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1.0 ABSTRACT

Voltage stability problem has been one of the major concerns for electric utilities as a result of

system heavy loading and needs to be solved. This paper presents the development of Artificial

Intelligent technique in prediction of voltage stability in power system. The purpose of this paper

is to develop Artificial Neural Network (ANN) program code in MATLAB software to perform

ANN prediction process for voltage stability condition. In ANN, it considers load bus in order to

analyze the voltage stability. The different values are tested in different bus at one time to

analyze and collect historical data. The data will be trained and tested. Fast performance,

accurate evaluation and good prediction for voltage stability have been obtained. A 14-system

bus is used as input variables, which consists of real power value (PL) and reactive power (QL).

This system analyzes the concerned variables and shows the stabilized value for load power (L)

as the output.

Uncontrollable decay of system voltage at one or more load buses or even over a significant

portion of the network as a response to load variations, generation or structure disturbances etc

has been observed in Power systems worldwide. This has been termed as voltage Instability and

the process of voltage decrease has been termed as a voltage collapse process. Voltage collapse,

a form of voltage instability, commonly occurs as a result of power deficiency. The reasons that

cause voltage collapse is:

1. Weakness of the transmission network

2. The power transfer level

3. Generator reactive power or voltage control limits

4. The load characteristics (PL,QL)

5. Characteristics of reactive compensation device

6. The action of voltage control devices like transformer under load tap changing

There are two kinds of disturbances that can make a power system unstable:-

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a) The variation of system condition, like a change at load bus

b) Severe change of system conditions such as faults or losses of an important generator

as bus.

With the rest of the system conditions remaining in charged, if the load at a particular bus is

varied, the voltage at the bus will also vary. Voltage at other nodes will also vary as a response to

this load change. In other words voltage at a load bus is elastic with respect to the active power

and reactive power delivered at that node. P, Q, V are active power, reactive power and voltage

of the bus. Under stable conditions these factors are generally negative.

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LR Related info regarding the load flow, voltage stability and ANN is collected present in

Chapter 2.

NRLF The result analyses are collected and will be used as the training data to the ANN

analysis.

ANN the application of ANN in prediction the voltage stability where 2 algorithms are

chosen, namely, Back-Propagation and General Regression Neural Network.Using for

comparison to determine the acceptable error limits of the ANN applications.

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2.0 INTRODUCTION

Power flow studies, commonly known as load flow, form an important part of power system

analysis. They are necessary for planning, economic scheduling and control of existing system as

well as planning expansion. The problem consists of determining the magnitudes and phase

angle of voltages at each bus and active and reactive power flow in each line.

In solving a power flow problem, the system is assumed to be operating under balanced

conditions and a single-phase model is used. Four quantities are associated with each bus. These

are voltage magnitude IVI, phase angle , real powerP, and reactive powerQ. the system buses

are generally classified into three types:

a) Slack Bus

One bus, known as slack or swing bus, is taken as reference where the magnitude and

phase angle of the voltage are specified. This bus makes up the difference between the

scheduled loads and generated power that are caused by the losses in the network.

b) Load buses

At these buses the active and reactive powers are specified. The magnitude and the phase

angle of the bus voltages are unknown. These buses are called PQ buses.

c) Regulated buses

These buses are the generator buses. They are also known as voltage-controlled buses. At

these buses, the real power and voltage magnitude are specified. The phase angles of the

voltages and the reactive power are also specified. These buses called PV buses.

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Power Flow Equation

The real and reactive power at bus i is

Pi +jQi = ViIi* or Ii = Pi jQi / Vi*

Substituting for Ii in yield

Pi jQi / Vi* = Viyij yijV j j i

Load Flow Method

a) Gauss Iterative Method

b) Gauss-Seidel Method

c) Newton-Raphson Method

- Because of quadratic convergence

- More efficient and practical

- number of iteration

d) Fast-Decoupled Method

An artificial neural network is a system based on the operation of biological neural networks, inother words, is an emulation of biological neural system. Although computing these days is truly

advanced, there are certain tasks that a program made for a common microprocessor is unable to

perform; even so a software implementation of a neural network can be made with their

advantages and disadvantages.

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Advantages:

A neural network can perform tasks that a linear program can not performed. When an element of the neural network fails, it can continue without any problem by

their parallel nature.

A neural network learns and does not need to be reprogrammed.

It can be implemented in any application.

It can be implemented without any problem.

Disadvantages:

The neural network needs training to operate.

The architecture of a neural network is different from the architecture of microprocessors

therefore needs to be emulated.

Requires high processing time for large neural networks.

A artificial neural network is developed with a systematic step-by-step procedure which

optimizes a criterion commonly known as the learning rule. The input/output training data is

fundamental for these networks as it conveys the information which is necessary to discover the

optimal operating point. In addition, a nonlinear nature makes neural network processing

elements a very flexible system.

ANN can categorize the learning situations in two distinct sorts. These are:

Supervised learning or Associative learning in which the network is trained by

providing it with input and matching output patterns. These input-output pairs can be

provided by an external teacher, or by the system which contains the neural network

(self-supervised).

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Unsupervised learning or Self-organization in which an (output) unit is trained to

respond to clusters of pattern within the input. In this paradigm the system is supposed to

discover statistically salient features of the input population. Unlike the supervised

learning paradigm, there is no a priori set of categories into which the patterns are to be

classified; rather the system must develop its own representation of the input stimuli.

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3.0 METHODOLOGY

Development of ANN Model

Development of ANN training codes

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Development of ANN testing codes

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3.1 PROBLEM SOLVING TIME- LINE

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4.0 RESULTS AND DISCUSSIONS

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Test System

The test system for this study is 14- Bus Reliability Test System (RTS). This system

consists of two generators buses, four load buses and transmission lines.

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4.1 RESULT

function [basemva,accuracy,maxiter,busdata,linedata]=pbl14bus

basemva = 100; accuracy = 0.0001; maxiter =100;

% Bus code: 0 = load bus; 1 = slack bus; 2 = generator bus

% load generator Injected

% bus code voltage angle MW Mvar MW Mvar Qmin Qmax Mvar

busdata=[ 1 1 1.006 0.000 0.000 0.0 0 0.0 0.0 0.0 0

2 2 1.045 0.000 21.7 12.7 0 40.0 -40 50 0

3 2 1.010 0.000 94.2 19.0 0 0.0 -30 40 0

4 2 1.070 0.000 11.2 7.5 0 0.0 -40 50 0

5 2 1.090 0.000 0.00 0.0 0 0.0 -20 40 0

6 0 1.000 0.000 47.8 -3.9 0 0.0 0.0 0.0 0

7 0 1.000 0.000 0.0 0.0 0 0.0 0.0 0.0 0

8 0 1.000 0.000 76.0 1.6 0 0.0 0.0 0.0 0

9 0 1.000 0.000 29.5 16.6 0 0.0 0.0 0.0 0

10 0 1.000 0.000 9.0 5.8 0 0.0 0.0 0.0 0

11 0 1.000 0.000 3.5 1.8 0 0.0 0.0 0.0 0

12 0 1.000 0.000 6.1 0.6 0 0.0 0.0 0.0 013 0 1.022 0.000 13.5 5.8 0 0.0 0.0 0.0 0

14 0 1.015 0.000 14.9 5.0 0 0.0 0.0 0.0 0];

% In the 14 bus case, there is no Mvar injected since there is no capacitive compensation

%

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% line data

% from to R X 1/2B tr-tap

linedata=[ 1 2 0.0194 0.0592 0.0264 1

1 8 0.0540 0.2230 0.0246 1

2 3 0.0470 0.1980 0.0219 1

2 6 0.0581 0.1763 0.0187 1

2 8 0.0570 0.1739 0.0170 1

3 6 0.0670 0.1710 0.0173 1

6 8 0.0134 0.0421 0.0064 1

6 7 0.0000 0.2091 0.0000 1

6 9 0.0000 0.5562 0.0000 1

8 4 0.0000 0.2520 0.0000 1

4 11 0.0950 0.1989 0.0000 1

4 12 0.1229 0.2558 0.0000 1

4 13 0.0662 0.1303 0.0000 1

7 5 0.0000 0.1762 0.0000 1

7 9 0.0000 0.1100 0.0000 1

9 10 0.0318 0.0845 0.0000 19 14 0.1271 0.2704 0.0000 1

10 11 0.0821 0.1921 0.0000 1

12 13 0.2209 0.1999 0.0000 1

13 14 0.1709 0.3480 0.0000 1];

end

Program for 14 bus data

count=0

kira=0

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while count


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op_ok(kira,:)=[busdata(6,6) busdata(8,6) busdata(9,6) busdata(10,6)

busdata(11,6) busdata(12,6) busdata(13,6) busdata(14,6) busdata(6,5) busdata(8,5) busdata(9,5)

busdata(10,5) busdata(11,5) busdata(12,5) busdata(13,5) busdata(14,5) fit]

else

count=count+1

op_xok(count,:)=[busdata(6,6) busdata(8,6) busdata(9,6) busdata(10,6)

busdata(11,6) busdata(12,6) busdata(13,6) busdata(14,6) busdata(6,5) busdata(8,5) busdata(9,5)

busdata(10,5) busdata(11,5) busdata(12,5) busdata(13,5) busdata(14,5) fit]

end

ifNilai_Q==500 && Nilai_P==500 && bus_no==8

return

end

end

end

end

end

endprogram for generate training and testing data

Data are collected from Newton Raphson load flow analysis

Only consider load bus. The value of Pd, Qd and Vm from load flow was taking.

In targeted output, write 1 for converge and 0 for diverge.

Data will be get from array and called historical data

The historical data will divided into two, which is:-

i. Training data

ii. Testing data

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Control variable = 16 which is reactive power Q for each load bus (slack bus and

generator bus is not required) and indicator

Targeted output = 1-stable (converge)

0-unstable (diverge)

Patterns = 20 pattern data for training and another 24 pattern data for testing

% ANN3_norm.m

function [pn,minp,maxp,tn,mint,maxt] = pbltr_norm(p,t)

%MATMAX Preprocesses data so that minimum is -1 and maximum is 1.

%

% Syntax

%

% [pn,minp,maxp,tn,mint,maxt] = premnmx(p,t)

% [pn,minp,maxp] = premnmx(p)

%

% Description

%

% MATMAX preprocesses the network training

% set by normalizing the inputs and targets so that

% they fall in the interval [-1,1].

%

% MATMAX(P,T) takes these inputs,

% P - RxQ matrix of input (column) vectors.% T - SxQ matrix of target vectors.

% and returns,

% PN - RxQ matrix of normalized input vectors

% MINP- Rx1 vector containing minimums for each P

% MAXP- Rx1 vector containing maximums for each P

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% TN - SxQ matrix of normalized target vectors

% MINT- Sx1 vector containing minimums for each T

% MAXT- Sx1 vector containing maximums for each T

%

% Examples

%

% Here is how to normalize a given data set so

% that the inputs and targets will fall in the

% range [-1,1].

%

% p = [-10 -7.5 -5 -2.5 0 2.5 5 7.5 10];

% t = [0 7.07 -10 -7.07 0 7.07 10 7.07 0];

% [pn,minp,maxp,tn,mint,maxt] = premnmx(p,t);

%

% If you just want to normalize the input:

%

% [pn,minp,maxp] = premnmx(p);

%

% Algorithm%

% pn = 2*(p-minp)/(maxp-minp) - 1;

%

% See also PRESTD, PREPCA, POSTMNMX, TRAMNMX.

% Copyright (c) 1992-1998 by The MathWorks, Inc.

% $Revision: 1.3 $

ifnargin > 2

error('Wrong number of arguments.');

end

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load minp1

load maxp1

minp =minp1;%min(p')';

maxp =maxp1;%max(p')';

[R,Q]=size(p);

oneQ = ones(1,Q);

equal = minp==maxp;

nequal = ~equal;

ifsum(equal) ~= 0

warning('Some maximums and minimums are equal. Those inputs won''t be transformed.');

minp0 = minp.*nequal - 0.1*equal;

maxp0 = maxp.*nequal + 0.9*equal;

else

minp0 = minp;

maxp0 = maxp;

end

pn = 0.8*(p-minp0*oneQ)./((maxp0-minp0)*oneQ) +0.1;

ifnargin==2

mint = min(t')';

maxt = max(t')';

equal = mint==maxt;

nequal = ~equal;

ifsum(equal) ~= 0

warning('Some maximums and minimums are equal. Those targets won''t be transformed.');

mint0 = mint.*nequal - 0.1*equal;

maxt0 = maxt.*nequal + 0.9*equal;

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else

mint0 = mint;

maxt0 = maxt;

end

tn = 0.8*(t-mint0*oneQ)./((maxt0-mint0)*oneQ) +0.1;

end

end

program for normalize data training

After setting the parameter of the training, the next step is to train the ANN. We had loaded the

data from the previous which is load ztrain.mat.

clc

clear

% a=0

%

% if a


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[pn,minp,maxp,tn,mint,maxt] = pbltr_norm(p,t) % this is to normalise the input and target

training data

% The next step is to design the network

net = newff(minmax(pn),[8,5,1],{'logsig','logsig','purelin'},'trainlm');% minmax(pn) =

minimum & maximum value

% for normalised input p. i.e: pn.

% to initialise

net = init(net);

net.trainParam.show = 1;

net.trainParam.lr = 0.95;% Learning rate used in some gradient schemes

net.trainParam.mc = 0.3415; % Momentum is used for slight tolerence on the learning rate

net.trainParam.epochs =1000; % Max number of iterations

net.trainParam.goal = 1e-8; % Error tolerance; stopping criterion

%Train network

net = train(net, pn, tn); % TRain the network based on the normalised p and t

an = sim(net, pn)

%[p] = matmin_24_baru(an,mint,maxt) % denormalise the training output

[p] = postmnmx(an,mint,maxt) % denormalise the training output

% if net.trainParam.goal>1e-8

% return

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% a=a+1

% end

%

% end

net_baru=net

save net_baru

fprintf('Press enter to continue with testing')

pause

program for training data

This is the best results for the convergence performance (mse vs epochs) for training after we

had trained the program more than one time.

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Result for training

After that, we had written and run testing program as following:

% ANN3_norm.m

function [pn,minp,maxp,tn,mint,maxt] = pblts_norm(p,t)

%MATMAX Preprocesses data so that minimum is -1 and maximum is 1.

%

% Syntax

%

% [pn,minp,maxp,tn,mint,maxt] = premnmx(p,t)

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% [pn,minp,maxp] = premnmx(p)

%

% Description

%

% MATMAX preprocesses the network training

% set by normalizing the inputs and targets so that

% they fall in the interval [-1,1].

%

% MATMAX(P,T) takes these inputs,

% P - RxQ matrix of input (column) vectors.

% T - SxQ matrix of target vectors.

% and returns,

% PN - RxQ matrix of normalized input vectors

% MINP- Rx1 vector containing minimums for each P

% MAXP- Rx1 vector containing maximums for each P

% TN - SxQ matrix of normalized target vectors

% MINT- Sx1 vector containing minimums for each T

% MAXT- Sx1 vector containing maximums for each T

%% Examples

%

% Here is how to normalize a given data set so

% that the inputs and targets will fall in the

% range [-1,1].

%

% p = [-10 -7.5 -5 -2.5 0 2.5 5 7.5 10];

% t = [0 7.07 -10 -7.07 0 7.07 10 7.07 0];

% [pn,minp,maxp,tn,mint,maxt] = premnmx(p,t);

%

% If you just want to normalize the input:

%

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% [pn,minp,maxp] = premnmx(p);

%

% Algorithm

%

% pn = 2*(p-minp)/(maxp-minp) - 1;

%

% See also PRESTD, PREPCA, POSTMNMX, TRAMNMX.

% Copyright (c) 1992-1998 by The MathWorks, Inc.

% $Revision: 1.3 $

ifnargin > 2

error('Wrong number of arguments.');

end

load minp2

load maxp2

minp =minp2;%min(p')';maxp =maxp2;%max(p')';

[R,Q]=size(p);

oneQ = ones(1,Q);

equal = minp==maxp;

nequal = ~equal;

ifsum(equal) ~= 0

warning('Some maximums and minimums are equal. Those inputs won''t be transformed.');

minp0 = minp.*nequal - 0.1*equal;

maxp0 = maxp.*nequal + 0.9*equal;

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else

minp0 = minp;

maxp0 = maxp;

end

pn = 0.8*(p-minp0*oneQ)./((maxp0-minp0)*oneQ) +0.1;

ifnargin==2

mint = min(t')';

maxt = max(t')';

equal = mint==maxt;

nequal = ~equal;

ifsum(equal) ~= 0

warning('Some maximums and minimums are equal. Those targets won''t be transformed.');

mint0 = mint.*nequal - 0.1*equal;

maxt0 = maxt.*nequal + 0.9*equal;

else

mint0 = mint;

maxt0 = maxt; end

tn = 0.8*(t-mint0*oneQ)./((maxt0-mint0)*oneQ) +0.1;

end

end

program for normalize data testing

clc

clear

load ztest

load zt2

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p=ztest

t=zt2

y= minmax(p)

minp2=[min(p')']

maxp2=[max(p')']

save minp2

save maxp2

[pn,minp,maxp,tn,mint,maxt] = pblts_norm(p,t)

load net_baru

%Setting the minimum and maximum training target

mint = [0];%min(t')'

maxt = [1]; %max(t')'

an = sim(net, pn) % output

[p] = postmnmx(an,mint,maxt)

[m,b,r] = postreg(p,t);

an=sim(net,pn); %a) Provide the outputs (an) based on the trained network

[m,b,r]=postreg(an,tn); %a) Regression analysis which computes the correlation coefficient

% between the outputs and the targets.

results=[an' tn'] %a) To compare between the network outputs and the targets

Program for testing

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This is the results of the testing:

results=[an' tn']

Bil an tn Bil an tn

1 0.9 0.9 1 0.1 0.1

2 0.9 0.9 2 0.1 0.13 0.9 0.9 3 0.1 0.1

4 0.9 0.9 4 0.1 0.1

0.906 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

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0.9 0.9 0.1 0.1

0.8998

0.9 0.1 0.1

0.9001

0.9 0.1 0.1

0.9 0.9 0.1 0.10.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.10.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1 0.1

0.9 0.9 0.1002

0.1

0.9 0.9 0.0997

0.1

188 0.9003

0.9 288 0.1002

0.1

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Result for testing

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5.0 CONCLUSION

From this ANNprogram code in MATLAB software, we learned on how to perform

ANN prediction process for voltage stability condition. The training process produced result for

the convergence performance (mse vs epochs) and the testing process produced results of

results=[an' tn'], where if the targeted output is 1 = stable (converge) and 0 = unstable (diverge).

Post regression analysis showed that we were manage to get the best line (R=1), and the

comparison of each bus outputs showed that the output obtained were accurate. The performance

of this testing and training process also depends on the size of the power system network under

consideration.

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6.0 REFRRENCES

[I] P. A. Lof, et aI., "Voltage Stability Indices For Stressed Power Systems", IEEE Irans. On

Power System, Vol. 8. no_ I, Feb 1993, pp.326-335.

[2] B. Gao, ct aI., "Voltage Stabilily Evalualion Using Modal Analysis", IEEE trans. On Power

System. Vol. 7, nO .. 4, Nov 1992, PI'. 1529-1542.

[3] N. Flatabo, et aI., "Voltage Stability Condition in a Power Transmission Calculated by

Sensitivity Method", IEEE trans. On Power Systems, Vol.5, no. 4,Nov. 1990, pp. 12861293.

[4] M. M. Begovic, A. O. Phadke, "Control of Voltage Stability using sensitivity Analysis",

IEEE trans. On Power Systems, Vol. 7, no. I, Feb 1992, pp. 1 14123.

[5] T. K Abdul Rahman and G. B Jasmon, "A New Technique for Voltage Stability Analysis In

A Power System and Improved Loadnow Algorithm For Distribution Network",

Intrcll1ation.1Conference on EMPD, Vol.2, pg 7 I 4-719, Nov. I 995.

[6) A.A. ElKeib, X.Ma, "Application of Artificial Neurat Networks in Voltage stability

Assessment" IEEE tr3ns. on power system. 1

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