fault current docs

Study on Voltage Unbalance Improvement Using SFCL in Power Feed Network With Electric Railway System

1

Abstract

This paper presents a novel approach to determine the power system stability using resistive superconducting fault current limiter (SFCL) of an electric power grid (EPG). In addition, the electric railway system has rapidly changing load characteristics in time. An unbalance is generated owing to the rapidly changing large single-phase loads. Subsequently, the unbalanced load causes an unbalanced transmission line. A voltage unbalance in the source influences the power equipment by causing a reduction in the power generation capacity of the generator and a decrease in the output of the other facilities in the transmission line. In addition, many flexible ac transmission systems are applied to transmission lines to compensate for and control electric power. A voltage unbalance causes a control error in these systems. In addition, we analyzed the effects of the proposed method using transient simulations. The angular separation of the rotors of synchronous machines present in the power system is introduced. It is shown that the SFCL can have different impacts (positive and negative) in function of its location in the EPG when a fault occurs. To evaluate the effectiveness of the proposed method, the IEEE benchmarked four-machine two-area test system is used to carry out several case studies. The results show that the transient stability using SFCL combined with its optimal resistive value reduces the angular separation of the rotors that improves effectively the system stability during a fault.

Index Terms—Damping performance, electric power grid,

superconducting fault current limiter, transient stability.

CHAPTER-I INTRODUCTION

WITH the increasing of system capacity, fault occurrence probability becomes higher, that can induce severe damages in electrical power system [1]. For example, the high value of the short circuit current can damage the insulation strength of electrical devices, synchronous generators, protective relays, lines transmission, and loads. In addition, the electrical power needed by the system when a fault occurs is modified and induced instable state of the power generators

[2]. Recently, the development of superconducting fault current limiters (SFCL) offers one of the most attractive alternatives to solve the fault current problems [3]–[5]. Thanks to their fast transition from a low to a high impedance, superconducting devices can limit, in a very short time, the value of any fault current. What is attractive is that the transition is due to an intransit behavior of the material itself [6]–[9].

The presence of the SFCL in a power system can increase the system stability and distributed energy quality [10]–[15].

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When an SFCL is introduced in an electric power grid (EPG), three important factors must be considered:

[1]optimal location of the SFCL in the EPG [16]; [2]optimal resistive value of the SFCL [17]; [3] protection-coordination problem with other existing de-vices (circuit breaker, OCR, etc.). This paper focuses on factors 1 and 2. Nowadays, the

optimal location of SFCL to improve the transient stability is studied for a simple power system like single machine infinite bus (SMIB) [2], [3], [15]. So far, the remaining open question is the selection of optimal location of the SFCL in a large scale power system to improve its transient stability. In this paper we consider a multi- generator system and we use their rotor angular difference to define a sensitivity index which leads to finding the best location of the SFCL in the grid. This sensitivity index is calculated with respect to the resistive value of the used SFCL. The effectiveness of the proposed method is evaluated on the IEEE benchmark four-machine two-area test system. The toolbox Sim Power Systems of MATLAB/SIMULINK software is used to carry out simulations studies.

The simulation results show the effectiveness of the proposed method. In fact, the optimal location determined for the SFCL improves the transient stability of the power system

and decreases the low frequency oscillation of the generators speed when a severe damage is introduced (three-phase fault). The advantage of the proposed method is that the selected location of the SFCL takes into account the fact that the fault can occur anywhere in the studied grid.

package.

CHAPTER-2

II. SFCL MODEL APPLIED TO POWER SYSTEM The operation of an SFCL is based on the natural transition of the superconducting state to normal state by exceeding the critical current I of the material. This transition from the super conducting to the normal state must be done in a very short time, generally, to limit the first current peak to a threshold value not exceeding three to five times the rated current, below the short-circuit current without limitation.

The SFCL is placed in series with a circuit breaker. During the fault, the current increases up to reach the threshold of

transition from superconducting wire. This transition from the super conducting element to normal state causes the development of resistance that limits or triggers the current limit. The time between threshold crossing and the limitation

3

T.Sravani, G. Hari Krishna,Sk.Jan Basha 81

5

is small (a few microseconds). The circuit breaker isolates the line as soon as possible after the beginning of the limitation. These super conducting fault current limiters use one of the fundamental properties of superconductors.The qualifications of SFCL are:

1. Very low impedance during normal operation. The current limiter must be “invisible” in this mode. Some transients such as those caused during the switching of a transformer should not inadvertently cause a transition of the limiter.

2. High impedance system during short circuit. The limiter must perform its function in the case of massive short circuit but also in the case of low short circuit fault.

3. Very good dynamic. The system must transit in very quickly (with in millisecond) to effectively limit the value of the short circuit.

There are several types of SFCL; the main ones include:1. The resistive limiter.

This is a coil of superconductive material, non-inductive by construction, mounted in series on the line. In case of fault, the winding initially at the superconducting state changes to the normal state. Its impedance appears in the line, which limits the fault current. This limiter can be applied in AC or DC systems.

2. The inductive limiter. It consists in its simplest form, two windings connected in parallel. This association is made so that the impedance of all is the lowest possible. In case of fault, one of the coils (made of superconducting material) returns to its normal state. The other winding made either copper or superconducting material limit the current through the inductance.

3. The limiting transformer. It consists of a superconducting secondary short-circuit and primary winding of a conventional copper. In normal Operation, the impedance of this transformer is mainly due to the coupling between the windings and may be very low. Under fault, the secondary winding quenches under the effect of fault current and acts as a switch that opens the secondary of the transformer. Therefore, we obtain the no load impedance of a transformer which is very important. As we said, the first function of an SFCL is to limit the

fault current induced in the faulty line. In this case, the passage to its superconducting state to its normal state can only be achieved if the fault appears in the line where the limiter is placed. The probability that a fault appears at a specific location in the power system is very low. Consequently, if the fault appears at a different location in the power system, the SFCL cannot be used for its first function because the current value through the SFCL will be not sufficient to ensure a transition of this last. The originality of the presented work is that the SFCL is used if the fault appears anywhere in the system. In this case, the SFCL can be seen as a rapid switch that introduces a resistance in the power system. The presence of this additional resistance improves the power system stability in case of short-circuit and this, regard-less of the position of the fault. The SFCL is not used to limit the Fault current but to improve the stability of the power system. If the fault appears in the line where the limiter is placed, the two functions of the SFCL are used (limitation of the fault cur-rent in the line and improvement of the power system stability). By cons, if a fault appears at a different location, the SFCL introduce its resistance in the power system to improve the transient stability of generators. In this case, the passage to its superconducting state to its normal state will be accomplished by applying a magnetic field superior to its critical magnetic field after the detection of the fault in the EPG. The results presented in this paper show the effectiveness of the proposed method. We can represent the SFCL by impedance, which depends on current, or by a resistance, which varies during time. The SFCL used in simulation represented resistance which varies with time as

6

(1) Where represents the maximum resistance that the

SFCL can introduce in the lines of the power system. Also, is the time of transition from the superconducting state

to the normal state, which is assumed, in this study, to be 1 ms [16].

III. DESCRIPTION OF THE PROPOSED METHOD

For an EPG with more than one generator, a necessary condition for satisfactory system operation is that all synchronous machines remain in synchronism when a severe transient disturbance appears (loss of transmission line, important increase of load, three-phase short circuit). This aspect of stability is influenced by the dynamics of generators rotor angle and power-angle relationships.

When a fault occurs in the system, the operating point of generators suddenly changes. Owing to inertia, the angular separation between the rotor positions of each generator is modified until the fault is cleared. At the beginning of the perturbation, this angular separation increases with a magnitude that depends on the time necessary to clear the fault. If the fault clearing time is small, the power system is perturbed but a stable point is found again after a few seconds. Otherwise, the synchronism of the power system is lost.

Fig. 1 presents the evolution of the angular separation of a simple power system (2 generators and 1 load) when a three-phase short-circuit occurs at 1 sec near one of the generators. In the presented figure, the angular separation represents the difference between the angular positions of the rotors of the two generators. If the fault is cleared at 1, 2 sec, the power system remains stable and the angle oscillates between two extreme values. On the other hand, if the fault is cleared at 1,3 sec, the kinetic energy gained during the time of fault has not been yet completely expended to the system. The angle continues to increase after the fault cleared. The power system is not capable to return to a stable position, leading to loss of synchronism. Sung et al. in [15] have demonstrated

Fig.1. Evolution of the angular separation of the rotors with a fault cleared at 1, 2 s (stable case) and a fault cleared at 1, 3 s (unstable case).

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Fig. 2. IEEE benchmarked four-machine two-area test system. When a fault occurs consequently, the transient stability of the system is increased.

Starting from this observation, we propose a method to select the optimal location of the SFCL in EPG based on the study of the angular separation of the rotors of synchronous generators in case of fault. Many studies have dealt with the increase of transient stability in power systems thanks to SFCL but most of them have limited the study to a simple power system such as generator, transmission line, and infinite bus. Now, the remaining open questions are the selection of optimal location of the SFCL in a power system with more than 2 generators. We present a method which is not limited to a simple system like an SMIB but extended to the IEEE benchmarked four-machine two-area test system presented in Fig. 2. This power system is composed of four generators, two loads and a long transmission line (220 km), that is a advantage to study the optimal location of an SFCL in a power system in comparison with SMIB.

The details on this system, including the systems parameters, are given in [19]. All generators (G1 to G4) are equipped with power system stabilizers (PSSs).

IV. SIMULATIONS RESULTS

To evaluate the effectiveness of the proposed method, ten locations (L1 to L10 in the middle of each line) are considered in Fig. 2. For a given position of the SFCL (m=1 to 10), a 100ms three-phase short-circuit is applied at corresponding value of the SFCL resistance used in simulation. When the SFCL will be positioned at each location, the study of indexes SMDm and TSIm will give us the best location of the SFCL in the system in case a three-phase fault can appear at any position in the system. The time simulation required until the system is restored to its original steady-state operation point after applying the fault is considered to be equal to 20 s. Before calculating values of index, it is necessary to compute the load flow of the presented power system. The results show that the power generated by generatorsG1 and G2 is mostly consumed by Load 1. In area 2, the power generated by generators G3 and G4 is consumed by Load 2 but it is not sufficient. The rest of the power required by Load 2, i.e., 413 MW, is transferred from area 1 to area 2 by the 220-km transmission line.

Therefore, if the value of (3) is greater for a given resistive value, the corresponding location becomes more optimal. The determination of optimal resistive value of SFCL is presented in the next sub-section.

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A. TCSC-Compensated Transmission

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Power transmitted between a sending-end bus and a receiving-end bus in an AC

transmission system is dependent on the series impedance. Further, impedance of a

transmission line consists mainly of inductive reactance, with resistance

accounting for only 5–10% of impedance [5], [6]. If a series capacitor is inserted

into transmission line, the inductive reac-tance of transmission line could be

compensated by a capacitive supply. This concept of series compensation is

illustrated in Fig. 1 [6]. Typical configuration of a TCSC from a steady-state

perspective involves a fixed capacitor (FC) with a thyristor-controlled reactor

(TCR). TCSC structure is shown in Fig. 2.

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Fig. 3. TCSC closed-loop constant current control methodology.

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Fig. 5. Transmission system connected with a railway.

CHAPTER – 3

MODELING THE SFCL AND FAULT OF THE TRANSMISSION LINE IN AN

ELECTRIC RAILWAY

Control of α typically applies open-loop control or closed-loop control. Fig. 3 details a

schematic of a constant current closed-loop control [8]. In Fig. 3, Iref is desired transmission

line current, IM is actual current, and Ierror is difference between Iref and IM . In particular,

Ierror is an important quantity in this control loop. A current unbalance can cause serious

issues for TCSC control.

. Unbalanced Load in an Electric Railway System

An electric railway characteristic that most utilities are concerned with is current

unbalance produced by large single-phase loads These unbalanced currents cause 3-phase

voltage unbalance. To minimize voltage unbalances in 3-phase power feed networks, Scott

transformers are widely used. Nevertheless, an unbalance can be generated owing to large

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rapidly changing single-phase loads. Fig. 4 shows an

In order to limit a fault current, many models for the SFCL have been developed: resistor-

type, reactor-type, transformer-type, etc. In this study, we modeled a resistor-type SFCL

that is mostly basic and used widely which represents the exper-imental studies for

superconducting elements of SFCL. Quench characteristics and recovery characteristics of

a resistor-type SFCL are modeled based on [11] and [12]. An impedance of the SFCL

according to time t is given as follows:

0 1 (t < t0)

t

t

02

Z(t)

=

Zn1

ex

p − (t0 t < t1)

(2)

−

T

F

≤−

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a1(t − t1) + b1 (t1 ≤ t < t2)

a2(

t

t2) +

b2 (t t2)

− ≥

where Zn and TF are the impedance saturated normal tem-perature and time constant. In

addition, t0, t1, and t2 are the quench-starting time, first recovery-starting time, and sec-

ondary recovery-starting time, respectively. a1, a2, b1, and b2 are coefficients of the first-

order linear function to denote the experimental results of the recovery characteristics of

the SFCL The values used for the parameters are listed in Table I. The recovery time of the

SFCL is set to the value until fault clearing to protect the TCSC and transmission line.

B. Fault Modeling of the Transmission Line in the Electric Railway

An electric railway is connected to a 154 kV transmission line through a Scott

transformer in Korea. Fig. 5 shows a trans-mission system connected with railway

equivalent model. A

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TABLE II

PARAMETERS OF TRANSMISSION LINE FAULT SIMULATION

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Fig. 6 Voltage and current results from the simulation: (a) without railway and (b) with

railway.

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Fig7. Transmission line three-phase fault simulation equivalent circuit and fault location

TCSC facility is installed to control power flow in transmission line, and an electric railway

includes a single phase load that causes a voltage unbalance. Table II shows the

transmission and electric railway system parameters of simulation. In addition, the self- and

mutual impedance of transmission and rail of the Korean electric railway system were

considered Here, in order to analyze the influence of an electric railway connection on the

transmission line fault, we simulated a fault situation. Fig. 6 shows fault location on the

transmission line with TCSC. Fault starting time is 0.4 s and fault duration time is 0.1 s.

Fig. 7(a) and (b) show simulation results for a 3-phase fault for an electric railway

connection, respectively. In case of fault on the transmission line without electric railway,

3-phase voltage decreased owing to fault and after fault removal, there is a transient

phenomenon that has a small offset voltage but returned to a steady state. In addition, this

simulation showed a small magnitude difference between offset voltages. Current is

generated a large transient current during fault and reach to steady state, load current, after

fault removal. In contrast, large offset voltages are represented in simulation result about

fault on transmission line with electric railway such as Fig. 7(b). Especially, voltage of

phase B is increased up to 350 kV in a moment. In addition, voltage unbalances of

transmission line became more serious compared with above case. Line currents are also

increased and caused unbalance owing to transient voltage.

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We think that closing phase angle control of TCSC system is influenced by generated

transient voltage and current as the cause of these results. These phenomenon will cause

problem about voltage stability and malfunction of protection scheme in the transmission

grid. These results show that an electric railway connection aggravates voltage unbalance

in the transmission line.

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CHAPTER -4

METHOD FOR IMPROVING THE VOLTAGE UNBALANCE

USING THE SFCL FROM THE LINE FAULT

We propose a method to improve voltage unbalance using an SFCL. If a transmission line

fault occurs, fault current is decreased by the SFCL. After fault is cleared, voltage unbal-

ance produced by railway’s single-phase loads can quickly be reduced. As a result, a

transmission and electric railway system return to the steady state. In particular, SFCL has

advantage of fast operation within 1/4 cycle. The operation characteristics of conventional

relay and breaker are greater than 5–15 cycles [1].

A. Case Study

As mentioned in the fault modeling, a single-phase load in an electric railway is one of

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the causes of voltage unbalance in the transmission system. However, the proposed method

using SFCL can alleviate this problem. SFCL was installed in the transmission line

between TCSC and electric railway in the case study simulation using the PSCAD/EMTDC

software package. SFCL decreased the voltage unbalance.

Fig. 8 shows the transmission system including an elec-tric railway and SFCL. Fig. 9(a)

and (b) show the results

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when SFCL has an impedance of 10 and 20 Ω, respectively. The results showed fault

current limiting characteristics and improvement in voltage unbalance. In addition, we

discov-ered following features: 1) the larger resistance of a resistor-type SFCL, the more

voltage unbalance was improved. 2) In SFCL operating process, there are differences of

recovery time between superconducting elements owing to unbalance fault current shown

in Fig. 7(b). If a fault occurs, the proposed method clears voltage unbalance and protects

TCSC. Thus, transmission system can quickly return to operating in a con-ventional state.

As a result, we will expect improvement effect for the problems about voltage stability and

protection scheme malfunction.

CHAPTER 5

MATLAB PROGRAMS

4.1 Introduction to Mat Lab:

MATLAB stands for MATrix LABoratory which has been developed by Math Works Inc. Mat

Lab provides matrix as one of the basic elements. It is dynamically decided depending on what value we

assigned to it.

MATLAB is case sensitive and so we have to be careful about the case of the variables while using

them in our programs. The combination of analysis capabilities, flexibility, reliability and powerful

graphics makes MATLAB the main software package for power system engineers

MATLAB gives an interactive environment with hundreds of reliable and accurate built – in

function. These functions help in providing the solution to a variety of mathematical problems including

matrix algebra, linear system, differential equation, optimization, non - linear system and many other types

of scientific and technical computations. The most important feature of MATLAB is its programming

capability, which supports both types of programming – object oriented and structured programming and

is very easy to learn and use and allow user developed functions.

4.2 Program

clc

close all

clear all

tic

% A B C

gendata = [ 1.2 0.0025 0.00032

1.15 0.0022 0.00028

1.1 0.002 0.00026];

genn=[1

2

3];

genno=gendata (:,1);

A=gendata(:,1);

B=gendata(:,2);

C=gendata(:,3);

gn=max(genn);

fprintf( ' pd lamda pg( 1) pg(2) pg(3)\n ');

j=1;

for lamda=1.873:0.05:4.35

for n=1:gn

p(n)=-(B(n)/C(n))+sqrt((B(n)/C(n))^2-4*(A(n)-lamda)/C(n));

pg(n)=p(n)/2;

pd=sum(pg);

end

disp([pd,lamda,pg( 1 ),pg(2),pg(3)]);

pg1(j)=pg(1);

pg2(j )=pg(2);

pg3(j )=pg(3);

pdn(j )=pg( 1 )+pg(2)+pg(3);

lam(j )=lamda;

j =j +1;

end

toc

plot (pg1, lam,'--', pg2, lam,'-', pg3, lam,'--', pdn, lam,'--');

xlabel ('LOAD IN MW');

ylabel ('INCREMENTAL FUEL COST (LAMDA)');

title ('INCREMENTAL COST CURVES TO MEET THE TOTAL SYSTEM LOAD DEMAMD AT

MINIMUM COST');

grid on

(a)Case Study 1:

clc

%nntwarn off

%ECONOMIC LOAD SCHEDULING WITHOUT TRANSMISSION LOSSES BY ANN

input = [0.3580 0.3919 0.4233 0.4527 0.4804 0.5067 0.5318 0.5558 0.5789 0.6011 0.6226

0.6434 0.6635 0.6831 0.7022 0.7208 0.7390 0.7567 0.7741 0.7911 0.8077 0.8240 0.8401 0.8558

0.8712 0.8864 0.9014 0.9161 0.9306 0.9449 0.9589 0.9728 0.9865 1.0000];

Pd=input*910;

tt = [0.3407 0.3764 0.4093 0.4399 0.4686 0.4958 0.5217 0.5465 0.5702 0.5931

0.6151 0.6364 0.6571 0.6772 0.6967 0.7157 0.7343 0.7524 0.7701 0.7874

0.8044 0.8210 0.8373 0.8533 0.8691 0.88450.8998 0.9147 0.9295 0.9440

0.9583 0.9724 0.9863 1.0000;

0.3577 0.3917 0.4231 0.4525 0.4802 0.5065 0.5316 0.5556 0.5787 0.6009

0.6224 0.6432 0.6634 0.6830 0.7021 0.7207 0.7389 0.7566 0.7740 0.7910

0.8076 0.8240 0.8400 0.8557 0.8712 0.8864 0.9013 0.9161 0.9306 0.9448

0.9589 0.9728 0.9865 1.0000;

0.3736 0.4060 0.4361 0.4644 0.4911 0.5166 0.5409 0.5642 0.5867 0.6084

0.6293 0.6496 0.6694 0.6886 0.7073 0.7255 0.7433 0.7607 0.7777 0.7944

0.8108 0.8268 0.8425 0.8580 0.8732 0.8882 0.9029 0.9174 0.9316 0.9457

0.9595 0.9732 0.9867 1.0000];

pg1=tt(1,:)*467;

pg2=tt(2,:)*320;

pg3=tt(3,:)* 140;

disp(' PG1 PG2 PG3 PD=PG1+PG2+PG3 ')

disp([pg1' pg2' pg3' Pd'])

disp ('DATA USED FOR TRAING THE NEURAL NETWORK')

pause

clc

% INTIALIZATON OF NEURAL NETWORK %

net = newff ([minmax (input)], [10 3], {'tansig','purelin'}, 'trainlm');

disp ('NEURAL NETWORKS WEIGHTS AND BIAS BEFORE TRAINING')

net.iw {1, 1}

net.b {1, 1}

net.b {2, 1}

pause

clc

% TRAINING PARAMETERS%

net.trainParam.epochs = 1000;

net.trainParam.goal = 0;

%

net= train (net, input, tt);

clc

disp

net.iw {1, 1}

net.lw {2, 1}

net.b {1}

net.b {2}

pause

clc

% SIMULATION OF ANN FOR TRAINED INPUT-OUTPUT %

ysim = sim (net, input);

disp ('SIMULATION OF ANN FOR TRAINED INPUT-OUTPUT')

pgs1 = ysim (1, :)*467;

pgs2 = ysim (2, :)*320;

pgs3 = ysim (3,:)* 140;

disp ([pg1' pgs1' pg2' pgs2' pg3' pgs3'])

pause

clc

%TESTING OF ANN%

test = [0.4358 0.4959 0.5560 0.6162 0.6763 0.7363 0.7965 0.8566 0.8867];

tic

a=sim (net, test);

toc

pgt1=a(1,:)*467;

pgt2 = a (2,:)*320;

pgt3 = a (3, :)* 140;

test = test*910;

disp ('SIMULATION FOR TEST INPUT')

disp ([test' pgt1’ pgt2’ pgt3’])

save annstu net

(b)Case Study 2:

warning off

close all

clc

lsg;

%nntwarn off

input=pdn;

Pd=input/max(input);

Pgs= [pg1' pg2' pg3' pdn'];

tt= [pg1/ 94.9605;pg2/102.5964;pg3/ 107.5583];

disp(' PG1 PG2 PG3 PD=PG1+PG2+PG3')

disp([pg1' pg2' pg3' input'])

disp('DATA USED FOR TRAING THE NEURAL NETWORK')

pause

clc

% INTIALIZATON OF NEURAL NETWORK %

net=newff([minmax(input)],[10 3],{'tansig','purelin'},'trainlm');

disp('NEURAL NETWORKS WEIGHTS AND BIAS BEFORE TRAINING')

net.iw{1,1}

net.lw{2,1}

net.b{1,1}

net.b{2,1}

pause

clc

% TRAINING PARAMETERS%

net.trainParam.epochs = 1000;

net.trainParam.goal = 0;

%ANN TRAINING %

net= train(net,input,tt);

clc

disp

net.iw{1,1}

net.lw{2,1}

net.b{1}

net.b{2}

pause

clc

% SIMULATION OF ANN FOR TRAINED INPUT-OUTPUT %

tic

ysim=sim(net,input);

toc

disp('SIMULATION OF ANN FOR TRAINED INPUT-OUTPUT')

pgs1=ysim(1,:)*94.9605;

pgs2=ysim(2,:)*102.5964;

pgs3=ysim(3,:)* 107.5583;

pds=pgs1+pgs2+pgs3;

pdact=input*305.1152;

format short g

disp([pg1' pgs1' pg2' pgs2' pg3' pgs3'])

pause

clc

CHAPTER 5

RESULTS

5.1 Graphical Method

PD LAMDA PG (1) PG (2) PG (3)

139.9728 1.8730 42.1197 47.0379 50.8153

145.0944 1.9230 43.7869 48.7606 52.5469

150.0535 1.9730 45.3977 50.4288 54.2269

154.8646 2.0230 46.9576 52.0472 55.8597

159.5403 2.0730 48.4711 53.6202 57.4490

164.0915 2.1230 49.9420 55.1513 58.9982

168.5276 2.1730 51.3738 56.6437 60.5100

172.8569 2.2230 52.7694 58.1003 61.9871

177.0868 2.2730 54.1315 59.5234 63.4319

181.2238 2.3230 55.4624 60.9152 64.8462

185.2739 2.3730 56.7640 62.2779 66.2320

189.2423 2.4230 58.0384 63.6130 67.5909

193.1337 2.4730 59.2870 64.9222 68.9


196.9525 2.5230 60.5114 66.2070 70.2340

200.7025 2.5730 61.7130 67.4687 71.5208

204.3875 2.6230 62.8930 68.7085 72.7860

208.0106 2.6730 64.0524 69.9275 74.0306

211.5748 2.7230 65.1925 71.1267 75.2557

215.0831 2.7730 66.3140 72.3070 76.4621

218.5378 2.8230 67.4179 73.4693 77.6506

221.9414 2.8730 68.5050 74.6144 78.8220

225.2961 2.9230 69.5760 75.7431 79.9771

228.6040 2.9730 70.6316 76.8560 81.1164

231.8669 3.0230 71.6724 77.9538 82.2407

235.0866 3.0730 72.6991 79.0370 83.3505

238.2649 3.1230 73.7123 80.1063 84.4463

241.4032 3.1730 74.7123 81.1622 85.5287

244.5031 3.2230 75.6999 82.2051 86.5982


241.4032 3.1730 74.7123 81.1622 85.5287

244.5031 3.2230 75.6999 82.2051 86.5982

247.5659 3.2730 76.6753 83.2355 87.6551

250.5929 3.3230 77.6390 84.2539 88.7000

253.5854 3.3730 78.5915 85.2607 89.7332

256.5445 3.4230 79.5332 86.2562 90.7552

259.4713 3.4730 80.4643 87.2408 91.7662

262.3668 3.5230 81.3852 88.2150 92.7666

265.2320 3.5730 82.2963 89.1789 93.7568

268.0679 3.6230 83.1979 90.1330 94.7370

270.8753 3.6730 84.0902 91.0775 95.7076

273.6551 3.7230 84.9736 92.0127 96.6688

276.4080 3.7730 85.8483 92.9388 97.6209

279.1349 3.8230 86.7146 3.8562 98.5641

281.8365 3.8730 87.5726 94.7651 99.4988


279.1349 3.8230 86.7146 3.8562 98.5641

281.8365 3.8730 87.5726 94.7651 99.4988

284.5134 3.9230 88.4227 95.6656 100.4251

287.1663 3.9730 89.2650 96.5581 101.3432

289.7959 4.0230 90.0998 97.4428 102.2533

292.4027 4.0730 90.9272 98.3198 103.1558

294.9874 4.1230 91.7475 99.1893 104.0506

297.5504 4.1730 92.5608 100.0515 104.9381

300.0924 4.2230 93.3672 100.9067 105.8185

302.6139 4.2730 94.1671 101.7549 106.6918

305.1152 4.3230 94.9605 102.5964 107.5583

Figure 5.1

Elapsed time is 0.531000 seconds.

0000000000000000000000000000000000000000000000000000000000000

Case Study 1:

PG1 PG2 PG3 PD=PG1+PG2+PG3

159.1069 114.4640 52.3040 325.7800

175.7788 125.3440 56.8400 356.6290

191.1431 135.3920 61.0540 385.2030

205.4333 144.8000 65.0160 411.9570

218.8362 153.6640 68.7540 437.1640

231.5386 162.0800 72.3240 461.0970

243.6339 170.1120 75.7260 483.9380

255.2155 177.7920 78.9880 505.7780

266.2834 185.1840 82.1380 526.7990

276.9777 192.2880 85.1760 547.0010

287.2517 199.1680 88.1020 566.5660

297.1988 205.8240 90.9440 585.4940

306.8657 212.2880 93.7160 603.7850

316.2524 218.5600 96.4040 621.6210

325.3589 224.6720 99.0220 639.0020

334.2319 230.6240 101.5700 655.9280

342.9181 236.4480 104.0620 672.4900

351.3708 242.1120 106.4980 688.5970

359.6367 247.6800 108.8780 704.4310

367.7158 253.1200 111.2160 719.9010

375.6548 258.4320 113.5120 735.0070

383.4070 263.6800 115.7520 749.8400


391.0191 268.8000 117.9500 764.4910

398.4911 273.8240 120.1200 778.7780

405.8697 278.7840 122.2480 792.7920

413.0615 283.6480 124.3480 806.6240

420.2066 288.4160 126.4060 820.2740

427.1649 293.1520 128.4360 833.6510

434.0765 297.7920 130.4240 846.8460

440.8480 302.3360 132.3980 859.8590

447.5261 306.8480 134.3300 872.5990

454.1108 311.2960 136.2480 885.2480

460.6021 315.6800 138.1380 897.7150

467.0000 320.0000 140.0000 910.0000

Ans =

-43.6137

-43.6137

43.6137

-43.6137

43.6137

43.6137

-43.6137

43.6137

-43.6137

-43.6137

Ans =

43.6137

40.5026

-37.3915

34.2804

-31.1693

-28.0582

24.9470

-21.8359

18.7248

15.6137

Ans =

0.3853

-0.8318

-0.0913

Figure 5.3 (a)

WEIGHTS AND BIAS AFTER TRAINING

Ans =

-18.3671

-6.9487

21.3496

-25.2423

16.1732

10.4797

-10.3463

12.5184

-38.8156

-42.8783

Ans =

Columns 1 through 7

-0.0163 -0.1359 0.0072 -0.0062 0.0197 0.0585 -0.0584

-0.0163 -0.1335 0.0070 -0.0062 0.0193 0.0573 -0.0567

-0.0162 -0.1313 0.0070 -0.0061 0.0189 0.0561 -0.0552

Columns 8 through 10

0.0540 -0.0066 -0.0225

0.0520 -0.0062 -0.0213

0.0500 -0.0059 -0.0202

Ans =

18.8009

6.4658

-18.1833

20.2644

-12.1753

-7.0560

5.8538

-5.8304

16.8740

16.4497

Ans =

0.7128

0.7210

0.7285

SIMULATION OF ANN FOR TRAINED INPUT-OUTPUT

PG1 PG1 PG2 PG2 PG3 PG3

Actual Obtained Actual Obtained Actual Obtained

159.1069 159.1054 114.4640 114.4655 52.3040 52.3038

175.7788 175.7834 125.3440 125.3397 56.8400 56.8405

191.1431 191.1394 135.3920 135.3954 61.0540 61.0537

205.4333 205.4322 144.8000 144.8021 65.0160 65.0154

218.8362 218.8351 153.6640 153.6602 68.7540 68.7564



231.5386 231.5435 162.0800 162.0807 72.3240 72.3205

243.6339 243.6447 170.1120 170.1125 75.7260 75.7272

255.2155 255.1895 177.7920 177.7876 78.9880 78.9892

266.2834 266.3055 185.1840 185.1887 82.1380 82.1403

276.9777 276.9620 192.2880 192.2940 85.1760 85.1700

287.2517 287.2514 199.1680 199.1638 88.1020 88.1032

297.1988 297.2125 205.8240 205.8229 90.9440 90.9497

306.8657 306.8587 212.2880 212.2781 93.7160 93.7115

316.2524 316.2517 218.5600 218.5689 96.4040 96.4049

325.3589 325.3656 224.6720 224.6766 99.0220 99.0212

334.2319 334.2275 230.6240 230.6182 101.5700 101.5673

342.9181 342.9182 236.4480 236.4479 104.0620 104.0662

351.3708 351.3654 242.1120 242.1176 106.4980 106.4972

359.6367 359.6347 247.6800 247.6728 108.8780 108.8802

367.7158 367.7250 253.1200 253.1139 111.2160 111.2154

375.6548 375.6553 258.4320 258.4521 113.5120 113.5079

383.4070 383.4026 263.6800 263.6685 115.7520 115.7497

391.0191 391.0236 268.8000 268.7992 117.9500 117.9561

398.4911 398.4936 273.8240 273.8271 120.1200 120.1194

405.8697 405.8466 278.7840 278.7761 122.2480 122.2493

413.0615 413.0828 283.6480 283.6472 124.3480 124.3458

420.2066 420.1998 288.4160 288.4390 126.4060 126.4081

427.1649 427.1742 293.1520 293.1358 128.4360 128.4296



434.0765 434.0645 297.7920 297.7772 130.4240 130.4274

440.8480 440.8632 302.3360 302.3587 132.3980 132.3996

447.5261 447.5130 306.8480 306.8420 134.3300 134.3300

454.1108 454.1090 311.2960 311.2922 136.2480 136.2468

460.6021 460.6094 315.6800 315.6819 138.1380 138.1384

467.0000 466.9976 320.0000 319.9999 140.0000 140.0000

Elapsed time is 0.016000 seconds.

SIMULATION OF ANN FOR TEST INPUT

Pd PG1 PG2 PG3

396.5780 197.0694 139.2940 62.6943

451.2690 226.3212 158.6186 70.8542

505.9600 255.2858 177.8516 79.0164

560.7420 284.1897 197.1187 87.2297

615.4330 312.9971 216.3887 95.4713

670.0330 341.6280 235.5822 103.6950

724.8150 370.3041 254.8496 111.9607

779.5060 398.8754 274.0841 120.2300

806.8970 413.2253 283.7432 124.3871

Case Study 2:


42.12 47.038 50.815 139.97

43.787 48.761 52.547 145.09

45.398 50.429 54.227 150.05

46.958 52.047 55.86 154.86

48.471 53.62 57.449 159.54

49.942 55.151 58.998 164.09

51.374 56.644 60.51 168.53

52.769 58.1 61.987 172.86

54.132 59.523 63.432 177.09

55.462 60.915 64.846 181.22

56.764 62.278 66.232 185.27

58.038 63.613 67.591 189.24

59.287 64.922 68.924 193.13

60.511 66.207 70.234 196.95

61.713 67.469 71.521 200.7

62.893 68.709 72.786 204.39

64.052 69.928 74.031 208.01

65.192 71.127 75.256 211.57

66.314 72.307 76.462 215.08

67.418 73.469 77.651 218.54

68.505 74.614 78.822 221.94

69.576 75.743 79.977 225.3

70.632 76.856 81.116 228.6

71.672 77.954 82.241 231.87

72.699 79.037 83.35 235.09

73.712 80.106 84.446 238.26


74.712 81.162 85.529 241.4

75.7 82.205 86.598 244.5

76.675 83.236 87.655 247.57

77.639 84.254 88.7 250.59

78.592 85.261 89.733 253.59

79.533 86.256 90.755 256.54

80.464 87.241 91.766 259.47

81.385 88.215 92.767 262.37

82.296 89.179 93.757 265.23

83.198 90.133 94.737 268.07

84.09 91.077 95.708 270.88

84.974 92.013 96.669 273.66

85.848 92.939 97.621 276.41

86.715 93.856 98.564 279.13

87.573 94.765 99.499 281.84

88.423 95.666 100.43 284.51

89.265 96.558 101.34 287.17

90.1 97.443 102.25 289.8

90.927 98.32 103.16 292.4

91.747 99.189 104.05 294.99

92.561 100.05 104.94 297.55

93.367 100.91 105.82 300.09

94.167 101.75 106.69 302.61

94.96 102.6 107.56 305.12

DATA USED FOR TRANING

WEIGHTS AND BIAS BEFORE TRAINING

ans =

0.16955

0.16955

-0.16955

0.16955

0.16955

0.16955

-0.16955

0.16955

0.16955

-0.16955

ans =

Columns 1 through 7

0.31106 0.39816 0.31043 -0.14949 0.43308 -0.021309 0.96542

-0.21619 -0.20563 0.67517 0.18933 0.022623 -0.62819 0.61328

0.25463 -0.17274 -0.25678 0.13148 0.5528 0.40127 0.40714

Columns 8 through 10

-0.030073 -0.26925 0.64602

-0.77077 -0.71991 0.3479

0.32971 0.13355 0.99889

ans =

-51.732

-48.621

45.51

-42.399

-39.288

-36.177

33.066

-29.955

-26.844

23.73

ans =

0.92327

-0.88228

-0.27938

WEIGHTS AND BIAS AFTER TRAINING

ans =

0.0683

-0.0627

0.0525

-0.0428

0.0401

0.0368

-0.0265

-0.0307

0.0220

-0.0358

ans =

Columns 1 through 9

0.0307 -0.0175 0.0210 -0.0310 0.0251 0.0213 -0.0671 -0.0203 0.1081

0.0301 -0.0172 0.0206 -0.0305 0.0245 0.0208 -0.0655 -0.0198 0.1042

0.0296 -0.0169 0.0202 -0.0299 0.0240 0.0204 -0.0640 -0.0193 0.1005

Column 10

-0.0448

-0.0418

-0.0392

ans =

-21.4224

18.7187

-15.0221

11.6138

-10.1758

-8.6791

5.6815

5.7437

-3.4178

4.3214

ans =

0.6809

0.6916

0.7013

SIMULATION OF ANN FOR TRAINED INPUT-OUTPUT



42.12 42.12 47.038 47.038 50.815 50.815

43.787 43.786 48.761 48.76 52.547 52.547

45.398 45.398 50.429 50.429 54.227 54.227

46.958 46.958 52.047 52.047 55.86 55.86



48.471 48.471 53.62 53.62 57.449 57.449

49.942 49.942 55.151 55.151 58.998 58.998

51.374 51.374 56.644 56.644 60.51 60.51

52.769 52.77 58.1 58.1 61.987 61.987

54.132 54.132 59.523 59.524 63.432 63.432

55.462 55.462 60.915 60.915 64.846 64.846

56.764 56.764 62.278 62.278 66.232 66.232

58.038 58.038 63.613 63.613 67.591 67.591

59.287 59.287 64.922 64.922 68.924 68.924

60.511 60.511 66.207 66.207 70.234 70.234

61.713 61.713 67.469 67.469 71.521 71.521

62.893 62.893 68.709 68.709 72.786 72.786

64.052 64.052 69.928 69.927 74.031 74.031

65.192 65.192 71.127 71.127 75.256 75.256

66.314 66.314 72.307 72.307 76.462 76.462

67.418 67.418 73.469 73.469 77.651 77.651

68.505 68.505 74.614 74.615 78.822 78.822

69.576 69.576 75.743 75.743 79.977 79.977

70.632 70.632 76.856 76.856 81.116 81.116

71.672 71.672 77.954 77.954 82.241 82.241

72.699 72.699 79.037 79.037 83.35 83.35

73.712 73.712 80.106 80.106 84.446 84.446

74.712 74.712 81.162 81.162 85.529 85.529



75.7 75.7 82.205 82.205 86.598 86.598

76.675 76.675 83.236 83.235 87.655 87.655

77.639 77.639 84.254 84.254 88.7 88.7

78.592 78.591 85.261 85.261 89.733 89.733

79.533 79.533 86.256 86.256 90.755 90.755

80.464 80.464 87.241 87.241 91.766 91.766

81.385 81.385 88.215 88.215 92.767 92.767

82.296 82.296 89.179 89.179 93.757 93.757

83.198 83.198 90.133 90.133 94.737 94.737

84.09 84.09 91.077 91.077 95.708 95.708

84.974 84.974 92.013 92.013 96.669 96.669

85.848 85.848 92.939 92.939 97.621 97.621

86.715 86.715 93.856 93.856 98.564 98.564

87.573 87.573 94.765 94.765 99.499 99.499

88.423 88.423 95.666 95.666 100.43 100.43

89.265 89.265 96.558 96.558 101.34 101.34

90.1 90.1 97.443 97.443 102.25 102.25

90.927 90.927 98.32 98.32 103.16 103.16

91.747 91.747 99.189 99.189 104.05 104.05

92.561 92.561 100.05 100.05 104.94 104.94

93.367 93.367 100.91 100.91 105.82 105.82

94.167 94.167 101.75 101.75 106.69 106.69

94.96 94.96 102.6 102.6 107.56 107.56

CHAPTER 5

CONCLUSION

This paper proposed a method to reduce voltage unbalance for a TCSC-compensated

transmission line using an SFCL. First, the configuration and operation of a compensated

trans-mission line and connected electric railway system were mod-eled and detailed. Next,

voltage unbalance in transmission line was studied when line fault occurs. Finally, the

method for alleviating this problem with SFCL was considered.

The proposed method showed the following improvements for transmission line faults: 1)

the fault current was decreased as compared to the existing system fault current and 2)

voltage unbalance in the transmission system was quickly improved after the fault was

removed. In future, we will study a protection scheme using an SFCL for a compensated

transmission system to improve system stability.

REFERENCES

[4] H.-S. Shin, S.-M. Cho, J.-S. Huh, J.-C. Kim, and D.-J. Kweon, “Applica-tion on of

SFCL in automatic power changeover switch system of elec-tric railway,” IEEE Trans.

Appl. Supercond., vol. 22, no. 3, p. 5600704, Jun. 2012.

[5] S. T. Senini and P. J. Wolfs, “Novel topology for correction of unbalanced load in

single phase electric traction systems,” in Proc. IEEE Power Electron. Spec. Conf.,

2002, vol. 3, pp. 1208–1212.

[6] T. Uzuka, S. Ikedo, and K. Ueda, “A static voltage fluctuation compen-sator for AC

electric railway,” in Proc. IEEE Power Electron. Spec. Conf., 2004, vol. 3, pp. 1869–

1873.

[7] A. D. Del Rosso, C. A. Canizares, and V. M. Dona, “A study of TCSC controller

design for power system stability improvement,” IEEE Trans. Power Syst., vol. 18, no.

4, pp. 1487–1496, Nov. 2012.

[8] S. S. N. Singh and A. K. David, “Optimal location of FACTs devices for congestion

management,” Elect. Power Syst. Res., vol. 58, no. 2, pp. 71– 79, Jun. 2001.

[9] J.-U. Lim, J.-C. Seo, and S.-I. Moon, “Selection of optimal TCSC location to keep

the steady-state voltage profile within limits,” presented at the KIEE Conf., 1998.

[10] A. Kazemi and B. Badrzadeh, “Modeling and simulation of SVC and TCSC to study

their limits on maximum loadability point,” Int. J. Elect. Power Energy Syst., vol. 26,

no. 8, pp. 619–626, Oct. 2004.

[11] Y. Tang, R. Yu, and M. Yan, “Research on the synchronous voltage reversal control

model of TCSC,” in Proc. Int. Conf. Power Syst. Technol., Oct. 24–28, 2010, pp. 1–6.

[12] T.-H. Chen, “Criteria to estimate the voltage unbalances due to high-speed railway

demands,” IEEE Trans. Power Syst., vol. 9, no. 3, pp. 1672–1678, Aug. 1994.

[13] S.-H. Chang, K.-H. Oh, and J.-H. Kim, “Analysis of voltage unbalance in the electric

railway system using two-port network model,” KIEE Trans., vol. 50A, pp. 248–254,

May 2001.

[14] J.-S. Kim, S.-H. Lim, J.-F. Moon, J.-C. Kim, and O.-B. Hyun, “Analysis on the

protective coordination on neutral line of main transformer in power distribution

substation with superconducting fault current limiter,” KIEE Trans., vol. 58, no. 11, pp.

2089–2094, Nov. 2009.

[15] H. R. Kim, S.-W. Yim, O.-B. Hyun, J. Sim, and S.-Y. Oh, “Analysis on recovery

characteristics of superconducting fault current limiters,” presented at the Proc. Conf.

Magn. Technol., Philadelphia, PA, USA, Aug. 27–31, 2007, MT-20.

[16] S.-H. Lim, S.-R. Lee, H.-S. Choi, and B.-S. Han, “Analysis of operational

characteristics of flux-lock type SFCL combined with Power compen-sator,” IEEE

Trans. Appl. Supercond., vol. 15, no. 2, pp. 2043–2046, Jun. 2005.

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