 50 hp grinder drive from the field investigation described in Chapter 4.
The capacitor switching transient is created by three voltage sources in series with GEN3.
Seventeen milliseconds into the simulation, the transient voltage sources add a damped
24% transient at 450 Hz (see Figure 24). This transient is the same as the transient
measured at the 50 hp grinder drive during the field investigation. The 17 ms delay

allows the circuit to settle into steady state operation.

 

 

 

 

 

 

RL XL RL

+ E +

RSX LSX VCX I '
x 0 RC
0 w .

LSZ VCY
VCZ
LLOAD

Figure 23. SPICE circuit diagram

VOLTAGE Vbc VOLTAGE Vab

VOLTAGE

39

 

 

 

 

 

 

 

 

 

 

 

200

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. /../
0d
-200: x Ur]
-400'.... ..fik..r.--. ...
0.01 0.015 0.02 0.025 0.03
TIME (SEC)

Figure 24. Drive ac input voltage

40
The current then enters a three phase full-wave bridge with uncontrolled rectifiers.

The LC filter uses a series inductor shunted by a capacitor with actual inductor and
estimated capacitor losses included as equivalent resistances. Inductor saturation appears
to be a factor in the transient performance of the field tested drive. Therefore, the
simulation circuit includes a saturable inductor model for the filter inductor developed by
Rumseyo[11]. The desired behavior is obtained from linear circuit elements as shown in
Figure 25. The voltage controlled current source G and capacitor CB integrate the
applied voltage to produce an output voltage proportional to the flux at node 3. The
voltage controlled voltage source E isolates the integration elements from subsequent
stages. The current out of E is the inductor current which, when unsaturated, is
determined by resistor RB. This current drives the current controlled current source F
which produces the inductor's terminal current. Element F isolates the model's circuitry
from the inductor terminals. When the current through RB exceeds the inductor
saturation level, the voltage across the resistor is high enough to exceed VP and VN and
forward bias diodes D1 and D2. The subsequent saturation current is determined by RS.
Frequency dependent losses are modelled by the parasitic capacitance across diodes D1
and D2. That capacitance, viewed through the integration network, is seen as a frequency

dependent resistance.

 

 

 

 

 

 

 

 

Figure 25. Circuit model for saturating inductor

41

Since voltage out of the LC filter is of primary interest, the drive inverter and motor
were not directly modelled. Instead, a series resistor and inductor provides an equivalent
load representing the 5 hp motor's mechanical output and leakage inductance. Two of the
quantities of interest from the simulation results are input and output voltages for the LC
filter (V l and V2 in Figure 23) to evaluate the effectiveness of the filter and whether the
inverter dc over-voltage limit is exceeded. The other quantity of interest is the inductor
current (I in Figure 23) during the transient to determine if the diodes are damaged or

over-current pl‘OICCLIOI‘l operates.

5.2 Simulation Results

The results of three cases are presented with different LC inductor operating modes:

linear operation, saturation, and no inductor.

5.2.1 Drive with Linear Inductor

The results of the first case to be considered with the drive fully loaded and a linear
inductor in the LC filter are shown in Figures 26 and 27. The input voltage to the LC
filter exceeds 400 V yet the output Shows little effect of the transient. Scaling down from
480 V drives, the typical dc trip level to protect the inverter would be 380 V. Over
voltage protection would not be actuated in this case. There is a low frequency
oscillation apparent in both the filter output voltage and the inductor current. This
oscillation is due to the interaction of the filter capacitor and inductor which have a
combined resonant frequency of 70 Hz. The 70 Hz voltage component does not appear at

the ac source but does appear at the motor.

42

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 27. Inductor current with and without transient

 

 

J
400 ‘
350 ' A
111 ”‘ '
x“
g , ./ l I/ :4
_I 300 -
O . V
> .
‘ FILTER
250 .. _ INPUT
‘ FILTER
: .......... OUTPUT
200 . . . r A t t
0.01 0.015 0.02 0.025 0.03
TIME (SEC)
Figure 26. Filter transient voltage response with linear inductor
40
- WITH
- _ TRANSIENT
- A WITHOUT
A 30 “' '°' " TRANSIENT
(I) .
CL .
E .
5 20
w it
E I “I":
D i
0 th. :: ! 3’3“?)
10 . — f, g . j" in. .r \
- fig. . 2' ‘
o d I I I I I I I I r j I I I I f I
0.01 0.015 0.02 0.025 0.03
TIME (SEC)

43
To better demonstrate the effect of the transient, the inductor current graph shows the

current with and without the transient. The capacitor switching transient at 17 ms shows
a corresponding 8 A transient current. Since ac input current for the drive is about 14 A
at full load, the peak would not cause over-current protective devices to trip the drive.
However, because the filter capacitor acts as a short circuit at the u'ansient frequency, the

magnitude of that transient current is entirely dependent on the filter inductor. The

transient current would be
V
i = — 24
' coL ( )

where V is the transient voltage (80 V in this case) at the transient frequency (0 (450 Hz).
For the above simulation, 1'; would be 8.4 A which agrees with the results. If the LC filter
were designed for a higher ripple than the Vee Arc, the inductor would be smaller and the
current transient would be larger. Depending on the ac over-current devices utilized, the

resulting transient current could trip the feed to the drive.

5.2.2 Drive with Saturating Inductor

The next case examines the consequence of designing the filter inductor to Operate
just below saturation at full load. A transient voltage applied to the inductor could
readily force the core into saturation. An inductor was created with the Intusoft model
with the resulting magnetization characteristics at the transient frequency (450 Hz) shown
in Figure 28. The vertical axis is relative flux density and the horizontal axis is inductor
current. The inductor core is assumed to be United States Steel M19 transformer iron
with a saturation flux density of 1.0 T. The actual inductor has 20 cm2 core area and 64

turns. The saturation level of the inductor was adjusted by varying the number of turns.

300

 

I

200

 

\
\

100

 

 

8
'\

 

 

RELATIVE FLUX DENSITY
o
\
\ \

1b
8
'\

 

 

1111

 

 

 

 

 

 

-00
3 IIII IIIleIIIlIIII IIII IITT

-120 -80 -40 0 40 80 120
CURRENT

Figure 28. SPICE inductor B/H curve

The simulation result for the LC filter input and output voltages are shown in Figure
29. In this case the peak filter output voltage is 385 V and the over-voltage protection
limit of 380 V is exceeded for 500 us. The drive will trip because the voltage applied to
the inverter section exceeds the over-voltage protection limits for magnitude and
duration. Furthermore, since the capacitor voltage exceeds the peak LC filter input
voltage, the transient voltage integrated across the filter capacitor. As described in
Chapter 3, with the inductor saturated, the filter acts as a RC integrating network. The
peak dc voltage is still less than the peak three phase transient voltage of 420 V (see
Figure 24).

45

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

400
350 . 2; M
g 3*“ . j I
75 300:
5 1
> I
250 ' _ FILTER .
. INPUT
: FILTER
.4 m OUTPUT
200 . . . . . . . . . . =|=v—u——=—r—
0.01 0.015 0.02 0.025 0.03

TIME (SEC)

Figure 29. Filter transient voltage response with inductor saturation

The inductor current is shown in Figure 30 to peak at 148 A as a result of the
transient. With the inductance reduced to almost a tenth of its non-saturated value, a very
low impedance is presented to the voltage transient. The magnitude of the current

transient is sufficient to operate over-current protection or damage diodes.

46
1 50

 

1111
g

125

 

 

é

 

11JJ

 

CURRENT (AMPS)
V
0'!

 

 

 

 

 

 

 

 

 

50 .
I;
25 j
0 1 I I I fi r I I I f I IAr
0.01 0.015 0.02 0.025 0.03
TIME (SEC)

Figure 30. Inductor transient current with saturation

At light load the inductor current is reduced and the capability to operate with
transient voltages without saturating is improved. Shown in Figure 31 are the LC filter
input and output voltages with the same applied capacitor voltage transient except the
drive is operating at 10% load. There is a slight increase in filter output voltage as the
capacitor is charged to a greater voltage but not sufficient to interfere with drive
operation. The 70 Hz oscillation is absent is this case because the diodes are not

conducting continuously at light load.

47

 

 

 

 

 

 

 

 

 

VOLTAGE
OJ
8

 

 

 

 

 

 

 

 

 

 

 

FILTER
250 — INPUT
: FILTER
2m I I I I I I I 1 I I
0.01 0.015 0.02 0.025 0.03
TIME (SEC)

Figure 31. Filter transient voltage response with saturable inductor at light load

5.2.4 Drive with No Inductor

The last case to be considered is a drive with no filter inductor. The inductor is
sometimes omitted in small drives to decrease cost. Although none of the field tests
involved such a drive, they are sufficiently common to merit examination. Here, the filter
input and output voltages are identical since there is only a shunt filter capacitor. Figure
32 shows the capacitor voltage as a result of the transient with other conditions identical
to the previous cases. As in previous cases, the filter capacitor and parasitic resistances
behave like an RC integrating network for the transient voltage. The dc voltage peaks at
420 V which is the magnitude of the three phase transient peak and more than enough to

operate the inverter over voltage protection.

48

 

 

 

 

 

 

 

 

 

 

 

400 l‘
350 l
w 3 \/\l
2 W
5 300 '
O I
> a
,
250
200 - I I I I fi T j I I I I I j j I I
0.01 0.015 0.02 0.025 0.03
TIME (SEC)

Figure 32. Filter transient voltage response without an inductor

The resulting dc current is shown in Figure 33. Since the filter capacitor presents a
very low impedance to the transient frequency, the source impedance determines the
resulting transient current. In this case it is very high and could operate over current
protection or damage diodes. A drive without the filter inductor is very vulnerable to

over voltage and over-current problems due to capacitor switching transient.

49

 

 

 

CURRENT (AMPS)
a
o

 

 

 

 

 

 

 

 

 

. I 1 . . .
0.01 0.015 0.02 0.025 0.03
TIME (SEC)

 

Figure 33. Filter transient current without an inductor

5.3 Comparison with Experimental Results

The simulation results from the previous sections are now compared to the
experimental results from Chapter 4. The linear and saturated inductor simulations are
compared to the results form field and laboratory tests. Since there were no tests of

drives without a LC filter inductor, this simulation case is not compared.

5.3.1 Drive with Linear Inductor

If the linear inductor drive simulation results are compared with gantry drive results
and the Vee-Arc laboratory test results, the dc transient voltage at the LC filter output is
similar. The results from the gantry and Vee-arc drives are repeated here for the

convenience of the reader in Figures 18 and 22. The 70 Hz voltage oscillation present in

SO

 

 

 

 

300 '
Drivedc
0 1
go aclnput
g 700‘
.m l
0 20 40 00

Time (ms)

Figure 18. Gantry drive transient waveforms

the simulation output is absent from the experimental results. However, the gantry and
Vee-Arc drives were tested at light load and the simulation showed that the 70 Hz
oscillation is absent when the diodes are not continuously conducting at light load. If the
experimental results are compared to the simulated light load case (Figure 31), the results
are identical. The increase in filter output voltage is greater in the simulation than the
laboratory test of the Vee-Arc drive. This may be because the voltage transient was only
applied to one phase in the laboratory test whereas it was applied to all three phases in the

simulation.

5.3.2 Drive with Saturating Inductor

The simulation of a drive with a saturating filter inductor tested the hypothesis that

saturation was responsible for the observed response of the grinder drive from the field

investigation to the capacitor switching transient. The DC filter output dc voltages for the

1000

500

Voltage

 

51

Filter Output

I

 

Rectifier Output

1

I

 

ac Input
1

l l l

8 16 24 32

Time (ms)

Figure 22. Laboratory test response of PWM drive

52
50 hp grinder drive and the corresponding simulation are repeated here in Figures 19 and

29. The simulation verified that when the voltage transient forces the filter inductor into
saturation, the LC filter effectively passes the transient to the inverter section. After the
dc peak voltage was reached in the simulation, the voltage quickly decayed to normal.

For the actual drive, the over-voltage protection immediately trips the inverter and the

peak dc voltage decays over a much longer time.

 

 

 

”‘JA
Drivedc
D
.5.“ °‘
o
> acInput
m ‘m
.m a
0 fl ‘0

Time (ms)

Figure 19. Grinder drive ac and dc transient waveforms

53
400

 

1 1 1 1

Ni

350

 

 

 

V5»
‘00...» ‘ to.

#1
‘5'
mm"! “A

 

 

 

 

 

VOLTAGE
o)
o
o

 

 

1411'

 

 

 

 

 

 

250 _ FILTER
.. INPUT
: FILTER
. W OUTPUT
200 I I I I I I I I I i
0.01 0.015 0.02 0.025
TIME (SEC)

Figure 29. Filter transient voltage response with inductor saturation

 

 

 

0.03

CHAPTER 6
MITIGATION

There are three approaches to mitigating capacitor switching transient problems. The
first is to reduce the magnitude of the transient at the utility capacitor that is switched.
The second is to design the drive with the necessary characteristics to reduce
susceptibility to the transient. Third, is to add a filter ahead of each drive to reduce the
magnitude of the transient. The method selected depends on whether the issue is
addressed at the equipment design, selection, or operating stage. Each of the methods is

considered separately.

6.1 Utility Switching Options

The utility can reduce the magnitude of the transient with different capacitor
switching methods. As utility capacitor banks increased in size in the 1950's and restrikes
became an increasing problem, a common method of reducing the switching transient
was to use pre-insertion resistors. These resistors were momentarily placed in series with
the capacitor as the switch was closed and shorted afterwards to reduce losses (see Figure
34). However, situations where the capacitor bank was frequently switched (such as for
testing) sometimes exceeded the thermal duty cycle rating of the resistors and caused
failure. The development of special purpose capacitor switchers that eliminated the

restrike problem eliminated as well the need for the resistors.

54

 

Switch A Closes After Switch B

Figure 34. Operation of pre-insertion resistors

As the effect of the low level capacitor switching transients on equipment became
apparent to utilities. they sought a solution with readily available equipment. One
inexpensive solution was the pre-insertion inductor developed to prevent the capacitor
bank inrush current for large banks from exceeding the switch capability. This device
operated in the same manner as the pre-insertion resistor without the thermal problems.
Rather than increase damping, the inductor shifts the transient frequency away from the
resonant frequency of the intermediate networks that propagate the transient. As utility
experience has shown, the change in transient frequency may not be sufficient in all cases
to eliminate tripping of drives. The pre-insertion inductors for 40 kV capacitors are 3 ml!
and cause the greatest frequency change on low impedance networks. For the network
feeding the automotive plant discussed in the field investigation, the pre-insertion
inductor would decrease the resonance frequency by 15 % from the calculated value of
525 Hz. Clearly, pre-insertion inductors do not completely eliminate the problems due to

capacitor switching for the utility

Although more expensive and not available for all voltage classes, a complete
solution is offered by the synchronous capacitor switcher. This device closes the three

phases separately with a vacuum switch as the voltage crosses zero almost eliminating the

56
transient. The resulting transient can be calculated from equation (1) by adding the

closing angle, T, in the differential equation and solving for the capacitor voltage.

di . 1‘.
E cos((ut- r): 1.5+ Rl +Ejzd: (25)

 

 

(Cu), cos (out - a), sin 0),,t)
(26)

E Sin((Dt-9-‘C)+ ' 7’
Z C [(Cmn )2 + (”42] Z

__l_(cosr _ msin(6 + T) _ £0), cos(6 + r)
a), L Z Z

v _ E 6“" [cos(6 + T)

 

 

)(Cco, sin a); + and cos (out)

For example, a synchronous switch installed at the east utility station from the field
investigation would produce the transient shown in Figure 35 plotted from (26). The
plotted closing angle is 0.3 ms later than the voltage zero crossing which is the switch
manufacturer's specified tolerance for operation. Such a device would reduce the

capacitor switching transient to such a low level, that it would no longer be a problem.

1.5

 

A

\
7/

 

.0
on

 

 

5'3
01

 

\_/

I I r T I

0.006 0.012
TIME (SEC)

I
-l

 

 

CAPACITOR VOLTAGE (PU)
o
\

 

 

 

 

l
_L
C
0‘
d
1
d
d

 

0

Figure 35 Utility capacitor voltage with synchronous closing

57

6.2 Drive Design Options

It is possible to design the drive to reduce susceptibility of the capacitor switching
transient. The most important design factor in the performance of the drive is the filter
inductor capability. The results of the drive simulation in Chapter 5 demonstrate how the
inductor affects transient voltage and current. If the inductor is present and does not
saturate, the transient voltage and current are limited to reasonable levels that should not
cause the drive to malfunction. If the inductor saturates during the transient, the transient
voltage integrates across the filter capacitor until it exceeds the dc over-voltage trip
threshold. The resulting transient current may operate over-current protection or damage
diodes. If the filter inductor is omitted, the same over-voltage and over-current problems

exist. The inductor should be designed according to equation (23) which is repeated here.

I 4.44mRACN-10"8

8

B

 

(23)

The inductor dc current, Idc, should be the maximum expected under maximum load
and low ac voltage conditions. The ripple voltage, VR should perhaps be assumed to be a
maximum of l pu of the nominal ac voltage at the ripple frequency. From (23), the core
area, Ac, affects the ripple voltage capability without changing the dc flux density. By
selecting the appropriate core area, the vulnerability of the drive to the capacitor

switching transient can be minimized.

6.3 Transient Filters

There are situations where a susceptible drive is already in use and the source of the

capacitor switching transient is unalterable. In this case a filter may be added to the drive

58
in the form of an ac reactor ahead of the drive. Unlike noise filters with cut off

frequencies of approximately 10 kHz, this reactor must filter frequencies that closely
correspond to harmonic current frequencies of the drive. To prevent excessive insertion
loss, the reactor must be customer engineered for the drive and sized from 2 % to 3 % of

the drive base impedance.

To illustrate, a SPICE simulation was conducted with ac reactors, designated LR,
shown in Figure 36. These were sized to 2% impedance which corresponds to 562 (1H
and are between the transient voltage source and the drive The transient voltage into the .
drive terminals from the simulation is shown in Figure 37. The transient magnitude has
been reduced especially at the voltage crests where diode conduction occurs. However,
the voltage waveform has been flat-topped by the reactors. Since diode conduction
occurs at the voltage crest, the corresponding voltage drop across the reactors causes the
flat-topping. As a result of the flat-topping, the drive is operating at reduced voltage,

which reduces the drive's capability to withstand momentary voltage sags without

 

 

 

 

 

tripping.
RL L1 RLOAD
RSX LSX VCX LRX '
X 0 RC
® Y Rsy LSY VCY LRY
O
L Z
N 2 R82 8 VCZ LRZ C1
LLOAD

Figure 36. SPICE model with ac reactors added

59
400

 

 

 

VOLTAGE Vab
lb
0
o

 

 

 

 

 

 

 

 

 

 

VOLTAGE Vbc
lb
8

 

 

 

 

 

 

 

 

 

 

VOLTAGE Vca
I6
0
O

 

 

 

 

 

 

 

‘400 d I I r I I T f I I I I I I I I I
0.01 0.015 0.02 0.025 0.03
TIME (SEC)

Figure 37 . Three phase transient voltage at drive with ac reactors

60
Two SPICE simulations were run to determine the effect of the ac reactors to protect

the drive from the capacitor switching transient. The first was the fully loaded drive with
saturating filter inductor and the second was a fully loaded drive without a filter inductor.
The drive dc voltages and currents as a result of the transient are shown in Figures 38
through 41. In each case the dc voltage entering the inverter was well below the over-
voltage trip threshold and transient currents were below levels that could cause damage to

the drive.

 

400

 

350 "

 

 

 

 

 

 

 

 

VOLTAGE
(A)
8
>
is

 

 

 

 

 

 

 

 

 

. ' J V
I FILTER
25° . — INPUT
7 FILTER
1 ........ OUTPUT
200 . . . . . . . . . .
0.01 0.015 0.02 0.025 0.03
TIME (SEC)

Figure 37. Filter transient voltages with a saturable dc inductor and ac reactor

8 8 8 8

CURRENT (AMPS)

.5
o

0

I
0.01

Figure 39. Drive dc current with saturable dc inductor and ac reactor

400

350

VOLTAGE
on
o
o

250

200

61

 

1111

 

1111

 

 

 

 

 

 

 

1111

 

/‘

N

 

NM

 

V

 

V

 

I.

 

 

I I I I I

0.015

I r I

TIME (

0.02

' ' (1025'
SEC)

0.03

 

 

4L11

\J

\\

 

1 1 1 1

 

1 1 1 1

 

 

 

 

 

 

0.01

0.015

I I I

TIME

0.02

I I

(SEC)

I I

0.025

0.03

Figure 40. Drive dc transient voltage with ac reactor and no dc inductor

62

 

 

 

 

 

 

 

 

 

 

 

75

If 50

5 .

S,

F 1

Z .

UJ

m -I

g 25 A I‘

O ..
o I I I I I I I I i l 1 T I I I I I I I l
0.01 0.015 0.02 0.025 0.03

TIME (SEC)

Figure 41. Drive dc current with ac reactor and no dc inductor

 

CHAPTER 7
CONCLUSIONS

The preceding analysis, experimentation, and simulation explored how ac drives with
uncontrolled rectifiers respond to the capacitor switching transient. It also addresses how
the transient is generated at the utility capacitor and propagates to the drive. The results

may be summarized by the following:

0 Due to the low value of damping inherent in utility systems, the peak value of the
capacitor closing transient is always near the maximum theoretical value of 2 pu at

the capacitor bus.

0 The transient propagates only if the transient frequency is within the bandwidth of the

successive voltage step-down networks.

- PWM drives can be disrupted by the transient either by dc over-voltage at the inverter
input or by a current surge through the drive filter capacitor. The over-voltage
triggers an over-voltage trip to protect the inverter transistors. The current surge can

operate over-current devices or damage diodes.

0 A properly designed filter inductor that does not saturate during the transient
minimizes susceptibility of the drive. If the inductor saturates during the transient,
the transient voltages integrates across the filter capacitor. If the filter inductor has
been omitted from the drive, the filter capacitor operates in a similar manner. In both
cases, a large current surge is generated by the filter capacitor as a result of the

voltage transient.

63

64
The most effective method to reduce the magnitude of the transient at the utility

capacitor is to use synchronous switchers that close each phase separately at the

voltage zero-crossing.

A less desirable method is to add ac reactors ahead of the drive to filter the voltage
transient. Although these reduce the transient at the drive, they also cause flat-
topping of the ac voltage which increases the drive susceptibility to under-voltage

problems.

APPENDD( A

APPENDIX A

 

 

 

 

 

SPICE MODEL
XL VI
13 BL 15 16 . 17 RL
RSX LSX VCX
4 7 10
1 O RC "
2 RSV 5 LSY a 11
L82 OVCY 18 19
o 3, 5,32, 5nn9012 C1
VCZ -

Figure 42. SPICE PWM drive circuit with node numbers

Table 5. SPICE PWM drive circuit data

PWM CAP SWITCHING TRANSIENT RESPONSE
'LAST NODE: 20

' 9/19/92 - full load

'INCLUDE DIODE.LIB

'INCLUDE SIGNALLIB

‘INCLUDE DEVICE.LIB

'OTHER THAN LIMPTS. THESE OPTIONS AID PWR ELECTRONICS SOLUTIONS
.OPT ABSTOL=1UA VNTOL=1 UV LIMPTS=505 METHOD=GEAR RELTOL=.OG ITL4=500
+ ITL5=14000

.TRAN 0.2MS SOMS 5M8 0.05MS UIC

.PRINT TRAN V(13,14) V(18,14) I(V|), V(20,16)

65

66
Table 5 (cont'd)

'3-PHASE VOLTAGE SOURCE SUBCIRCUIT CALL

XV3 1 2 3 0 GEN3 {VGEN=196 FREQ=60 MAGERR=0 PHASE=0}
'THIS ADDS THE CAP SWITCH TRANSIENT

VCX 7 1O SIN 0V 80V 450HZ 17MS 125

VCY 8 11 SIN 0V ~40V 450HZ 17MS 125

VCZ 9 12 SIN 0V -40V 450HZ 17MS 125

VI 16 17

'RDUMMY CONNECTS THE NEUTRAL WHICH IS NOT USED IN THE DRIVE
RDUMMY 2 0 1K

D1 10 13 DN3495

D2 11 13 DN3495

D3 12 13 DN3495

D4 14 1O DN3495

D5 14 11 DN3495

06 14 12 DN3495

'CAPACITOR WITH LOSSES (RC)

C1 18 14 0.0015 IC=310V

RC 17 18 .05

‘NONLINEAR INDUCTOR CALL WITH LOSSES (RL)

'RLD CONNECTS THE FLUX TEST POINT

XL 15 16 20 CORE {VSEC=.130 IVSEC=.OOO LMAG=3.36MH LSAT=43UH FEDDY=1 KHZ}
RL 13 15 .041

RLD 20 16 100K

'THIS SIMULATES MOTOR THRU THE DRIVE INVERTER

RLOAD 17 19 22

LLOAD 19 14 29.1MH IC=10A

67
Table 5 (cont'd)

“SOURCE IMPEDANCE
RSX 1 4 2.56M

RSY 2 5 2.56M

RSZ 3 6 2.56M

LSX 4 7 0.02MH IC=0A
LSY 5 8 0.02MH IC=-1OA
LSZ 6 9 0.02MH IC=1OA
.END

 

 

 

 

 

V1

 

 

 

 

 

 

 

1 (2)

Figure 43. SPICE three-phase voltage source GEN3

Table 6. SPICE three-phase voltage source GEN3 data

'SYM=GEN3

.SUBCKT GEN3 3 7 1 20

'3 PHASE GENERATOR

* FREO = {FREQ}

° AMPLITUDE .. (VGEN)

C1 2 20 {1/(6.28319K‘FREQ)} IC={VGEN}
R1 2 20 1E6

I1 20 2 PULSE {VGEN‘1U}O

' MAKES UIc UNNECESSARV
E1 5 20 20 2 1

V1 3 2o SIN o {VGEN} {FREQ}

 

68
Table 6 (cont'd)

E2 7 20 POLY(2) 5 2o 3 20 o -866.00M -500.00M

E3 1 20 POLY(2) s 20 3 20 o

+ {(1+.o1'MAGERR)°(.366'(1-.5'(.0174533*PHASE)Az)-
.5'.0174533‘PHASE'(1+.166667'(.0174533*PHASE)"2))}
+ {(1+.01'MAGERR)'(-.5'(1-.5'(.O174533'PHASE)’\2)-
.866'.0174533‘PHASE‘(1+.166667‘(.0174533‘PHASEY‘2))}
G1 20 2 20 a 1M

R2 7 o 100MEG

R3 1 o 100MEG

R4 3 o 1OOMEG

R5 5 o 100MEg

.ENos

 

 

 

 

 

 

 

 

VM1 5 RS DI 6
Figure 44. SPICE nonlinear inductor model CORE

Table 7. SPICE nonlinear inductor model CORE data

‘SYM=CORE

'PARAMS ARE

‘ VSEC, VOLT-SEC CORE CAPACITY (23m)

' IVSEC, INITIAL CONDITION

' LMAG, MAGNETIZING INDUCTANCE

" LSAT, SATURATION INDUCTANCE

' FEDDY. FREQUENCY WHEN LMAG REACTANCE = LOSS RESISTANCE

' EXAMPLE CALL

‘ XCORE1 5 6 7 CORE {VSEC=50U IVSEC=-25U LMAG=10MHY LSAT=20UHY

69
Table 7 (cont'd)

+ FEDDY=20KHZ}

.SUBCKT CORE 1 2 a

RX 3 2 1 E12

' EXAMPLE MAKES CB=1E-7. IC=-250

ca 3 2 (VSEC/soo) IC={IVSECNSEC'500}

F1 1 2 VM1 1

G223121

E142321

VM145

° EXAMPLE MAKES Re=1ooK

Re 5 2 (LMAG‘SOONSEC}

RS 5 6 {LSAT‘SOONSEC}

* EXAMPLE MAKES RS=200

VP 7 2 250

D1 6 7 DCLAMP

VN 2 a 250

02 a e DCLAMP

'EXAMPLE MAKES CJO=238PF, MULTIPLIER 3 AND VJ=25 GO TOGETHER
.MODEL DCLAMP D(CJO={3'VSEC/(6.28'FEODY‘500‘LMAG)} VJ=25)
.ENDS

LIST OF REFERENCES

[1]

[2]

[3]

[4]

[5]

I6]

[7]

[8]

[9]

[10]

[11]

LIST OF REFERENCES

IEEE Committee Report, "Bibliography on Switching of Capacitor Circuits
Exclusive of Series Capacitors,” IEEE Transactions, PAS, Vol. 89, No. 6, pp
1203-1207, Jul/Aug 1970.

V. E Wagner, I. P. Staniak, and T. L. Orloff, ”Utility Capacitor Switching and
Adjustable Speed Drives," IEEE Transaction on Industry Applications, Vol. 27,
No. 4. pp. 645-651, Jul/Aug 1991.

G. T. Hensley, T. Singh, M. Samotyj, M. McGranaghan, and R. Zavadil, ”Impact
of Utility Switched Capacitors on Customer Systems, Part I - Magnification at
Low Voltage Capacitors," IEEE Transactions on Power Delivery, Vol. 7, No. 2,
pp. 862-868, Apr 1992.

M. McGranaghan, T. E. Grebe, G. T. Hensley, T. Singh, and M. Samotyj, "Impact
of Utility Switched Capacitors on Customer Systems, Part II - Adjustable Speed
Drive Concerns," IEEE Transactions on Power Delivery, Vol. 6, No. 4, pp. 1623-
1628, Oct 1991.

AN SI/IEEE Standard €62.41, IEEE Recommended Practice on Surge Voltages in
Low-voltage AC Power Circuits, 1991.

H. M. Planz and G. N. Lester, ”Control of Overvoltages on Energized Capacitor
Banks," IEEE Trans. Power App. Syst., Vol. PAS-92, No. 3, pp. 907-915,
May/Jun 1973.

W. S. Vilcheck and D. A. Gonzalez, ”Guidelines for Applying Shunt Capacitors
on Industrial Power Systems," presented at IEEE Ind. Comm Power Syst. Conf.,
Denver, CO, 1986.

J. Zaborszky and J. W. Rittenhouse, "Fundamental Aspects of Some Switching
Overvoltages on Power Systems," AIEE Trans. Power App Syst., Vol. PAS-81,
pp. 815-822, Feb 1963.

A. J. Schultz, K. B. Johnson, and N. R. Schultz, ”Magnification of Switching
Surges," AIEE Trans. Power App Syst., Vol. PAS-77, pp. 1418-1425, Feb 1959.

“9.8;. McLayman, Transformer and Inductor Design Handbook, Marcel Dekker,
1 .

D. L. Rumsey, "A Saturing Transformer Model for SPICE,” Proc 15th Intersoc
Energy Convers Eng Conf, Vol 1, Seattle WA, pp. 95-99, 1980.

70

"IIIIIIIIIIIIIIIIIIII