Citation
Analysis of the internal voltage distribution in a reactor using the electromagnetic transient program (EMTP)

Material Information

Title:
Analysis of the internal voltage distribution in a reactor using the electromagnetic transient program (EMTP)
Creator:
Montoya, Anthony H
Place of Publication:
Denver, Colo.
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
vii, 63 leaves : illustrations ; 29 cm

Thesis/Dissertation Information

Degree:
Master's ( Master of Science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Electrical Engineering, CU Denver
Degree Disciplines:
Electrical Engineering
Committee Chair:
Sen, Pankaj K.
Committee Members:
Roemish, William R.
Anderson, Marvin F.
Thomas, Joe E.

Subjects

Subjects / Keywords:
Electric reactors ( lcsh )
Electric circuit analysis ( lcsh )
Electric circuit analysis ( fast )
Electric reactors ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 43-46).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Department of Electrical Engineering.
Statement of Responsibility:
by Anthony H. Montoya.

Record Information

Source Institution:
University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
22947629 ( OCLC )
ocm22947629
Classification:
LD1190.E54 1990m .M66 ( lcc )

Full Text
ANALYSIS OF THE INTERNAL VOLTAGE DISTRIBUTION IN
A REACTOR USING THE ELECTROMAGNETIC TRANSIENT PROGRAM (EMTP)
by
Anthony H. Montoya
B.S., Colorado School of Mines, 1982
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Department of Electrical Engineering


This thesis for the Master of Science Degree by-
Anthony H. Montoya
has been approved for the
Department of
Electrical Engineering
by
YA
ft
ankaj K. Sen
William R. Roemish
Date GUI % A900
Joe E. Thomas


iii
Montoya, Anthony H. (M.S., Electrical Engineering)
Analysis of the Internal Voltage Distribution in a Reactor Using
the Electromagnetic Transient Program (EMTP)
Thesis directed by Associate Professor Pankaj K. Sen
A method is developed in this thesis to analyze the
internal voltage distribution in a single layer, air-core
reactor. The method is based on dividing a coil into a number of
equal segments and calculating the parameters of the equivalent
circuit. The equivalent circuit is then modeled using the
Electromagnetic Transient Program (EMTP) and solved for internal
voltage distributions.
The method is flexible and accuracy is dependent on the
ability to determine the equivalent circuit parameters and on the
40 coupled linear branch limitation of the EMTP.
The form and content of this abstract are approved. I recommend
its publication.
Pankaj K. Sen


iv
ACKNOWLEDGMENTS
The support and assistance provided by everyone at the
Western Area Power Administration is greatly appreciated.
Thanks.
To Madison, who is just beginning her adventure.


V
CONTENTS
CHAPTER
I. INTRODUCTION ............................. 1
II. EQUIVALENT CIRCUIT OF A REACTOR .......... 4
III. REACTOR MODELING USING THE EMTP...........11
IV. PROGRAM TO CALCULATE EQUIVALENT CIRCUIT
PARAMETERS...............................16
V. STEADY STATE FREQUENCY RESPONSE .......... 20
VI. ENERGIZATION TRANSIENT RESPONSE .......... 30
VII. DISCUSSION............................... 39
VIII. CONCLUSIONS...............................42
BIBLIOGRAPHY .......................................... 43
APPENDIX
A. VAX FORTRAN SOURCE CODE FOR REACTR PROGRAM 47
B. EMTP COMPATIBLE DATA FILE FOR
10-SEGMENT MODEL ........................ 60
C. EMTP DATA FILE FOR ENERGIZATION RESPONSE 62


vi
TABLES
Tables
5.1 Parameters for Degeneff's Coil ...........24
5.2 Self and Mutual Inductances for
Degeneff's Coil............................24
5.3 Resonant Frequencies of Grounded
Neutral Model ............................ 27
5.4 Resonant Frequencies of Ungrounded
Neutral Model ............................ 28


vii
FIGURES
Figures
2.1 Equivalent Circuit Model Diagram ............ 9
2.2 Diagram of Coil Parameters Used in
Inductance Equations ..................... 10
4.1 Flowchart of REACTR Program ................ 19
4.2 Input Data For REACTR Program................19
5.1 Frequency Response of Grounded Winding ... 25
5.2 Frequency Response of Ungrounded Winding . 26
5.3 Internal Voltage Distribution for
Grounded Neutral Model ................... 29
5.4 Internal Voltage Distribution For
Ungrounded Neutral Model ................. 29
6.1 Energize Grounded Winding .................. 35
6.2 Energize Ungrounded Winding ................ 36
6.3 Decomposition of Incident Pulse ............ 37
6.4 Energization Transient for Grounded Winding 38
6.5 Energization Transient for Ungrounded
Winding....................................38


CHAPTER I
INTRODUCTION
Shunt reactors are commonly used to compensate for the high
charging current on long transmission lines during light loading
conditions. Two common types of shunt reactor construction are
the oil-immersed reactor and the dry-type reactor.
Oil-immersed reactors are generally connected directly to
the line requiring compensation. The reactors are either single-
phase or three-phase units.
Dry-type reactors are usually limited to voltages through
34.5-kV. The reactors are commonly applied to the tertiary
winding of a transformer connected to the system requiring
compensation. The reactors are generally single-phase, air-core
units. This thesis will concentrate on dry-type, air-core
reactors.
Many shunt reactor failures were reported in a 1979, IEEE,
power industry survey [1,2]. One common failure mode for the
dry-type shunt reactors consists of an internal, turn-to-turn
fault which results in a very small change in phase current. If
not isolated promptly, the turn-to-turn fault can evolve into a


2
phase-to-neutral fault. The phase-to-neutral fault can place
line-to-line voltage across each phase of the reactor resulting
in possible damage to the unfaulted phases.
The nature of the internal faults makes it difficult to
determine the cause of the fault or to predict reactor
performance from field tests [3,4,5,6]. Special techniques are
required to analyze the internal voltage distribution in
windings. Traditionally, three methods have been used to
determine the internal voltage distribution; direct measurement
on an actual winding, direct measurement on a model of the
winding or calculating the response from a mathematical,
equivalent circuit model of the winding.
Direct measurement of the actual winding is the most
reliable method of determining the internal voltage
characteristics, however this method requires sophisticated
equipment and can not predict the performance of a winding before
it is built. Direct measurement of a model is a valuable method
but also requires test equipment and is inflexible.
Mathematical, equivalent circuit models, are a convenient,
flexible alternative to direct measurements. The mathematical
models have traditionally been solved manually or more recently,
using computer programs specifically developed to numerically
solve the model. The computer programs are generally limited
because they can not conveniently model the interaction between
the winding and other power system components. An alternative to
the existing programs is the Electromagnetic Transient Program
(EMTP). The EMTP is a general purpose, digital, transient


3
simulation program that is beginning to receive wide spread use.
The EMTP has the advantage that it is flexible and can accurately
model the interaction between a large number of power system
components.
The purpose of this thesis is to develop an equivalent
circuit for a single-layer air-core reactor, model the equivalent
circuit in EMTP and then use the model to analyze the steady
state frequency response and energization transient response of
the reactor.


CHAPTER II
EQUIVALENT CIRCUIT OF A REACTOR
An equivalent circuit to study the internal voltage
distribution of a coil can be developed by dividing the coil into
a number of segments that are electrically and magnetically
coupled. The circuit used in this study for a single layer air-
core reactor was developed by P. Abetti and F. Maginniss [7] and
is shown in Figure 2.1. Each segment is equal in length and
electrically approximated by lumped circuit parameters. The
lumped circuit parameters include self inductances, mutual
inductances between segments, ground coupling capacitances,
winding turn-turn capacitances and shunt, series and ground
leakage resistances.
Computation of Equivalent Circuit Elements
Capacitances
The computation of capacitances for the N-segment
equivalent circuit model in Figure 2.1 is straight forward. Let
Cgt be the total capacitance to ground and Cst the total series
capacitance of a distributed winding. If the winding is divided
into N segments, the capacitance to ground of each segment is
Cg=Cgt/N. Half of the capacitance to ground, Cg, is placed at


5
each end of the section. The series capacitance of each segment
is Cs = N Cst.
The computation of the total capacitances can be determined
by various methods and to various degrees of accuracy. The
values can often be supplied by the reactor manufacturer. One
method of determining the series capacitance Cst is by
calculating the capacitance, C, between two adjacent turns using
a parallel plate approximation [8]. The total series capacitance
is then Cst = C/turns. The total ground capacitance can be found
by treating each winding section as an equivalent cylinder. The
capacitance between each equivalent cylinder and ground is then
easily calculated [8, 9]. The total ground capacitance is
approximately equal to the sum of the capacitances of all
segments [10].
Resistances
Let rst be the total series loss resistance. The series
loss resistance is both current and frequency dependent. The
resistance includes the winding ohmic losses which are dependent
on skin effect, the proximity effect, the stray field losses
which are significant in air cored reactors, and the stray field
losses in the spiders and connecting bus bars. Rst is the total
shunt resistance and accounts for dielectric losses in turn-to-
turn insulation. Rgt is the total winding leakage resistance to
ground and accounts for the dielectric losses in the turn-to-
ground insulation. If the winding is divided into N- segments,
the per segment series loss and shunt resistances are rs = rst/N


6
and Rs = Rst/N. The ground resistance of a segment is Rg=N(Rgt).
Twice the ground resistance of a segment, 2 Rg, is placed at each
end of the segment.
The total resistances are difficult to calculate
analytically and are often found by testing. The resistances
have little effect on the natural frequencies of the winding,
however they cause damping and can considerably reduce the
magnitudes of the voltage oscillations. Resistances are often
neglected since they do not have a large effect on natural
frequencies and since the maximum magnitude of the voltage
oscillations is primarily of interest [7].
Inductances
The relationship between the total inductance of a coil and
the inductance of an individual segment within the coil is not as
simple as the relationships for the capacitance and resistance.
This is because every coil segment, n, has self inductance Lnn
and mutual inductances Mnm with all other segments. For a coil
divided into N segments there will be one self inductance for
each segment. The self inductance for the first segment is
designated L1]L, L22 for the second and Lnn for any segment n. If
the segments are equal in length, the self inductances of each
segment is equal and is referred to as L1X. For the coil divided
into N equal segments, there will be N-l mutual inductances. For
the first segment, M12 is the mutual inductance between the first
segment and the second segment. In air coils the self and mutual
inductances of a segment do not depend upon the segment's


7
position within the coil. Since the mutuals do not depend on the
position of the segment within the winding, the mutual inductance
between any two adjacent segments will have a value equal to
Mij M13 is therefore equal to the mutual inductance between any
two segments separated by one segment. In general, Mln is the
mutual inductance between any two segments separated by n-2
segments.
The self inductance of any coil segment and the mutual
inductance between any two coil segments can by accurately
calculated from the geometry of the coils. The general method
used in this thesis is based on Neumann's formula for inductance
[11]. Applying Neumann's formula, the mutual inductance between
two coaxial, infinitesimally thin concentric or nonconcentric
coils is
pS+1,
r1!
M = yonin2
R^R2Cos^ di|/
(1)
dz' dz"
,ii J, j
*
R^+R2+(z'-z")2-2R1R2Cos^
Where, as shown in Figure 2.2, nx and n2 are the number of turns
per unit length, Rx and R2 are the radii, s is the separation
between the two coils and \|*=0 is the azimuthal angle.
Integrating with respect to \jy, z' and z" gives
.3/2
(2)
M = 2Jt po(R1R2) n1n2[Ci(R1,R2,z1) Ci(R1,R2,z2)
+ Ci(R1,R2,z3) Ci(R1,R2,z4)]
where the function Ci is defined as


8
Ci(R^^2>z)
and,
m R1R2
2n
^ R^+R2+z^-2R^R2Cos\(/
Rl+R2-^RlR2^OS^
+ s
+ s
+ s
+ s
(3)
Sin \J> d\|/
The function Ci can be accurately solved numerically using
the computer algorithm developed by T. Fawzi and P. Burke [11].
Computer code to solve the function Ci and a subroutine to
calculate the inductances is listed in Appendix A and discussed
in Chapter IV.


NODAOO
9
FIGURE 2.1
Equivalent Circuit Model Diagram
Equivalent Circuit Elements
L1X Self inductance
Mnn Mutual inductance
Rs Shunt resistance
rs Series loss resistance
Rg Ground leakage resistance
Cs Winding capacitance
Cg Ground coupling capacitance


10
FIGURE 2.2
Diagram of Coil Parameters Used
in Inductance Equations


CHAPTER III
REACTOR MODELING USING THE EMTP
The Electromagnetic Transients Program (EMTP) is a computer
program used to simulate electromagnetic and elctromechanical
transients in multiphase electrical power systems. It was first
developed as a digital counterpart to the analog Transient
Network Analyzer (TNA). An EMTP simulation case is defined by
generating component models. The types of components that can be
modeled include:
1. Uncoupled resistance, inductance and capacitance.
2. Coupled resistance, inductance and capacitance.
3. Traveling wave line and cable models.
4. Nonlinear impedances.
5. Ideal switches.
6. Ideal current and voltage sources.
7. Machines.
8. Control systems.
Once the component models are defined, control parameters are
defined and the desired simulation is executed.
In this thesis, an EMTP model is developed for a single-
layer, air-core reactor based on the equivalent circuit described


12
in Chapter II. The reactor model is then connected to the
appropriate component models for simulation. The EMTP will be
used to simulate both steady state and transient response. The
frequency scan option, which systematically varies the frequency
of the sources for steady state solution will also be used.
From Chapter II, a single-layer air core reactor can be
modeled as a network of uncoupled resistances, uncoupled
capacitances and coupled inductances. A brief discussion of the
EMTP solution techniques for these elements follow. Refer to
[12,13,14,15] for additional information on EMTP simulations.
EMTP Solution for Lumped Elements
The basic EMTP time-domain solution starts with a known
steady state initial condition at t=t-At. A new solution is then
calculated for At seconds later. This new solution is used as
the t-At initial condition for the next calculation. The process
is repeated until the time domain simulation is complete.
Uncoupled linear lumped-element modeling
For an inductor, i = 1/L J v dt. Applying trapezoidal rule
integration with time step At to the differential equation
yields:
i(t) = i(t-At) + At(v(t) v(t-At))/2L (4)
Regrouping yields
i(t) = v(t)/R + I
(5)


13
Where R = 2L/At, I = i(t-At) + v(t-At)/R
(6)
The resistor R is a constant, while I represents a known current
source which varies with each time step.
Similar techniques can be used to model a resistor and a
capacitor. In each case the differential equations of R, L or C
elements are transformed into equivalent constant resistors and
time-varying current sources. Voltages sources can also be
represented by a Norton equivalent current source of a form
similar to the R,L,C elements. A system of R,L,C, branches and
voltage sources can therefore be represented by a network of R,I
equivalent branches which can be solved at each time step.
Coupled linear lumped-element modeling
The uncoupled model is a special case of the more general
coupled linear lumped-element- model. By switching from scalar to
matrix algebra, the same general formulas apply.
For coupled inductances, [v] = [L] d[i]/dt. Applying
trapezoidal rule integration as before yields:
[i(t)] = [i(tAt)] + At [L]-1[v(t) v(t-At)]/2
(7)
Regrouping yields
[ i (t) ] = [vCOHR]"1 + [I]
(8)
Where
[R] = 2[L]/At, [I] = [i(t-At)] + [R]1[v(t-At)]
(9)


14
Once again, the resistor matrix [R] is a constant, while [I]
represents a known current source which varies with each time
step.
Similar techniques are used to model a coupled capacitor or
a coupled R-L branch. In each case the differential matrix
equations of R, L or C elements are transformed into equivalent
constant resistors and time-varying current sources.
After the coupled or uncoupled elements are converted to
equivalent resitances and time-dependent current sources they are
connected together to form a circuit network. Kirchhoff's
current and voltage laws are then be applied to obtain a system
of simultaneous equations. EMTP solves the simultaneous
equations by setting them up as the nodal admittance matrix
[Y][v]=[i], where [Y] is the nodal admittance matrix and [v] and
[i] are the vectors of the node voltage and the injected current.
The node voltage vector is then found using Gaussian elimination
to solve the matrix equation.
Structure of the EMTP Model
The reactor equivalent circuit is entered into EMTP as
collection of lumped, linear impedance branches. An example of
the structure of the EMTP branches for a 10-segment reactor is in
Appendix B. The structure of the model is described in detail in
Section 6 of the EMTP Rule Book [16]. Each line of data in the
input file is referred to as a card since the file format is
FORTRAN fixed column format. Each branch card identifies the


15
parameter of the element being modeled and the two names of the
nodes that the branch is between. Two types of EMTP lumped
models are used to describe the reactor equivalent circuit.
The multiphase coupled R-L branch card is commonly used to
model coupling between phases and to model sequence components.
In the reactor model it is used to represent the self inductance,
the mutual inductance and the series loss resistance. In general
the multiphase coupled R-L model can be used to specify up to 40
mutually-coupled, series R-L elements. The data is specified as
an R-L matrix. Since the matrix is always symmetrical, a
diagonal matrix representation is used.
All other reactor equivalent circuit elements are specified
as lumped, uncoupled, series R-L-C branch cards. The format
shown in Appendix B is the alternate high-precision format. The
high precision format is specified by the use of the $VINTAGE,1
card. After this card is read, all subsequent branch cards
require the higher precision format. The $VINTAGE,0 card
switches to the standard format. The terminal node names are
specified in columns 3-8 (BUS1) and 9-14 (BUS2). If any of these
node names are blank, that node will be treated as a ground
connection. The R-L-C information is specified in columns 27-42
(R), 43-58 (L) and 59-74 (C).


CHAPTER IV
PROGRAM TO CALCULATE EQUIVALENT CIRCUIT PARAMETERS
REACTR is a Fortran computer program that was developed to
calculate the parameters of the elements in the equivalent
circuit model. The program also creates a data file that can be
directly included into an EMTP simulation. Source code for the
program and subroutines is in Appendix A. The program was
written and compiled on a DEC, VAX computer. Figure 4.1 contains
a flowchart of the main program and subroutines. A description
of the program follows.
Program REACTR
This is the main body of the program. REACTR calls four
subroutines that input data, calculate parameters for the
equivalent circuit, output a text data file and creates a data
file that can be read by the EMTP.
Subroutine REDATA
This subroutine will input the data necessary to model the
reactor. Figure 4.2 is a diagram of the coil and lists the data


17
that is required to model the reactor. In addition to reading in
data, this subroutine divides the coil into segments and
calculates all of the equivalent circuit elements except for the
self and mutual inductances. The subroutine will except a value
of zero for any of the total resistances or capacitances. Any
circuit element that is zero will be neglected.
Subroutine INDCTN
INDCTN calculates the self inductance of each coil segment
and the mutual inductances between all other sections. A
function CI(RR1, RR2, Z) is called to calculate the inductances
as described in Chapter 2 and [11].
Subroutine DTABLE
This subroutine creates a file summarizing the input and
output data. The format is not EMTP compatible but is easy to
interpret.
Subroutine MODOUT
MODOUT creates an EMTP compatible data file. The file lists
the parameters for each of the equivalent circuit elements in the
form of EMTP branch cards. The file can be directly read by
EMTP using the $INCLUDE statement. In addition to listing the
circuit element parameters, the subroutine connects the branch


18
elements together to create the equivalent circuit.
Inductances and capacitances listed by MODOUT are in units
of mH and yF. EMTP can use either reactances in ohms or
inductances and capacitances in mH and yF. To allow EMTP to
properly interpret the units used, the X option (XOPT) and C
option (COPT) columns, in the first miscellaneous data card, must
be entered as zeros. All linear branch cards will then be
interpreted in units of mH and yF. Resistances are always in
ohms.
The convention used for naming the nodes is that the first
node is named N0DA00, the next is N0DA01. The names continue in
a similar fashion until the last node is reached. The last node
is always N0DA99. Terminal nodes N0DA00 and N0DA99 are therefore
always named the same regardless of the number of segments in the
model. This way the terminal connections in EMTP do not have to
change even if the reactor model is changed.
The A in the node name allows for phase designations. If a
three phase model is required, the data file can be copied to
create three files. A text editor can then be used to change
NODA to NODB and NODC thereby creating files with unique node
names for all three phases.
The maximum number of segments allowed is 40. This is a
limit of the EMTP and not a limit of the method used to create
the model. The minimum number of segments is one.


19
FIGURE 4.1
Flowchart of REACTR program
Main program code
Subroutine to read input data and
to calculate resistances and
capaci tances
Subroutine to calculate self and
mutual inductances.
Subroutine to write input and
output data to a text file.
Subroutine to write EMTP compatible
branch card file for reactor model
Normal end of REACTR program
FIGURE 4.2
Input data for REACTR program
Axial length (1)............m
Radius (R)..................m
Number of turns (n) .... integer
Shunt resistance (Rs) . ohms
Ground leakage resistance Rg ohms
Series loss resistance (rs) ohms
Winding capacitance (Cs) . F
Grnd coupling capacitance Cg F


CHAPTER V
STEADY STATE FREQUENCY RESPONSE
The steady state frequency response is simulated by modeling
the coil described in Table 5.1 and using the EMTP frequency scan
option. The simulation is verified by comparing the results with
data published by Abetti [7, 17, 18] and Degeneff [19] for the
same coil.
Self and mutual inductances for the coil are determined
using the REACTR computer program listed in Appendix A.
Inductances found using the program for a 10 and 20-segment
equivalent circuit model are listed in Table. 5.2. Self and
mutual inductances published by Degeneff are also listed in Table
5.2 for comparison. The remainder of the parameters used in the
equivalent circuit model are taken directly from Degeneff.
Appendix B lists the EMTP compatible data file for a 10-segment
equivalent circuit model of the Degeneff coil. This data file
was produced by the REACTR program and can be directly included
into an EMTP file.
To calculate the frequency response of the model an EMTP
frequency scan is performed. One ampere of current is injected
into the model at node N0DA00. The frequency of the current is
then increased from 50 Hz to 200 kHz in 50 Hz steps. The steady


21
state node voltage at N0DA00 is examined at each frequency.
Since a one ampere source is used, the voltage is equivalent to
the terminal impedance of the equivalent circuit. Figure 5.1
shows plots of the terminal impedance versus frequency for a 1,
10, 20 and 40-segment equivalent circuit model with the neutral
(N0DA99) grounded. Figure 5.2 shows the frequency response for
the same models except the neutral is not grounded.
Resonant frequencies occur at the points on the plots where
the impedance is zero. Anti-resonance occurs where the impedance
is a maximum.
A computer program was developed for this thesis to read
EMTP frequency scan plot files, of the type used to create the
plots in Figures 5.1 and 5.2, and detect zero crossings. The
zero crossings correspond to,the resonant frequencies and also to
the anti-resonant frequencies since the impedance changes from a
positive maximum to a negative maximum. Table 5*3 lists the
resonant and anti-resonant frequencies for the 10, 20 and 40
segment grounded neutral models found using the zero crossing
program. Measured frequencies from Degeneff are also listed for
comparison. The resonant and anti- resonant frequencies found
using the EMTP compare well with the measured results for all the
models at the lower frequencies. As the frequencies increase,
models with more segments are required to accurately model the
reactor.
Table 5.4 lists the resonant and anti-resonant frequencies
for the ungrounded model from Figure 5.2. The frequencies are


22
slightly different than those for the grounded model due to the
change in the equivalent circuit.
Internal Voltage Response
To check the internal voltage response, a one volt (1 pu)
source was connected to the EMTP models. Three runs were made
for the grounded and ungrounded neutral models with the frequency
of the voltage source at 60-Hz and at the first two resonant
frequencies. A 20-segment model was used since the frequencies
are relatively low. The absolute value of the maximum voltage at
each node of the reactor model is shown in Figure 5.3 and Figure
5.4.
For the 20-segment grounded neutral model, the source
frequencies used were 60-Hz to represent the power frequency,
7350-Hz for the first resonant frequency and 16775-Hz for the
second resonant frequency. For all three sources the voltage
profile is one volt at the source node and zero at the grounded
neutral. As expected, the 60-Hz steady state response is linear.
With a 7350-Hz source, the profile rises to a maximum of 26 volts
(26 pu) at 50% of the coil length. With the 16750-Hz source, the
profile has a zero node at 50% and two 10 volt (10 pu) peaks at
25% and 75%. These profiles compare well with profiles
published in Degeneff. The profiles also have the classic form
of standing waves as described in Rudenberg and in Bewley [20,
21]. For a grounded winding an integral number of half waves fit
into the length of the winding.


23
For the ungrounded coil, standing waves would also be
present at the resonant frequencies, except that an odd number of
quarter waves would fit into the winding length. Source
frequencies of 60-Hz, 3225-Hz and 10975-Hz were used to obtain
the voltage profile for the ungrounded reactor model at power
frequency and the first and second resonant frequencies. In all
three cases the voltage distribution found at the source node was
1 volt. The neutral voltage varied since it was ungrounded. For
the 60-Hz source, the voltage was 1 volt all along the reactor.
At 3225-Hz a profile corresponding to a quarter wave was present.
The voltage maximum was 53 volts (53 pu) at the ungrounded
neutral. A three quarter wave was obtained with the 10975-Hz
source. The voltage was zero at 2/3 of the winding length and a
17 volt (17 pu) maximum at the 1/3 and neutral points.
The steady state frequency response of the equivalent
circuit reactor model duplicates results published by Degeneff.
The internal voltage profile duplicates published results for the
grounded neutral model and matches the theoretical standing wave
distributions for both the grounded and ungrounded neutral model.


24
TABLE 5.1
Parameters for Degeneff's Coil
Axial length (1) ...............
Radius (R) .....................
Number of turns (n) ..........
Shunt resistance (Rst) .........
Ground leakage resistance (Rgt).
Series loss resistance (rst) .
Winding capacitance (Cst) . .
Ground coupling capacitance (Cgt)
1.2192 m
0.292 m
1794
1.65 x 106 ohms
2.10 x 1010 ohms
226 ohms
3.4 x 10-13 F
8.5 x lO"9 F
TABLE 5.2
Self and Mutual Inductances for Degeneff's Coil
(All inductances in mH)
10-Segment : model 20-Segment model
Degeneff REACTR Degeneff REACTR
Lll 28.998 29.185 9.301 9.308
Ml-2 13.537 13.668 5.250 5.284
Ml-3 6.231 6.223 3.135 3.133
Ml-4 3.379 3.372 2.120 2.118
Ml-5 1.987 1.982 1.505 1.503
Ml-6 1.242 1.238 1.101 1.100
Ml-7 0.817 0.814 0.824 0.823
Ml-8 0.560 0.558 0.628 0.627
Ml-9 0.398 0.397 0.487 0.486
Ml-10 0.292 0.291 0.383 0.383
Ml-11 0.306 0.305
Ml-12 0.247 0.246
Ml-13 0.201 0.201
Ml-14 0.166 0.168
Ml-15 0.139 0.138
Ml-16 0.116 0.116
Ml-17 0.099 0.099
Ml-18 0.084 0.084
Ml-19 0.072 0.072
Ml-20 0.063 0.062


Terminal Impedance of 1-segment Grounded Neutral Coil
As a Function of Frequency
150
100
0.50
0.00
-0.50
0
H -1.00
s
-150.
0.00
30.00 60.00 90.00 120.00
FREQUENCY IN KILOHERTZ
150.00
+0FVEI
FK0EEGR4
NOOAOO -SAL
+QFVE2:
FKQEGP14
HDAOO HAG
Terminal Impedance of 10-segment Grounded Neutral Coil
As a Function of Frequency
+0WVE1
FKQHSEGR4
KDAOO -DEAL
+CWVE2:
FSQPSE0R4
HCDAm -HAG
FREQUENCY IN KILOHERTZ
ro
tn
Frequency Response of Grounded Winding


Terminal Impedance of 1-segment Ungrounded Neutral Coil
As a Function of Frequency
150
100
0.50
0.00
I
M
P in
b
N x
C
E -0.50
0
H -1.00
s
-150






0.00
30.00 60.00 90.00 120.00
FREQUENCY IN KILOHERTZ
150.00
+0WEt
FSEQHGH.4
KSAOO HEAL
*MVE2
FEEGNGA4
WOAOO HUG
Terminal Impedance of 10-segment Ungrounded Neutral Coil
As a Function of Frequency
150
100
I
~ 0.50
P in
b
A
N x
C
E
0.00
-050
0
H -l0o
s
-150


J .-A X A
t ( ( V


0.00
30.00 60.00 90.00 120.00
FREQUENCY IN KILOHERTZ
150.00
+OORVEt
FKQIICIU
KSAOO -m.
*ami
mmau
KSAOO HUG
Terminal Impedance of 40-segment Ungrounded Neutral Coil
As a Function of Frequency
150
100
0.50
0.00
I
M
P S?
b
N x
C
E -050
0
H -100
s
-150


J A , 1 i ,A, , A - / W-
+ J\ n S


0.00
30.00 60.00 90.00 120.00
FREQUENCY IN KILOHERTZ
150.00
+QHVE t
FffiHGKPW
KSAOO HEAL
+QRVE2
FH04OBP14
KSAOO HUG
s
a
%
Q
0
t-h
|
s*
8.
1
m
ro
cn
FIGURE 5.2


27
TABLE 5.3
Resonant Frequencies of Grounded Neutral Model
Harmonic Measured 10 20 40
Order Frequency Segment Segment Segment
1/2 3.15 3.22 3.22 3.22
1 7.35 7.35 7.35 7.35
1 1/2 10.8 10.92 10.97 10.97
2 16.5 16.77 16.77 16.77
2 1/2 20.5 20.87 21.02 21.07
3 28.0 28.37 28.52 28.57
3 1/2 32.9 32.77 33.32 33.42
4 41.4 41.87 42.42 42.47
4 1/2 47.5 46.12 47.52 47.72
5 57.5 56.67 58.17 58.32
5 1/2 60.12 63.32 63.77
6 76.0 72.27 75.57 75.87
6 1/2 73.67 80.37 81.17
7 94.0 94.42 94.97
7 1/2 98.32 99.82
8 119.0 115.12 115.72
8 1/2 116.37 119.27
9 139.5
9 1/2
10 164.0
10 1/2
11 188.0
11 1/2
12 214.0
12 1/2
Note: Integer harmonic orders correspond to resonant
frequencies. 1/2 harmonics correspond to anti-
resonant frequencies. Frequencies are in kHz.


28
Table 5.4
Resonant Frequencies of Ungrounded Neutral Model
Harmonic 10 20 40
Order Segment Segment Segment
1 3.22 3.22 3.22
1 1/2 6.27 6.35 6.35
2 10.92 10.97 10.97
2 1/2 14.62 14.77 14.77
3 20.92 21.07 21.12
3 1/2 25.02 25.47 25.52
4 32.92 33.47 33.57
4 1/2 37.17 38.27 38.52
5 46.47 47.82 48.07
5 1/2 50.27 52.87 53.32
6 61.02 63.97 64.42
6 1/2 63.72 68.87 69.72
7 81.67 82.42
7 1/2 85.97 87.42
8 100.87 102.07
8 1/2 103.72 106.22
9 123.67
9 1/2 125.32
Note: Integer harmonic orders correspond to resonant
frequencies. 1/2 harmonics correspond to anti-
resonant frequencies. Frequencies are in kHz.


29
Figure 5.3
Internal Voltage Distribution for Grounded Neutral Model
Internal Voltage Distribution for Ungrounded Neutral Winding


CHAPTER VI
ENERGIZATION TRANSIENT RESPONSE
Upon energizing a winding, a wave travels at a finite
velocity from the source into the winding. When the wave reaches
the remote terminal it is reflected according to the terminal
impedance. The wave then undergoes a series of reflections
between the two winding terminals until the steady state solution
is reached.
Figures 6.1 and 6.2 show the initial wave propagation, due
to energization, for a grounded and ungrounded neutral winding.
The wave propagation is shown both in the time and space domain
and are consistent with published waveforms [20, 21, 22].
Energization is simulated using the EMTP file listed in
Appendix C and a 40-segment model of the reactor described in
Table 5.1. A 10-kV crest, 60-Hz, voltage source is switched at
5-iisec. Switching occurs at the peak of the 60-Hz voltage
waveform.
During the short, 75-ysec, simulation period the 60-Hz wave
appears as a constant 10-kV step pulse. The pulse travels down
the winding at a maximum propagation velocity given by:
v = lco m/sec
(10)


31
where 1 is the winding length in meters and w is the fundamental
angular frequency. The minimum time for the pulse to travel to
the remote terminal is then:
T = 1/v or 1/w sec (11)
For the grounded reactor in Chapter V, f = 7350-Hz and the
minimum travel time is 22-ysec. This is consistent with Figure
6.1.
As the pulse travels down the winding, it's shape is
distorted. The slope of the leading edge is flattened and an
oscillation which precedes the pulse develops. This pulse
distortion is characteristic of traveling waves in windings.
When a traveling wave impinges on the terminal of a winding,
reflections and refractions occur. Waves that are at a natural
resonant frequency of the winding enter the winding and are
amplified to create the standing waves shown in Chapter V. Other
waves are totally reflected or only enter a short distance into
the winding. In a winding there is a critical frequency, due to
the winding capacitance, above which all waves are reflected [20,
21, 22]. The reflections, refractions and the critical frequency
combine to distort the waveform.
A step pulse of the form generated by switching the 60-Hz
source consists of the sum of an infinite series of sinusoid
waves. From Fourier analysis, a step pulse is given by:


32
e
E
2
+
E r sin cot
IX J0 w
doo
(12)
Where E is the maximum voltage of the step pulse. Solving the
equation gives e = 0 for t < 0 and e = E for t > 0.
In a winding only frequencies below the critical frequency
wc can propagate through the winding. Frequencies above coc are
reflected back into the system. The Fourier integral can
therefore be separated into two components, e' which consists of
the. sum of the frequencies below coc and e" which consists of the
frequencies above coc. The component e' travels into the winding
and is given by:
e'
E
2
+
E
It
Wc
r sin Mt
J0
doo
(13)
The other component, e", is reflected and given by:
_ e r
' n
sm cot
CO
dco
(14)
This decomposition of the step pulse into a reflected and a
transmitted wave, due to the turn-turn capacitance, is the main
difference between the traveling pulse behavior of windings and
of homogeneous lines [20].
Figure 6.3 shows the three waves. The transmitted wave e',
has a flattened leading edge and damped oscillations on both
sides of the rise. The reflected wave e" is exponential and also
has the damped oscillations.
At t=0, the reflected and transmitted waves sum to give the
original step pulse. At t=0+, the transmitted wave starts to
enter the winding and the reflected wave starts to enter the


33
system. The sum of the two result in the leading edge of the
pulse starting to flatten and oscillations starting to precede
the leading edge. As time continues, the two waves move further
apart and the leading edge of the pulse continues to flatten and
the oscillations continue to increase. If the winding is
infinite in length the reflected wave will disappear into the
system and the pulse will consist only of the transmitted wave.
A winding of finite length will cause successive
reflections at the winding terminals. For a grounded neutral
winding, the reflection is negative. Positive reflections would
occur for open windings. The reflections cause the waveforms to
contort in a complicated manner and continue until the steady
state voltage distribution occurs.
After 22-ysec, the effects of the reflections start to
become apparent in Figures 6.1 and 6.2. The waveforms in the
Figures are identical in the time period that it takes the pulse
to travel to the remote terminal and return. After the reflected
wave returns, it combines with the original pulse and starts to
contort.
Figure 6.4 and 6.5 show the energization simulations for
the grounded and ungrounded windings for 8-msec. Node 10 (25%)
is shown for the grounded winding and node 99 (100%) is shown for
the ungrounded since these nodes experience the maximum node
voltages. For the grounded winding a maximum voltage of 1.47 pu
occurs at node 10 at 91.2-ysec. A maximum voltage of 2.70 pu
occurs at the neutral at 182-ysec for the ungrounded winding.


34
In Figures 6.4 and 6.5, the initial waveform contortions
last for about 1.6-msec. The waveform then appears as a sinusoid
that damps to the steady state solution. If the maximum value of
the steady state solution were plotted in space instead of time,
the 60-Hz linear distributions shown in Chapter V would result.


35
Figure 6.1a - Energize Grounded Winding
Initial Response to Energizing the Winding
With a 10-kV crest, 60-Hz, Source Applied at 5-usec
Node Voltages at 0%, 5%, 25%, 50% and 98% of the Winding Length
0.00 .15.00 30.00 45.00 60.00
TIME IN MICROSECONDS
75.00
+CURVE t
swiratpu
N0DA02
* CURVE t
SWTTCRPL4
NODAW
X CURVE 3:
SWITCRPL4
N0DA20
0 CURVE 4:
SWTTCHPL4
N0DA39
CURVES:
SWITCHPL4
NOOAOO
Figure 6.1b - Energize Grounded Winding


36
Figure 6.2a - Energize Ungrounded Winding
Initial Response to Energizing the Ungrounded Winding
With a 10kV crest, 60-Hz, Source Applied at 5-usec
Node Voltages at 0%, 5%, 25%, 50% and 100% of Winding Length
0.00 15.00 30.00 45.00 60.00
TIME IN MICROSECONDS
75.00
+CURVE t
swilchngPU
N00A02
curve t
sm'tdngPU
NODAK)
XCURVEJ
swilctrgRA
N0DA20
BCURVE 4:
switchngPL4
N0DA99
CURVE 5:
stitchngJU
HODAOO
Figure 6.2b - Energize Ungrounded Winding


37
Figure 6.3
Decomposition of the Incident Pulse
e
At t=0i the incident pulse is at the terminal of the winding.
The incident pulse is the sum of the transmitted wave e' and the
reflected wave e". At t=0+, the transmitted wave moves into the
winding at velocity v. The reflected wave enters the system with
velocity v". The pulse, which is the sum of the reflected and
transmitted waves, begins to distort. If the winding is infinite
in length, the reflected wave disappears into the system and the
pulse only consists of the transmitted wave.


38
Figure 6.4 - Energize Grounded Winding
2.00 1.50 o 1' o 0.50 Ld V 0.00 0 X L * T -0.50 A £ -1.00 -1.50 o nr\ ENERGIZATION TRANSIENT FOR GROUNDED WINDING VOLTAGE AT NODE 10
+CURVE t L0NGGR4 N0DA00 CURVE 2: L0NGGR4 NOOAIO
IL
Id -
V l |l M 'MVV\f
% S



"'o.oo 1.60 3.20 4.80 6.40 8.00 TIME IN MILLISECONDS
Figure 6.5 - Energize Ungrounded Winding
ENERGIZATION TRANSIENT FOR UNGROUNDED WINDING
NEUTRAL TERMINAL VOLTAGE (NODE 99)
+ CURVEE
L0NGNGR4
N0DA00
CURVE 2:
L0NGNGR4
N0DA99
TIME IN MILLISECONDS


CHAPTER VII
DISCUSSION
A method is developed in this thesis to analyze the
internal voltage distribution in a single layer, air-core
reactor. The method is based on dividing the coil into a number
of equal segments, and calculating the parameters of the
equivalent circuit. The equivalent circuit is then modeled in
EMTP and solved for the internal voltage distribution. Possible
refinements and limitations are discussed in this chapter.
The method accurately determines the resonant frequencies
of a coil, especially at the lower harmonics. The model also
adequately describes the transient response due to propagation
velocity, reflections, refractions and critical frequency. The
critical frequency in rad/sec of the winding is given by:
w-fyl
Where w is the winding length in meters, y is the turn-turn
capacitance in Farads per meter and 1 is the self inductance in
Henries per meters. The equation suggests that the accuracy of
the impulse response due to the critical frequency can be
improved by improving the accuracy of the inductance or


40
the winding capacitance calculations. The self and mutual
inductance are accurately calculated but only the capacitive
effects of one turn on an adjacent turn is included. One
refinement would be to include coupled capacitances between all
the turns or segments in a manner similar to the coupled
inductances. The coupled capacitances and inductances could
easily be modeled in EMTP using the the coupled Pi-circuit branch
[16]. Another refinement is to use a more accurate method to
calculate the winding capacitance. Alternative methods of
calculating the capacitances are discussed in [10, 23].
The choice of the number of segments to be used in the
equivalent circuit is dependent on the desired accuracy of the
analysis. For resonant frequency calculations it is sufficient
to choose the number of segments somewhat larger than the
required number of natural frequencies [7]. For transient
analysis, more segments are necessary to accurately model the
higher frequency behavior. It has been suggested that a 50-
segment model can accurately model the impulse response of a coil
[10]. The EMTP model described in this thesis can model a device
with a maximum of 40 mutually-coupled elements [16]. Therefore
the maximum number of mutually coupled segments that can be
modeled in one reactor is 40. This is close enough to the 50-
segment model to be adequate for most analysis. If additional
accuracy is required, the reactor can be divided into segments
that are unequal in length. The shorter segments are placed at
the terminal where the impulse is to be applied. This will
improve the high frequency response at the location where the


41
high frequency component of the pulse interacts with the winding.
This refinement is easily modeled and solved using the EMTP.
Other refinements pertain to the physical construction of
reactors. Reactors often have graded insulation with greater
insulation at the source terminal. Graded insulation effects the
losses and capacitances of the winding and generally increases
the severity of the voltage distribution [22]. Grading rings are
often used to equalize the voltage distribution under impulse
conditions. The grading rings are designed so that capacitive
current flowing between the rings and the winding tend to
compensate for the ground capacitive current. This makes the
current through the turn-turn capacitance more uniform. The
effects of the graded insulation and the grading rings can easily
be modeled in the EMTP once the circuit parameters are developed.
The EMTP solution method could also be applied to multilayer
reactors although the equivalent circuit will be much more
complex.
In general the method presented is extremely flexible. The
accuracy is dependent on the ability to calculate parameters for
the equivalent circuit and the 40-segment limit of the EMTP.


42
CHAPTER VIII
CONCLUSIONS
The EMTP can be used to accurately analyze the internal
voltage distribution of a single layer air-core reactor under
steady state and transient conditions. The method proposed is
based on dividing the reactor into a number of segments equal in
length and calculating the parameters of the equivalent circuit.
The equivalent circuit is then modeled in EMTP and solved for the
internal voltage distribution.
The method is flexible and accuracy is dependent on the
ability to determine the equivalent circuit parameters and on the
40-segment limit imposed by the EMTP.


BIBLIOGRAPHY
[1] "Summary of 1979 Survey of Shunt Reactor Protection," Shunt
Reactor Protection Working Group, Transformer and Bus
Protection Subcommittee of the IEEE Power System Relaying
Committee, January 1980.
[2] "Shunt Reactor Protection Practices," Power System Relaying
Committee Report, IEEE Trans. on Power Apparatus and
Systems, vol. PAS-103, no. 8, August 1984.
[3] Preliminary Report on White and Huron Substation Shunt
Reactor Field Tests, Prepared by Trench Electric for Western
Area Power Administration, Golden, CO, May 3, 1989.
[4] Cleaveland, G. W., "Reactor Switching Field Tests, Pinnacle
Peak Substation, Colorado River Storage Project," Research
Report No. EP-28, Bureau of Reclamation, Denver, CO, October
1968.
[5] Cleaveland, G. W., and R. R. Fillenberg, "Reactor Switching
Tests of an Oil Circuit Breaker Shiprock Substation,
Colorado River Storage Project, February 16-17, 1966,"
Research Report No. EP-17, Bureau of Reclamation, Denver,
CO, August 1966.


44
[6] Eilts, L. E., "Reactor Model Tests to Determine Internal
Stresses and Examine Possible Relaying Methods," M.S.
Thesis, University of Colorado, Boulder, CO, June 1969.
[7] Abetti, P. A., and F. J. Maginniss, "Natural Frequencies of
Coils and Windings Determined by Equivalent Circuit," AIEE
Transactions Power Apparatus and Systems, pp. 495-504, June
1953.
[8] Salama, M. M. A., "A Calculation Method for Voltage
Distribution on a Large Air Core Power Reactor," IEEE
Transactions on Power Apparatus and Systems, vol. PAS-100,
no. 4, April 1981.
[9] Maruvada, P. M., and N. Hylten-Cavallius, "Capacitance
Calculations for Some .Basic High Voltage Electrode
Configurations," IEEE Transactions on Power Apparatus and
Systems, vol. PAS-94, no.5, pp. 1708-1718, 1975.
[10] Dahab, A. A., P.E. Burke, and T.H. Fawzi, "A Complete Model
of a Single Layer Air-Cored Reactor for Impulse Voltage
Distribution," IEEE Transactions on Power Delivery, vol. 3,
no. 4, October 1988.


45
[11] Fawzi, T. H., and P. E. Burke, "The Accurate Computation of
Self and Mutual Inductances of Circular Coils," IEEE
Transactions on Power Apparatus and Systems, vol. PAS-97,
no.2, March/April 1978.
[12] Dommel, H. W., "Digital Computer Solution of Electromagnetic
Transients in Single and Multi-Phase Networks," IEEE
Transactions on Power Apparatus and Systems, vol. PAS-88,
pp. 388-399, April 1969.
[13] Dommel, H. W., and W. S. Meyer, "Computation of
Electromagnetic Transients," Proceedings of the IEEE, vol.
62, no. 7, July 1974.
[14] "Digital Simulation of Electrical Transient Phenomena," IEEE
Tutorial Course Text, 81 EH0173-5-PWR, 1980.
[15] Dommel, H. W., Electromagnetic Transients Program Reference
Manual, (EMTP Theory Book), Bonneville Power Administration,
Portland, OR, August 1986.
[16] Electromagnetic Transients Program (EMTP) Revised Rule Book
Version 2.0, Report EL-6421-L, EPRI, Palo Alto, CA.
[17] Abetti, P. A., "Correlation of Forced and Free Oscillations
of Coils and Windings," AIEE Transactions Power Apparatus
and Systems, pp. 986-996, December 1959.


46
[18] Abetti, P. A., and F. J. Maginniss, "Fundamental
Oscillations of Coils and Windings," AIEE Transactions
Power Apparatus and Systems, pp. 1-10, February 1954.
[19] Degeneff, R. C., "A General Method for Determining Resonance
in Transformer Windings," IEEE Transactions on Power
Apparatus and Systems, vol. PAS-96, no. 2, March/April 1977.
[20] Rudenberg, R., Electrical Shock Waves in Power Systems,
Harvard University Press, Cambridge, MA, 1968.
[21] Bewley, L. V., Traveling Waves on Transmission Systems,
Second Edition, Dover Publications, New York, NY, 1963.
[22] Greenberg, A., Transients in Power Systems, John Wiley and
Sons, Inc., New York, NY, 1971.
[23] Chowdhuri, P., "Calculation of Series Capacitance for
Transient Analysis of Windings," IEEE Transactions on Power
Delivery, vol. PWRD-2, no. 1, January 1987.


APPENDIX A
VAX Fortran Source Code for REACTR Program
PROGRAM REACTR PROGRAM TO FIND EQUIVALENT CIRCUIT MODEL OF COIL
PROGRAM REACTR
C
C Anthony H. Montoya
C December 29, 1989
C
C The purpose of this program is to find a distributed parameter
C model for a given reactor. The reactor may be modeled as a
C series of sections, each section containing the following:
C a series inductance and resistance in parallel with a series
C resistance and a series capacitance between the two nodes,
C and a shunt resistance and capacitance to ground from each
C end of the segment (node).
C Two outputs are obtained. The first is a table or list of the
C data input and the resultant model values. The second is a
C punched .MOD file to be included in an EMTP input file.
C The theory and equations used to determine the self and mutual
C inductances may be found in the reference listed below.
C
C Reference:
C Fawzi, T.H. and P.E. Burke, "The Accurate Computation of Self
C and Mutual Inductances of Circular Coils," IEEE Trans, on PAS
C Vol. PAS_97, no. 2, March/April 1978.
C
CALL REDATA
CALL INDCTN
CALL DTABLE
CALL MODOUT
WRITE (6,10)
10 FORMAT (//,2X,'Normal end of REACTOR MODELLING')
END


ooo oooo oooo ooono ooo ooooo
SUBROUTINE INDCTN CALCULATES THE SELF AND MUTUAL L OF A COIL
SUBROUTINE INDCTN
IMPLICIT NONE
This subroutine calculates the self inductance of each
coil segment as well as the mutual inductance with all
other coil sections in the distributed model.
INCLUDE 'DTBLOK.CMN'
REAL Z1, Z2,Z3,Z4,PI,PERM
INTEGER I
REAL Cl
Define pi and permeability constants.
PI=3.141592654
PERM=PI*4.OE-7
Calculate the separation between one coil and each of the others.
Then use the function Cl to find the values to be used in the
expression for the inductances.
DO 10 I=1,NUMSEG
IF (I.GT.100) GOTO 20
SEPAR=(L1+L2)*(I-1)
Numeric corrections are needed for the self inductance (1=0)
and the mutual inductance with the next coil (1=1).
IF (I.EQ.l) SEPAR=1.0E-8
IF (I.EQ.2) SEPAR=SEPAR+1.OE-8
Find the parameters Z1,Z2,Z3,Z4 and then use the Cl function
to find the inductance.
Z1=SEPAR+L1+L2
Z2=SEPAR+L1-L2
Z3=SEPAR-L1-L2
Z4=SEPAR-L1+L2
INDUCT(I)=CI(R1,R2,Z1)-Cl(Rl,R2,Z2)+CI(R1,R2,Z3)-Cl(Rl,R2,Z4)
INDUCT(I)=INDUCT(I)*2.0*PI*PERM*N1*N2*((R1*R2)**1.5)
IF (I.EQ.l) INDUCT(I)=INDUCT(I)*2.0
10 CONTINUE
The inductance values have been calculated.
20 RETURN
END


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SUBROUTINE REDATA READ INPUT DATA FROM THE CONSOLE
SUBROUTINE REDATA
IMPLICIT NONE
This subroutine will read in all of the data necessary to
perform the calculations necessary to model a reactor
(or any coil, in general) as a distributed element.
INCLUDE 'DTBLOK.CMN'
INTEGER INDX
Read in all of the necessary information for the inductances.
10 FORMAT (F)
20 FORMAT (I)
30 WRITE (6,40)
40 FORMAT (//,5X,'PLEASE ENTER THE FOLLOWING INFORMATION:',/)
50 WRITE (6,60)
60 FORMAT (/,2X,'THE NUMBER OF SECTIONS TO BE USED IN MODEL ')
READ (5,20,ERR=50) NUMSEG
IF (NUMSEG.LT.1) GOTO 50
70 WRITE (6,80)
80 FORMAT (/,2X,'THE RADIUS OF THE COIL IN METERS ')
READ (5,10,ERR=70) R1
IF (R1.LE.0) GOTO 70
90 WRITE (6,100)
100 FORMAT (/,2X,'THE TOTAL HEIGHT OF THE COIL IN METERS ')
READ (5,10,ERR=90) LENGTH
IF (LENGTH.LE.O) GOTO 90
110 WRITE (6,120)
120 FORMAT (/,2X,'THE NUMBER OF TURNS ON THE COIL ')
READ (5,10,ERR=110) N1
N1=N1/LENGTH
IF (Nl.LT.l) GOTO 110
130 WRITE (6,140)
140 FORMAT (/,2X,'THE PER SEGMENT LOSS RESISTANCE ',
* /,4X,'(IN SERIES WITH DIST. INDUCTANCE) ')
READ (5,10,ERR=130) RLOSS
IF (RLOSS.LT.O) GOTO 130
The segmented coil sections have the same radius and turns ratios.
However, the length of the coil sections are 1/n of the length of
the total coil. However, all equations use half the length of
each coil section, so this number must be divided by two.
R2=R1
N2=N1
L1=LENGTH/(2.0*NUMSEG)
L2=L1
Now obtain the other (total) parameters needed, such as series and


ooo ooo oooo oo
shunt capacitances and resistances.
150 WRITE (6,160)
160 FORMAT (/,2X,'THE TOTAL SERIES RESISTANCE (IN OHMS) ')
READ (5,10,ERR=150) RSERIS
IF (RSERIS.LT.O) GOTO 150
170 WRITE (6,180)
180 FORMAT (/,2X,'THE TOTAL SHUNT RESISTANCE (IN OHMS) ')
READ (5,10,ERR=170) RSHUNT
IF (RSHUNT.LT.O) GOTO 170
190 WRITE (6,200)
200 FORMAT (/,2X,'THE TOTAL SERIES CAPACITANCE (IN FARADS) ')
READ (5,10,ERR=190) CSERIS
CSERIS=CSERIS*1.OE+6
IF (CSERIS.LT.O) GOTO 190
210 WRITE (6,220)
220 FORMAT (/,2X,'THE TOTAL SHUNT CAPACITANCE (IN FARADS) ')
READ (5,10,ERR=210) CSHUNT
CSHUNT=CSHUNT*1.OE+6
IF (CSHUNT.LT.O) GOTO 210
The distributed resistances and capacitances may be calculated
from the values just entered.
SERRE S=RSERIS/NUMSEG
SHTRES=RSHUNT*NUMSEG
SERCAP=CSERIS*NUMSEG
SHTCAP=CSHUNT/NUMSEG
Allow the user to enter comment cards.
WRITE (6,230)
230 FORMAT (//,2X,'ENTER FIVE COMMENT LINES FOR .MOD FILE:',
* /,IX,1 ***************************************' j
k >***************************************')
DO 250 INDX=1,5
READ (5,240) COMM(INDX)
240 FORMAT (A78)
IF (COMM(INDX).EQ.' ') GOTO 260
250 CONTINUE
All of the data has been entered.
260 RETURN
END


ooo ooo ooo ooo oooo
FUNCTION CI(RR1,RR2,Z) FUNCTION USED TO FIND INDUCTANCES
REAL FUNCTION CI(RRl,RR2,Z)
IMPLICIT NONE
This function is used to calculate values needed
to find inductances for the reactor distributed model.
REAL RR1,RR2,Z,K,KSQR,Q,0LDQ,A,0LDA,B,0LDB,C,0LDC,D,0LDD
REAL ALPHA,OLDALP,BETA,OLDBET,GAMMA,TEMP
INTEGER I
Calculate and initialize values.
Q=(RR1-RR2)/(RR1+RR2)
K=SQRT(((RR1-RR2)**2+Z**2)/((RR1+RR2)**2+Z**2))
KSQR=((RR1-RR2)**2+Z**2)/((RR1+RR2)**2+Z**2)
GAMMA=Z**2/(4*RR1*RR2)
A= SQRT(1-KSQR)*(1/(3*(1-KSQR))-GAMMA)
B=0.0-KSQR/ (3*SQRT (1-KSQR) )
C=GAMMA* SQRT(1-KSQR)
When RR1=RR2, the values must be redefined as follows.
TEMP=ABS(RR1-RR2)
IF (TEMP.LT.1.OE-6) THEN
A=A+C
B=B+C
C=0.0
ENDIF
0LDALP=1.0
OLDBET=ABS(K)
OLDQ=ABS(Q)
OLDA=A
OLDB=B
0LDC=C
OLDD=0.0
1=0
Use the recursive procedure to find the functional value Cl.
10 TEMP=ABS(1.0-0LDBET/0LDALP)
IF ((I.GT.50).OR.(TEMP.LT.1.0E-14)) GOTO 20
1=1+1
The procedure is different for the case RR1=RR2.
ALPHA=0LDALP+0LDBET
BETA=2*SQRT(0LDALP*0LDBET)
A=0LDA+0LDB/0LDALP
B=2*(0LDB+0LDBET*0LDA)
TEMP=AB S(RR1-RR2)


o o o o o
IF (TEMP.LT1.OE-7) THEN
C=0.0
D=0.0
IF (Z.LT.l.OE-7) THEN
01=0.2122065908
GOTO 30
ENDIF
ELSE
C=OLDC+OLDD/OLDQ
D=2*(OLDD+OLDC/OLDQ*OLDALP*OLDBET)
Q=OLDQ+OLDALP*OLDBET/OLDQ
ENDIF
OLDALP=ALPHA
OLDBET=BETA
OLDQ=Q
OLDA=A
OLDB=B
OLDC=C
OLDD=D
GOTO 10
The numerical iteration has either converged to a number
within 1.0e-14 of the value, or the maximum number of
iterations (50) have been computed.
20 CI=(A*ALPHA+B)/(2*ALPHA**2)+(C*ALPHA+D)/(ALPHA*(ALPHA+Q))
30 RETURN
END


o o o o
53
SUBROUTINE DTABLE WRITE DATA FILE TO THE SCREEN AN OUTPUT FILE
SUBROUTINE DTABLE
IMPLICIT NONE
This subroutine will write all of the data (both input and
calculated) to the screen and then to an output file.
INCLUDE 'DTBLOK. CMN'
INTEGER INDX,CNT,LU
10
20
30
40
50
60
DO 120 INDX=1,2
IF (INDX.EQ.1) THEN
LU=6
ELSE
LU=12
OPEN (UNIT=LU,STATUS='NEW',FILE='REACTOR.DAT')
ENDIF
WRITE (LU,10)
FORMAT (//)
DO 30 CNT=1,5
IF (COMM(CNT).EQ.' ') GOTO 40
WRITE (LU,20) COMM(CNT)
FORMAT (2X,A78)
CONTINUE
WRITE (LU,50)
FORMAT (//,5X,'THE FOLLOWING DATA WAS USED TO COMPUTE THE',
k /,7X,'VALUES TO BE USED IN THE REACTOR MODEL:')
WRITE (LU,60) R1,LENGTH,N1,RSERIS,RSHUNT,CSERIS,CSHUNT
*
*
*
*
*
*
70
80
*
*
*
*
*
90
100
- ',F8.5,' meters',
',F8.5,' meters',
',F8.1,' turns/meter',
FORMAT (/,2X,'RADIUS OF COIL
/,2X,'LENGTH OF COIL
/,2X,'TURNS PER METER OF COIL
/,2X,'TOTAL SERIES RESISTANCE ',E12.6,
/,2X,'TOTAL SHUNT RESISTANCE -',E12.6,
/,2X,'TOTAL SERIES CAPACITANCE ',E12.6,
/,2X,'TOTAL SHUNT CAPACITANCE ',E12.6,'
WRITE (LU,70)
FORMAT (/,5X,'THE PER SECTION DISTRIBUTED VALUES ARE AS
'FOLLOWS:')
WRITE (LU,80) NUMSEG,RLOSS,SERRES,SHTRES,SERCAP,SHTCAP
FORMAT (/,2X,'NUMBER OF SEGMENTS FOR MODEL ',13,
ohms',
ohms',
micrc
microfarads')
ohms',
ohms',
ohms',
microfarads',
microfarads')
/,2X,'RESISTANCE IN SER. WITH IND. ',E12.6,'
/,2X,'RESISTANCE IN PAR. WITH IND. ',E12.6,'
/,2X,'SHUNT RESISTANCE TO GROUND ',E12.6,'
/,2X,'CAPACITANCE IN PAR. WITH IND. ',E12.6,'
/,2X,'SHUNT CAPACITANCE TO GROUND ',E12.6,'
WRITE (LU,90)
FORMAT (/,5X,'THE SELF AND MUTUAL INDUCTANCES ARE AS FOLLOWS:',
/,7X,'(VALUES ARE GIVEN IN MILLIHENRIES)')
WRITE (LU,100) INDUCT(1)*1000.0,INDUCT(2)*1000.0
FORMAT (/,2X,'L = ',E12.6,7X,'Ml- 2 = ',E12.6)
IF (NUMSEG.LT.3) GOTO 120


WRITE (LU,110) ((CNT,INDUCT(CNT)*1000.0), CNT=3,NUMSEG)
110 FORMAT (2(2X,'M1-',I2,' = ',E12.6,5X))
IF (INDX.EQ.2) CLOSE (UNIT=LU)
120 CONTINUE
RETURN
END


ooo ooo ooo o o o o o o o o o
SUBROUTINE MODOUT CREATES EMTP COMPATIBLE DATA FILE
SUBROUTINE MODOUT
IMPLICIT NONE
This subroutine will punch the EMTP .MOD file which may be
included in an EMTP run.
INCLUDE 'DTBLOK.CMN'
CHARACTER REC0RD*80,TEM(3)*18
INTEGER CARD,INDX,LU, N
If more than fourty sections have been requested, then the
output file will not be punched (EMTP has a 40 element
limit for this model).
5 FORMAT (A80)
IF (NUMSEG.GT.40) THEN
WRITE (6,10)
10 FORMAT (//,2X,'T00 MANY SECTIONS FOR EMTP TO HANDLE
* /,4X,'NO .MOD FILE CREATED.')
GOTO 520
ENDIF
Open up the output file.
45 LU=12
OPEN (UNIT=LU,CARRIAGECONTROL='LIST',
* STATUS='NEW',FILE='REACTOR.MOD')
Write the comment lines to the output file.
50 FORMAT ('C ',78X)
60 FORMAT ('C ',A78)
WRITE (LU,50)
DO 70 INDX=1,5
IF (COMM(INDX).EQ.' ') GOTO 75
WRITE (LU,60) COMM(INDX)
70 CONTINUE
75 WRITE (LU,50)
Write the self and mutual inductance cards to the output file.
WRITE (RECORD,80)
80 FORMAT ('C SELF. INDUCTANCE AND MUTUAL R-L BRANCHES',39X)
WRITE (LU,5) RECORD
WRITE (RECORD,90)
90 FORMAT ('C < RX L >',
* '< R X L X R X L >')
WRITE (LU,5) RECORD
CARD=0


o o
56
100 CARD=CARD+1
IF (CARD.GT.NUMSEG) GOTO 210
INDX=CARD
TEM(1)=' '
TEM(2)=' '
TEM(3)=' '
DO 130 N=l,3
IF (INDX.EQ.1) THEN
WRITE (TEM(N),110) RLOSS,INDUCT(INDX)*1000.0
110 FORMAT (F6.2,E12.6)
INDX=INDX-1
GOTO 140
ELSE
WRITE (TEM(N),120) INDUCT(INDX)*1000.0
120 FORMAT (6X,E12.6)
INDX=INDX-1
ENDIF
130 CONTINUE
140 IF (CARD.LT.10) THEN
WRITE (RECORD,150) CARD+50,CARD-1,CARD,TEM(l),TEM(2),TEM(3)
150 FORMAT (12,'NODAO',11,'NODAO',I1,12X,A18,A18,A18)
ELSE IF (CARD.EQ.10) THEN
WRITE (RECORD,160) CARD+50,CARD-1,CARD,TEM(l),TEM(2),TEM(3)
160 FORMAT (12,'NODAO',11,'NODA',I2,12X,A18,A18,A18)
ELSE
WRITE (RECORD,170) CARD+50,CARD-1,CARD,TEM(l),TEM(2),TEM(3)
170 FORMAT (12,'NODA',12,'NODA',12,12X,A18,A18,A18)
ENDIF
IF (CARD.EQ.NUMSEG) WRITE (REC0RD(13:14),172)
172 FORMAT ('99')
WRITE (LU,5) RECORD
IF (INDX.EQ.0) GOTO 100
175 TEM(1)=' '
TEM(2)=' '
TEM(3)=' '
DO 180 N=l,3
IF (INDX.EQ.1) THEN
WRITE (TEM(N),110) RLOSS,INDUCT(INDX)*1000.0
INDX=INDX-1
GOTO 190
ELSE
WRITE (TEM(N),120) INDUCT(INDX)*1000.0
INDX=INDX-1
ENDIF
180 CONTINUE
190 WRITE (RECORD,200) TEM(l),TEM(2),TEM(3)
200 FORMAT (26X,A18,A18,A18)
WRITE (LU,5) RECORD
IF (INDX.EQ.O) GOTO 100
GOTO 175


ooo ooo ooooo
57
Use high precision format for the rest of the file.
210 WRITE (LU,50)
WRITE (LU,220)
220 FORMAT ('$VINTAGE, l',69X)
Now write the series resistance cards to the output file.
IF (SERRES.EQ.O) GOTO 300
WRITE (LU,50)
WRITE (LU,230) SERRES
230 FORMAT ('C SERIES RESISTANCE Rs = ',E12.6,' OHMS',34X)
WRITE (LU,240)
240 FORMAT ('C < RESISTANCE >',
* '< INDUCTANCE X CAPACITANCE > ')
DO 280 INDX=1,NUMSEG
IF (INDX.LT.10) THEN
WRITE (RECORD,250) INDX,INDX-1,SERRES
250 FORMAT (2X,'NODAO',11,'NODAO',I1,16X,E12.6,38X)
ELSE IF (INDX.EQ.10) THEN
WRITE (RECORD,260) INDX,INDX-1,SERRES
260 FORMAT (2X,'NODA',12,'NODAO',I1,16X,E12.6,38X)
ELSE
WRITE (RECORD,270) INDX,INDX-1,SERRES
270 FORMAT (2X,'NODA',12,'NODA',I2,16X,E12.6,38X)
ENDIF
IF (INDX.EQ.NUMSEG) WRITE (REC0RD(7:8),172)
WRITE (LU,5) RECORD
280 CONTINUE
Now write the series capacitance cards to the output file.
300 IF (SERCAP.EQ.O) GOTO 370
WRITE (LU,50)
WRITE (LU,310) SERCAP
310 FORMAT ('C SERIES CAPACITANCE Cs = ',E12.6,' MICROFARADS',24X)
WRITE (LU,240)
DO 360 INDX=1,NUMSEG
IF (INDX.LT.10) THEN
WRITE (RECORD,330) INDX,INDX-1,SERCAP
330 FORMAT (2X,'NODAO',11,'NODAO',I1,48X,E12.6,6X)
ELSE IF (INDX.EQ.10) THEN
WRITE (RECORD,340) INDX,INDX-1,SERCAP
340 FORMAT (2X,'NODA',12,'NODAO',I1,48X,E12.6,6X)
ELSE
WRITE (RECORD,350) INDX,INDX-1,SERCAP
350 FORMAT (2X,'NODA',12,'NODA',I2,48X,E12.6,6X)
ENDIF
IF (INDX.EQ.NUMSEG) WRITE (REC0RD(7:8),172)
WRITE (LU,5) RECORD
360 CONTINUE
Now write the shunt resistance cards to the output file.


o o o o o o
58
370 IF (SHTRES.EQ.O) GOTO 430
WRITE (LU,50)
WRITE (LU,380) SHTRES
380 FORMAT ('C SHUNT RESISTANCE Rg = ',E12.6,' OHMS',36X,
* /,'C R = 2*Rg AT TERMINALS',57X)
WRITE (LU,240)
WRITE (RECORD,390) 2*SHTRES
390 FORMAT (2X,'NODAOO',22X,E12.6,38X)
WRITE (LU,5) RECORD
DO 420 INDX=1,NUMSEG-1
IF (INDX.LT.10) THEN
WRITE (RECORD,400) INDX,SHTRES
400 FORMAT (2X,'NODAO',I1,22X,E12.6,38X)
ELSE
WRITE (RECORD,410) INDX,SHTRES
410 FORMAT (2X,'NODA',I2,22X,E12.6,38X)
ENDIF
WRITE (LU,5) RECORD
420 CONTINUE
WRITE (RECORD,425) 2*SHTRES
425 FORMAT (2X,'N0DA99',22X,E12.6,38X)
WRITE (LU,5) RECORD
Now write the shunt capacitance cards to the output file.
430 IF (SHTCAP.EQ.O) GOTO 490
WRITE (LU,50)
WRITE (LU,440) SHTCAP
440 FORMAT ('C SHUNT CAPACITANCE Cg = ',E12.6,' MICROFARADS',27X,
* /,'C C = Cg/2 AT TERMINALS',57X)
WRITE (LU,240)
WRITE (RECORD,450) SHTCAP/2.0
450 FORMAT (8X,'NODAOO',48X,E12.6,6X)
WRITE (LU,5) RECORD
DO 480 INDX=1,NUMSEG-1
IF (INDX.LT.10) THEN
WRITE (RECORD,460) INDX,SHTCAP
460 FORMAT (8X,'NODAO',I1,48X,E12.6,6X)
ELSE
WRITE (RECORD,470) INDX,SHTCAP
470 FORMAT (8X,'NODA',I2,48X,E12.6,6X)
ENDIF
WRITE (LU,5) RECORD
480 CONTINUE
WRITE (RECORD,485) SHTCAP/2.0
485 FORMAT (8X,'N0DA99',48X,E12.6,6X)
WRITE (LU,5) RECORD
Turn off the high precision format.
490 WRITE (LU,50)
WRITE (LU,500)
500 FORMAT ('$VINTAGE, 0',69X)
WRITE (LU,50)


o o o
C
WRITE (LU,510) NUMSEG
510 FORMAT ('C END OF ',12,' SECTION REACTOR MODEL',47X)
WRITE (LU,50)
Close the output .MOD file if one has been created.
CLOSE (UNIT=LU)
C
520 RETURN
END


APPENDIX B
EMTP Compatible Data File for 10-segment Model
This data file was created using the REACTR program listed in
Appendix A. The coil modeled is described in Table 5.1. The
file is written in the form of EMTP branch cards and can be read
directly by EMTP using the $INCLUDE command.
10SEGMENT.MOD EMTP BRANCH CARD FILE FOR 10-SEGMENT MODEL
C
C 10-SEGMENT MODEL OF THE DEGENEFF COIL
C
C SELF INDUCTANCE AND MUTUAL R-L BRANCHES
C < R X L
>< R X
X R X
51NODA0 0NODA01 22.600.291724E+02
52NODAO1NODAO 2 0.136648E+02 22.600.291724E+02
53NODA0 2NODAO 3 0.622384E+01 0.136648E+02 22.600.291724E+02
54NODA03NODA04 0.337353E+01 0.622384E+01 0.136648E+02
22.600.291724E+02
55NODA04NODA05 0.198315E+01 0.337353E+01 0.622384E+01
0.136648E+02 22.600.291724E+02
5 6NODAO 5NODAO6 0.123936E+01 0.198315E+01 0.337353E+01
0.622384E+01 0.136648E+02 22.600.291724E+02
5 7NODA0 6NODA0 7 0.814617E+00 0.123936E+01 0.198315E+01
0.337353E+01 0.622384E+01 0.136648E+02
22.600.291724E+02
58NODA07NODA08 0.558816E+00 0.814617E+00 0.123936E+01
0.198315E+01 0.337353E+01 0.622384E+01
0.136648E+02 22.600.291724E+02
59NODA0 8NODA09 0.397364E+00 0.558816E+00 0.814617E+00
0.123936E+01 0.198315E+01 0.337353E+01
0.622384E+01 0.136648E+02 22.600.291724E+02
6 ONODAO 9NODA9 9 0.291319E+00 0.397364E+00 0.558816E+00
0.814617E+00 0.123936E+01 0.198315E+01
0.337353E+01 0.622384E+01 0.136648E+02
C 22.600.291724E+02
SVINTAGE, 1
C
C SERIES RESISTANCE Rs =
C <
NODAO1NODA0 0
NODAO 2NODAO1
NODAO 3NODAO 2
NODAO 4NODAO 3
NODAO 5NODAO 4
NODA06NODA05
NODAO 7NODA0 6
NODAO 8NODAO 7
NODAO 9NODA0 8
NODA9 9NODAO 9
0.165000E+06 OHMS
RESISTANCE > < INDUCTANCE
0.165000E+06
0.165000E+06
0.165000E+06
0.165000E+06
0.165000E+06
0.165000E+06
0.165000E+06
0.165000E+06
0.165000E+06.
0.165000E+06
> < CAPACITANCE >


C SERIES CAPACITANCE Cs = 0.340000E-05 MICROFARADS
C < RESISTANCE X INDUCTANCE
NODAO inodaoo
NODA0 2NODAO1
NODAO 3NODAO 2
NODAO 4NODA0 3
NODAO 5NODA0 4
NODA06NODA05
NODAO 7NODA0 6
NODA08NODA07
NODAO 9NODA0 8
NODA9 9NODA0 9
C
C SHUNT RESISTANCE Rg =
C R = 2*Rg AT TERMINALS
C <
NODAO 0
NODA01
NODAO2
NODAO 3
NODAO4
NODAO 5
NODAO 6
NODAO 7
NODAO8
NODAO 9
NODA99
0.210000E+12 OHMS
RESISTANCE > < INDUCTANCE
0.420000E+12
0.210000E+12
0.210000E+12
0.210000E+12
0.210000E+12
0.210000E+12
0.210000E+12
0.210000E+12
0.210000E+12
0.210000E+12
0.420000E+12
C
C SHUNT CAPACITANCE Cg = 0.850000E-03 MICROFARADS
C C = Cg/2 AT TERMINALS
C < RESISTANCE X INDUCTANCE
NODAO0
NODAO 1
NODAO2
NODAO 3
NODAO 4
NODAO 5
NODAO6
NODAO7
NODAO 8
NODAO9
NODA99
C
$VINTAGE, 0
C
C END OF 10 SECTION REACTOR MODEL
C
X
X
X
CAPACITANCE >
0.340000E05
0.340000E05
0.340000E05
0.340000E05
0.340000E05
0.340000E05
0.340000E05
0.340000E-05
0.340000E05
0.340000E-05
CAPACITANCE >
CAPACITANCE >
0.425000E03
0.850000E-03
0.850000E03
0.850000E03
0.850000E-03
0.850000E03
0.850000E03
0.850000E-03
0.850000E03
0.850000E03
0.425000E03


62
APPENDIX C
EMTP Data File for Energization Response
This file runs the grounded reactor energization simulation
described in Chapter VI.
SWITCH. DAT EMTP ENERGIZATION SIMULATION
BEGIN NEW DATA CASE
C
C a****************************************************************************
C
C ENERGIZE REACTOR
C GROUND REACTOR NEUTRAL
C
Q ****************************************************************************
C
c
£ *************************** jU3C DATA CARDS *******************************
C
C ** FIRST MISC. DATA CARD.**
C
C T-STEP T-MAX X-OPT C-OPT EPSILON TOLMAT T-START
C (SEC) (SEC) (0=mH) (0=uF)
c 1-8 9-16 17-24 25-32 33-40 41-48 49-56
(. 7.5E-9 7.5E-5 0. 0. 0.0 0.0 0.0
c p ** SECOND MISC . DATA CARD **
c I OUT IPLOT IDOUBL KSSOUT MAXOUT IPUN MEMSAV ICAT NENERG IPRSUP
c 1-8 9-16 17-24 25-32 33-40 41-48 49-56 57-64 65-72 73-80
C OOOOOOPPPPPPPPDDDDDDDDKKKKKKKKMMMMMMMMIIIIIIIIMMMMMMMMCCCCCCCCNNNNNNNNPPPPPPPP
500 111100100
C
c
c **********************
C BRANCH CARDS *
C **********************
C
£ **************************** 4Q SEGMENT REACTOR MODEL ************************
C
C TURN OFF OUTPUT FILE LIST OPTION AND READ IN REACTOR MODEL
C THIS MAKES THE OUTPUT FILE EASIER TO READ
$LISTOFF
$INCLUDE 4 0 SEGMENT.MOD
$LISTON
C
c


C HIGH RESISTANCE MEASURING BRANCH REF. RULE BOOK 6-4
C BBBBBBDDDDDDCCCCCCCCCCCCRRRRRRLLLLLLCCCCCC
NODAO0NODA20 1.E18 3
NODA2 0NODA9 9 1.E18 3
NODAO ONODAO 1 1.E18 3
NODAO 1NODA0 2 1.E18 3
NODAO2NODA03 1.E18 3
NODAO 3NODAO 4 1.E18 3
NODAO 4NODA0 5 1.E18 3
NODAO 5NODA0 6 1.E18 3
NODA06NODA07 1.E18 3
NODAO 7NODAO 8 1.E18 3
NODAO 8NODAO 9 1.E18 3
NODAO 9NODA10 1.E18 3
NODA10NODA20 1.E18 3
C
BLANK CARD END OF BRANCHES
C
£ **********************************
C ** TIME CONTROLLED SWITCH CARDS **
£ **********************************
c
C GROUND NEUTRAL THROUGH A SWITCH
C
C BUS 1 BUS 2 T-CLOSE T-OPEN N-STEP V-FLASH SPECIAL REFERENCE
C REQUEST BUS-5 BUS-6
C 3-8 9-14 15-24 25-34 35-44 45-54 55-64 65-70 71-76
C BBBBBBbbbbbbCCCCCCCCCCOOOOOOOOOONNNNNNNNNNVWWVWWSSSSSSSSSSBBBBBBbbbbbb***I
C
NODA99 -1.0 1.0
SOURCENODAO 0 5E-6 1.0
C
BLANK CARD ENDING SWITCH DATA
C
q ************************* 60-HZ, 10KV SOURCE ****************************
C
C REFERENCE: EMTP THEORY BOOK SECTION 7.5
c
14SOURCE 10000. 60.
C
BLANK CARD ENDING SOURCE DATA
C
C VOLTAGE REQUESTS
C
C 111111222222333333
NODAO ONODAO1NODA0 2
NODA0 3NODA0 4NODAO 5
NODAO 6 NODAO 7NODAO 8
NODAO 9NODA10NODA11
NODA12NODA13NODA14
NODAl 5NODA16NODA17
NODA18NODA19NODA20
NODA21NODA22NODA23
NODA2 4 NODA2 5NODA2 6
NODA27NODA28NODA29
NODA3 ONODA31NODA3 2
NODA3 3NODA3 4NODA3 5
NODA3 6NODA3 7NODA3 8
NODA3 9NODA9 9
C
BLANK CARD END OF NODE VOLTAGE OUTPUT REQUESTS
BLANK CARD END OF PLOTTING REQUESTS
BLANK CARD TERMINATING STATISTICS OUTPUT REQUESTS
C
BEGIN NEW DATA CASE
BLANK