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NEURAL NETWORKS

Application of Artificial Neural Network (ANN) technique for

the measurement of voltage stability using FACTS Controllers

BY

V.RAVITEJA

P.VENKATESH3RD YEAR

ASCET

AUDISANKARA COLLEGE OF ENGINEERING & TECHNOLOGY

GUDUR

Email: [email protected]: [email protected]

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mailto:[email protected]




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Application of Artificial Neural Network (ANN) technique for

the measurement of voltage stability using FACTS Controllers

Abstract: A Methodology is

proposed for the online monitoring and

assessment of voltage stability margins,

using artificial neural networks and FACTScontrollers with a reduced input data set

from the power system. In this

methodology, first the system model is

reduced using self – organized artificial

neural networks and an extended AESOPS

algorithm. Then supervised learning of

multilayered artificial neural networks is

carried out on the basis of this reduced

model. Finally, on the basis of trained

network and the reduced set of system

variables, monitoring is carried out along

with the assessment of voltage stabilitymargins. This methodology is tested

comparatively with a methodology for

monitoring and assessing voltage stability

using a complete input data set. The tests

were carried out on a real power system with

92 buses. The results obtained indicate the

justifiability of using a reduced system

because of the increased efficiency and

accuracy of calculation, both in the learning

stage and in the recall stage of the artificial

neural network.

I) Introduction: Most of the large

power systems are badly suffered due the

phenomena of voltage instability. The basic

method of preventing such severe system

incidents is timely identification of voltage

instability. In this sense, the development ismade by using suitable computer producers

in online environment for monitoring and

assessing the voltage stability margins. Two

method are adopted to solve the stability

problems I) static method ii) dynamic

method the. This approach of static methodis based on the steady state load flow model

for calculating power flow and assessing

how far the Jacobian matrix is true from the

singularity function, that is, from classis

static voltage collapse the practical

implementation of this method is carried out

while defining an entire series of simple

indicator which show the static voltage

stability margins. Some of this indicators

can be used in an online environment,

however such a simplified approach renders

good results. The dynamic method of

approach is based either on a lineariseddynamic method of the power system and

Eigen value analysis or on a non-linear

dynamic model of the power system and

direct methods. Such as dynamic bifurcation

and numeric transient simulations. The

method based on the dynamic approach give

a much more real picture of voltage stability

margins. However, methods based on the

dynamic approach are time consuming in

terms of computer time for the online

environment. The most attractive means for

solving this problem is found in artificialneural network (ANNs). These networks can

be trained offline for complicated mapping,

such as the difficult problem of determining

voltage stability margin, and can be used in

an efficient and timely way in the online

environment to monitor and assess the same.

In this paper, an entire series of efficient

methods are proposed which are based on

artificial neural networks (ANNs) and on

various indicators of voltage stability

however all the methods proposed are

mostly based on the complete vector of system variables, which significantly

diminishes their efficiency.

This paper deals with the

development of a new methodology for

monitoring and assessing voltage stability

margins, it is a methodology based onartificial neural networks (ANNs) with a

reduced input data set. The motive of this

research is to establish what minimal

necessary input data set is for the precise

monitoring and assessment of voltage

stability. The methodology proposed is based on static and dynamic stability

margins, which are determined by eigen

value analysis of the linearised static and

dynamic models of a power system, and also

on the use of multilayered and self

organized artificial neural networks (ANNs).

This methodology is composed, as in the

practice of a learning stage and a recall

stage. In the learning stage, first reduction of

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the model of the observed power system is

carried out using self-organized artificial

neural network (ANNs) and an extended

AESOPS algorithm. This reduction is made

for all relevant configurations, while

defining the relevant configurations, all

outages of lines and generators are

considered. As well as the most portable

combinations of double outages. Second, the

training of multilayered feed forwardartificial neural networks (ANNs) is carriedout on this reduced model, by varying the

load power over the range of the nighttime

minimum and daytime peak value. During

the training, mapping is established betweenthe reduced input set of system variables and

the voltage stability margin. Finally, during

recall or exploitation based on reduced set of

system variables, the monitoring and

assessment of voltage stability margins of

the considered operating regime is

performed. The proposed methodology istested with a methodology for monitoring

and assessing voltage stability based on the

complete input set. The results obtained

indicate the justifiability of using a reduced

system in the learning stage through the

increased efficiency and quality of leaning

of the artificial neural networks (ANNs) andin the exploitation stage through the

increased efficiency and reduction of

measurements required from the system.

2) Concept of Proposed Methodology:

(a)

(b)

Fig-1. Configuration of artificial neural

network (ANNs) considered

a) UR b) NT

The proposed methodology for monitoring

and assessment voltage stability is based on

self-organized and multilayered feed

forwarded artificial neural networks

(ANNs). It consists of four stage: 1)

configuration and design procedure. 2)

Stability analysis. 3) Reduction of system

model using a self organized artificial neural

network (ANN) and an extended AESOPS

algorithm, and training the multilayeredartificial neural network (ANN) over such areduced model. 4) Exploitation – that is the

monitoring and assessment of voltage

stability margins. In the text that follows the

basic steps in the proposed methodology are briefly elaborated.

2.1) Configuration and design procedure

of the artificial neural networks (ANNs)

(a): NY

(b): NR

Fig-2. Configuration of artificial neural

networks (ANNs) considered

In the learning stage, four artificial neural

network (ANN) configurations are

considered as in figures 1(a2b), 2(a2b)

i) UR-is a self-organized ANN intended for

the reduction of the vector of system

variables the input to this ANN is the

complete vector of system variables (Y) and

the out put is the reduced vector of system

variables (YR ) reduction of the vector of

system variables is carried out for each

relevant topology.

ii) NT-is a multilayered ANN for detecting

system topology, the input to this ANN is

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the complete vector of system variables, and

the out put is binary identification code of

the topology.

iii) NY-is a unified multilayered ANN for

evaluating voltage stability margins for each

considered topology of the power system.

The input to this ANN is the complete

vector of system variables and the

identification code of the topology. Theoutput is the real part of the critical Eigenvalue (Sc) and also the voltage stability

margin M.

iv) NR- is a multilayered ANN for evaluation of the voltage stability margin for

the considered topology of the power

system. The input to this ANNs is a reduced

vector of system variables and the output is

the real part of the critical Eigen value and

also the voltage stability margin.

By combining these four configurations two global algorithms for

analyzing stability are obtained.

AY-an algorithm based on a combination of

‘NT’ and ‘NY’ configurations of the neural

network as in fig-3.

AR-an algorithm based on a configuration of

‘NT’ ‘UR’ and ‘NR’ configurations of

neural network as in fig-4

Fig-3. Algorithm ‘AY’ based on the

complete input set of system

Fig-4. Algorithm ‘AR’ based on the reduced

input set of system variables

All the artificial neural networks

(ANNs) mention ed were configured with

one input layer, one out put layer, and one

hidden layer each. If the number of hidden

layers is increased to two, the learning time

is increase significantly and there is no

increase in accuracy. The number of neurons

in the hidden layer for all absorbed networks

was designed so that a minimal square error

was obtained. For most of the artificial

neural network observed in this paper, the

number of neurons in the hidden layer is30% less than the number of neurons in theinput layer. The artificial neural networks

(ANNs) for detecting system topology had a

sigmoid activation function for the neurons

in the hidden layer and for the neurons at theoutput layers the activation function was a

pure linear function. The (ANNs) for

evaluating system stability had a tangent

hyperbolic activation function for the

neurons in the hidden layer, and for the

neurons at the out put layer the activation

function is a pure linear function.

2.2) Analysis of stability:

The basic stability analysis model is

referred in this paper. In addition, this model

is extended to accept the following

components. Standard types of turbines and

governing systems, basic types of automaticvoltage regulators (AVRs) including the

power system stabilizer (PSS) and finally an

aggregate model of an induction machine

are also included. In this model the fast

transient processes in all machinesstator/network is ignored. The elimination of

these transient leads to standard singular

perturbation form of the description:

x=f(x,y) ………… (1)

0=-g(x,y) …………(2)

Where x & y are the vectors of dynamic

state variables and algebraic system

variables, respectively.

x1=(xM, xAVR , xG) ... (3)y=(θ ,V,P,Q) ………(4)

Where the meaning of following

symbols is i.e., xM, xAVR , xG – the sub vector

of dynamic state variables of synchronousand induction machines, the sub vector of

AVR dynamic state variables including the

pss and dynamic state variables of the

turbine and governing system respectively;

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θ ,V,P,Q – the sub vector of voltage phaseangles, the sub vector of voltage

magnitudes, the sub vector of injected active

powers and the sub vector injected reactive

powers of all nodes in the observed power

system, respectively. Monitor and

assessment of voltage stability in this paper

are actually based on the algebraic system

variable vector and on various combinations

of its sub vectors-(θ ,V,P,Q).

For analysis of stability, the

algorithm of fig-5 is used. Both the static

and dynamic aspects of voltage stability are

considered. The static aspect is based on the

distance of operating point from the saddle

node bifurcation point which corresponds to

the singularity of the linearised matrix of the

static power system model, while the

dynamic aspect is based on the distance of the operating point from the critical node

bifurcation point which corresponds to the

null real parts of the pair of complex eigen

values linearised the matrix of the dynamic

power system model.

Fig-5. Flow chart

Stability analysis is basically

differentiated for the ‘AR’ algorithm that is

based on a reduced system model and for the

‘AY’ algorithm, which is based on the

complete system model. Stability analysis

for the ‘AR’ algorithm is carried out in six

steps as in fig-6. The calculation of stability

analysis begins by taking the night

minimum as the starting system load, thisload is then distributed to all loaded busesaccording to the specified distribution co-

efficient and a random number generators.

In the first step the observed load level ‘P’

determine the stationary point (x0,y0). In thesecond step, linearisation of the dynamic

model is carried out using the defined

stationary point. Then, elimination is carried

out of the algebraic system variable vector

(y0) for dynamic stability analysis, and then

the elimination of the dynamic state variable

vector (x0) for the analysis of the staticstability. In this way, linear models are

obtained for dynamic and voltage stability.

In this way linear models are obtained for

dynamic and static voltage stability analysis.

In the third step system reduction is carried

out first by applying the self organized ANN

from the vector of dynamic and algebraicvariables (x,y) the reduce dynamic and

algebraic vectors (xR , yR ) are obtained, and

then by applying an

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Fig-6. Measurement of the real part of the critical Fig-8. Measurement of the voltage stability margin for

Eigen values for the algorithms AY and AR the algorithm AY and AR

a) AY-(θ ,V) (----), AR-(θ ,V),(----), simulation a) AY-(θ ,V) (----), AR-(θ ,V),(----),

simulation

b) AY-(P,Q) (----), AR-(P,Q),(----), simulation b) AY-(P,Q) (----), AR-(P,Q),(----), simulation

Fig-7. Measurement of the real part of the critical Fig-9. Measurement of the voltage stability margin

Eigen values for the algorithms Ay & AR for the algorithm AY & AR

a) AY-(V,P,Q) (----), AR-(V.P,Q),(----), simulation a) AY-(V,P,Q) (----), AR-(V,P,Q),(----), simulation

b) AY-(θ ,V,P,Q) (----), AR-(θ ,V,P,Q),(----), simulation b) AY-(θ ,V,P,Q) (----), AR-(θ ,V,P,Q),(----),

simulation

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Extended AESOPS algorithm from the

dynamic and static system matrix E & F, a

reduced system matrices ER & FR are

obtained. In this way reduced dynamic and

static models are obtained. The application

of self organized ANNs for the reducing

vector x & y is described in the next section,

while the application of the extended

AESOPS algorithm for system reduction isdescribed in the section 4.1. In the fourthstep by applying QR algorithm to the

reduced static and dynamic models the

Eigen values (λ i, vi) are determined. In the

fifth step the smallest Eigen values (ψ f ) are

determined and then the following variables

are recorded: actual load level (p), the

reduced vector of algebraic system variables

(yR ) and the smallest critical Eigen value

(ψ f ). In the final step testing is done to see

if the critical load level (Pcrit) has been

reached and if all condition for completing

the calculation have been fulfilled.When all condition for completing

the calculation have been fulfilled the

voltage stability margin is determined for all

operating points using the following

equation:

M = Pcrit – p ………(5)

Pcrit

Calculation of the stability analysis

for the AY algorithm is standard and is

different from the described calculation in

that it does not contain step 3 for system

reduction. In this way stability analysis and

determination of Eigen values is done for

the entire system model.

2.3) Supervised and unsupervised learning

of Artificial Neural Networks (ANNs):

The multilayered and self-organized

artificial neural networks are used in the

proposed methodology. Self-organized

ANNs are used for reduction of the system

model and of the input set for multilayered

artificial neural network learning, while

multilayered ANNs are used for detecting

topology and for monitoring and assessment

of voltage stability.

i) System reduction using self organize

ANN: The self organized ANN is introduce

in order to reduce the learning time of the

ANN and to reduce the number of system

variables needed for voltage stability margin

monitoring and assessment. According to

this method the problem of reducing the

vector of system variables from the ANN

can be presented as a problem of extractingcharacteristics variables and the variables,which differ from one another. In other

words the algorithm developed for the

reduction of vector system variables groups;

its coordinates, which are sufficiently,approximate in time, and separate the

dissimilar once. The straight variable, which

is closes to the calculated center of group, is

taken as the characteristic representatives of

the group. Finally by grouping all

characteristics representative of the group in

one vector, the reduced system vector (yR ) isobtained. If only the chosen representative

of each group is observed during the

formation of the system model, the

dimension of the system description can be

decrease. A more detail review of the ANN

algorithm used is to be found in the, section

4.2.

ii) Supervised learning of the ANNs:

After system reduction using the

result of stability analysis on a reduced set

of system variables learning is carried our.Supervise learning of multilayered ANN is a

process which the correction of synaptic

weights between neurons in proximate

layers to learn carry out. The error back

propagation algorithm with a variable

learning rate is used for these purposes. The

general expression for the correction of the

synaptic weights is well known as the

generalized delta rule.

2.4) Exploitation of artificial neural

network (ANNs):After selecting required ANN configurationwith the most suitable characteristics, it is

possible to move on to the next stage is

called exploitation. First, the system

topology is detected.

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Next, and evaluation of the stability

of the power system with the identified

topology on the basis of complete or

reduced vectors of the system variables is

carried out. A schematic over view of the

considered variants of the exploitation

stages shown in fig-3 and fig-4.

Monitoring of voltage stability

margins is performed by introducing

measured and estimated system variablevalues into the input of the correspondingneural network with algorithm ‘AY’ and

‘AR’. Voltage stability assessment is carried

out by testing, if there is an outage of any

single element that is lines or generators or if any of there probable combinations leads

to a disruption of the voltage stability

margins. For the simulation of the

considered outages two approaches are

followed.

i) Indirect stability assessment (ISA):

The first approach is indirect and is performed so that for each outage the

evaluation is first done for the vector of

system variables by applying the fast-

decoupled load flow calculation. Then on

the basis of the vector of system variables

and the specified identification code for the

topology of the outage in question, thevoltage stability margin of the observed

outage is tested by applying one of the

suggested ANNs.

ii) Direct stability assessment (DSA):The second approach is direct, and

is performed so that the input of the ANN is

the input vector y = (P,Q) consisting of

actual injected active and reactive powers in

all buses and the identification code of the

outage. In these way voltage stability

margins of the observed outage is directly

evaluated with out the fast-decoupled load

flow calculation.

3) Application of the methodology:

The proposed methodology for stability analysis is based on ANNs withcomplete and reduced sets of input data. It

can be tested on high voltage power system

about 92 buses 12 number of generator

buses and 174 lines. In doing so the

following four cases may be considered for

the complete input vector of system

variables.

i) Vector y=(θ ,V), state variable

system

ii) Vector y=(P,Q), directly

measured system variables

iii) Vector y=(V,P,Q), directly

measured variables

iv) Vector y=(θ ,V,P,Q), all system

variables.

By combining this input vector by

combining this input vector with the

proposed algorithm or detecting the

topology ‘NT’ and monitoring and

evaluating voltage stability ‘AY’ and ‘AR’

the following configurations/algorithms are

obtained which are tested in this paper:

NT-(θ ,V), AY-(θ ,V),

AR-(θ ,V),

NT-(P,Q), AY-(P,Q), AR-(P,Q),

NT-(V,P,Q), AY-(V,P,Q), AR-(V,P,Q),

NT-θ ,V,P,Q), AY-(θ ,V,P,Q), AR-

(θ ,V,P,Q),

As, such, of special interest are the

algorithms which are based on the vector of

system variables y=(V,P,Q) which are

directly measurable from the system, while

the remaining input vectors require

estimated values of the sub vector of the

voltage phase angles of the buses (θ ).

3.1) System reduction and ANN learning

on a test sample:

The following relevant configurations areconsidered in this paper: base configuration,

all single outages of lines and generators,

and most probable combinations of double

outages. For each relevant configuration,

first the reduced set of system variables is

determined using the self-organized neural

network UR. This reduction renders an

average reduction of the system variablevector by 95%, so that the reduced vector

represents only about 5% of the whole

vector. In forming these vectors as separate

groups, the following are usually set apart:

i) Voltage phase angles and magnitudes in

buses where low, rated power generators are

connected;

ii) Active and reactive powers in generators

buses;

iii) active and reactive powers in loaded

buses of a single region;

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iv) voltages in load buses of single compact

region.

It is interesting to note that it was

actually those buses which would be

assigned as pilot buses, according to the

secondary voltage regulation algorithm

(7,16), which were chosen as characteristic

representatives of the group with the

voltages of load buses. In this way, the proposed algorithm for reduction of the system variable set can also be used for

selecting a candidate for the pilot buses of

secondary voltage regulation.

On the basis of the complete andreduced vectors of system variables,

supervised learning of ANNs was carried

out. The ANNs were trained using either one

network for all relevant configurations

(algorithm AY), or a single network for each

relevant configuration AY), or a single

network for each relevant configuration(algorithm AR). For each relevant

configuration, the load was varied over the

range of the nighttime minimum to the

daytime peak value, during which 100

different margins were observed. The basic

characteristics are presented in Table-1.

Table-1. Basic learning

characteristics of the observed ANNs

In Table 2, the relationship is

presented comparatively of the time needed

for stability analysis, system reduction and

ANN learning for algorithms AY and AR.

Learning was done on a workstation

ALPHA 4100/300 MHz. From the Table itcan be seen that the AR algorithm is

significantly more efficient in the learning

phase. This efficiency is achieved because

of the shorter time necessary for calculating

the stability analysis for the reduced system

model. The other more significant reduction

in computer time was achieved in

the shorter learning time for several smaller

ANNs that for the one large ANN. However,

the obstacle is the application of algorithm

AR that is necessary for the configuration of

the large number of smaller ANNs. This

number is approximately equivalent to the

number of relevant configurations.

Table-2. Comparative computer

learning time for algorithms AY and AR

3.2) Testing the methodology in

exploitation:

The testing of ANNs on a real

power system was carried out for the all

configurations for topology detection, and

for monitoring and assessing voltage

stability margins. Testing of the trainedANNs for the detection of system topology

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was carried out on an unknown set of 12960

samples (40 each for every topology

observed). In doing so, the following four

ANNs for topology detection were

considered:

NT-(θ ,V), NT-(P,Q), NT-(V,P,Q), NT-

(θ ,V,P,Q). On the observed test set, all four

networks detected all the considered

topologies with a high degree of accuracy.

Namely, the output neurons of neural

network NT were so designed that they give

a binary code for each topology considered.

The mean square errors calculated from the

real values at the output neurons are given in

table-3.

Table-3. Mean square errors for output

neurons and for the considered power

system topology:

The test results of the neural

networks for the monitoring and assessment

of the voltage stability margin are shown in

figs. 6-9. In figs. 6 & 7 there is a

comparative presentation of the dependence

of the real part of the critical Eigen values

on the system load level for algorithms AY

and AR. In figs. 8 & 9 there is comparative

presentation of the dependence of the

voltage stability margin on the system load

level for algorithms AY and AR. From Fig.6a and Fig. 8a, it can be seen that in the

situation where the input set contains only

system state variables (θ ,V), greater

precision is achieved by using algorithm AY

with the whole input set, than by using

algorithm AR with a reduced input set.

When the input set consist of input vectors

(P,Q), the precision achieved with reduced

or complete input set, is almost equal with

reference to fig-6(b) and fig-8(b). Finally

from fig-7 (a), 9(a) and fig-9(b). It can b e

seen that when the input set contains enough

data input vectors (V,P,Q) and (θ ,V,P,Q),

greater precision is achieved by using

algorithm AR with a reduced input set then

by using algorithm AY with the entire input

set. In addition algorithm AR is one order of

magnitude faster in exploitation than

algorithm AY in terms of ms, which is

exceptionally important because exploitation

is done in an online environment.As mention above, when assessing

voltage stability, both the ISA and DSA

approaches were analyzed the computer

time needed for analyzing stability in bothapproach are given in table-4. From the table

it can be seen that the direct calculation of

stability using DSA and AR-(P,Q),decreases computer time remarkably without

significant loss in precision.

Table-4. Computer time for assessing

voltage stability using the indirect

approach ISA and the Direct approach

DSA

4) Details of Model:

4.1) System Reduction

The basic model for system

reduction is a linearised mathematical model

of power system

x=Ax+By ………….. (1)0=cx+Dy …………….(2)

It the vector of state x is divided into two

sub vectors xR is the sub vector which

contains the variables of state whose

dynamics are under consideration and x0 is

the sub vector which contains the variables

of the state whose dynamics are not under

consideration the equations above obtain the

following form:

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xR = ARR xR + AROx0+ BR .y ……. (3)

xO= AOR xR + AOOxO+ BO .y …..... (4)

0= CR xR + COxO + D.y ……… (5)

Where

ARR , ARO, AOR , AOO, correspond to the sub

matrix of matrix A

BR , BO correspond to the sub matrix of

matrix B

CR , CO, correspond to the sub matrix of

matrix CThat is the system of equations 3 – 5 in theLaplace frequency domain are

sxR = ARR xR + AROx0+ BR .y ……. (6)

sxO= AOR xR + AOOxO+ BO .y …..... (7)

0= CR xR + COxO + D.y …………. (8)

In order to observed the dynamics of only

relevant state variables, which are contained

in sub vector xR , it is necessary to eliminate

the sub vector of variables of state x0 from

models equations 6-8, and the vector of

algebraic variable y. After these elimination,which are realized using the gauss method, a

reduced system model is obtained

sx=[ARR -B1.D1-1(s)C1] xR ……….. (9)

Where the following symbols are used:

B1=[ARO BR ], D1(s)= A RR -SI Bo

Co D

C1= AOR

CR …………………….. (10)

To analyze the dynamic reduce modelequation-9 it is necessary to detetemine its

Eigen values. Determining these Eigen

values is done by an iterative approach (1)

individual or (2) simultaneous.

In this paper the individual method

is used which is based on the following

iterative approach

sK+1=Aii-B1D-1(SK )C

1, k=1,2, ….. n (11)

Where SK SK+1 is the approximation of the

required Eigen values in the and k and k+1

iteration. For improving the convergence of these iterative methods product linearisation

B1D-1(SK ) is used.

With this iterative method the Eigen

value is determined which predominantly

associated to the ith component of the sub

vectors of xR . By varying the index I=1, …..,

R it is possible to determine all Eigen values

of the reduced model as in equation 9 with

great efficiency.

4.2) Artificial neural network (ANN)

algorithm:

The goal of unsupervised

classification is to group the state variables

of the system which are characteristic by

similar dynamic in the process the cosine of

angle covered by vectors of individual state

variables at all interval is taken as the

measure of similarity between them. If twoarbitrary state variables are observed over a period of time, for example xi=[x1i, x2i, ….

xmi]T and x j=[x1j, x2j,…. Xmj]

T, They will be

similar if they both cover a small angle. In

order the measure there similarity thefollowing express is used

cosθ ij = xiTx j (1)

xi xi

If equation (1) is larger than the given value,represented by the similarity threshold

(cosθ 0), that is if the condition θ ij < θ 0

then the vectors xi and xij are similar and

belong to the same group. Keeping the

criterion for defining similar vector as in

equation (1) it is necessary to normalize

them before hand by using the formula

i = xi I=1,2, …. n (2)

xi

The grouping of similar variables is

achieved in the following way. The arbitrary

group g(g=1, … , G) is observed consistingof k variables. The arbitrary ith variable x i,

that is its normalized value i, will belong

to this group if it satisfies the condition that

θ ig < θ 0 where θ 0 is the threshold of group

membership, θ ig is the angle between ith

vector i and the center of the gth group Cg.

As the new element enters the

group, the center of group moves toward the

position of the variable i according to the

formula

Cgk+1= Cg

k +á∆ Cgk …….. (3)

Where Cgk and Cg

k+1 are the centers of g

group before and after vector i enters this

group. The coefficient ‘a’ is a factor of

proportionality define by the intuitiveexpression ‘a’=1/k+1, where k is the number

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of variables making of the group, and the

coefficient ∆ Cgk is the correction of the

position of the group center (∆ Cgk =xi- Cg

k ).

By replacing ‘a’ and ∆ Cgk finally we get

Cgk+1=a i+ Cg

k (1-a) i.e.,

Cgk+1= KCg

k + i ….. (4)

K+1

The calculated group centers of equation 4serve for the basis for finding the closest

state variables for them, which become the

characteristic representatives of the group.

5) Conclusion & Result:

These paper deals with the developments of

new methodology for monitoring and

assessment the voltage stability, which is

based on artificial neural networks (ANNs)with a reduced input system data set. The

input data set is reduced using a self-

organized neural network, and then amultilayered feed forward neural network is

trained using this reduced data set to

monitor and assess the voltage stability

margins. The proposed methodology tested

comparatively with a method for monitoring

and assessing the voltage stability, which is

based on a complete input data set. Tests are

carried out on a power system with 92

buses. The obtained results indicate that,

both in the learning and exploitation stages

the efficiency of the methodology is

significantly increase by reducing the inputdata set. More over, when the input data set

is representative enough, the ANNs based

on the reduced data set achieved greater precision in calculating voltage stability than

did the ANNs, which is based on the

complete input data set. In addition, by

using the reduction of input data, there is a

significant reduction also in the demand for

the measurements within the power system.

6) References:

1. Voltage stability and security in bulk

power systems voltage phenomena-voltage

stability and security, engineering

foundation conference, Potosi, Missouri

USA, sep-1988 – by CONCOR DIA, C.

2. Neural network and fuzzy system by Bard

Kosco.

3. Understanding of FACTS – by narain.

G.Hingorani, Laszlo Gyugyi.

4. Monitoring and assessment of voltage

stability margins using artificial neural

network with a reduced input set IEEE,

june-1997 by D.Popovic/D.Kukalj and

F.Kulid.

5. Reactive power controller inelectronic systems by T.J.E. Millers.

149

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