EVALUATION OF SHUNT CAPACITOR SWITCHING IN POWER
SYSTEMS USING THE ELECTROMAGNETIC
TRANSIENTS PROGRAM
by
Jeffrey David Selman
B.S., Pennsylvania State University, 1974
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado at Denver in partial
fulfillment of the requirements for the degree of
Master of Science
Department of Electrical Engineering
and Computer Science
1990
This thesis for the Master of Science degree by
Jeffrey David Selman
has been approved for the
Department of
Electrical Engineering and Computer Science
by
William R. Roemish
Marvin F. Anderson
Date
Ill
Selman, Jeffrey David (M.S., Electrical Engineering)
Evaluation of Shunt Capacitor Switching in Power Systems Using the
Electromagnetic Transients Program
Thesis directed by Associate Professor Pankaj K. Sen
When a high voltage shunt capacitor bank is energized alone, or a bank is
switched with a parallel bank in service, voltage and current transients are produced
which can affect the bank and the connected power system elements. These
transients may damage equipment due to their high magnitudes and frequency
determined by the rise time. It is, therefore, necessary to be aware of Basic Lightning
Impulse Insulation Levels (BIL) and Basic Switching Impulse Insulation Levels
(BSL) which define allowable levels of overvoltage to avoid damaging insulation in
transformers and other equipment.
The main purpose of this thesis is to discuss, in detail, complex shunt
capacitor switching problems. A PC version of the Electromagnetic Transients
Program (EMTP) is used to provide numerical solutions. Methods of reducing the
magnitudes and frequencies of voltage and current transients are also discussed.
Two case studies are discussed: (1) energization and restrike of a single,
isolated capacitor bank and (2) backtoback switching of adjacent shunt capacitor
banks.
The form and content of this abstract are approved. I recommend its publication.
Sign
CONTENTS
ACKNOWLEDGMENTS......................................................vi
CHAPTER
I. INTRODUCTION....................................................1
Review of Literature..........................................2
H. EMTP SIMULATION AND MODELLING TECHNIQUES........................6
Brief History.................................................6
Numerical Solution Techniques and Uncoupled Linear Elements...6
System Equivalents (Linear Coupled Elements).................10
Transmission Lines...........................................12
Transformer Models...........................................26
Surge Arresters..............................................36
Switches.....................................................41
EMTP Input Data Structure....................................41
m. THEORY AND SYSTEM MODELLING......................................45
Case 1 System Model..........................................45
Case 2 System Model..........................................50
Representation of Stray Capacitance..........................53
Circuit Switcher Representation..............................56
Deenergization and Switch Restrike..........................59
Methods of Reducing Transients...............................62
Surge Withstand Standards and Insulation Coordination........66
V
IV. DIGITAL SIMULATIONS, ANALYSIS, AND RESULTS................72
Selection of Time Step (At).............................72
Analysis and Results Case 1...........................73
Numerical Oscillations.................................103
Analysis and Results Case 2..........................107
Bypass of Preinsertion Impedance......................123
V. SUMMARY AND CONCLUSION...................................125
APPENDIX
A. SYSTEM PARAMETERS, CALCULATIONS, AND
INPUT DATA FOR CASE 1...................................128
B. SYSTEM PARAMETERS, CALCULATIONS, AND
INPUT DATA FOR CASE 2..................................141
REFERENCES
148
VI
ACKNOWLEDGMENTS
This thesis is submitted to the University of Colorado at Denver as the final
requirement for the Master of Science Degree in Electrical Engineering. The work
could not have been completed without the cooperation and assistance of several
people.
I especially wish to thank my academic and thesis advisor, Dr. Pankaj K. Sen,
Associate Professor of Electrical Engineering and Computer Science at the University
of Colorado at Denver, whose clear and practical thinking are always the best
encouragement and whose efforts have made the Electric Power Engineering
Graduate Program at UCD a worthwhile pursuit.
I am also grateful to the following people for their support and assistance with
the EMTP/ATP software used to run the simulations: Drs. Tsuhuei Liu and W. Scott
Meyer of The Bonneville Power Administration, Portland, Oregon; Robert Zavadil
of Electrotek Concepts, Knoxville, Tennesee.
I would also like to thank Terry Belei and Ray OLeary of the S & C
Company, Chicago, Illinois, for providing technical information on the circuit
switching devices discussed and simulated in the case studies.
Finally, I wish to thank Trina Van Patten of TriState Generation and
Transmission Association, Denver, Colorado, for creating the illustrations and
providing the necessary graphics support.
CHAPTER I
INTRODUCTION
There are a number of concerns associated with the application of shunt
capacitor banks on a transmission system, namely: voltage magnification at remote
capacitor banks, voltage magnification and high frequency transients at transformer
terminals remote from the switched capacitor, surge arrester duties, inrush current for
backtoback switching (energization of a second bank while the first adjacent bank is
already energized).
The case of energizing a capacitor bank radially at a remote location from a
transformer is of special interest. Transient voltages may be seen at the transformer
terminals, caused by the travelling waves on the transmission line between the
transformer and the remotely switched capacitor. Despite the fact that surge arresters
are usually located at line and/or transformer terminals and will limit the peak lineto
neutral overvoltage of the transient, certain high frequencies can excite internal
resonances of the transformer winding sections resulting in internal voltage
magnification and tumtotum failure [1]. In addition, restriking (arcing over
following deenergization) of the capacitor switching device can cause high
magnitude/ffequency voltage transients due to the trapped charge left on the capacitor
bank.
The backtoback switching of capacitor banks results in a high frequency
inrush current which flows between the banks. This transient current does not usually
contain sufficient energy to cause damage to high voltage equipment, but may cause
2
nuisance clearing of individual capacitor can link fuses.
In both cases of capacitor switching, devices such as preinsertion resistors
and preinsertion inductors, which are mounted on the switching device, and current
limiting inductors hardwired in the bus (in series with each phase of the capacitor
bank) are available to minimize the severity of the transients. Severity of transients is
measured by magnitude, frequency, and rise time of voltage/current. High rateof
rise of voltage (dv/dt) can damage insulation in transformer windings.
The intent of this thesis is to first model the capacitor switching scenerios as
accurately and in as much detail as possible, and secondly to demonstrate that the
devices previously mentioned can effectively reduce the severity of the transient
voltages and/or currents.
Review of Literature
The case of energization and restrike of a single, groundedwye capacitor
bank with an autotransformer connected to the remote end of a transmission line
emanating from the capacitor bank bus was examined in [1]. Of particular interest is
the voltage waveform at the transformer terminals when energization/restrike of the
remote capacitor bank takes place.
The purpose of the study was to determine the cause of a tumtotum failure
in one of the series winding sections on one phase of the remotely connected
autotransformer. Restriking of an oil circuit breaker not rated for capacitor switching,
connected in series with the capacitor bank circuit switcher which false tripped was
suspected. EMTP was used to run the simulations on a mainframe computer. The
transmission line connecting the capacitor bank to the transformer was modelled with
frequency dependent parameters. A simplified transformer model was used for the
first run to get the voltage waveform. A detailed, distributed LC, 7winding section,
single phase transformer model was built for a separate EMTP simulation with the
3
known design parameters. Using the frequency scan option in EMTP, the natural
resonant frequency of the transformer model was determined to be in the vicinity of 5
to 6 kHz depending on the values used for stray capacitance from winding to tank.
An actual frequency scan was also performed on the physical transformer with the
core and coils out of the tank. The resonant frequency was measured to be 8 kHz,
indicating that the stray capacitance has a significant effect. When the semi
oscillatory transient voltage waveform caused by the capacitor bank energization/
restrike was injected at the terminal of the transformer model, an internal voltage
magnification occurred in the subject winding section on the order of 3.5 per unit.
The transient voltage is actually higher when superimposed on the steady state 60
cycle voltage. Exciting this internal natural frequency has been called partwinding
resonance.
No further studies of this case were run to examine methods of reducing the
magnitude and frequency of the transient voltage seen at the transformer location.
Discussion of the paper by a major manufacturer of high voltage switching devices
makes reference to preinsertion resistors and inductors and permanently installed bus
inductors as methods of transient voltage reduction.
A second capacitor switching scenerio was also examined in [1]. This case
involved a tumtotum winding failure of a deltaconnected phase shifting
transformer remotely connected from the capacitor location. Again, travelling
voltage waves appeared on the line as a result of energizing the capacitor bank. What
was unique about this case was the fact that peak transient voltages of opposite
polarity on two different phases arrived at the transformer terminals at the same time.
Even when limited to 2.0 per unit phase to ground by surge arresters, 4.0 per unit
voltage appeared across one of the deltaconnected windings which exceeded the
basic switching impulse insulation level (BSL) of the transformer and caused a
4
winding failure. In this particular case, field measurements of the voltages appearing
at the transformer location were taken and compared extremely well with digital
simulations from EMTP. As in the first case, frequency dependent parameters were
used to model the transmission line connecting the capacitor bank to the transformer.
60 and 1000 ohm preinsertion resistors as well as 2.5 ohm (6.63 mH) bus inductors
were studied as effective methods of reducing the transient voltages.
Cases involving the energization of an isolated capacitor bank and the
resultant transient voltages at a remote location were also examined in [2]. A
comparison between the effects on transient voltage reduction using a 40 ohm pre
insertion resistor versus a 10 mH preinsertion inductor was illustrated in detail.
Cases of energizing ungrounded shunt capacitor banks versus grounded shunt banks
were examined as was synchronous closing (controlled energization at or near voltage
zero) for both cases. Also of special interest, variation of system parameters such as
capacitor size, number of transmission lines connected to the capacitor bank bus,
length of the transmission line between the capacitor bank and the bus of interest, and
the effects of load were examined.
Reference [3] deals specifically with the subject of synchronous closing as
applied to backtoback switching of adjacent capacitor banks. It was demonstrated
by field measurements that an electronic control scheme which senses voltage zero
crossings could be used to effectively reduce the transient voltage and inrush current
when the second capacitor bank is energized.
The classical problem of backtoback switching of capacitor banks as well as
solutions to the problem are discussed and demonstrated in [4]. These solutions
include the use of a 35 ohm preinsertion resistor and several values of current
limiting bus inductors. Two unique scenerios were also examined: outrush current of
an energized capacitor bank during a closein fault, and energization of a transformer
5
connected to an adjacent bus with energized capacitors. Of special interest in this
paper was the field measurement of the phase and neutral currents in a capacitor bank
during a restrike in one of the phases of the switching device. This was determined to
be the cause of failure of the capacitor bank neutral instrument transformer.
In reference [5], the problem of phasetophase surges caused by capacitor
bank energization was investigated both at the capacitor and remote locations. EMTP
was used for the simulations; however, it is not known if frequency dependent
parameters were used to model the radial transmission line connected to the capacitor
bank bus. Variation of system parameters such as line length and number of sources
connected to the capacitor bus were evaluated as was transient voltage reduction
using preinsertion resistors ranging in value from 40 to 300 ohms. Surge arresters
were not considered in this study.
Reference [6] contains parameters such as self inductance of typical capacitor
banks and sample calculations of bus inductance which are necessary to perform a
backtoback capacitor bank switching study. Also included are formulas for
calculating peak inrush current and inrush frequency (neglecting damping) for both
the isolated bank and backtoback cases. This standard publication is a result of the
efforts of the I.E.E.E. Power Engineering Society Switchgear Committee.
CHAPTER II
EMTP SIMULATION AND MODELLING TECHNIQUES
Brief History
Tools to model transient phonomena in power systems, including capacitor
switching, have been around for many years. The Transient Network Analyzer
(TNA) is actually a scaled down analog model of the power system using actual
resistors, inductors, capacitors, transformers, switches, etc. to model linear and
nonlinear elements. A program designed to run on large mainframe digital
computers known as the Electromagnetic Transients Program (EMTP) was originally
developed in the late 1960s by Dr. Hermann Dommel [7]. The program was
considered to be the digital computer replacement for the TNA. Over the years, many
program improvements have been made by the Bonneville Power Administration
(BPA) and other utilities and universities. More recently, a version of the EMTP
known as the Alternative Transients Program (ATP) which will run on a personal
desk top computer, evolved as a result of the efforts of certain BPA personnel and the
Leuven (Belgium) EMTP Center (LEC). The ATP program, suitable for the PC, is
used in this thesis to perform the digital simulations discussed later.
Numerical Solution Techniques and Uncoupled Linear Elements
The digital computer can not give a continuous solution or representation of
transient phenomena. The concept of sequential discrete solution is utilized in the
EMTP [8]. The solution is actually given as a sequence of snapshot pictures of
7
voltage and current at discrete time intervals (At). Each linear element of the power
system (resistance, inductance, and capacitance) is modelled by representing it with a
first order differential equation. These first order differential equations are then
transformed to a series of linear algebraic difference equations using the method of
Trapezoidal Integration [9].
Consider first the resistive branch representation shown in figure 2.1.
Figure 2.1 Resistive branch representation
A linear algebraic equation is used to solve for the current from node k to node m.
The time domain solution is given by the nodal equation
k
WW
Jk.mvt) R
m
k
vk(t)
v(t)
(i)
Figure 2.2 illustrates the inductive branch.
k
m
L
Vk
Figure 2.2 Inductive branch
The differential equation for the voltage across the inductance is given by
Vk(t)Vm(t) = L^k,m
(2)
8
This equation is then integrated from a known state: (t A t) to an unknown state: (t)
to obtain the following equation for current through the inductive branch.
i k,m (t) = 1 k,m (tAt) + f [ Vk(t) Vm (t)] dt (3)
L /tAt
The application of the Trapezoidal Rule of Integration yields the algebraic branch
equation in nodal form used to solve for the current through the inductor.
ifcm W = [Â£] [Vk(t)Vm (t)] +Itn (tAt) (4)
Figure 2.3 is the EMTP representation for the inductive branch.
Vk(t)
k ijc,m (t) (DIk m (tAt)
m
w u vwv At i
Vm(t)
Figure 2.3 EMTP representation of inductive branch
Equation 4 agrees with figure 2.3 where I^m(t A t) is the equivalent current source
known from past history
Ik,m (tAt) =ik,m (tAt) +[At] [Vk(tA t)Vm (tA t)] (5)
and
Atl = 1
2LJ R
(6)
9
The capacitance branch representation is similar to that of the inductive
branch as illustrated in figures 2.4 and 2.5.
Vk
Figure 2.4 Capacitive branch
k ik,m (t) ^ Ik \ m (tAt)
O' VWV R = 2C m
* i Vk(t) < w w k 1 i < k Vm(t)
Figure 2.5 EMTP representation of capacitive branch
The integral equation describing the voltage across the capacitive branch is
Vk(t)Vm(t)=i [ik,m(t)] dt+Vk(t4t)Vm(tAt) (7)
^ .ftAt
Once again, integrating with the Trapezoidal Rule results in a time domain solution
for the current through the capacitive element
where
and
k.m (t)=[2Â£l[Vk(t)Vm(t)]+It,m (tAt) (8)
At J
Ik,m (tAt) = ik,m (tAt) [2Â£][Vk(tAt)Vm (tAt)] (9)
2C
. At.
1
R
(10)
10
System Equivalents (Linear Coupled Elements')
System equivalents or driving point impedances are the Thevenin equivalent
impedances of the network at any given point. The number and location of system
equivalents is dictated by the size of the system and the bus or busses of interest
inwhich the transient phenomena is to be studied. There are no hard or fast rules as to
where to locate equivalents. Common sense should be used. Transient waveforms at
a given bus are affected by travelling waves on all of the transmission lines connected
to that bus, and saturation caused by nonlinear devices such as transformers. It is
customary to attach system equivalents at least one bus removed. The size of the
system (number of busses, lines, etc.) however, is usually limited by the amount of
computer memory available which is more of a concern when using the PC version of
EMTP.
Unlike many short circuit and load flow studies, which usually perform
computations on a single phase basis, the EMTP computes all parameters on a three
phase basis using the three phase model. Positive and zero sequence impedance
values used in the equivalents are derived from a short circuit study at the selected
busses. (Negative sequence values are the same as positive sequence.) The EMTP
model used for system equivalents is the linear, mutuallycoupled, lumped RL circuit
shown in figure 2.6 in which the three phase source voltages are connected to one
side, and the system connected to the other.
A
B
C
system
awvnmm.
L
AfW\orm
AWvarm
source
i_..________.j
mutual coupling
Figure 2.6 EMTP source equivalent representation
11
Sequence values are converted to phase values to be used in EMIT simulation
by means of Karrenbauers transformation [10] as shown in figure 2.7.
Figure 2.7 Karrenbauers transformation
The resultant phase matrix is symmetric and triangular as a result of Karrenbauers
transformation and inverse transformation matrices.
[T] =
1 1 1 1
1 (1M) 1 1
1 1 (1M) 1
1
1 1 1 0Mi
'1 1 1 r
1 1 0 . 0
1 0 1 0 0
1 0 0 0 l
(11)
(12)
M represents the number of phases in the system. Therefore, for a threephase
system, the transformation and inverse transformation matrices become
' 1 1 r
[T] = 1 2 1
. 1 1 2.
' 1 1 r
1 1 0
3
. 1 0 1.
(13)
(14)
12
The transformation of impedances from sequence or mode quantities to phase
quantities is accomplished by
[Zpta!e]=[T][Zmo
Direct equations for converting from mode values to phase values with = Z^ result
from equation 15.
Zs =I(Zo+2Zj) (16)
zm = J (Zo Zi) (17)
Zs represents the selfimpedance and Zm represents the mutualimpedance of the
source element.
Other transformation techniques can be used such as symmetrical components
and a, (3, O components, however the Kairenbauer transformation is best suited for
the solution of electromagnetic transients [9]. The advantage over symmetrical
components lies in the fact that the Kairenbauer transformation matrix is real whereas
the symmetrical component transformation matrix contains complex quantities. The
advantage over a, P, O transformation is mainly simplicity.
Transmission Lines
Threephase overhead transmission lines are modelled in EMTP as mutually
coupled circuits containing R, L, and C elements. Three possibilities exist: lumped
parameter Pimodel, distributed constant parameter, and frequency dependent.
The simplest model for transmission lines is the lumped parameter Pimodel
inwhich short cascaded PI circuits as shown in figure 2.8 are connected together to
represent a transmission line of a certain length.
13
AA/v\nnnnrv
R L
o
C
2
Figure 2.8 Lumped Pimodel for transmission lines
The lumped Pimodel is adequate for steadystate and low frequency analysis, but is
not the best representation for highfrequency transient analysis. The reason for this
is the Picircuit is actually a low pass filter and the transient analysis produces a
natural cutoff frequency. Also, occasional numerical instabilities are encountered in
EMTP when a large number of Picircuits are cascaded together. Therefore, the PI
model is generally not used in EMTP simulation, except for very short lines and
steadystate solutions.
A more widely used model for EMTP is the distributed constant parameter
line representation. This model eliminates artificial natural resonances of the lumped
elements, therefore eliminating the natural cutoff frequency, making the model valid
for high frequency transient simulation [11]. The term constant parameter refers to
the fact that the R, L, and C elements of the transmission line are frequency
independent. To further understand the concept of distributed parameters, consider
an incremental section of one phase of a lossless (no resistance and shunt
conductance) transmission line shown in figure 2.9.
/ (x,t)
e(x,t)
 nnnook
) i \ L'Ax C'Ax . V /
Ax
Figure 2.9 Incremental section of lossless line
14
x represents distance and t represents time. L' and C' are the incremental inductance
and capacitance respectively. Since there are two variables x and t, partial differential
equations governing the voltage and current on the line can be expressed.
3e j / 3/
Bx dt
(18)
= C' (19)
Bx dt
The general solution to the voltage and current equations are given by dAlembert [9].
I (*,t) = fl (xvt) + f2 (x+vt) (20)
e(*,t) = Zof!(j:vt)Zof2 (*+vt) (21)
These solutions are actually the travelling wave equations for the transmission line
where fj (x vt) is the forward wave travelling at velocity v and f2(x + vt) is the
reverse wave travelling at velocity v. From the differential equation solution, v is
defined as
<22)
The travel time, T, of the line can be derived by
x = l =Vl'C'/ (23)
where / is the length of the transmission line. Zq is the characteristic or surge
impedance and is defined as
(24)
15
~VS
A visualization of the relationship between the parameters previously described is
shown in the single phase, twoport transmission line of figure 2.10.
fl(xvt) XA ,
k 1 k, m (0

Vk(t)
t f2(^ + vt)
*"m,k(t) m

v(t)
Figure 2.10 Twoport transmission line
Implementation of the distributed line model into EMTP is accomplished by
deriving the equations for two equivalent current sources at each end of the line
connected across the characteristic impedance, Zo as shown in figure 2.11.
t"m,k(t) m
1 1 4
p i Ezo
Im(tX) <
Vm(0
Figure 2.11 EMTP transmission line representation
^o
<, = + (tt)
^ o
(25)
(26)
(27)
16
I(tt)=Jk,(tT)^2l (28)
The equivalent current sources Ik and Im are known at state t from the past history at
time (t x), where x was previously defined as the travel time of the transmission line.
For most accurate distributed line modelling of transmission lines, a lossy
model (containing series resistance and shunt conductance) should be used.
Resistance introduces damping which has a major effect on transient waves.
Consider now an incremental section of a lossy distributed parameter line shown in
figure 2.12.
Figure 2.12 Incremental section of lossy line
The exact partial differential equations governing the voltage and current on a three
phase lossy transmission line are [10]
?V =[l']+[r<1/ (29)
dx dt
~ = [C']7+[G/]V (30)
[ R' ], [ L' ], [ C' ], and [ G'] are vector matrix quantities and are typically
determined by a line constants program. In actual EMTP simulation, the series
17
resistance of the line is not distributed, but rather is lumped, and the conductance G is
considered negligible and is left out as shown in figure 2.13.
m WA vwv
R7 distributed R7 V distributed R7
4 L',C' 2 L' C' 4
(lossless) (lossless)
Figure 2.13 Distributed parameter line model with lumped resistance
The reasoning behind the lumped resistance model lies in the fact that the transient
solution becomes more complicated when the resistance is distributed and numerical
instability may exist. Field test results have shown close correlation to the model
shown in figure 2.13 [12].
To understand the overall effect of resistance, one should consider the exact
steadystate Pimodel for a transmission line (figure 2.14) and the associated
equations.
Figure 2.14 Exact steadystate Pimodel
Zseries = z0 sinh yl (31)
\ Yshunt = ^tanh^
(32)
18
The two important parameters for wave propagation are the characteristic impedance,
Zo and the propagation constant, y which are defined as
I R'+jcoL7
V G'+jcoC'
(33)
Y V(R'+joiL')(G'+jo)C') <34)
where to is frequency. The propagation constant, yis complex and can be separated
into real and imaginary parts.
y = a + j P (35)
a = Re[y] = Attenuation Constant (36)
P = Im [y] = Phase Constant (37)
The influence of resistance can now be seen and it is again noted that for the
distributed constant parameter model, R', I/, and C' are frequency independent (G' =
0). The overall functions, ZQ and y however, are influenced by frequency (cd).
Physical construction of three phase transmission lines have an important
effect on transient waves because of intercoupling between phases. Two line
configurations are considered: fully transposed and untransposed.
H H
Figure 2.15 Fully transposed 3phase line
19
a 
b 
C0
Figure 2.16 Untransposed 3phase line
The idea behind the fully transposed line is to balance the three phases by allowing
each phase to share an equal space in the horizontal plane. In matrix form, the phase
impedance per unit length of the transmission line is given by
[Z'phj =[R/]+j[L/]
(38)
and the phase admittance is
[Y'ptaJ = jd)[c']
(39)
where
R ac
[r'] = Rb> vRbc
. R'ca R^ vR^_
[L'] = ^ab L'ac'
Lb> '^bb' sLbc
i' ^ ca T 'V sL'CC _
[c] = nC^ ^ab C'ac'
^bc
. C'ca
(40)
(41)
(42)
For a fully transposed line, the off diagonal elements of [ R' ], [ L' ], and [ C' ] will
be equal. Performing a Karrenbauer transformation from phase to modal quantities
20
will result in fully decoupled modal matrices (all off diagonal elements are zero).
This was previously illustrated in figure 2.7.
The distributed constant parameter line model in EMTP assumes continuous
transposition which for all practical purposes is the same as full transposition, unless
nontransposition is specified. Like the linear coupled elements, modal quantities are
converted to phase values via the Kairenbauer transformation.
Untransposed lines present a more difficult transformation problem. The off
diagonal elements of the [ R' ], [ L' ], and [ C' ] matrices are now unequal and are a
function of the tower geometry and configuration of the transmission line. Even
though the matrices are still symmetric, full decoupling from phase to mode values
using the Karrenbauer transformation is not possible. The Eigenvector method has
been proven to be successful in such case [10]. The diagonalized matrices [ Z'mode ]
and [ C'mode] are obtained from
[z'mcKfe] = [ T,]'1 [z'ptaj [ T, ] (43)
[ C'md=] = t T( l'1 [C'phj [ Tv] (44)
where
[Ti]1[TV] (45)
The columns of [ Ty ] are the eigenvectors of the matrix product [ Z phase] x
[ j co C'ftose]. Voltage and currents in phase quantities are obtained from modal
quantities with [ Ty ] and [ T. ] as follows:
[ phase ] = [ Tj ] [ i mode ] (46)
[ vphase ] [Ty] [ vmode ]
(47)
21
The transformation matrix is frequency dependent and complex which leads to
difficulties in the transient analysis. Two assumptions are made: the transformation
matrix is constant over a certain range of frequencies, and the transformation matrix
is approximately real. For overhead lines, it has been found that the matrix [ T. ] can
be approximated by a frequency independent matrix over a frequency range from 10
Hz to 10 kHz with sufficient accuracy [10]. When setting up an untransposed,
constant parameter distributed line model in EMTP, the imbedded line constants
program calculates the phase parameters based on entered tower geometry and
conductor data. In addition, up to three frequency cards are specified. The
transformation matrix is then calculated at these frequencies in order to approximate a
frequency range. A similar procedure is used to enter the data for the frequency
dependent line model described next.
The parameters of overhead transmission lines with ground return are highly
dependent on frequency. Accurate modelling of this frequency dependence over the
entire frequency range of the signals (transients) is of essential importance for the
correct simulation of electromagnetic transients conditions [13]. One would normally
assume that the inherent per mile line resistance, inductance, and shunt capacitance
are constant over a given frequency range. In reality, these parameters are not
constant over broad frequency ranges because of variation in the depth of penetration
of ground currents and because of conductor skin effect. The characteristic
impedance and propagation constant of the frequency dependent transmission line are
given by the following equations:
(48)
V (r '(g))+j 001/(00)) (g'(o))+j o)C '(cn))
22
Carsons equations for earth return indicate that the zero sequence resistance and
inductance are primarily affected by frequency, with R'o increasing dramatically with
frequency [7].
In the early 1980s, a frequency dependent transmission line model was
developed for the EMTP by Jose Marti of the University of British Columbia. A
supporting program, as part of EMTP, called JMARTI SETUP, is used to generate
data for simulation.
The first step in simulating the frequency dependent line involves the use of
an equivalent circuit in basic form for one end of the line as shown in figure 2.17.
k 
o 
 i k(t) L~
network C^) bk(t)
o
Figure 2.17 Frequency dependent line model basic form
The objective is to duplicate the frequency response of the characteristic impedance,
Zo(co) where the modal parameters are generated using the imbedded line constants
program within the JMARTI SETUP, and ZQ(o)) is calculated at various
frequencies using equation 48 so that Z^co) = Zq(co). Marti selected a technique to
synthesize the characteristic impedance known as the series Foster network [13]. The
network consists of a series of RC blocks as shown in figure 2.18.
WA WA
Ri r2
It 1(
Ci
C2
Figure 2.18 Foster network to synthesize ZQ(co)
Ci
23
The number of RC blocks and the parameters of the network result from the
approximation of Zo(s) (s is the complex variable) by a rational function of the form
, (s+zi)(s+z2) (s+Zj)
**'' (s+pi)(s+p2)**(s+pi)
(50)
where the zeros (Zj) and the poles (p) are real, negative, and distinct. The actual
values of R and C are determined by performing a partial fraction expansion on
equation 50.
z,(s) +s+p2 (51)
Ro = k0 R,. = i C,X (52)
The next step involves evaluating the voltage source, bk(t) in figure 2.17. The
voltage source must represent the weighted effect upon end k of the line from past
values of current and voltage at end m. This weighting accounts for the different
travelling times ( t ) and attenuations (y) of the different frequency components in
the travelling waves. The source, bk(t) is the convolution integral
bk(t)=J fm(tu) ai(u)du (53)
where fm(t), the travelling wave function, is defined as
fm(t) = 2Vm(t)bm(t) (54)
at(t) is the weighting function which is the time domain form of the line response
function
24
A1(Q)eJ,<) ()
In order to avoid the numerical difficulties involved in obtaining a^t) from an inverse
Fourier transform of Aj(co), and the numerical burden of accurately evaluating the
convolution integral for the voltage at each time step of the network solution, the
function is approximated in the complex plane by a rational function of the same form
as Z ((D). y (cd) is calculated at various frequencies using the line constants
program and equation 49.
A curve fitting process known as asymptotic tracing is used to obtain the
corresponding rational approximations for Zq(co) and Aj(cd). This is done for both
zero and positive sequence modes. The zeros and poles of the partial fraction
expansion of these functions and time delay, x define the parameters of the equivalent
circuit. An example of the curve fitting process for the zero sequence mode of Zo(cd)
is illustrated in figure 2.19 where I Zq(
scales [10].
The magnitude function is expressed in dB (201og I Zq(cd) I). Straight line segments
25
with a slope of either zero or a multiple of 20 dB per decade constitutes an envelope
for the rational function. In other words, the rational function, Z ((D) is contained
between Zo(co) and the asymptotes. The comers of the asymptotic envelope define
the location of the zeros and poles of the rational function. A Fourier transform is
used to transform the pole/zero data to the time domain.
The JMARTI SETUP routine automatically punches card images
containing the output parameters and places them in an output file for use in a
transient simulation. Once the JMARTI model for a particular transmission line is
built, it can be used over and over again for various simulations and moved between
various system models. The JMARTI output file is brought into the system model
data base for transient simulation using the $INCLUDE Fortran statement. Once
the data has been transferred, the parameters are evaluated using the reduced line
model of figure 2.11. The past history current vectors, Ik and Im are updated at each
time step in the network solution.
Input data for the JMARTI SETUP program consists of two parts: line
parameters for the imbedded line constants program, and frequency cards. The line
parameter data consists of tower geometry for the transmission line, and phase
conductor/shield wire dc resistances and physical dimensions. The frequency card
group consists of either 2 or 3 frequency data cards. If the line is untransposed, a first
card bearing the single frequency at which the diagonalizing transformation matrix is
to be calculated must be included since it is frequency dependent A common value
for overhead lines is 5000 Hz [10]. The second frequency card contains the
frequency of the steady state solution, which in many cases is 60 Hz. A third
frequency card is necessary to request the logarithmic looping over all frequencies
that are required by the Fourier transformation in the program. Typically, this will
cover 8 or 9 frequency decades starting from 0.01 Hz, with 10 points per decade. For
26
the transposed line, only the second and third frequency cards are needed. Additional
data included on the frequency cards are the length of the transmission line and the
soil resistivity, p, which is used in Carsons equations to calculate zero sequence
resistance and inductance. A typical value of p is 100 ohmmeter.
Transformer Models
Detailed single phase and three phase transformer models including
nonlinearities such as the effects of saturation, are included in EMTP. The use of an
appropriate model is based on the physical construction of the core and windings of
the transformer. Three phase transformers can be classified into two types of core
construction: core form and shell form. Three possible designs exist and are shown
in figure 2.20.
3Legged 5Legged core Shell
core
Figure 2.20 Three phase transformer core designs
Both the 5legged core and shell transformers have zero sequence return flux paths,
therefore allowing the phases to be magnetically independent. Positive and zero
sequence impedances of these transformers will be equal. The 3legged core unit has
no zero sequence return flux path through the iron. Zero sequence flux will therefore
flow through the air and steel tank of the transformer. The phases are magnetically
dependent and the positive and zero sequence impedances will be different.
One of the more commonly used transformer models in EMTP simulation is
27
the single phase saturable transformer model which most closely represents 3phase,
5legged core and shell type units because of independent magnetic action as well as
single phase units. A 3winding representation is shown in figure 2.21.
Figure 2.21 Single phase saturable transformer model
Winding resistances and leakage inductances (or inductive reactances) are calculated
from the short circuit impedances and copper losses typically found on transformer
test reports and the following equations:
R= per phase) (56)
I2
base
* = VIZ^R* (57)
The winding impedances are calculated in ohms on their perspective kV base.
Transformation or reflection of the impedances is accomplished by the ideal
transformers. Connected across winding 1 is the magnetizing resistance (Rmae) or
core loss resistance as it is commonly called. Rmag is calculated in ohms based on the
open circuit test data.
28
_ y2 (phasetophase)
mag_P^ (3phase)
(58)
In parallel with the magnetizing resistance is a nonlinear inductance which represents
the magnetic properties of the transformer iron core. This element, often called the
saturation branch, is necessary to model the nonlinear effects of saturation during
EMTP simulation.
During the transient period, transformers connected to a particular system may
be driven into the saturation region due to overvoltages. When this happens, the
excitation current wave will have a nonsinusoidal shape, which in turn will cause
other current and voltage wave distortions [11]. This phenomena is illustrated in
Voltage and magnetic flux are related by Faradays Law
29
V(,) = l4M (59)
v dt
where N is the number of turns of the perspective transformer winding. Flux linkage
in voltseconds (\t) is the unit actually used for the saturation representation in
EMTP simulation and is defined as
< II e (60)
v5E dt (61)
The saturation effects of transformers are handled in EMTP by use of the
pseudononlinear inductance branch, which uses piecewise linear segments to
represent the nonlinearity. Transformer test reports sometimes include a saturation
curve which is plotted as RMS voltage versus RMS exciting current. A conversion
must be made to flux linkage in voltseconds versus peak exciting current for the
piecewise representation as illustrated in figure 2.23.
Figure 2.23 Conversion of curve to \j//ie curve
For the conversion, it is necessary to assume that the flux varies sinusoidally as a
function of time.
Y = Ymax sin ( t)
(62)
30
With this assumption, the voltage will also be sinusoidal and the conversion of
Vjy^s values to flux values becomes a simple rescaling.
VrmsYI (63)
T (0
The rescaling of currents is more complicated, except for point B at the end of the
linear region AB.
b = IrmsB VI (54)
In order to make the conversion of current in the nonlinear region, segments BC, C
D, DE, etc., it becomes necessary to utilize the equation defining RMS current.
I RMS =
i2(t)dt
(65)
To evaluate this integral equation for the portion of the saturation curve of interest,
equation 65 becomes
I
2 _2
RMS ft
i2d(cot)
(66)
Applying the Trapezoidal Rule of Integration segment by segment results in
1s=a + bi+ci2 <67>
where a, b, and c are known constants. Since Ij^ is also known, ie can now be
determined by the quadratic equation. Trapezoidal Rule is used because the
31
conversion process is done recursively in an EMTP supporting program called
Saturation.
Modem high voltage transformers with grain oriented steel cores typically
saturate somewhere around 1.1 to 1.2 times rated flux, with a sharply defined knee as
Figure 2.24 Typical transformer saturation curve
More often than not, a twoslope piecewise linear inductance is sufficient to model
this curve. The slope in the saturated region above the knee is the aircore
inductance. This inductance is almost linear and fairly low compared with the slope
in the unsaturated region. Harmonic studies using EMTP have shown that in most
cases, a twoslope piecewise linear inductance was accurate enough. Going to a more
detailed 5slope inductance changed the results very litde [14].
A transformer model to represent a 3phase, 3legged core unit where the phases
are magnetically dependent is available in the version of EMTP/ATP presently being
used. The parameters and model of the 3phase saturable transformer are similar to
the single phase unit with the difference being in the fact that the saturation branches
of each phase are coupled together through ideal transformers and a zero sequence
inductance, Lq as illustrated in figure 2.25.
32
Figure 2.25 3Phase saturable transformer model
Certain problems exist in the application of this particular transformer model. First,
the value of L is difficult to obtain. L is determined by the reluctance of the zero
sequence airreturn path for flux through the tank of the transformer, and the
expression
L
(68)
where Nj is the number of turns of winding 1. It is not common to see values of Lo or
3^ on transformer test reports. Secondly, a problem involving numerical instability
has been encountered when using a 3winding model [10].
Another transformer model known as BCTRAN can be built using an
EMTP supporting program. BCTRAN was developed by British Columbia Hydro
(BC Hydro) and produces a linear, coupled model of the transformer. This is
33
accomplished by building [ R ] and [ L ] matrices based on phase impedance values
transformed from positive and zero sequence short circuit test data that is entered into
the program directly. In addition, open circuit test data is converted to linear R and L
values for the excitation branch which can be placed on any selected winding.
BCIRAN has no provision for the nonlinear saturation branch previously
described. A separate pseudononlinear branch can, however be added external to
the model on any selected winding. A 3winding, 3phase transformer model using
BCTRAN is illustrated in figure 2.26.
wdg.
1
A<
B'
C<
9x9 linear matrices
[R] + j[coL]
onrrp
AW
m
nrrrr
WAr
nrmn
/w
V.
wdg. 3
Figure 2.26 Transformer representation using BCTRAN
A
B wdS
2
C
For this example, the linear magnetizing branches are connected to winding 3. The 9
x 9 linear matrices, [ R ] and [ L ] contain both self and mutual impedances
between phases and windings. The mutual impedances are inductive (to L) and will
approach infinite value as frequency is increased. Therefore, the main advantage of
BCTRAN over the previously discussed transformer models is accuracy at very
low frequencies.
Presently, there are no transformer models in EMTP/ATP to directly
accomodate autotransformers. These devices are typically 2winding, consisting of a
34
series/common winding connected groundedwye and a tertiary winding connected in
delta as shown in figure 2.27.
Figure 2.27 2Winding autotransformer (1phase)
Short circuit and open circuit impedances are usually provided on autotransformer
test reports as hightolow (HL), hightotertiary (HT), and lowtotertiary (LT).
One suggested representation in EMTP using BCTRAN involves splitting the
series/common winding into 2 separate windings.
Figure 2.28 Autotransformer representation using BCTRAN
This representation is close to the actual physical connections of the autotransformer.
The complication, and possible consequent errors arise from the conversion of the test
value impedances of the actual autotransformer of figure 2.27 to the model in figure
2.28 (ie: winding voltages must equal perspective winding ampereturns).
As an alternative, the autotransformer test impedances can be converted to the
Tequivalent, a popular representation used in other power system studies.
35
H ^ ^ L
=czz]
Zp
T
Figure 2.29 Tequivalent representation of an autotransformer
2 (ZHL + ZhT ZlT ) (69)
j (Zhl + Zlt Zht) (70)
^ (Zht + Zlt Zhl) (71)
This representation lends itself well to the 3winding saturable transformer model in
figure 2.21 where the windings connect to a common point or node. The main
discrepancy from the true autotransformer lies in the internal winding connections.
Using the saturable transformer model, typical winding connections for a 3winding
representation are shown in figure 2.30.
Figure 2.30 Autotransformer 3winding representation
If the autotransformer is treated the same way as a regular transformer, that is, if the
details of the internal connections are ignored, the saturable transformer model will
produce reasonably accurate results, except at very low frequencies [12]. At dc, the
voltage ratio between the low and high side of a full winding transformer will be zero,
36
whereas the voltage ratio of the autotransformer arrangement in figure 2.28 becomes
the ratio of the resistances of winding 2 to winding 1 (dc voltage divider effect).
Interwinding capacitances and windingtotank stray capacitances which
become predominate at higher frequencies are not considered in any of the
transformer models discussed. EMTP development in this area is in progress
however.
To summarize transformer modelling for transient analysis, one must consider
how detailed of a model is necessary and where the transformer is located in relation
to the switching or the bus of interest If the intent is to observe internal transformer
transients, a detailed distributed model should be used as was done in [1]. Data to
construct such a model is often difficult to obtain. If a particular transformer is
located 2 or 3 busses away from the point of switching or observation, it may be
appropriate to ignore the nonlinear effects of saturation; whereas if the transformer is
connected adjacent to these points, modelling the saturation branch in detail would be
prudent.
Surge Arresters
Devices to protect generators, transformers, and other power system devices
against levels of transient overvoltage which can permanently destroy their nonself
restoring insulation are called surge arresters and can be modelled in EMTP. The
earliest versions of surge arresters were spark or rod gaps and consisted of air gaps
between electrodes of various shapes. Rod gaps protect against overvoltages by
collapsing the voltage to practically zero after sparkover and creating a short circuit
which must then be interrupted by circuit breakers. With the exception of protective
spark gaps for series capacitors, these devices are seldom used in todays modem
power systems.
37
Two basic types of surge arresters are commonly used: siliconcarbide (SiC)
and zincoxide (ZnO) or metaloxide varistors (MOV) as they are commonly called.
Until about 10 years ago, only siliconcarbide arresters were used. The MOV type
arresters have quickly replaced the older type to the extent that some manufacturers
presently produce only metaloxide arresters [12].
SiC arresters consist of a siliconcarbide resistor or series of resistor blocks
which have a nonlinear voltagecurrent characteristic or resistance, R(i) in series with
a spark gap as illustrated in figure 2.31.
Figure 2.31 Siliconcarbide arrester
The spark gap completes the path from the system through the resistor to ground
when the overvoltage exceeds the sparkover voltage of the gap. The resistor then
limits the followthrough current allowing the arrester to reseal or interrupt the
current in the gap. To facilitate the resealing, so called active spark gaps were
designed in which the arc voltage builds up after a defined time [12]. The series gap
is necessary in the SiC arrester due to the fact that siliconcarbide disks cannot
withstand continuous linetoground system voltage.
Advances in semiconductor technology brought about the MOV arrester,
which can be gapless and rated for continuous system voltage. A specified maximum
continuous overvoltage (MCOV) in RMS is provided by the manufacturer and must
be adhered to in order to avoid thermal damage. Actually, two types of MOV
38
arresters are available and can be modelled in EMTP. The gapless and shunt gap
MOV arresters are shown in figure 2.32.
Figure 2.32 MOV arresters
The shunt gap version allows a higher MCOV rating before sparkover of the gap,
Rj(i) + R2(0, and a lower discharge voltage characteristic following sparkover, R^i).
Since both the gapless and shunt gapped MOVs are solidly connected linetoground,
a leakage or grading current of a few milliamps will be present during steady state
conditions.
MOV arresters are highly nonlinear resistors, with an almost infinite slope in
the normalvoltage region, and an almost horizontal slope in the overvoltage
protection region [12]. The MOV device has a greater nonlinear characteristic than
the SiC device as can be seen from the discharge curves of figure 2.33.
39
Intuitively, one can see that the MOV arrester provides an almost ideal characteristic
for overvoltage protection, similar to a zener diode in electronic circuits. Actually,
small MOV devices are now almost exclusively being used to protect computers and
other sensitive electronic equipment.
The curves of figure 2.33 are provided by the arrester manufacturer and are
based on a measured discharge voltage across the arrester for a specified current
wave. The magnitude of the current wave is a function of the arrester and source
impedance and the applied voltage of the source. Typically, the source voltage is
varied to obtain currents ranging from lkA to 40kA. The shape of this current wave
is controlled by an impulse generator and is intended to represent a steepfront
lightning surge. The American National Standards Institute (ANSI) and Institute of
Electrical and Electronic Engineers (IEEE) have accepted an 8 x 20 microsecond
current wave as a standard. By definition, the wave reaches peak or crest in 8
microseconds and reduces to half crest in 20 microseconds as illustrated in figure
2.34.
Figure 2.34 Surge arrester 8 x 20 test current wave
An additional standard current wave of 45 x 90 microseconds, representing a
slower rise time switching surge is applied to the arrester at a magnitude of either 500
or 1000 amps in order to obtain a discharge voltage which is representative of the
maximum switching surge protective level of the arrester. It is this voltage value
40
along with a value picked off the curve of figure 2.33 representing lightning surges
which are used for insulation coordination in devices such as transformers. Insulation
coordination is discussed in a later chapter.
Modelling of the MOV arrester in EMTP is accomplished with the use of a
supporting program known as ZNO FITTER. Because of the extreme nonlinearity
of the MOV, a piecewise linear representation of the discharge curve, which is used
to represent the SiC arrester, and transformer saturation curves, cannot be used. The
nonlinear resistance of the MOV is expressed as an exponential function of the form
where p, vref, and q are constants. Typical values for q are 20 to 30 [12]. Several
points are picked off the manufacturers discharge curve for a particular arrester and
entered in ZNO FITTER along with the steady state voltage rating and a value for
vref which is arbitrary. Typically, the value used here is the maximum switching
surge level.
Using a closedform solution technique known as the Newton Iterative
Method, which is actually a least squares exponential curve fit, the entered voltage
and current data are converted to the form of equation 72 for each pair of data. ZNO
FITTER automatically punches the card images or lines of data in this form to be
used in transient simulation. In addition, the flashover voltage of the shunt gap, if it
exists, is entered. If the arrester is gapless, a negative value for Vflash is entered.
Energy absorption or duty of a surge arrester is measured in Joules (watt
seconds), or more precisely, kilo or MegaJoules depending on the size. This rating is
provided by the manufacturer and becomes a concern when performing transient
overvoltage simulations. A plot of energy versus time can be obtained for a particular
41
case by requesting such output on the ZNO data cards.
Switches
Switches are used in EMTP to simulate circuit breakers, circuit switchers, and
gaps. Three types of switches are available in the ATP/EMTP program: time
controlled, voltage controlled or flashover, and statistical.
The time controlled switch is most commonly used to represent circuit
breakers and other circuit interrupting devices such as circuit switchers. The actual
switch closing time is specified. The switch will automatically open at the first
current zero, simulating actual arc extinction. A time before which opening will not
be allowed (Topen) can be specified to allow interruption at a later current zero.
Also, a current margin can be specified allowing the switch to open below an absolute
value before passing through zero simulating current chopping.
A voltage controlled or flashover switch is used to simulate spark gaps and
any other devices which may flash over during transient simulation. Three
parameters are entered: time before which the switch is prevented from flashing over
(Tclose), time period after flashover before which opening will not be allowed (T
delay), and the voltage which must be exceeded for the switch to flash over (Vflash).
Statistical switches simulate random closing of circuit breaker poles within a
specified pole span. By running a series of random shots (up to 200 on mainframe
computers) in which the three poles close at different points along the voltage wave,
an overvoltage probability profile can be obtained for a particular transient switching
study.
EMTP Input Data Structure
Input data for an EMTP case is built using a text editor to create the card
42
images or lines of data containing all of the system parameters and commands
necessary to run the case. These lines of data must be arranged in data groups in a
specific order as indicated in figure 2.35.
Figure 2.35 EMTP input data structure
With the exception of the miscellaneous and initial conditions, the data groups are
followed by a BLANK card which signals the program to look for a different type
of data.
There are usually two miscellaneous data cards. The first card contains the
time step (At) and maximum time in seconds for the transient simulation. Also
included are XOPT and COPT* values. XOPT is a value that indicates whether
inductance in milliHenries (mH) or inductive reactance in ohms (Â£2) is entered on the
linear branch cards. If XOPT = 0, the inductances are entered in mH. If XOPT5 >
0, the values are in ohms at the frequency, XOPT in hertz. The same rule applies to
COPT, which is the capacitance data. If COPT = 0, capacitances are entered in
microFarads (iF) and if COPT > 0, the data is entered as micromhos (iU), coC at
the particular frequency. A second miscellaneous data card contains various output
43
requests such as the frequency of printed output from the time step loop, frequency
for saving solution points of the time step loop for plotting, and printout of the steady
state solution. (As a check for proper network connections, a steady state solution is
done before the transient simulation).
Branch data consists of linear coupled elements such as system equivalents,
linear uncoupled circuit elements such as capacitors and reactors, lumped or
distributed parameter transmission line models, and linear or nonlinear transformer
models. Also included here are modularized data fries brought into the case by use of
the $INCLUDE statement. These fries include JMARTI frequency dependent
transmission line models, BCTRAN transformer models, and nonlinear surge
arrester models such as ZNO FTITER.
All switches in the network are listed in the next data group. Details of
various switches were previously described.
Source data cards are next and consist of all voltage and/or current sources in
the network. Typically, voltage sources are used to represent equivalent system
generation behind source impedances at various locations in the modelled system.
Voltage sources are represented in EMTP by the following equation:
V(t) = Epcos(cot + e) (73)
where Ep is the peak linetoneutral voltage, to is frequency in hertz, and 0 is the
relative phase angle. Nonsinusoidal sources such as pointbypoint multisloped
impulse waves, ramps, and step functions can also be represented.
Data for overriding the internally calculated initial conditions (which come
from the steady state network solution) are listed next. This would include such data
as trapped charges on capacitors and transmission lines.
44
The output node voltage requests occupy the last data group in the overall
EMTP data structure. Names of those busses inwhich voltage output data is required
are listed. Current, power, and energy through branches and switches, and voltage
across open switches are requested on their perspective data cards or card images.
CHAPTER m
THEORY AND SYSTEM MODELLING
Two capacitor switching scenerios were examined. Both cases involved
portions of the TriState Generation and Transmission Association 115 kV system.
The objective was to model each system in as much detail as deemed practical using
the modelling techniques discussed in the last chapter.
Case 1 System Model
The first case involved the switching of an isolated 115 kV, 15 MVAR,
groundedwye capacitor bank at the Western Area Power Administration (Western)
Pilot Butte substation. A portion of the TriState and Western 115 kV systems in the
Riverton, Wyoming area were modelled as well as part of the Pacific Corporations
230 kV system. A complete oneline diagram of the system as entered in the EMTP
input data file for simulation is shown in figure 3.1. The letters and numbers in
parenthesis are the alphanumeric node names of the various busses and connecting
points for the sources and capacitor bank.
With the exception of the RivertonPilot Butte 115 kV line, all of the
transmission lines were represented by the distributed constant parameter model
assuming transposition. The RivertonPilot Butte line was modelled using the
JMARTI frequency dependent model (untransposed) in order to accurately
represent the transient voltage waves seen at the Riverton 115 kV bus during
switching of the capacitor bank at Pilot Butte. This was necessary because of
concerns of the transformer connected radially at Riverton. Tables of input data for
46
Atlantic
Figure 3.1 System oneline diagram for case 1
47
the distributed line models and system equivalents, as well as tower geometry and
other input data for the JMARTI model are included in appendix A.
Two transformers connect the 230 and 115 kV systems together as shown in
figure 3.1. Both are 2winding autotransformers. Test reports for both banks list only
positive sequence short circuit data, so it could not be determined if they are core or
shell type designs. The single phase saturable transformer model (3winding) was
used to represent both autotransformers. Whether or not the autotransformers are
core form is actually insignificant. If saturation is modelled, interaction between the
saturation branches of each phase will occur due to the interconnection of the delta
tertiary windings.
Effects of saturation were not considered for the Thermopolis unit for two
reasons: the bank is removed from the main bus of interest (Riverton), and the RMS
test saturation curve was not available. Steady state operating values (excitation
current at 100% voltage) from the test report were entered for the Thermopolis unit
since a linear representation of the magnetizing branch is needed for the steady state
solution.
The test report for the Riverton transformer includes the RMS saturation
curve, therefore a complete nonlinear excitation branch was modelled. This is
appropriate since the transformer is connected to the bus of interest. A twoslope,
piecewise linear representation was used to closely resemble the actual saturation
curve. Figure 3.2 is the RMS saturation curve for the Riverton unit reproduced from
the test report and figure 3.3 is the converted peak fluxcurrent curve used in the
EMTP simulations.
48
RMS exciting current
simulation
From figure 3.2, the knee is approximated to be 135% of nominal voltage. By
use of a 9999 card following the knee point saturation data, the nonlinear or air
core segment is assumed to have zero slope or be parallel to the current axis. This
greatly simplifies the data conversion from RMS to peak values and still gives an
accurate representation of the actual saturation curve. By only having to specify two
49
points (operating point and knee point) the use of the SATURATION conversion
program described in the last chapter was unnecessary. Conversion of excitation data
for both transformers as well as calculation of winding impedances are included in
appendix A.
Surge arresters are connected at each end of the RivertonPilot Butte 115 kV
line and are modelled in order to show the effects of voltage limiting and energy
absorption (duty) during transient simulations. Similar arresters are connected at the
Riverton transformer bushings but were omitted because they have basically the same
voltage discharge characteristics as the line arresters and will simply share the energy
following discharge from a transient overvoltage wave. No arresters are connected
directly at the Pilot Butte capacitor bank, however this is occasionally done to control
overvoltages associated with switching a bank. The arresters at both ends of the line
are gapless, MOV type. Ratings, specifications, discharge characteristics, input data
listing for the ZNO FITTER supporting program, and punched output data for the
exponential curve fit are included in appendix A.
Parameters such as bus inductance, resistance, and switch/contact resistances
were omitted in the isolated capacitor bank energization case. The reason for this
becomes obvious when considering the equivalent circuit of figure 3.4.
Figure 3.4 Equivalent circuit for energizing an isolated capacitor bank
Values of resistance and inductance associated with the bus and switches connecting
50
the bank to the system are very small compared to the system values and since they
are in series with each other, the system values predominate. Source resistance is
usually small compared to the source inductive reactance and provides damping of
the inrush current when the switch is closed.
Peak inrush current and inrush frequency can be calculated by the following
equations, neglecting resistance:
Ipeak = Es Ec (74)
f = (75)
where Es is instantaneous system voltage, Ec is the instantaneous capacitor voltage, C
is capacitance in Farads, and L is the system inductance in Henries [15]. Typically,
on small isolated banks such as the case being modelled, the initial peak inrush
current is limited to several hundred amperes by the system inductance. Inrush
frequency is also limited to several hundred hertz by the inductance. In the case of
reenergizing the capacitor with a trapped charge of opposite polarity from the source
voltage (restrike), the peak inrush current may be significantly higher. This is
demonstrated in the next chapter.
Case 2 System Model
Backtoback switching of shunt capacitor banks was examined in case 2. By
definition, backtoback refers to the energization of one bank with a second
energized bank in close proximity. For this case, the Grant substation and a portion
of the TriState 115 kV system in western Nebraska was modelled, and is shown in
figure 3.5.
Ogallala
115kV
Lamar
115kV
51
nrrrp
(SRCl)
21.3 mi.
19.1 mi.
(OGAL)
srrw
(LAMR)
(SRC1)
24.3 mi.
(GRN2)
^Tnnnn
_
(GRNl)
115kV
bus impedance
(GRC2)
7.5MVAR
(bank #1)
A
T4,
81kV
Grant
(25/33/42MVA)
(GRN6)
69kV
7.5MVAR
(bank #2) (ungrounded banks)
U_l
Figure 3.5 System oneline diagram for case 2
Both shunt capacitor banks at Grant are 7.5 MVAR and connected wye
ungrounded. The three transmission lines were represented by distributed constant
parameter line models assuming transposition. The transformer connected to the
Grant 115 kV bus is a 115/69 kV autotransformer with a 4.81 kV delta connected
tertiary winding. A linear representation of the Grant transformer similar to the
Thermopolis unit in case 1 was used. Transformer parameters and tables showing
input data for the system equivalents and distributed line models for case 2 are
included in appendix B.
Backtoback switching of capacitors is typified by the reduced system model
shown in figure 3.6.
52
S
system
+
t
V
c
Figure 3.6 Backtoback capacitor switching reduced system model
When C2 is energized, the energy already stored in Cj is transferred into C2 initially
and a high inrush current results. This current is limited only by the inductance and
resistance between and C2 which is usually very small. As in the case of
energizing an isolated bank, R produces the damping in the circuit. Figure 3.6
reduces to the equivalent circuit of figure 3.7.
Figure 3.7 Backtoback capacitor switching equivalent circuit
Lj and L2 are the self inductances of the two capacitors, L, is the inductance of the
buswork between the two banks, and R is the total resistance consisting of the bus,
bus connectors, switch contacts, fuses, and inherent values of the capacitors
themselves (if available).
Unlike the case of switching an isolated bank, bus impedance parameters are
S
necessary to accurately simulate backtoback switching. A layout of the 3inch,
53
hollow aluminum bus connecting the two capacitor banks at Grant is shown in
appendix B as are the bus impedance calculations. Mutual impedances of the bus are
omitted due to the short length involved.
Based on the circuit in figure 3.7, the maximum inrush current occurs when
the switch closes at peak system voltage and is given by [6]
where
and
I peak = ( Yo) I Ceq
V Leq
Leq = Li + L2 + L3
_ Cl C2
* Cl+C2
(76)
(77)
(78)
Equation 76 neglects resistance. Similar to the case of the isolated bank, inrush
frequency can be calculated using equation 75 where and are substituted for L
and C. From equations 75 and 76, it becomes apparent that with very small
inductances, both magnitude and frequency of the inrush current will be very high.
Magnitudes of 10 to 20 kA and frequencies ranging from 20 to 30 kHz are not
uncommon. It is this high magnitude of current when distributed among individual
capacitor cans within the bank that causes nuisance clearing of fuses.
Representation of Stray Capacitance
Stray capacitance to ground of outdoor bushings of apparatus such as circuit
breakers, circuit switchers, transformers, disconnects, and instrument transformers are
often added together and represented as a single capacitance to ground connected at
the bus of interest. Typical values of outdoor bushing capacitances at 115 kV are 250
 420 picoFarads (pF) as compared to 500 550 pF for 345 and 500 kV bushings [16].
55
explained in more detail in the next chapter.
Ungrounded capacitor banks are typically grounded through a high impedance
resistive potential device (4 MÂ£2) as shown in figure 3.8.
ABC
Figure 3.8 Ungrounded capacitor bank with potential device
The potential device is used to detect unbalances in voltage on the bank caused by
fuse operations on individual capacitor cans and/or unbalanced faults. The neutral
capacitance of the banks is representative of the stray capacitance of these potential
devices. A typical value at 115 kY is 600 pF [16]. This value was used in the
simulations for case 2. The EMTP model for ungrounded banks is shown in figure
3.9.
l
T
Cn = 600 pF
Figure 3.9 EMTP model of ungrounded capacitor bank
56
Delta tertiary windings such as those associated with the Riverton,
Thermopolis, and Grant autotransformers are electrically isolated (although not
magnetically) from the main network. Without a path to ground or a ground
reference, EMTP cannot calculate voltages at the tertiary nodes. As a matter of
convenience, the stray capacitance of the tertiary bushings can be represented as
shown in figure 3.10.
Figure 3.10 Transformer tertiary with stray bushing capacitances
Stray capacitance of bushings up to 15 kV ranges from 190 to 220 pF [16]. For the
Riverton and Grant transformers, 200 pF was used. As a measure to save computer
memory (due to the large size of case 1), one leg of the Thermopolis transformer
tertiary was grounded through a 10,000 ohm resistor which provided a sufficient
reference for EMTP computations.
Circuit switchers rather than circuit breakers are used exclusively to switch
capacitor banks in the TriState system due to economic considerations. Typically,
circuit switchers are onehalf the cost of circuit breakers, however their fault
interrupting capability is much less. A 115 kV circuit switcher can interrupt 4000 to
8000 amps whereas a 115 kV breaker may be rated to interrupt 20 to 40 kA. Circuit
switchers use sulphurhexafloride gas (SFfi) or vacuum as a dielectric medium for arc
Circuit Switcher Representation
57
interruption. These type of devices are well suited for interrupting capacitive current
due to their high dielectric strength in relation to the fact that higher than normal
transient voltages appear across the interrupter when deenergizing capacitor banks.
This voltage buildup is called transient recovery voltage (TRV) and is described in
more detail in the next section.
Figure 3.11 is an illustration of the circuit switcher most commonly used by
TriState to switch shunt capacitor banks [18].
system
Figure 3.11 Circuit switcher illustration
The interrupter consists of a sealed SF6 gas bottle with one or two interrupting
contacts in series (depending on the voltage rating). In parallel with the interrupting
contact(s) is a loadcarrying contact and grading resistors to equalize the voltage
when two interrupting contacts are used.
58
o
grading AW1 130MQ . 11 , resistors i 130MQ
11 11 interrupting contacts i 1 1 ;
load carrying contact
o
to brain
o
Figure 3.12 Circuit switcher interrupter
The brain is a mechanical device that coordinates the opening and closing of
the interrupter contacts and the external blade disconnect by means of a motor
operator (not shown in figure 3.11) and the motor operator linkage. Closing
(energization) and opening (deenergization) sequences of the circuit switcher are as
follows: 1) Closing: the interrupting contacts and loadcarrying contacts are closed
prior to the close signal. When the motor operator receives a close signal, the blade
disconnects close energizing the bank. Travel time of the blade is approximately 1
second. An arc occurs between the arcing horn of the blade, which is deenergized,
and the seat for the blade, which is energized at system potential, as the blade
approaches the closed position. Since the blade is relatively slow in closing
compared to system frequency, energization will enevitably always occur at or near
peak system voltage. 2) Opening: after the trip signal, the load carrying contacts are
opened followed by the interrupting contacts. Next, the blade disconnects open and
the interrupting/load contacts are reset for the close sequence.
Modelling of the circuit switcher for EMTP simulation was simple and
straight forward. The time controlled switch was used where Tclose corresponds to
approximate peak voltages on each phase (0100 psec., 2.30 msec., and 5.25 msec,
for phases A,C, and B respectively). This model was demonstrated in case 1 and used
exclusively in case 2.
59
A newer type circuit switcher inwhich the blade disconnects and loadcarrying
contacts have been eliminated has become available recently. One set of main con
tacts are used for all purposes, similar to a circuit breaker. The pole closing span for
all three phases is on the order of 1.5 msec. This device was demonstrated in case 1.
Deenergization and Switch Restrike
Circuit switchers deenergize a capacitor bank at a current zero as do all
circuit interrupting devices. Since the current is purely capacitive, the voltage at that
instant is at a peak value. Initial interruption of the capacitive circuit is generally easy
duty since the current magnitude is low compared to fault current. The current may
therefore be interrupted when the contacts have parted only a small amount. As a
result of interruption, the capacitor traps peak voltage on the load side of the switch
while the instantaneous voltage on the source side is of the same polarity. Figure
3.13 illustrates this occurance at time tr
Figure 3.13 Capacitor deenergization and subsequent restrike
60
Successful interruption depends on whether the interrupter can build up
sufficient dielectric strength to withstand the rateofrise of the recovery voltage
(RRRV) and the peak value of this voltage. From figure 3.13, the transient recovery
voltage (TRV) across the switch reaches a maximum of 2.0 times peak system
voltage at time, t^. This is only true however, for the grounded bank since all 3
phases are independent of each other. In the case of ungrounded banks, a higher TRV
can appear across the first opening phase after the remaining phases open due to a
trapped voltage on the stray neutral capacitance to ground. This phenomena is
demonstrated in the next chapter for case 2. Because of this higher voltage, circuit
switchers for ungrounded banks (115 kV and above) are supplied with two
interrupting contacts versus a single contact for grounded banks. Each contact is
rated for twice peak system voltage.
Closer examination of figure 3.13 shows that the TRV takes on the form
TRV = Vp( 1 coscot) (79)
RRRV can easily be determined from
RRRV = kV (peaktopeak) (80)
t2 ti
For the 115 kV, 60 Hz system, this value is calculated to be 0.0225 kV/psec. The
ANSI standard for circuit breakers refers to an exponential cosine envelope
inwhich a rise in voltage to 213 kV peak may occur in 275 psec. for a 121 kV, 20 kA
(interrupting) circuit breaker [19]. This equates to an RRRV of 0.775 kV/psec. No
standards presently exist for circuit switchers, however test results using the cosine
envelope have resulted in RRRV values in the range of 1.6 to 2.0 kV/ psec. for both
single and double gap units.
A restrike is defined as a resumption of current between the contacts of the
61
interrupting device during an opening operation after a zero current interval of 1/4
cycle or longer of nominal frequency. Reignition refers to the same phenomena
occurring at less than 1/4 cycle of nominal frequency [20]. The highest probability of
contact flashover occurs at ^ in figure 3.13 since this is the highest point of TRV.
Hereafter, this definition of restrike is used in the forthcoming simulations.
At ty when the restrike occurs, the capacitor attempts to recover to peak
voltage of the opposite polarity and, in so doing, will overshoot due to the fact that
the circuit is underdamped. The current waveform is actually the oscillatory inrush.
The high frequency voltage associated with the high frequency current is of the same
frequency but bears a phase relation to the current of 90 degrees. Thus, if a second
current interruption occurs at the first high frequency current zero, a peak voltage,
will be trapped at opposite polarity on the capacitor and can be as high in magnitude
as 3 times peak [21]. The scenario is now set for a second restrike which could occur
when system voltage reaches the next positive peak value. This restriking process
can continue every half cycle with subsequent buildup of even higher voltages until
surge arrester duties are exceeded and equipment is damaged.
Circuit switcher interrupters are designed not to restrike for capacitor
switching, fault interruption, or any other switching operations. Restriking may occur
for adverse conditions such as loss of gas or vacuum in an interrupter bottle or
misalignment/misadjustment of the contacts and brain. Restriking will enevitably
occur on a device not rated for capacitive current such as some oil circuit breakers,
since oil does not have the dielectric strength to handle the TRV previously
mentioned for capacitor deenergization.
A single restrike was simulated in case 1 to show the severity of the voltage
transient on the system, especially at the remote transformer bus, and the duty on the
surge arresters. The restrike model was created by first placing a positive, dc voltage
62
of 93.9 kV, representing the peak trapped charge, across one phase of the capacitor
bank using the initial conditions option. Next, the switch was closed when the system
voltage reached negative peak value.
Methods of Reducing Transients
Three methods of controlling overvoltages and limiting inrush current during
capacitor bank switching are demonstrated in the next chapter: 1) fixed bus
inductors, 2) preinsertion (closing) resistors, and 3) preinsertion inductors. A fourth
method, synchronous closing, is discussed in [3] but is not demonstrated. The
concept of synchronous closing will become obvious after description of the voltage
waveforms associated with energizing capacitor banks.
Fixed bus inductors are small, wound, aircore devices that are mounted in the
bus in series with each phase of the capacitor bank. For mechanical and economical
reasons, the inductors are often mounted on the capacitor bank rack so that they are
physically between the bank and the circuit switcher. By doing so, the inductors are
deenergized when the capacitor bank is out of service. A small advantage is realized
here by the fact that there are I2R losses associated with the inductors inherent
resistance. Three standard size wound inductors are available from a major
manufacturer: 0.18 mH, 0.36 mH, and 0.5 mH. Other sizes can be specified,
however one should be aware of and I2X losses in relation to the size of the bank
before specifying an inductor larger than 0.5 mH.
As an example, TriState has installed 0.5 mH inductors at a few locations
where capacitor banks are switched backtoback. The 0.5 mH inductor is rated for
100 amps and has an inherent resistance of 0.0138 ohms. For a 15 MVAR bank, the
total 3phase I2R and I2X losses are 235 watts and 5.66 kVAR respectively, which
should not pose a problem related to heating or derating of the bank itself. The
63
inductor must also be rated for momentary fault duty. An advantage of the inductor
in relation to limiting transients is realized by the fact that it is frequency dependent
and offers a high impedance to high frequency inrush currents and step voltage waves
similar to a choke.
Preinsertion resistors and inductors have a distinct advantage over fixed bus
inductors. The preinsertion devices are inserted only during the closing sequence of
the switching device, meaning that they are only in the circuit a brief period, on the
order of several cycles. In the case of the circuit switcher with blade disconnects, the
insertion time is on the order of 7 cycles. Because of this brief insertion time, fR and
I2X losses are not a concern. Therefore, the size of the preinsertion inductor can be
much greater than the bus inductor on the order of 20 times, which results in a much
greater effect on reducing transients associated with capacitor bank switching.
Inherent resistance of the preinsertion inductor is not a concern. In fact, the device is
purposely designed with as much resistance as deemed practical to make it lossy (a
source of damping). Likewise, preinsertion resistors are designed with large
resistance values to provide significant damping to transient waves.
Physical size limits the values of R and L on the preinsertion devices when
applied to a circuit switcher such as the one previously illustrated in figure 3.11. The
resistors/inductors are mounted on the stationary portion of the circuit switcher blade
disconnects as illustrated in the photograph, figure 3.14.
64
preinsertion
inductors
Figure 3.14 Circuit switcher with preinsertion inductors
The inductors in figure 3.14 are inserted into the circuit as the blades travel toward
the closed position and catch the springloaded arcing rods at the top end of the
inductors.
Preinsertion inductors and resistors for circuit switchers similar to the one in
figure 3.14 are available from the circuit switcher manufacturer in one size only:
lOmH with a resistance of 2.5 ohms for the inductor, and 40 ohms for the resistor.
The inductor has only been available for the last two years. These devices are not
presently available for the newer, bladeless circuit switcher previously mentioned.
Larger sized preinsertion resistors can be specified for circuit breakers since they are
mounted external to the breaker tank and are inserted by means of internal, auxiliary
contacts.
Three disadvantages to using preinsertion resistors and inductors should be
65
noted: 1) no closeintofault capability (the resistor/inductor is not rated for the fault
duty encountered when the circuit switcher is closed into a fault on the capacitor bank
or bus work between the bank and the switcher), 2) ineffective in limiting transients
associated with restriking since the restrike occurs during deenergization when the
preinsertion device is not in the circuit, 3) a secondary transient, typically smaller in
magnitude than the initial energization transient, may occur when the preinsertion
device is bypassed. (This is examined in the next chapter).
Simulation of the preinsertion sequence can be handled in two different
manners. On large mainframe computers, where memory size is not a large concern,
a complete 7 cycle simulation can be run showing both energization and bypass
transients. For this simulation, the switch model shown in figure 3.15 is typically
used.
(PBC1A)
(PBX1A)
CD
R, L
(PBT1A)
C
*
Figure 3.15 EMTP switch model with preinsertion impedance
Sj is closed at a predetermined time followed by S2 after 7 cycles. As
demonstrated in the next chapter, the initial energization transient will last on the
order of 1/4 cycle (based on 60 cycle power frequency). Power frequency follows for
7 cycles before the bypass transient occurs, which for all practical purposes is steady
state. If a full 7 cycles is displayed on one plot, the initial 1/4 cycle transient will be
compressed to the point that much information may be lost not to mention the
enormous size of the plot file that will result. Given the fact that a personal computer
rather than a mainframe was used to run the simulations which follow, a simplified
66
switch model which lumps the preinsertion impedance with the capacitor impedance
was used for the energization transient simulations (figure 3.16).
(PBC1A)
(PBT1A)
Figure 3.16 Simplified EMTP switch model with preinsertion impedance
The bypass transient is observed in a separate simulation using the model of figure
3.15. Tclose for Sj was set for 1.0 meaning that the switch is closed in the steady
state, before transient simulation. S2 is then closed at a predetermined time, and the
bypass transient is observed.
Transformer specifications for power systems must include winding insulation
withstand limitations as related to transient overvoltages. Surge arresters, as
previously described in the last chapter, protect the windings and insulation from
these overvoltages. To coordinate insulation limits and surge arresters, test impulse
voltage levels have been established which the equipment can withstand repeatedly
without damage. These impulse levels are defined in terms of Basic Lightning
Impulse Insulation Level (BIL), which is intended to be representative of a lightning
surge, and Basic Switching Impulse Insulation Level (BSL), representative of a
switching surge. Conventional BIL and BSL for nonselfrestoring insulation are
defined as the crest value of a lightning or switching impulse test voltage at which the
insulation exhibits a complete withstand or zero flashover probability [22]. Crest
voltage, in relation to insulation coordination, always refers to peak linetoground
voltage, unless linetoline voltage is specifically addressed.
Surge Withstand Standards and Insulation Coordination
67
VP
= VrmS(LL)
w
iVsJ
(81)
The standard BIL test wave for insulation withstand on power transformers is
a full impulse voltage wave which reaches crest value in 1.2 psec. (frontofwave)
and decreases to onehalf crest value in 50 psec. (1.2 x 50) [22]. The BIL waveshape
is illustrated in figure 3.17.
Figure 3.17 Standard lightning impulse waveshape (BIL)
Permissible rateofchange of voltage (dv/dt) for the frontofwave portion of the BIL
curve can be determined by dividing the crest value by 1.2 psec.
The standard BSL test wave is also a full impulse voltage wave, however it
has a much slower front time and longer tail. Front time is 250 psec. and timeto
halfvalue is 2500 psec. (250 x 2500) as illustrated in figure 3.18 [22].
68
kV
Figure 3.18 Standard switching impulse waveshape (BSL)
A third test known as chopped wave, is performed on transformers to present
a more severe stress to the winding insulation. The chopped wave has a similar front
ofwave as the BIL, but abruptly chops just beyond crest value as illustrated in figure
3.19.
Figure 3.19 Standard chopped waveshape
The chopped wave test is accomplished by applying a 1.2 x 50 psec. wave with a
spark gap connected at the terminals of either the impulse generator or transformer
winding. The gap has a specified sparkover voltage and time to sparkover or chop
time (tc). The crest value for chopped wave is always 110% of the BIL crest value
and tc is 3 [isec. for BIL crest voltages greater than 110 kV [23]. The actual slope of
the chopped portion of the wave is not specified in any standards, however judging
69
from figure 3.19 and the fact that tc is 3 nsec., the time to zero voltage must be less
than 1 nsec. Chopped waves impose different stresses on transformer windings than
the frontofwave portion of BIL waves in that the wave penetrates into the winding
before abruptly collapsing to zero. This rapid drop in voltage particularly stresses the
tumtotum insulation.
The concept of insulation coordination is to compare or calculate margins
between the BIL, BSL, chopped wave crest values and the arrester discharge voltages
having comparable wave shapes. In other words, a comparison of strength and stress.
The coordination points for MOV arresters are summarized in table 3.1.
Table 3.1 Insulation coordination points
MOV arrester protective level (discharge voltage in kV) transformer withstand level (kV)
1. 8x20 p.sec. current wave BIL
2. 45x90 p.sec. current wave BSL
3. current wave producing a voltage wave cresting in 0.5 nsec. chopped wave
The 8 x 20 current waves which form the arrester characteristic curve
described in the last chapter consist of current magnitudes typically ranging from 1.5
to 40 kA. Such a curve for the Riverton/Pilot Butte MOV arresters is plotted in
appendix A. There is no universally accepted surge current level on which to base
insulation coordination, however currents in the 10 20 kA range are usually used
[24]. The current magnitude for the slower 45 x 90 wave is typically either 500 or
1000 A depending on the voltage rating of the arrester. This magnitude may vary
between arrester manufacturers as it is not addressed in the standards. The 0.5 isec.
arrester discharge voltage, which is intended to represent the chopped wave, is
70
produced by a fast current wave having a typical shape of 0.6 x 1.5 jisec. and a
magnitude ranging from 10 to 20 kA depending on the voltage rating of the arrester.
Once again, standards do not specifically address the size and shape of this current
wave, so values may vary between manufacturers.
Margin calculations for points 1,2, and 3 in table 3.1 are performed using the
following equation:
[(transformer) I arrester \ 1 v im
mar n 1 withstand '' \ protective level /J (g2)
o margin arrester protective level
Industry standard minimum margins are 20% for BIL and chopped wave, and 15%
for BSL [24].
Insulation coordination and rateofchange of voltage (dv/dt) were examined
only in case 1. There are two reasons for this: first, surge arresters were modelled
only in case 1, and secondly, in the case of energizing an isolated capacitor bank, as
demonstrated in the next chapter, transient overvoltages are generated at a remote
location (Riverton) where arresters and a transformer are connected. In case 2, where
backtoback energization of banks was examined, it will be shown that high current
transients are generated between the banks. Voltage transients will be mitigated to
some extent by support given the bus voltage by the energized bank.
Since the Riverton transformer 115 kV winding is subjected to transient
overvoltages at the 115 kV bus, and arresters are connected there, insulation
coordination was examined at this point. Table 3.2 lists the standard transformer
withstand voltages and dv/dt for the 115 kV winding, arrester discharge voltages
(from the manufacturers catalog), and calculated protective margins [23,25].
71
Table 3.2 Riverton 115 kV insulation protective margins
transformer withstand tests transformer withstand level (kV) rateofchange of voltage dv/dt (kV/psec.) arrester protective level (kV) protective margins (%)
1. BIL 450 375 204 120.6
2. BSL 375 177 112
3. chopped wave 495 >495 231 114.3
As indicated in table 3.2, much more than minimum margins exist for all three points
meaning that there is adequate insulation coordination at the Riverton 115kV
location.
CHAPTER IV
DIGITAL SIMULATIONS. ANALYSIS. AND RESULTS
EMTP simulations for cases 1 and 2 were run on a personal desk top computer
using the MSDOS based ATP software. The computer of choice was an IBM 80286
AT compatible running at a CPU clock speed of 10 MHz with an 8 MHz, 80287 math
coprocessor. The coprocessor is required to run ATP. The computer was also
equipped with a 32 Mbyte hard disk drive and 640 kbytes of RAM memory, the
minimum requirement to run ATP. An interactive plotting program, PCPLOT,
written by Mustafa Kizilcay of Hannover, Germany, for ATP, was used to plot all of
the waveforms for the simulations which follow.
Selection of Time Step ('At')
Selection of a suitable time step for simulation involves the consideration of
three factors: 1) In order for EMTP to compute currents and voltages on transmission
lines based on past history values (tx), At must be smaller than the travel time, x, of
the shortest line in the network. In both cases 1 and 2, the shortest line length is 19.0
miles which equates to a travel time of 100 psec. 2) Computer memory size, in the
case of personal computers, may dictate the size of a particular plot file. The smaller
the time step, the greater number of sampled points for a given time frame (Tmax).
3) Theoretically, the highest displayed frequency for a given At is based on the
Nyquist interval of 2 samples per cycle [12].
(83)
73
fNyquist
2At
From a practical standpoint, 8 or more samples per cycle is considered the
minimum to obtain reasonable accuracy. Computations using the trapezoidal method
of solution in EMTP have shown errors of 5.2% and 0.8% for sample rates of 8 and
20 respectively [12]. Based on a sample rate of 20 and a At of 5 psec., frequencies in
the range of 10 kHz are observable with minimum error.
A time step of 5 psec. was selected for all of the simulations which follow.
The voltage waveform at the Riverton 115 kV bus (case 1) for single phase
energization of the Pilot Butte capacitor was used as a benchmark (figure 4.2 in the
next section) because of the high frequency components in the wave. At was varied
from 50 psec. down to 2 psec. Trial by inspection revealed no noticeable difference
between 5 and 2 psec.
Analysis and Results Case 1
The objectives of case 1 were to observe and analyze the voltage and current
transient waves seen at Pilot Butte and Riverton 115 kV busses for energization/de
energization of the 15 MVAR isolated capacitor bank at Pilot Butte. A single restrike
on phaseA of the capacitor circuit switcher was also simulated. Methods of reducing
transient voltages generated by capacitor switching were also examined. For all of
the voltage waveforms that follow, per unit (pu) voltage refers to a base value of
93.89 kV which is peak linetoneutral voltage for the 115 kV (RMS) power system.
Energization of one phase (A) of the capacitor bank is examined first and is
used as a benchmark for analysis of all the voltage waves for case 1. Much emphasis
and importance was given to modelling of transmission lines and use of the
74
JMARTT frequency dependent line model in chapter two. A comparison was made
between the use of constant distributed parameters and frequency dependent
parameters for the Riverton Pilot Butte 115 kV line. Figure 4.1 shows the Pilot
Butte and Riverton 115 kV phaseA voltages for energization of the phaseA
capacitor using constant parameters (assuming full transposition). Figure 4.2 is the
same energization with frequency dependent parameters (line is untransposed).
v [kV]
Figure 4.1 Energization of phaseA capacitor at Pilot Butte, constant line parameters
75
Figure 4.2 Energization of phaseA capacitor at Pilot Butte, frequency dependent line
parameters
A significant difference between the two waveforms is noted and is due
mainly to the fact that more damping is seen at the higher frequencies in the wave of
figure 4.2. This is to be expected since the zero sequence resistance increases
dramatically with frequency for the frequency dependent model. For all of the case 1
simulations which follow, the JMARTl model was used to represent the Riverton 
Pilot Butte 115 kV line.
The numbered points on figure 4.2 correspond with the following sequence of
events: 1) The capacitor switch at Pilot Butte is closed energizing the bank at peak
voltage. The initial voltage on the capacitor is zero and cannot change
instantaneously so the capacitor looks like a short circuit at the instant the switch is
closed. Consequently, the Pilot Butte bus voltage collapses to zero almost
instantaneously. This voltage change generally occurs in a fraction of a microsecond
to several microseconds depending on the inductance and surge impedance (L/R time
76
constant) of the system at that point [26]. The momentary short circuit caused by
energizing the capacitor results in an inrush current which is shown in a later trace.
2) The step wave generated by the capacitor energization travels along the
Pilot Butte Riverton 115 kV line and arrives at the Riverton 115 kV bus in 159 p
sec., the travel time, x, of the line. At this point, the surge sees a discontinuity or
change of surge impedance from the line to the transformer connected to the line.
The voltage does not simply collapse to zero but rather swings toward the opposite
polarity of the bus voltage prior to the collapse. The amount of overshoot is a
function of what is known as coefficent of reflection, a. This concept, as related to
travelling waves is illustrated in figure 4.3.
A
T"
r
Figure 4.3 Effects of impedances on travelling waves
The coefficent of reflection is given as
_ Z2^Zi
Z! +Z2
(84)
and the reflected voltage, V2 is
V2 = aVi (85)
A portion of Vj is also refracted through by a similar coefficient of
refraction, however only the reflected portion of the wave is of interest concerning the
77
composition of figure 4.2. From equations 84 and 85 it is apparent that if bus B is
open circuited, that is = , then a will be 1 and the reflected voltage, V2 will be
equal to the incoming voltage, Vr The net result at bus B is that V2 adds to Vj
resulting in a doubling effect. If the surge impedance at bus B looks like a short
circuit, such as a capacitor, a will be 1 and the net effect will be a cancellation of
the two voltages at bus B.
In the case of the Riverton 115 kV bus, a much larger overshoot or doubling
effect would be seen if the transformer were open circuited on the 230 kV side. In
this case, the arriving surge would see only the magnetizing impedance to ground
which is very high (360 kf2). The actual system configuration however, has three 230
kV transmission lines and the 230 kV system connected to the 230 kV side of the
transformer. The net result is the arriving surge sees the parallel combination of the
transformer magnetizing impedance and the lumped sum of the transformer winding
impedance and 230 kV system Thevenin equivalent as illustrated in figure 4.4.
(RIV1) 115kv (RIV2) 230kv
Figure 4.4 Equivalent surge impedance at Riverton 115 kV bus
The combined impedance is much lower than the magnetizing impedance
alone resulting in a lower coefficient of reflection which tends to mitigate the
doubling effect of the surge. The same effect would be accomplished by adding
transmission lines to the Riverton 115 kV bus since the parallel combination of surge
impedances of the lines (300 400 ohms each) would lower the overall surge
impedance at the bus.
78
3) The surge returns to the Pilot Butte 115 kV bus and is barely discernible
due to the very low surge impedance of the capacitor bank. At this point, the
reflection coefficient is 1 resulting in a cancellation of the voltages at the bus and a
surge of opposite polarity that is on its way back to Riverton.
4) The surge returns to Riverton giving a transient surge in the opposite
direction, resulting in the peak value for the complete wave. This value is 1.39 per
unit and is not high enough to cause discharging of the Riverton surge arrester.
(From the arrester discharge curve in appendix A, the voltage at which discharge
begins is approximately 1.77 pu). Subsequent reflections occur after point 4 causing
high frequency components in the wave and dampen out due to the effects of
resistance at the higher frequencies.
5) The bus voltage at Pilot Butte attempts to recover to the 60 Hz value and in
so doing overshoots the source voltage. The actual value is 1.49 pu which also is
below the arrester discharge level. The overshooting is a result of the equivalent
circuit being underdamped.
Since the transient wave at Riverton is superimposed on the 60 Hz voltage, the
peak transient will always occur when the switch is closed at or near peak system
voltage. The maximum step change at the capacitor location also occurs when
closing at peak voltage and also affects the peak transient at the remote bus.
Conversely, it becomes apparent that no step change or transient will occur if the
switching device were to close or make up at a voltage zero. In this case, the
capacitor charges as system voltage increases. Consequently, little or no inrush
current flows. This is the theory behind controlled synchronous closing which is
discussed in detail in [4].
Figure 4.2 can be summarized as follows: The Pilot Butte voltage wave has
two key characteristics a fast front surge or step wave that occurs initially and an
79
oscillatory transient that follows. The parameters affecting these characteristics are
the capacitor value, R and L circuit constants at the bus, and where the switch is
closed in relation to the 60 Hz source voltage. The Riverton voltage wave also begins
with a fast front surge and ends with an oscillatory transient, which by inspection
contains high frequencies in the range of several kHz. The factors that mainly
influence the characteristics of this wave are the surge impedance at the Riverton bus
and the length of the line between Pilot Butte and Riverton.
In reference [1], the frequency of the voltage wave appearing at the
transformer terminal was examined in detail and determined to be coincident with the
natural frequency of one of the winding sections (part winding resonance). This
resulted in an internal voltage magnification and subsequent winding failure. It is not
in the scope of this thesis to examine this phenomena. No straight forward method to
examine exact frequency content of a particular waveform exists in the version of
EMTP/ATP used here. Nor could the detailed distributed transformer model be built.
Inrush current for energization of the phaseA capacitor is shown in figure 4.5.
80
i [A]
Figure 4.5 Inrush current for energization of phaseA capacitor at Pilot Butte
Large discontinuities or notches are seen in the current trace and correspond with
reflected voltage waves returning to the Pilot Butte bus. The peak magnitude of
current is 500 amps and the inrush frequency is approximately 345 Hz.
The composite voltage waves for 3phase energization of the capacitor bank
are quite similar to the single phase energization. Figures 4.6 and 4.7 are the Pilot
Butte and Riverton bus voltages for staggered 3phase closing of the bank.
81
v [kV]
Figure 4.6 3Phase staggered capacitor energization Pilot Butte bus voltage
v [kV]
Figure 4.7 3Phase staggered capacitor energization Riverton bus voltage
82
Staggered closing refers to the switch on each phase closing at its perspective voltage
peak. This simulates the arcing over of each blade contact of the conventional circuit
switcher described in the last chapter. Since the capacitor bank neutral is solidly
grounded, each phase closes independently.
The main difference between the waves of figure 4.2 and those of figures 4.6
and 4.7 is the additional discontinuities and spikes caused by the effects of mutual
coupling between phases on the transmission line, and the fact that the waves on each
phase arrive at each bus at different times. In figure 4.6, the highest overshoot is 1.65
pu and occurs on phaseC. The highest transient value in figure 4.7 is also 1.65 pu
and occurs on phaseB.
In the last chapter, a newer circuit switcher without blade disconnects was
discussed. Energization occurs through the highspeed, highdielectric interrupter
contacts and the manufacturer specifies a maximum pole closing span of 1.5 msec. A
series of random pole closures of the capacitor bank switcher within the 1.5 msec,
window were run to determine the maximum transient overvoltage at the Riverton
bus. Simulations were run first without surge arresters in order to determine which
pole closure sequence yielded the highest overvoltage. The highest transient voltage
at Riverton was 1.81 pu and occurred on phaseA when all three poles closed
simultaneously at 100 psec. This simulation is shown in figures 4.8 and 4.9.
83
v [kV]
Figure 4.8 3Phase simultaneous capacitor energization Pilot Butte bus voltage
v [kV]
Figure 4.9 3Phase simultaneous capacitor energization Riverton bus voltage
84
From figure 4.8, it is apparent that the energization occurs while phaseA
system voltage is at peak value and phases B and C are at half peak. The amount of
overshoot of the oscillatory wave at Pilot Butte following the step change for phaseA
is the same as previous simulations. Phase B and C differ substantially because
phaseB system voltage is decreasing and phaseC is increasing. Overshoot of the
phaseA step wave as it arrives at the Riverton bus in figure 4.9 is substantially
greater than previous simulations. This is attributed to the fact that the waves of each
phase arrive at the Riverton bus at precisely the same time. B and C phases have an
additive effect on phaseA.
The previous simulation was run again with the surge arresters connected.
Figure 4.10 is a plot of only phaseA voltages at Pilot Butte and Riverton.
Figure 4.10 3Phase simultaneous capacitor energization Pilot Butte and Riverton
phaseA voltage
Close comparison of figure 4.10 with 4.9 shows the peak transient at Riverton has
85
been reduced slightly by the arrester. Figure 4.11 is a plot of the phaseA arrester
energies at Riverton and Pilot Butte for this simulation.
W [J]
40
20
0
20
I
40
0 500 1000 1500 2000 2500 3000 3500 4000
RTV1AGND PBT1AGND t[ISec]
Figure 4.11 PhaseA arrester duty at Riverton & Pilot Butte for 3phase capacitor
energization
No noticeable energy is absorbed in the Pilot Butte arrester. At Riverton, the arrester
duty is 55 Joules which is very low compared to its 659 kJ rating.
The Riverton phaseA voltage wave in figure 4.10 is the most severe of the
capacitor energization simulations. Although surge arresters limit the peak voltage of
the transient to a safe level below the BIL rating of the transformer, there is concern
for the rateofchange in voltage of the initial step change and rise of the oscillatory
transient that follows. Figures 4.12 and 4.13 are these portions of the wave with the
time scales magnified in order to measure rateofchange.
86
v [kV]
Figure 4.12 Riverton phaseA voltage expanded time scale for initial portion of
wave
v [kV]
Figure 4.13 Riverton phaseA voltage expanded time scale for second portion of
wave
87
The initial step change of the Riverton voltage in figure 4.10 appears to chop
from peak system voltage (93.89 kV) to 50 kV almost instantaneously. As
illustrated in figure 4.12, this time is actually 10 psec. (2 time steps) which results in
a rateofchange (dv/dt) of 14.39 kV/psec. A discontinuity occurs between the 5 p
sec. time steps. The validity of evaluating an individual slope for one time step is
questionable, therefore only the aggregate slope from peaktopeak is considered.
This value is well below the Riverton transformer standard for chopped wave (table
3.2). From figure 4.13, the oscillatory transient rises from 50 kV to 165 kV in 305 p
sec. resulting in a dv/dt of 0.705 kv/psec. which also is well below the transformer
standard for BIL as indicated in table 3.2.
With the possible exception of high frequency components in the Riverton
voltage waves, none of the transients exhibited thus far appear to pose any threat to
the winding insulation of the Riverton transformer. Never the less, the use of pre
insertion impedances is demonstrated next as a method of reducing the magnitude and
frequency of the energization transients. The 3phase simultaneous closing case is
used because the most severe transients were generated and it is easiest to see the
effects of the preinsertion impedances on all 3 phases.
Simulation using 40 ohm preinsertion resistors is examined first and the
results are shown in figures 4.14 and 4.15.
88
Figure 4.14 Pilot Butte bus voltages for capacitor energization 40 ohm pre
insertion resistors
v [kV]
 RTV1A RTV1B  RIV1C t [p.Sec]
Figure 4.15 Riverton bus voltages for capacitor energization 40 ohm preinsertion
resistors
89
In this case, the bus voltage at Pilot Butte does not collapse to zero. The extent to
which the bus voltage collapses depends upon the ratio of the resistance of the pre
insertion resistor to the equivalent surge impedance of the transmission lines
connected to the capacitor bank bus (voltage divider). From figure 3.1, two
transmission lines with surge impedances of 370 ohms each are connected to the Pilot
Butte bus resulting in an equivalent surge impedance of 185 ohms. This reduced
voltage dip at Pilot Butte results in less overshooting of the step wave at Riverton.
The peak transient voltage at Riverton is reduced to 1.49 pu (phaseA) and the
reflected waves following the peak transient are dampened somewhat by the effects
of the additional resistance.
At Pilot Butte (figure 4.14), the oscillation following the voltage collapse
reveals a series of small discontinuities. These discontinuities occur because the
travelling waves returning to Pilot Butte now see the 40 ohm preinsertion resistor
rather than the very low surge impedance of the capacitor. The reflection coefficient
is now approximately 0.64 resulting in a less than perfect cancellation of the incident
wave.
Simulations were run for other values of preinsertion resistors. A dramatic
difference was seen using resistors of a much larger value which would be expected.
Figures 4.16 and 4.17 show the effects of 200 ohm preinsertion resistors.
90
Figure 4.16 Pilot Butte bus voltages for capacitor energization 200 ohm pre
insertion resistors
v [kV]
Figure 4.17 Riverton bus voltages for capacitor energization 200 ohm preinsertion
resistors
91
Voltage collapse at the Pilot Butte bus is further mitigated since a larger portion of
the voltage is dropped across the 200 ohm resistors (half). Overshooting of the
oscillatory transient following the collapse in voltage is now nonexistent because the
circuit is closer to being critically damped. Larger discontinuities are seen in the
latter portion of the wave due to a reflection coefficient which now approaches 0.04.
At the Riverton bus, the arriving step wave is reduced to the point that very
little overshoot is seen. The reflected transient waves which follow are dramatically
reduced to where they are barely discernible due to the effects of greater damping and
the fact that the reflections from Pilot Butte are greatly reduced. The peak transient
voltage at Riverton on phaseA is now 1.17 pu.
The next simulation involves the energization of the capacitor bank through
the preinsertion inductor. Three values of inductors were examined: 5,10, and 20
mH. Since the 10 mH device is the only one commercially available, results are only
shown for this value. The 5 and 20 mH inductors were found to exhibit either a
smaller or larger effect. Figures 4.18 and 4.19 are the bus voltages for 3phase
energization of the capacitor bank through the 10 mH preinsertion inductors.
92
Figure 4.18 Pilot Butte bus voltages for capacitor energization 10 mH preinsertion
inductors
Figure 4.19 Riverton bus voltages for capacitor energization 10 mH preinsertion
inductors
93
The main difference in bus voltage at Pilot Butte from previous simulations is now
there is no abrupt step change when the capacitor is energized. The reason for this is
the inductor has a very high surge impedance relative to the surge impedance of the
lines connected to the Pilot Butte bus. This results in an exponential decay in voltage
as determined by the equivalent RL circuit. This exponential decay of the step wave
is seen at the Riverton bus as well, but to a lesser extent.
An important difference seen at Riverton is the reduction of the high
frequency content in the voltage wave (rounding off of the sharp peaks and reduction
in the number of peaks) caused by the detuning effect of the inductor. Also, since
the preinsertion inductors have a relatively low resistance, the transient oscillations
are not significantly damped as they are with the preinsertion resistors. The peak
transient voltage at Riverton (phaseA) has been reduced to 1.28 pu for this
simulation.
Bus inductors were not examined for the energization simulations because
their inductance values (0.18 0.5 mH) are much smaller than the preinsertion
inductors and consequently, their effect on mitigation of the transient voltages are
small in comparison. Table 4.1 summarizes the overall effects of the preinsertion
impedances on the Riverton 115 kV bus voltage for energization of the capacitor
bank.
94
Table 4.1 Effects of preinsertion impedances on Riverton voltage for capacitor
energization
preinsertion device peak transient voltage (phase Apu) reduction of high frequency components damping
none 1.77 pu*
40 ohm resistor 1.49 pu moderate moderate
200 ohm resistor 1.17 pu significant significant
10 mH inductor 1.28 pu significant minimal
* limited by surge arrester
Deenergization of the capacitor bank is examined next. Since the bank
neutral is solidly grounded, each phase clears at its own current zero which
corresponds to peak voltage. Capacitor deenergization normally results in no system
transients. This is illustrated in figure 4.20 and 4.21 where figure 4.20 is the voltages
on the capacitor side of the switch and figure 4.21 is the Pilot Butte bus voltages.
Figure 4.20 Capacitor voltages for 3phase deenergization of capacitor bank
95
Figure 4.21 Pilot Butte bus voltages for 3phase deenergization of capacitor bank
Figure 4.20 shows the trapped voltages on each phase of the capacitor bank following
interruption. In this simulation, the clearing sequence is CBA. The bus voltages in
figure 4.21 indicate small discontinuities at and following interruption. This is due to
regulation of the 60 Hz source voltages when the capacitive load is dropped.
The last series of simulations for case 1 involve a single restrike on phaseA
of the circuit switcher at Pilot Butte following deenergization of the capacitor bank.
Figure 4.22 shows the phaseA voltages at Pilot Butte and Riverton for the restrike.
