Citation
Modeling techniques in simulating power system transients using the electro-magnetic transient program

Material Information

Title:
Modeling techniques in simulating power system transients using the electro-magnetic transient program
Creator:
Mudarres, Mohammed Kamal
Publication Date:
Language:
English
Physical Description:
57 leaves : illustrations ; 28 cm

Subjects

Subjects / Keywords:
Transients (Electricity) ( lcsh )
High voltages ( lcsh )
Digital computer simulation ( lcsh )
Digital computer simulation ( fast )
High voltages ( fast )
Transients (Electricity) ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 51-52).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Department of Electrical Engineering, Department of Computer Science and Engineering.
Statement of Responsibility:
by Mohammed Kamal Mudarres.

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:
19782932 ( OCLC )
ocm19782932
Classification:
LD1190.E54 1988m .M82 ( lcc )

Full Text
This thesis for the Master of Science degree by
Mohammed Kamal Mudarres
has been approved for the
Department of
Electrical Engineering and Computer Science
by
£ankaj K. Sen
William R. Roemish
Marvin F. Anderson
Date:


Ill
Mudarres, Mohammed Kamal (M.S., Electrical Engineering)
Title: Modeling Techniques in Simulating Power System
Transients Using The Electro-Magnetic Transients
Program
Thesis directed by Associate Professor Pankaj K. Sen
The importance of power system transients and the
extreme stresses produced during transients in high
voltage systems was recognized very early. The analysis
of power system transient conditions is most significant
in determining power apparatus insulation levels, current
interrupting device characteristics and ratings, and surge
protection requirements, particularly at the high voltage
(HV), extra high voltage {EHV) and ultra high voltage
(UHV) levels.
The digital simulation technique is most commonly
used for studying such problems. One of the best known
programs is the Electro-Magnetic Transient Program (EMTP).
The purpose of this thesis is to discuss various
techniques in modeling power system apparatus for
transient studies. A non-linear transformer model is
developed. Digital simulations are performed and
discussed on number of case studies to enhance the
understanding of EMTP studies.
The forms and contents of this abstract are approved. I
recommend its publication,
Signedl
Panlkaj K. Sen


This thesis is dedicated to
my father
Kamal Muneir Mudarres


V
ACKNOWLEDGMENTS
This thesis is submitted to the University of
Colorado at Denver as the final requirement for the Degree
of Master of Science in Electrical Engineering. This
study would not have been possible without the cooperation
and contributions of many people.
I especially wish to thank Dr. Pankaj K. Sen,
Associate Professor of Electrical Engineering and Comuter
Science at CU-Denver for serving as my academic and thesis
advisor and providing me with his suggestions, criticism,
and encouragement.
I also wish to thank Mr. Richard W. Wall of the
Power Products Incorporated in Boise, Idaho for providing
me with a PC-EMTP program, without which I would not have
been able to do this thesis.
Finally, I would like to thank all my family
members for supporting me emotionally to complete this
work and to whom I would be grateful forever. I also wish
to thank an array of close friends for some stimulating
discussions and helping me a great deal in editing it.


VI
CONTENTS
ABSTRACT............................................. iii
DEDICATION............................................. iv
ACKNOWLEDGMENTS......................................... v
CONTENTS............................................... vi
FIGURES.............................................. vi i
CHAPTER
1. INTRODUCTION...................................... 1
2. THE ELECTRO-MAGNETIC TRANSIENT PROGRAM............ 4
2.1 History of Transient Simulation............. 4
2.2 Modeling Procedures in the EMTP............. 6
2.2.1 Uncoupled Linear Elements............ 6
2.2.2 Coupled Linear Elements............. 10
2.2.3 Transmission Lines and Cables....... 13
2.2.4 Non-Linear Elements................. 17
3. TRANSIENT PHENOMENA............................ 2 6
3.1 Data Preparation........................... 26
3.2 System Energization........................ 30
3.3 Capacitor Switching........................ 33
3.4 Transients Caused by Faults................ 36
3.5 Transients Caused by Lightning............. 39
3.6 Simulation of Ferroresonance............... 44
4. CONCLUSION....................................... 49
REFERENCES...................................... 51
APPENDICES
53


7
7
9
11
12
14
15
16
19
20
21
22
23
24
25
27
30
34
37
37
40
41
FIGURES
Resistive Branch.............................
Inductive Branch.............................
Inductor Representation in EMTP..............
Multi-Winding Transformer....................
EMTP Representation of Transformer..........
Transmission Line Section....................
Transmission Line............................
Transmission Line Representation in EMTP.....
Equivalent Circuit of Magnetization Admitance
Saturation Curve of a Transformer............
First and Third Harmonics....................
Conversion from RMS Values to Volt-sec.......
Determination of Inductances from Slopes.....
Core Representation..........................
Switching Action.............................
General Power System.........................
System Energization..........................
Capacitor Switching..........................
Fault Switching..............................
Transients Caused by Faults..................
Lightning Surge According to IEEE Standards..
Switches Operation...........................


VI11
3.8 Transients Caused by Lightning................. 41
3.9 System Used for Ferroresonance Study........... 45
3.10 Thevenin Equivalent Representation............. 45
3.11 Ferroresonance Simulation...................... 46
3.12 BPA Simulation................................. 47


CHAPTER I
INTRODUCTION
The study of power system transients has been
growing rapidly. It has become essential to understand
the behavior of power systems under transient conditions,
especially in designing high voltage (HV) extra high
voltage ( EHV ) and ultra highe voltagte ( UHV.) systems.
The task of studying power system transients is
very complex and tedious. The need for a sophisticated
mathematical treatment is essential. The process for
developing an engineering tool to better analyze and
understand transients began a long time ago. Since the
early 1900s, engineers have been trying to develop such
a tool. There has been a tremendous amount of work done
and there is still more work that needs to be done.
The introduction of digital computers in the
1960s has opened new and fascinating fields to study the
transient phenomena. Computer programs were developed to
model different power apparatuses and then simulate
transient actions by proper switching of different
elements as desired. Such programs are very hard to
develop and require a lot of programming knowledge. Clear


2
understanding of the theory of power system analysis is
also an essential requirment.
Results obtained from such computer studies help
a great deal in designing and writing specifications for
power system applications. Design for HV, EHV and UHV
systems is seldom dictated solely by the steady-state
performance of the system. Extreme conditions usually
occur during transient phenomena. Therefore, a need for a
tool to study power systems during these transients is
considerably important. Transient studies are used to
determine the design for transmission line towers,
clearance for transmission line conductors, insulation of
windings in power apparatuses, rating of circuit breakers,
loading capability of equipment, protection scheme design
and many others.
The representation of the power system components
can differ from one application to another. This is
considered one of the real advantage of EMTP in transient
analysis. For instance, a transmission line may be
treated as a short bus section, or as an infinitely long
line, or as an inductance, or as a capacitance or as a
resistance, depending upon the specific transient
phenomena being studied. This concept applies for many
other components as well. It is very difficult to
determine a mathematical model for a component which
represents it correctly under all circumstances. The task
of selecting the right model is left to the expertise of


the engineer working on the problem. However, one must
know or at least assume what the outcome should look like.
This ability to pre-determine the proper system model can
come only with experience in the field of transient
analysis.
This thesis will discuss various techniques used in
power system modeling for transient studies. A non-linear
transformer model is developed. Digital simulations are
performed for number of case studies including different
models to enhance the understanding of EMTP studies.


CHAPTER II
THE ELECTRO-MAGNETIC TRANSIENT PROGRAM (EMTP)
2.1 History of Transient Simulation
Since the early 1900s electrical engineers have
been trying to study the phenomena of power system
transients. In the early years, the use of the Transient
Network Analyzer (TNA) was very helpful [2]. The idea was
to build a miniature power system by using simple
components such as resistors, inductors, capacitors and
sources to represent the real power system under
investigation. Switching action or faults were simulated
manually to represent various abnormalaties. Currents and
voltages at strategic locations were measured by
appropriate equipment in all of the systems for detail
analyses.
Though the process is simple conceptually, it is
quite cumbersome and difficult to build a different
miniature power system each time to investigate a
transient case. In addition to this, the high cost of the
study has limited the use of the TNA to large utility
companies and to extremely important cases.
The search for better tools to study transient
phenomena continued for the next decades. In the early


0
1960's, with the introduction of digital computers,
engineers began to think about using computers to simulate
power system transients.
Originally, many short programs were developed to
study small special cases and then build a large network,
piece by piece. One version of these programs, called the
Electro-Magneteic Transient Program (EMTP), was considered
to be more reliable and easier to build on to.
The EMTP, originally, was developed by Dr. Hermann
Dommel [8] in the late 1960's at the Bonneville Power
Administration (BPA). The code of the program has grown
from a few hundred lines to several thousand lines through
the years. It is designed for a large main frame
computer.
With the rising use for personal computers in the
1980s a need for a PC version of the EMTP became
essential. Number of programs were developed and are
available for general use. Due to the limitations of the
PC memory and speed, these programs impose certain
restrictions on the size of the system being modeled.
However, the PC version is easier to use, more convenient
and provides a good basic understanding for any transient
problem.
In recent years, the use of the EMTP has become
essential to many utilities and manufacturing companies.
In fact, the use of the program is not limited to the


industry, many universities have incorporated teaching and
using the program for research purposes.
2.2 Modeling Procedures in the EMTP
Since the digital computer can not give a
continuous solution or representation of the transient
phenomena, the concept of the sequential discrete solution
is utilized. The solution given by the EMTP is presented
in time steps rather than continuous time analysis.
Modeling is done by representing each of the
components in the system by their algebraic or
differential equations. These differential equations are
solved by using the trapezoidal rule of integration. The
solution of such equations can be found by solving from
initial conditions and then progress the analysis one time
step At until the desired time is achieved.
According to the EMTP, most power apparatuses can
be categorized under the following four main areas.
1. Uncoupled Linear Elements
2. Coupled Linear Elements
3. Transmission Lines and Cables
4. Non-Linear Elements
Fundamentals of modeling these elements in a PC version of
the EMTP are discussed next.
2.2.1 Uncoupled Linear Elements
These are the most basic elements in the EMTP.
They can be represented easily by an algebraic or


7
differential equation relating voltage across the element
and current flowing through the branch.
First, consider a resistive branch as shown, in
Figure 2.1.
k *-
Vk

*km
vV'A
R
m

Figure 2.1 Resistive Branch
The current can be solved by using the following equation,
1
i (t) = --- [ V (t) V (t) ] (2.1)
km R k m
this is a simple algebraic equation and can be represented
as is in the EMTP.
The equation for an ideal inductive branch is,
d i (t)
km
V (t) V ( t) = L ------- (2.2)
km dt
k *" *kro
----- ^WY\
vk L
m
Figure 2.2
Inductive Branch


8
The differential equation can be replaced by an algebraic
equation in the EMTP using the trapezoidal expansion form,
and is given by,
At
i (t) = ---- [ V (t) V (t) ] + i (t At) +
km 2L k m km
At
---- [ V (t At) V (t At) ] (2.3)
2L k m
From the above equation, we can see that the first term is
dependent upon the node voltage at any time t, while the
last two terms are dependent on voltage and current one
time step At before t, i.e. at time (t At). It is
assumed that the value of the voltage and the current are
already known at time (t At). The expression of the
current can be re-written slightly different as a
resistance term and a current source calculated one time
step back.
i (t)
km
where,
and ,
I ( t
km
---- [ V (t) V (t) ]
Req k m
+ I (t At)
km
2L
Req = ----
At
1
At) = i (t At) + ------- [ V (t
km Req k
V (t At) ]
m
At)
(2.4)
(2.5)


The current I is known from the past history. So, we
km
can replace the inductor with an equivalent current source
and a resistor as shown in Figure 2.3.
Req
Figure 2.3 Inductor Representation in EMTP
We can derive the equations for an ideal
capacitive branch in the same manner as the inductive
branch, yielding,
1
i (t) =
km
----- [ V (t) V (t) ] +
Req k m
I ( t A t)
km
(2.7)
where,
Req
and,
A t
2 C
(2.8)
I (t At
km
---- [ V (t At) V (t At) ]
Req k m
i (t
km
A t)
(2.9)


10
As before, the capacitor can be replaced by a current
source and a resistor.
The ordinary differential equations of the
uncoupled linear L or C elements are transformed by the
trapezoidal rule of integration into equivalent constant
resistors and known time-varying current sources [8].
Simultaneous solution then requires the interconnection of
such resistors and current sources, resulting in a linear
resistive network that must be solved at each time step
A t.
2.2.2 Coupled Linear Elements
The application of the coupled linear elements is
very useful in modeling for the EMTP. This concept can
be applied in case of multi-winding transformers or "PI"
circuit modeling for multi-phase distributed transmission
lines or cables.
The modeling of the coupled elements is very
similar to that of the uncoupled. The only difference is
the switching from scalar quantities to matrix quantities.
This means that all branches are considered multi-phase
branches and they are represented by matrices. In this
analysis the matrix quantities will be denoted by
brackets.


11
Figure 2.4 Multi-Winding Transformer
The voltage-current relationships of the windings in the
transformer (neglecting losses) can be written as,
' VI ' " Lll LI 2 LI 3 d " il
V2 L21 L22 L23 i2
dt
L V3 J L31 L32 L33 i3 _
where, Lll, L22 and L33 are the self inductances of the
windings and L12, L13, L21, L23, L31 and L32 are the
mutual inductances of the windings.
d
[ V ] = [ L ] . ---- [ i ] (2.10)
dt
Applying the trapezoidal rule of integration with
incorporation of the time step concept yields,
At -1
[ i(t) ] = ---- [ L ] [ V(t) + V(t At) ] +
2
[ i (t At) ]
(2.11)


As before, we are assuming that values of the voltage and
current are known at time It At). Therefore, we can
re-write the above equation as an equivalent resistance
and known current source,
where,
-1
[ I ] = [ilt At)] + [R] [V(t At)] (2.13)
2 [L]
R = ------- (2.12)
A t
i(tj]


Figure 2.5 EMTP Representation of Transformer
Equation for the coupled capacitors can be described in a
similar fashion, as a resistance term and a current
source.
-1
At [C]
R =
(2.14)
-1
= (i (t At)] [R] [V(t At)]
[ I ]
(2.15)


13
2.2.3 Transmission Lines and Cables
There are several ways one to represent overhead
transmission lines and cables in digital simulations. One
common method is the use of lumped parameters and cascaded
short Pi-circuits to represent a long transmission line.
This method is ideal for steady-state and very low
frequencies analysis. The fact that the Pi-circuit model
is no more than a low pass filter, this analysis will
produce a natural cut-off frequencuy and therefore the
model will not be usefull at higer frequencies. The
distributed parameter model is more realistic for
reasonablly high frequenies. This model is preferred for
most transient studies because it eleminates all
artificial natural resonances of the lumped elements,
there is no natural cut-off frequency, and it provides a
substantial numerical stability. The last of these models
is the frequency-dependent line model. This model
provides an ideal representation for transmission lines in
transient studies. It is an excellent tool for high
frequency simulations and especially when the study
requires a detailed representation for transmission lines.
Unfortunately, the PC version of the EMTP being used for
this thesis does not have this model.
The modeling of transmission lines and cables in
this section will utilize the concept of distributed
parameters. This concept is directly derived from the
solution of the well-known Wave Equations.


J. 1
Consider the most basic case, a small section of a
lossless transmission line. Assuming that this section
has inductance of L' henries and capacitance of C' farads
per meter. If this section has a length of Ax, then its
inductance and capacitance will be L'Ax and C'Ax as
shown.
i (x,t)
------>*
v (x,t)
L'AX
C'ax ziz
--- A X
Figure 2.6 Transmission Line Section
The digital computer representation of the
transmission line can be derived from the differential
equation of the line known as the Wave Equations. These
equations solve for the voltage and current as a function
of time and position.
^v
3x
(x, t)
^i
L --- ( x t)
^i
(2.16)
3i
^x
( x t )
3v
C ------- ( x t )
at
(2.17)
The solution of these equations is given by,


A %J
i1x,t) = f + (x st) + f_(x + st) (2.18)
v(x,t) = Zo f_|_(x st) Zo f_(x + st) (2.19)
where,
r Zo = / (characteristic V c* impedance) (2.20)
and,
1 s = (speed of wave propagation) (2.21)
'I L C '
The functions f_|_(x st) and f_(x + st) are the waves
traveling, with velocity s, in the forward and backward
direction respectively.
For the transmission line used in this analysis
and shown in Figure 2.7,
k -----------1 --------- m
(t) Surge Impedance vm (t)
= Z0
Figure 2.7 Transmission Line
the solution of the Wave Equations is implemented in the
EMTP by looking from one end of the transmission line to
the other, yeilding the following two-port equations for
the current going through the line.


X u
i ( t )
km
v (t)
k
--------- + I (t t)
Zo k
i (t)
mk
where,
I (t .tr)
k
and,
I (t -tr)
ra
d
t = ----
v (t)
m
Zo
+ I (t t)
m
v (t T)
m
- i (t -tr) - ----------------
mk Zo
- i (t tr)
km
(travel time of
v (t t)
k
Zo
the line).
s
d : the length of the line.
(2.22)
(2.23)
(2.24 )
(2.25)
(2.26)
These equations can be modeled as a resistor term and a
known current source as shown. Further analysis on
the development of the solution can be found in refernce
[4].
ikm (t) *-mk. (t)
(t-
Figure 2.8 Transmission Line Representation in EMTP


The EMTP requires the line parameters R', L', and
C* to be used as an input for the program. In most cases,
with complicated line configuration, calculating the line
parameters is more complex. The EMTP has a supplemental
program called "Line Constants" to calculate the line
parameters. This routine can calculate the line
parameters for any multi-phase transmission lines.
2.2.4 Non-Linear Elements
The most common types of nonlinear elements used
in power systems transient calculations include nonlinear
inductances for the representation of transformer and
reactor saturation, and nonlinear resistance for the
representation of surge arresters. For some special
studies, the representation of the nonlinear arc
resistance in circuit breakers can also be useful.
This section will discuss only the modeling of non-
linearity in transformers due to core saturation and its
effect on transient studies.
During the transient period, transformers
connected to a given system may be driven into the
saturation region due to overvoltages. When that happens
the output current wave will have a non-sinusoidal shape,
which in turn will cause some other distortions and
possibly will resonate with some adjacent components on
the system. To study these problems, a nonlinear
transformer model is required. Unfortunately, the PC
version being used in this thesis does not have a built-


18
in model for the saturated transformer. A nonlinear
transformer model is developed by switching the
magnetization inductance consecutively, at certain voltage
levels, to represent the saturation in the transformer.
operating conditions, the steady-state leakage impedance
values of the transformer is used for performance
calculations. The magnetization impedance (or admittance)
of the transformer, if used, can be determined from the
open circuit test as follow [5]. The equivalent circuit
is shown in Figure 2.9.
When a transformer is running under normal
I
Y
G j B
(2.27 )
V
P
G
(2.28)
2
V
B
G
2
(2.29)
where
Y : the open circuit admittance
I : rms value of the exciting current
V : the impressed voltage during the test
P : the power input measured from the primary side


19
Figure 2.9 Equivalent Circuit of the Magnetization
Admitance
However, when the transformer is driven into the
saturation region, the transformer behavior is largely
controlled by the magnetization characteristics of the
core material. The relationship between the current and
the voltage in the transformer during saturation is
related by the flux in the iron core at any time t.
d V
v (t) = ------- (neglecting the sign) (2.30)
d t
or,
't
If (t) = v (t) dt and, (2.31)
J o
If ( t) = f ( i(t) ) = Flux Linkage (2.32)
The instantaneous (|J-i relationship can be represented by
what is called the saturation curve of the magnetic core
as shown in Figure 2.10.


V (v-s)
Figure 2.10 Saturation Curve of a Transformer
The saturation curve for any transformer can be
obtained from its manufacturer. It can be expressed as
rms voltage as a function of rms current, or flux linkage
in volts-sec as a function of instantaneous current. One
form can be converted into the other form by using the
following assumptions and algorithm.
1. hysteresis and eddy current losses in the iron core
are ignored,
2. resistance in the winding is neglected,
3. the flux-current curve is to be generated point by
point at such distances that linear interpolation is
acceptable between points, and
4. The voltage wave is a perfect sinusoid.
Assume, v (t) = V cos (wt), then
m


21
V sin (wt)
m
1|J (t) = -------------- = y sin (wt)
w m
but, for a sine wave,
V
rms \/ 2
then,
TjJ w
m
V = ;-----
rms V 2
(2.33)
(2.34)
(2.35)
To convert the instantaniouse current to rms value, the
first and third harmonics (higher order of harmonics are
neglected for simplicity) have to be taken into
consideration because the current waveform is no longer
sinusoidal. This can be best illustrated as follows.
i (t)
Figure 2.11 First and Third Harmonics of
the Current Wave


22
Assume that the transformer current has the first and
third harmonics as the predominant harmonics, then
i (t) = II sin (wt) + 13 sin (3wt) (2.36)
Equation (2.36) can be represented by an equivalent sine
wave which its rms value is calculated as follows,
Using equations (2.35) and the equivalent sine wave given
by equation (2.37), the conversion to rms values of the
flux and current can be performed.
TjJ ^rros
Figure 2.12 Conversion from Volts-Sec to RMS values


The magnetization inductance of the transformer
for any specific portion of the saturation curve can be
calculated from the slop of the curve at any operating
z z
point. The appropriate inductance values can be switched
on at the corresponding voltage level to simulate
transformer core saturation.
Figure 2.13 Determination of Inductances from Slopes
The saturation characteristic is devided into three
regions for simplicity in this particular case as shown in
Figure 2.13. Different inductance values are calculated
as follows:
A V
A (rms)
L = slope A = ------------- = tan a (2.38)
A A I
A (rms)


L. **
L = slope B
B
L = slope C
C
A V
B (rms)
A I
B (rms)
A V
C (rms)
A I
C (rms)
tan b
tan c
(2.39)
(2.40)
However, L is the magnetization inductance of
A
the transformer during the linear part of the saturation
curve, which can be calculated from the open circuit test
of the transformer as discussed before. Typically,
L > > L
A B
and,
L > > L
B C
The transformer equvalent circuit is then
represented as follows:
Leakage Impedance
Figure 2.14 Core Representation


25
SI and S2 are switched on, if the instantaneous value of
the transformer terminal voltage is larger than VI and V2,
consecutively, and switched off if the terminal voltage is
less than VI and V2.
Figure 2.15 Switching Action


CHAPTER III
TRANSIENT PHENOMENA
In this section some cases where transient
occurrence played an important role in the behavior of the
system will be discussed.
Some of the topics that will be covered are:
- system energization,
- capacitor switching,
- transients caused by faults,
- transients caused by lightning, and
- simulation of ferroresonance
To keep the analysis fairly simple, one main
hypothetical system will be assumed and most of the
studies will be performed on it. For the ferroresonance
study, the system used is obtained from reference [4].
3.1 Data Preparation
Data preparation for the EMTP can be done
according to the given standard information. It must be
noted here that the EMTP requires all components to be
represented in actual quantities, that is in ohms, henries
and farads, etc.


27
230 kV

200 MV A 200 MVA
X = 0.12 X, 101
d t
13-8 kV
X Connected
(2)
230 kV
120 mile
15 mile
--^
69 kV
(3)2SVA W
500 MVA
X -10*
(fc)
,1(00 MVA
0.9 (lag) p.f.
230 kV
69kV
t> 160 MW
__ 0.8 (lag) p.f.
7 | Corrected to 0.95 (lag)
/
Figure 3.1 General Power System
Sources: All sources are considered ideal voltage
sources,
v(t)=V sin (wt + 0)
m

V
* 13.8 KV = 11.27 kV/phase
m \/ 3
w = 377 r/s
Transformers: The data for the transformers in the system
are obtained from the specification sheet of the
transformers. Those are the self and mutual impedance of
the windings.
Transmission Lines: The Line Constant program is used
here to find the parameters of the lines. As it was


28
mentioned in chapter two, to calculate the line
resistance, inductance and capacitance, the following data
is needed for each line:
- the length of the line,
- the elevation of the line from ground, including the
sag,
- the GMR of each conductor including the shield wire,
- the diameter of each conductor,
- phase spacing of conductors,
- transposition of line,
- frequency of steady-state operation, and
- dc resistance of each conductor.
Capacitor Banks and Loads: The value of the capacitor
banks are determined from the load ratings. For example,
at bus 4 the load initially was 160 MW at 0.8 (lag) power
factor. It has been corrected by using capacitors to
operate at 0.95 (lag) power factor.
So, at 0.8 pf,
2
69
Z = ----- = 23.81 ohms
200
R = 23.81 0.8 = 19.04 ohms
-1
23.81 sin (cos 0.8)
L = ------------------------ = 3 7.9 mH
377
At 0.95 pf, the VARs in the system can be calculated by,
160 -1
Q = ---- sin (cos 0.95) =52.59 MVAR
0.95


29
At 0.8 pf,
-1
Q = 200 sin (cos 0.8) = 120 MVAR
Therefore, the VARs supplied by the capacitor
Qc = 120 52.59 = 67.41 MVAR
The impedance of the capacitor is,
2
69
Zc = -------- = 70.63 ohms
67.41
C
1
377 70.63
37.56 uF
is,
At bus 6,
Z
2
69
----- = 11.9 ohms
400
R = 11.9 0.9 = 10.71 ohms
-1
11.9 sin (cos 0.9)
L = ------------------------- = 13.76 mH
377
Time Specification: Since the EMTP utilizes the concept
of discrete solution, the time step has to be specified at
the beginning of the program. This should be small enough
to reduce the error margin. Generally speaking, the time
step should be smaller than one half of the smallest
traveling time of any transmission line in the system [4].


30
3.2 System Energization
The first simulation is the case where the system
is operating under normal conditions with the load at bus
4 operating at 160 MW and 0.8 (lag) power factor. The
system is energized and its behavior is observed. For
this simulation, as well as the next three, the simulation
time is 100 milliseconds (0.1 seconds). The results are
shown in Figure 3.2.1 thru Figure 3.2.6.
BUSl-U
Figure 3.2.1 System Energization at BUS 1


31
BUS 2 U ikV)
Figure 3.2.2 System Energization at BUS 2
BUS 3 u (kV)
Figure 3.2.3 System Energization at BUS 3
BUS4-U (kV)
Figure 3.2.4 System Energization at BUS 4




i 3
As it was demonstrated in the previous plots, the
initial transients caused by the system energization can
be harmful to the system. At bus 1 a sinusoidal source
supplying energy to the system is seen. Both of buses 3
and 4, have encountered about 1.5 per unit voltage during
energization, which may cause some problems. It could
affect the load connected at bus 4. Due to the long
transmission line connected between buses 2 and 5, it is
obvious that energizing long lines causes worse transients
than short ones. The plots of the voltage at bus 5 and 6
show that the magnitude of the initial transient was equal
to about 2.0 per unit. This is a situation where a need
for some means of protection for limiting transient
overvoltage is necessary. A delay is observed on buses 5
and 6, which is due to the length of the transmission
line. This delay in time is controlled by the traveling
time of the line, which in this case is about 20
microseconds.
3.3 Capacitor Switching
A capacitor will be used at bus 4 to correct the
power factor from 0.8 to 0.95. The capacitor is switched
at about 16 milliseconds and the system behavior is
observed at all buses. The bus voltage plots are shown in
Figure 3.3.


c(4
0.1 sec
BUS3-U (kV)
328 T
Figure 3.3.1 Capacitor Switching at BUS 2
0.1 sec
Figure 3.3.2 Capacitor Switching at BUS 3
0.1 sec
Capcitor Switching
Figure 3.3.3 Capacitor Switching at BUS 4


35
BUS5-U ^V)
Figure 3.3.4 Capacitor Switching at BUS 5
BUS6-U (kV)
Figure 3.3.5 Capacitor Switching at BUS 6


36
Transients caused by capacitor switching are more
severe on buses 4 and 3, simply because the capacitor was
connected to bus 4 to improve the power factor at the
load, and there is less inductance between the capacitor
and bus 2. The rest of the buses are indeed affected by
the capacitor switching as shown in Figure 3.3. Looking
at the plot at bus 4, it is obvious that at the instant
the capacitor was switched, the system sees that exactly
as a short circuit. This is due to the physical nature of
the capacitor.
It must be mentioned here that the capacitor
switching is a very complex procedure. There are several
techniques one may use to minimize the damage caused by
capacitor switching. Further discussion on protection
against capacitor switching is beyond the scope of this
thesis.
3.4 Transients Caused by Faults
For this simulation, a three-phase to ground fault
occurs in the middle of the 15 mile long line. The fault
is simulated by connecting the middle of the line to
ground through a very small resistor. The resistor is
used to eliminate numerical instability, which is purely a
computational problem.


37
BUS 3
BUS 4
1 juohms

close @ 15 msec
Figure 3.4 Fault Switching
BUS2-U (kV)
Figure 3.5.1 Fault at BUS 2


38
BUS3-U (kV)
0.1 sec
Figure 3.5.2 Fault at BUS 3
BUS4-U ( kV )
0.1 sec
BUS3-U OtV )
Figure 3.5.4 Fault at BUS 5


39
BUS6-U (kV)
Figure 3.5.5 Fault at BUS 6
Three phase fault is one of the most severe
problems that a power system may encounter. As it is
shown in the previous plots, the system encountered a
fault at the middle of the short line. At buses 3 and 4,
the voltage is suppressed immediately. The voltage at bus
2 was reduced considerably due to the fault. Buses 5 and
6 were also greatly affected by the fault. Single line to
ground faults and line to line faults can be simulated in
the EMTP in a similar manner.
3.5 Transients Caused by Lightning
For this study a lightning stroke hits the middle
of the 120 mile line. The lightning is simulated by two
large high frequency current sources injecting current at
the middle of the line. The first source has higher
frequency and rise time to represent the left side of the
strike, while the second source has lower frequency. Both
sources are connected to the system, consecutively, for a


40
duration of 100 microseonds. The selection of the
lightning surge was obtained from the IEEE standards (see
Figure 3.6). Switching configuration for lightning
simulation is shown on Figure 3.7. The switches in the
figure are closed or opened in the order of their numbers.
SI is closed at 14 milliseconds, S2 is opened after 1.2
microseconds to simulate the first part of the lighting,
S3 will close at the same time S2 opens. This is the
start of the second source. Finally, S4 opens after 98.8
microseconds to complete the full lightning strike. The
behavior of the system is observed at the six buses and
results are shown.
usee
Figure 3.6 Lightning Surge According to IEEE standards


41
S0URCE1 SOURCE2
Figure 3.7 Switches Operation
Busa-u (kV)
0.1 sec
Figure 3.8.1 Lightning at BUS 2


42
BUS3-U (kV)
Figure 3.8.2 Lightning at BUS 3
BUS4-U (kV)
Figure 3.8.3 Lightning at BUS 4
Figure 3.8.4 Lightning at BUS MID


43
BUS5-U (kV)
Figure 3.8,5 Lightning at BUS 5
BUS6-U
Figure 3.8.6 Lightning at BUS 6


3.6 Simulation of Ferroresonance
Ferroresonance is a special type of resonance due
to transformer core saturation that can give rise to large
overvoltages in power systems, and its effect can range
from as little as abnormal transformer humming, all the
way to equipment failure, due to insulation breakdown.
This phenomenon is very common in transformers
that have an ungrounded primary, have considerable
capacitance to ground connected to them and are switched
to a power source with single-phase interruptive devices,
which will result in series capacitance and nonlinear
inductance. [11]
A power system encounters ferroresonance in a
certain area when transformers adjacent to that area are
driven into saturation. To simulate that effect a
computer model that accounts for non-linearities in
transformers should be used.
Using the nonlinear transformer model developed
earlier one can simulate the ferroresonance phenomenon.
The following case was simulated by the Bonnevile
Power Administration on their 1100 kV test line.
Ferroresonance occurred in phase A when this phase was
switched off on the low-voltage side of the step-up
autotransformer (see Figure 3.9). Phase C was not
connected to a transformer at that time. [4]


t J
Figure 3.9 System Used for Ferroresonance Study
This system can be simulated by representing the
dotted portion by its Thevenin equivalent, referred to the
high side. The Thevenin equivalent was found, by BPA, to
be a voltage source behind a capacitance. This equivalent
circuit is accurate enough over the frequency range
encountered in ferroresonance studies.
Figure 3.10 Thevenin Equivalent Representation


46
The above system was modeled and simulation
results are shown in Figure 3.11.
T Ifl-U
Figure 3.11.1 Transformers Voltage
T Ift-I
Figure 3.11.2 Transformers Current


47
The same system was simulated by BPA and results are shown
in Figure 3.12.
Figure 3.12 BPA Simulation
The results from the model developed in this
thesis produces very similar results as those obtained by
BPA, except for some oscillation during the voltage peak.
This is due to the simplification of the problem assuming
ideal inductive branches, resistance was neglected. Also
BPAs version of the EMTP has an averaging technique,
where the program will average the oscillation values and
uses the average in the output plot.
Generally, numerical oscillation is a common
problem with most numerical simulation programs. The time
step size and initial conditions are the major factors
contributing to the magnitude of the oscillation.


48
Selecting the right numbers can save a lot of time and
effort.
Numerical oscillation are produced due to
switching capacitors or inductors. The problem can be
resolved by using a small resistor in series with the
capacitor, the size of the resistor can differ according
to the time step size and is given by [4],
0.15 At
R = ----------
2 C
while for the inductor, the resistor is connected in
parallel and it is estimated by [4],
13.3 L
R = --------
A t
Once these resistors are used in the appropriate places,
the problem of numerical oscillation is resolved
considerably.
In the ferroresonance study performed for this
thesis, these resistors were used to reduce the numerical
oscillation problem.


CHAPTER IV
CONCLUSION
The use of the PC version of the EMTP is utilized
here. As it was shown in the study cases discussed above,
the existence of the transients can be harmful to the
power system apparatuses and personnel.
It should be noted that the modeling of the power
systems can be more detailed than it was done. However,
the results may be slightly different. The reason of
these simulations is to identify the transients and get a
general feeling of their existence and their magnitude.
This thesis also have discused various techniques in
modeling physical phenomena such as faults and lightning.
The PC version of the EMTP offers a good and easy
application for that purpose.
One of the most important factors in studying
transients analysis is the switching time, the time at
which an apparatus or an external effect was imposed on
the system. Generally, if the switching occurred at the
instant where the voltage is at its maximum point,
producing a maximum change in voltage across capacitance,
the resulting transient has a larger magnitude. For all
of the transients simulated in this thesis, the switching


occurred at maximum voltage to observe the system under
the worst possible situation.
ou
No surge arrestors or other types of voltage
limiting devices were used for this study.
As far as the transformer nonlinear model
developed here, it was found to be valid and can be used
for any transformer once its saturation curve is known.
This model can be more exact by using more piece-wise
linear segments to represent the saturation curve.
However, only three linear segments were used and the
results were very reasonable. One can note that a non-
linear resistor model can be developed similarly to
represent surge arrestors.
In summary, the PC-EMTP is a relatively new
tool, but its use is growing considerably. There are many
publications on this topic that can explain it in further
detail. This thesis has discussed some basic aspects of
power system transient simulation.


REFERENCES
1. Bayless, R. S., Selman, Jeff D., Truax, D. E. and
Reid, W. E., "Capacitor Switching and Transformer
Transients", IEEE paper presented at the PES Summer
Meeting, Mexico City, Mexico, 1986.
2. Clerici, Alessandro and Marzio, Leonardo,
"Coordinated Use of TNA and Digital Computer for
Switching-Surge Studies: Transient Equivalent of a
Complex Network", IEEE Paper presented at the PES
Winter Meeting. New York, New York, 1970.
3. Dommel, Hermman W., "Digital Computer Solution of
Electromagnetic Transients in Single and Multiphase
Networks", IEEE paper presented at the PES Summer
Power Meeting. Chicago, Illinois, 1968.
4. EPRI Course, EMTP Workbook, University of Wisconsin
at Madison, Madison, Wisconsin, 1987.
5. Fitzgerald, A. E., Kingsley Jr., Charles and Umans,
Stephen, Electric Machinery, 4th edition, McGraw
Hill, 1983.
6. IEEE Tutorial Courses, Digital Simulation of
Electrical Transient Phenomena, New York, 1981.


7. Morched, A. S. and Brandwajn, V., "Transmission
Network Equivalent for Electromagnetic Transient
Studies", IEEE paper presented at the PES Winter
Meeting, New York, New York, 1982.
8. Sen, Pankaj K. and Mudarres, Mohammed K., "PC Version
of the Electro-Magnetic Transient Program (EMTP) in
Power System Analysis", IEEE paper presented at the
Region V Conference. Colorado Springs, Colorado,
March, 1988.
9. Stevenson Jr., William D., Elements of Power System
Analysis, 4th edition, McGraw Hill, 1982.
10. Wall, Richard W., PC-EMTP Manual and Program, Power
Products Inc., Boise, Idaho, 1987
11. Perez, Manuel A., Ferroresonance, Its Causes and
Effects on Power Systems. M.S. Report, University of
Colorado, Boulder, Colorado, 1976.


APPENDIX A
The following are the data used for the
simulations performed in this thesis.
A.1 System Energization
; Time Specification
1000 0.000E+00 1.000E-01 2.500E-05
; Branch Data R L C
1 BUS1 BUS2 4.800E+00 8.966E-03 0.000E+00 0
/ 0.000E+00 0
-1 BUS2 BUS3 2.640E+00 3.900E-02 2.367E-07 0
/ 0.000E+00 0
11 BUS3 BUS4 0.000E+00 2.345E-02 3.000E-01 0
/ 0.OOOE+OO 0
0 BUS4 / 1.900E+01 3.700E-02 0.OOOE+OO 0
/ 0.000E+00 0
-1 BUS 2 BUS 5 2.115E+01 3.100E-01 1.893E-06 0
/ 0.000E+00 0
11 BUS 5 BUS6 0.OOOE+OO 4.536E-01 3.000E-01 0
/ 0.000E+00 0
0 BUS 6 / 1.070E+01 1.376E-02 0.OOOE+OO 0
/ 0.000E+00 0
; Source Data
1 BUS1 1.38000E+04 6.00000E+01 0.00000E+00
; Output Data
999 BUS1 BUS2 BUS3 BUS4 BUS5 BUS6


54
A.2 Capacitor Switching
; Time Specification
1000 0.000E+00 1 .000E-01 2 .500E-05
; Branch Data R L C
1 BUS1 BUS 2 4.800E+00 8.966E-03 0.OOOE+OO
/ 0.000E+00 0
-1 BUS2 BUS3 2.640E+00 3.900E-02 2.367E-07
/ 0.000E+00 0
11 BUS3 BUS4 0.000E+00 2.345E-01 3.000E-01
/ 0.000E+00 0
0 BUS4 / 1.900E+01 3.700E-02 0.OOOE+OO
/ 0.OOOE+OO 0
; Capcitor Switching at BUS 4
0 BUS4 / 0.OOOE+OO 0.OOOE+OO 3.756E-05
/ 1.600E-02 0
-1 BUS2 BUS5 2.115E+01 3.100E-01 1.893E-06
/ 0.000E+00 0
11 BUS5 BUS6 0.OOOE+OO 4.536E-01 3.000E-01
/ 0.000E+00 0
0 BUS6 / 1.070E+01 1.376E-02 0.OOOE+OO
/ 0.OOOE+OO 0
; Source Data
1 BUS1 1.38000E+04 6.00000E+01 O.OOOOOE+OO
; Output Data
999 BUS1 BUS2 BUS3 BUS4 BUS5 BUS6
0
0
0
0
0
0
0
0


A.3 Transients Caused by Faults
; Time Specification
1000 0.000E+00 1.OOOE-O1 2.500E-05
; Branch Data R L C
1 BUS1 / 0.000E+00 BUS 2 0 4.800E+00 8.966E-03 0.000E+00 0
-1 BUS2 / 0.000E+00 MID 0 1.320E+00 1.950E-02 1.184E-07 0
-1 MID / 0.000E+00 BUS3 0 1.320E+00 1.950E-02 1.184E-07 0
: Fault Switching at the Middle of the Line
0 MID / 1.667E-02 / 0 1.000E-06 0.000E+00 0.000E+00 -10
11 BUS3 / 0.OOOE+OO BUS4 0 0.000E+00 2.345E-01 3.000E-01 0
0 BUS 4 / 0.000E+00 / 0 1.900E+01 3.700E-02 0.000E+00 0
-1 BUS2 / 0.000E+00 BUS 5 0 2.115E+01 3.100E-01 1.893E-06 0
11 BUS5 / 0.000E+00 BUS 6 0 0.000E+00 4.536E-01 3.000E-01 0
0 BUS6 / 0.000E+00 / 0 1.070E+01 1.376E-02 0.000E+00 0
; Source Data
1 BUS1 1.38000E+04 6.00000E+01 0.00000E+00
; Output Data
999 BUS1 BUS2 BUS3 BUS4 BUS5 BUS6


56
A.4 Transients Caused bv Lightning
; Time Specification
1000 0.000E+00 1 .000E-01 2 .500E-05
; Branch Data R L C
1 BUS1 BUS2 4.800E+00 8.966E-03 0.OOOE+OO
/ 0.000E+00 0
-1 BUS2 BUS3 2.640E+00 3.900E-02 2.367E-07
/ 0.OOOE+OO 0
11 BUS3 BUS 4 0.OOOE+OO 2.345E-01 3.000E-01
/ 0,000E+00 0
0 BUS4 / 1.900E+01 3.700E-02 0.OOOE+OO
/ 0.000E+00 0
-1 BUS2 MID 1.058E+01 1.550E-01 9.465E-07
/ 0.000E+00 0
-1 MID BUS5 1.058E+01 1.550E-01 9.465E-07
/ 0.OOOE+OO 0
; Lightning Model
0 LIT1 MID 1.000E-04 0.OOOE+OO 0.OOOE+OO
/ 1.501E-02 0
0 SRC1 LIT1 1.000E-04 0.OOOE+OO 0.OOOE+OO -
/ 1.500E-02 0
0 SRC1 / 1.000E-06 0.OOOE+OO 0.OOOE+OO
/ 0.OOOE+OO 0
0 LIT2 MID 1.000E-06 0.OOOE+OO 0.OOOE+OO
/ 1.515E-02 0
0 SRC2 LIT2 1.OOOE-06 0.OOOE+OO 0.OOOE+OO -
/ 1.500E-02 0
11 BUS5 BUS6 0.OOOE+OO 4.536E-01 3.000E-01
/ 0.OOOE+OO 0
0 BUS6 / 1.070E+01 1.376E-02 0.OOOE+OO
/ 0.OOOE+OO 0
; Sources Data
1 BUS1 1.38000E+04 6.00000E+01 0.00000E+00
-1 SRC1 5.00000E+04 1.OOOOOE+03 9.OOOOOE+Ol
-1 SRC 2 5.00000E+04 5.00000E+02 1.20000E+02
; Output Data
999 BUS1 BUS2 BUS3 BUS4 BUS5 BUS6
999 MID
0
0
0
0
0
0
10
10
0
10
10
0
0


57
A.5 Simulation of Ferroresonance
; Time Specification
1000 0.000E+00 7.000E-02 2.000E-04
> Branch Data R L C
0 SRCA SI 0.OOOE+OO 4.440E-01 0.OOOE+OO 0
/ 0.000E+00 0
0 SRCA SI 5.905E+04 0.OOOE+OO 0.OOOE+OO 0
/ 0.000E+00 0
0 SI T1 1.OOOE+OO 0.OOOE+OO 0.OOOE+OO 11
/ 0.000E+00 0
0 T1 T2 1.130E+01 0.OOOE+OO 0.OOOE+OO 0
/ 0.000E+00 0
0 T2 T1A 0.OOOE+OO 1.968E+00 0.OOOE+OO 0
/ 0.000E+00 0
0 T2 T1A 2.617E+05 0.OOOE+OO 0.OOOE+OO 0
/ 0.000E+00 0
> Non-Linear Transformer Representation in EMTP
0 T1A / 4.500E+06 0.OOOE+OO 0.OOOE+OO 0
/ 0.OOOE+OO 0
0 T1A / 3.500E+04 3.439E+03 0.OOOE+OO 0
/ 0.000E+00 0
0 T1A Cl 3.500E+03 1.173E+02 0.OOOE+OO 0
/ 0.000E+00 0
0 T1A Cl 7.800E+06 0.OOOE+OO 0.OOOE+OO 0
/ 0.000E+00 0
0 Cl / 1.OOOE+OO 0.OOOE+OO 0.OOOE+OO 2
T1 5.716E+05 0
0 T1A C2 3.500E+03 4.199E+01 0.OOOE+OO 0 .
/ 0.000E+00 0
0 T1A C2 2.792E+06 0.OOOE+OO 0.OOOE+OO 0
/ 0.000E+00 0
0 C2 / 1.OOOE+OO 0.OOOE+OO 0.OOOE+OO 2
T1 6.351E+05 0
50 T1A LI 1.130E+01 0.OOOE+OO 0.OOOE+OO 0
/ 0.OOOE+OO 0
0 LI L2 0.OOOE+OO 1.968E+00 0.OOOE+OO 0
/ 0.OOOE+OO 0
0 LI L2 2.617E+05 0.OOOE+OO 0.OOOE+OO 0
/ 0.OOOE+OO 0
0 L2 SRCB 5.730E+02 0.OOOE+OO 2.618E-08 0
/ 0.OOOE+OO 0
) Sources Data
1 SRCA 6 . 35100E+05 6.00000E+01 0. 00000E+00
1 SRCB 6 .35100E+05 6.00000E+01 2. 40000E+02
; Output Data
999 T1
T1A