Artificial Intelligence and Neural Network Applications in Power Systems

ARTIFICIAL INTELLIGENCE AND NEURAL NETWORK  APPLICATIONS IN POWER SYSTEMS

Document By SANTOSH BHARADWAJ REDDY Email: [email protected]

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each of which may have an effect on

ABSTRACT:

The The elec electr tric ic powe powerr indus industr try y is currently

undergoing

the securi security ty of the syste system. m. Neural Neural

an

networks networks have shown great promise

unprecedente unprecedented d reform, reform, ascribable ascribable to,

for thei theirr abi ability to qui quickly ckly and and

one

accu accura rattely ely

of

the

most

potentially

exciting

profitable

and

pred prediict

the

syst system em

recent secu securi rity ty when when trai traine ned d with with data data

developments in increasing usage of 

coll collect ected ed from from a smal smalll subs subset et of 

artificia artificiall intelligenc intelligencee techniques. techniques. The

system variables.

artificial neural network approach has attr attrac acte ted d

numb number er

of

appl applic icat atio ions ns

The intention of this paper is to give an overview of application of 

espe especi cial allly in the the field eld of powe power  r 

arti artifi fici cial al inte intell llig igen ence ce

system since it is a model del free

network (NN) techniques in power 

estima estimator tor.. Neural Neural networ networks ks provid providee

syst system emss to progn prognos osti tica cate te load load on

solutions

 power plant and contingency in case

to

nonl nonliinear near

ver very

com comple plex

prob probllems ems.

and

Nonl Nonliinear  near 

and neura neurall

of any unexpecte unexpected d outage. outage. In this this

  probl problems ems,, like like load load forecas forecastin ting g that that

 paper we present the key concepts of 

cann cannot ot

artificial neural networks, its history,

be

solve olved d

wit with

stan standa darrd

algorithms but can be solved with a

imitation

neur neural al

architecture

netw networ ork k

accu accura racy cy..   pow power er

with with

Moder Modern n syst system emss

rema remark rkab able le

inte interc rconn onnect ected ed

oft often

cons consiist

brain and

neuron’s

finally

the

applic applicati ations ons (load (load foreca forecasti sting ng and

of  contingency

thous thousan ands ds of piec pieces es of equi equipm pment ent

of

analysis).

Th e

applications of artificial intelligence

in areas of load forecasting by error 

cont contrrol, ol,

Backpropagat Backpropagation ion learning learning algorithm algorithm

Management

Systems

and conting contingenc ency y analysi analysiss based based on

wide widely ly

in

Quality

cent center ers. s. The The abno abnorm rmal al mode modess of 

index

have

been

comp comput uter er base based d

used used

Ener Energy gy

are

ener energy gy

now cont contrrol

 perspicuously explained.

system operation may be caused by

INTRODUCTION:

networ network k fault faults, s, active active and reacti reactive ve

Modern power systems are required

  pow power er imbal mbalan ance cess,

to gener generat atee and and suppl supply y high high qual qualit ity y

deviations. deviations. An unplanned unplanned Operation Operation

electric energy to customers. To

may may lead lead to a mal mal or a comp comple lete te

achieve achieve this requirement requirement,, computers computers

syste ystem m

have have been been applied applied to power power syste system m

emergency

  pla plann nnin ing, g, moni monito tori ring ng and and contr control ol..

syst system emss are are rest restor ored ed back back to the the

Power system application application programs programs

normal state according to decisions

for analysing system behaviours behaviours are

made made

stored in computers. In the planning

engineers. There is also a need to

stag stagee of a powe powerr syst system em,, syste ystem m

develo develop p fast fast and effici efficient ent methods methods

anal analy ysis sis

for the pred prediicti ction of abno abnorm rmal al

prog progrrams ams

repe repeat ated edly ly.. modify

are are

Engi Engine neer erss

the

programs

input

adju adjust st

data

according

exec execut uted ed

to

and and

blac blacko kout ut..

by

Under nder

situations,

expe experi rien ence ced d

thes hese power 

oper operat atio ion n

system behaviour.

these

to

or freq freque uenc ncy y

Artifi Artificia ciall intell intellige igence nce (AI) (AI)

their  has

provided

reasoning

for 

experi experience ence and heuris heuristic tic knowled knowledge ge

encodin ding

about about the system system until until satisf satisfact actory ory

declarative declarative knowledge. The advent

 plans are determined.

of neur neural al net network workss

For sophisticat sophisticated ed approaches approaches

and

techniques

(NN" (NN"s) s),,

wit with

in

additi addition, on, provid provides es neural neural networ network  k 

to syste system m planni planning, ng, develo developme pment nt of 

modul modules es which which can be execu execute ted d in

meth method odol olog ogie iess

to

an online online enviro environme nment. nt. These These new

incorp incorpora orate te practi practical cal knowle knowledge dge of 

techniques supplement conventional

  pla plann nnin ing g

computing techniques and methods

and and

tech techni niqu ques es

engi engine neer erss into into prog progra rams ms

whic which h also also incl include ude the the nume numeri rical cal

for sol solving ving prob proble lem ms of powe power  r 

analysis programs are needed. In the

syst system em

area of power System monitoring and

control.

plan planni ning ng,,

oper operat atio ion n

and and

Unit Unit commit commitment ment,,

Areas of Applications:

Poss Possib ible le

appli applica cati tion onss

of

arti artifi fici cial al

Mainte Maintenanc nancee

scheduling, Load forecasting.

intelligence in power system planning and operati operation on were were invest investiga igated ted by   power titles titles and researchers. researchers. In the last

decade,

intelligence

many

systems

1. Artificial Neural Networks

artificial

and

expert

1.1 What is a Neural Network?

systems have been built for solving  problems in different areas within the field field of power power system systemss only. only. These These areas are summarized below.

An Artificial  Neural  Network  (ANN) is an information  processing paradigm that is inspired

System planning

  by by

Transmission planning and design, Generation Generation expansion, expansion, Distribut Distribution ion  planning.

the the

way way

biol biolog ogiical cal

ner nervous vous

systems, such as the brain, process information. The key element of this   parad paradigm igm is the novel novel struct structure ure of  the informatio information n processing processing system. system.

System Analysis

It is composed of a large number of 

Loadflow engine, Transient stability

highly highly

interc interconn onnect ected ed

elem elemen ents ts System Operation h Monitoring Alarm processing, processing, Fault diagnosis, diagnosis, Substa Substati tion on monito monitorin ring, g, System System and network network restorati restoration, on, Load shedding, shedding, Volt Voltag agee / reac reacti tive ve power power cont contro rol, l, Cont Contin inge genc ncy y

sele select ctio ion, n,

switching, Voltage collapse.

Netw Networ ork  k 

(neu (neuro rons ns))

proces processin sing g work workin ing g

in

unison unison to solve solve specif specific ic proble problems. ms. ANNs,

like

people,

learn

by

example. example. An ANN is configured configured for  a

speci pecifi ficc pattern

appl appliicati cation on,, recognition

such uch or

as data

classi classific ficati ation, on, throug through h a learni learning ng   pro proce cess ss..

Lear Learni ning ng

in

biol biolog ogic ical al

systems systems involves involves adjustments adjustments to the Operational Planning

syna synapt ptic ic

conn connec ecti tion onss

that that

exis existt

  between the neurons. This is true of 

is a speci pecial aliz ized ed cell cell whi which can can

ANNs as well.

 propagate an electrochemical signal. The neuron has a branching input structure (the dendrites), a cell body, and a branching output structure (the axon). The axons of one cell connect to the the dend dendri rite tess of anot anothe herr via via a synapse. When a neuron is activated, it fire firess an elec electr troc ochem hemic ical al signa signall along the axon. This signal crosses the synapses to other neurons, which may in turn fire. A neuron fires only if the total signal received at the cell

The major breakthrough in the fiel ield of ANN ANN occu occurrred wit with the inven vention

of

 body from the dendrites exceeds a certain level (the firing threshold).

Back ackpropagation

algorithm which enabled design and

To capture the essence of biological

learni learning ng techni technique quess of multil multilaye ayered red

neural systems, systems, an artifici artificial al neuron

neur neural al netw networ orks ks..

is defined as follows:

Since nce

then hen

the

development development and areas of applicatio application n in which ANN is applied has been

It rece receiv ives es a numb number er of inpu inputs ts (either from original data, or from

thriving.

the output of other neurons in the neural network). Each input comes

1.3 Biological inspiration:

via a connection that has a strength The brain is principally composed of

a

very

large

10,000,000,000)

number of

(circa

neurons,

mass massiv ivel ely y inte interc rcon onne necte cted d (wit (with h an average

of

several

thousand

interconnect interconnectss per  neuron neuron,, alth althoug ough h this varies enormously enormously). ). Each neuron

(or

weight);

these

weights

correspond to synaptic efficacy in a  biological  biological neuron. Each neuron also has has a sing single le thre thresh shol old d valu value. e. The The weighte hted sum of the inputs is formed, subtracted,

and to

the

threshold

compose

the

activation of the neuron (also known

algori orithmic

appro proach

as the post-synaptic potential, or PSP,

computer

of the neuron).

inst instru ruct ctio ions ns in orde orderr to solv solvee a

follows

i.e.

a

the

set

of  

 problem. •

The The acti activat vatio ion n signa signall is pass passed ed thro throug ugh h an activ activat atio ion n func functi tion on (also

known

as

a

Neural

networks

process

transfer  

info inform rmat atio ion n in a simi simila larr way way the the

function) function) to produce produce the output of 

human brain does. Neural networks

the

learn learn by example. example. They They cannot cannot be

neuron.

  progr programm ammed ed to perfor perform m a specif specific ic task.

On

the

conv conven enttional onal cogn cognit itiive

other

comp comput uter erss

appr approa oach ch

to

hand, use use

a

prob probllem

solving; the way the problem is to solved must be known and stated in smal smalll

unamb unambig iguou uouss

These

instructions

inst instru ruct ctio ions ns.. are

then

If a network is to be of any use, there

converted to a high level language

must ust be input nputss (whic which h carr carry y the

 program and then into machine code

values of variables of interest in the

that the computer can understand.

outsid outsidee world) world) and output outputss (which (which form predictions, or control signals).

  Neura Neurall networ networks ks and convent convention ional al

The input, hidden and output neurons

algor algorit ithm hmic ic comput computer erss are are not in

need to be connected together.

compet competiti ition on but comple complemen mentt each each other. other. Even more, a large number of 

1.4

Neural

networks

versus

conventional computers

task tasks, s, requi require re syst system emss that that use use a combination of the two approaches (normally (normally a conventional conventional computer  computer 

  Neu Neura rall netw networ orks ks take take a diff differ eren entt approach to problem solving than that of

conventional

Conv Conven enttional onal

comp comput uter erss

computers. use use

an

is used used to supe superv rviise the the neur neural al netw networ ork) k) in orde orderr to perf perfor orm m at maximum efficiency.

functi function on (tran (transfe sferr functi function) on) that that is

1.5 Features

1.

High co computational ra rates

specified for the units. This function

due to the massive parallelism.

typi typica call lly y fall fallss into into one one of thre threee

2.

Fault tolerance.

categories:

3.

Training

adopts pts

itself,

the

network  

bas based on

the

inform informati ation on receiv received ed from from the

Linear (or ramp) Threshold

environment. 4.

Programmed rules are

Sigmoid

not necessary. 5.

Primitive c om omputational

For  linear units, the output activity is proportional to the total weighted

elements.

output. threshold unit, the output is set For  threshold

1.6 The Learning Process

at one of two levels, depending on Supe Su perv rvis ised ed

lear learni ning ng

which

whet whether her the the tota totall input input is grea greate ter  r 

incorp incorpora orates tes an extern external al teacher teacher,, so

than than or less less than than some some thre thresh shol old d

that each output unit is told what its

value.

desi desire red d resp respon onse se to inpu inputt sign signal alss ough oughtt to be. be. Duri During ng the the lear learni ning ng   proce process ss global global inform informati ation on may be required.

For  sigmoid units, the output varies varies continuously but not linearly as the input changes. Sigmoid units bear a greater resemblance to real neurons

Unsupervised Unsupervised learning learning uses uses no

than do linear or threshold units, but

exte extern rnal al teac teache herr and and is base based d upon upon

all three must be considered rough

only only loca locall info inform rmat atio ion. n. It is also also

approximations.

referred to as self-organisation 2. APPLICATIONS 1.7 Transfer Function App1: Power Systems Load

The behaviour of an ANN depends on  both the weights weights and the input-output input-output

Forecasting

difficulty

to

find

functional

Commonly and popular problem that

relati relations onship hip betwee between n all attrib attribute ute

has an import important ant role role in econom economic, ic,

vari variab able le

financ financial ial,,

expansi expansion on

demand, difficulty to upgrade the set

and planni planning ng is load load foreca forecasti sting ng of 

of rules that govern at expert system

 power systems. Generally most of the

and is ability to adjust themselves

  papers and projects in this area are

with with rapid rapid nonline nonlinear ar syste system-l m-load oad

categorized into three groups:

changes. The NNs can be used to

develo developme pment, nt,

and and

inst instan anta tane neou ouss

load load

solve these problems. Most of the ‫ﻢ‬

Short-term (STLF)

load fore orecasting

ove over

an

interval

 projects  projects using NNs have considered considered many

such

as

weather 

rang rangiing from rom an hour hour to a

condit condition ion,, holida holidays, ys, weekend weekendss and

week is important for various

spec pecial

appl appliicati cation onss

fore foreca cast stin ing g

such such

commitment, dis dispat patch, ch,

as

uni unit

economic

ener energy gy

scheduli uling

and and

sport

matches

mode model, l,

day days

in

succ succes essf sful ully ly..

This is because of learning ability of 

tran transf sfer  er   NNs with many input factors. real

time

‫ﻢ‬

Mid-term

load

control. A lot of studies have

forec orecas astting( ing(M MTLF TLF)

 been done for using of short-

range from one month to five

term term load load fore foreca cast stin ing g with with

years,

diff differ eren entt

of 

enough fuel for power plants

be

afte afterr elec electr tric icit ity y tari tariff ffss are are

these

meth method ods. s. One One methods

may

classified as follow:

&

syst system ems, s,

Jenkins Fuzz Fuzzy y

model, infe infere renc nce, e,

used

to

that that

pur purchas hase

calculated.

Regression Regression model, model, Kalman Kalman filtering, filtering, Box

actors

‫ﻢ‬

Long-te -term load forecasting

Expert

(LTLF), covering from 5 to

Neur Neuro o

20 year yearss or more more,, used used by

fuzzy models and Chaos time series analysis. Some of these methods have main limitations such as neglecting of  some forecasting attribute condition,

planning

engineers

and

economists to determine the type

and

generating

the

size

plants

of   that

minimize

bot both

fixed

and

variable costs.

discrete time series over forecasting intervals. Sta Stand nda ard

standard

Load

load

:-The

curve

is

produce uced once nce a day . It needs needs resc rescal alin ing g over over time time . The

standard

load

characterizes the base load . It is cal calcul culated ated by usin using g histor historica icall load load data data .The .The standar standard d load load calcul calculati ation on can be div divided ded in two  parts. The first one makes an

average

using

all

common days in the same 2.1.1

Overview

of

STLF

Techniques:-

A

wide

  perio period. d. The holida holidays ys are includ included ed with with Saturd Saturdays ays and Monday Mondays. s. The

variety

of   seco second nd part part inve invest stig igat ates es on the the techniques/algorithms for STLF have  particular characteristic for each day  been reported in the literature (These of the week, separately. For this a  procedures typically make use of two simple weighted moving average is   basic models peak load models and

made.

load shape modes. (Load d Standard Standard Load Load Concept Concept :- (Loa Shape Model) The load forecasting is divided into two general general parts; parts; peak load load model model and load shape model .Former deals with with dai daily or weekl eekly y peak peak load load mode modeli ling ng & late laterr desc descri ribes bes load load a

Resi Residu dual al/D /Dev evia iati tion on

Load Load:-The

residual load is used to represent the most recent variation of the load . This value contains information for  last last 3 hour hours. s. Auto Auto regr regres essi sive ve and and exponential smoothing are the most common methods used to calculate the deviation of load value.

desi desirred 2.1. 2.1.2 2

Arti Artifi fici cial al

Neur Neural al

netw networ ork  k 

based short term load forecasting:

The deve devellopme opment nt of an ANN ANN

outp output ut for

traini aining ng

the

network. An initial input data set is   pr presen esente ted d

to

ANNS ANNSTL TLF F

whi which

 based STLF model is divided into two

adj adjusts usts the the weig weight ht val values ues for for a

  proce processe sses, s, the "learn "learning ing phase" phase" and

minimu minimum m error. error. Follow Following ing a new

the "recall phase". In learning phase,

input data set is presented and the

the

weight

neurons

are

trained

using

values

are

adjusted

in

hist histor oric ical al input input &out &outpu putt data data and and

acco accord rdan ance ce .The .The proc proces esss fini finish shes es

adju adjust stab able le

grad gradua uall lly y

when the difference between target

optimized to minimize the difference

output and the found output for all

  betwe between en the comput computed ed and desire desired d

the input sets is close to zero. The

output. The ANN allows outputs to be

feed forward Multilayer Perceptron

calc calcul ulat ated ed based based on some some form form of 

(MLP) neural network model is used

experiences,

than

for implem implement enting ing the STLF STLF model model

understanding the connection between

(ANN (ANNST STLF LF). ). Fig5 Fig5 shows shows a MLP MLP

input and output (or cause and effect).

wit with

In recall phase the new input data is

advantage of this model is that it is

appl applie ied d to the the netw networ ork k & and and its its

abl able

outputs are computed and evaluated

mappi ppings. gs.

for testing purpose. In the ANN based

trained by standard backpropagation

STLF

training algorithm and developed by

weig weight htss

model,

are are

rather

a

layered

ANN

structure structure (Input layer, layer, Hidden layer,

sing singlle

to

lear learn n The

hidd hidden en

high highlly MLP

1ay 1ayer.T er.Tli liee

nonnon-llinea inear  r  model

is

Rumelhart.

Output layer) is used. In this method the weig weight htss are are cal calcul culated ated by a learning

process

using

error 

  propa propagat gation ion in parall parallel el distri distribut buted ed   pro proce cess ssin ing. g. The The STLF STLF prob proble lem m is formulated with the past data as the input data and the latest data are the 2.1.3 2.1.3 Multila Multilayer yer Percept Perceptron ron and

Its application in load forecasting:-

instances ; which is achieved , thus

The multi layer Perceptron and the

avoidi avoiding ng overloa overloadin ding g of networ network k ,

associated backpropagation algorithm

  by by term termin inat atin ing g Lear Learni ning ng once once a

  pro propo pose sed d a sound sound meth method od to trai train n

  per perfo form rman ance ce

networks having more than two layers

reac reache hed d

of neur neuron onss. The The learn earniing rule ule is

network is capable of approximating

known as Backpropagation which is a

arbitrary mappings given a net of the

grad gradiient ent

output.

dece decent nt

techn echniique que

wit with

  backward error(gradient) propagation is

depicted

in

Fig.6. The

back 

.

pat pattern ern

The The

has has

been been

back backpr prop opag agal alio ion n

The name backpropagation comes from the fact that the error (gradient)

 propagation network in essence learns

of hidd hidden en unit unitss are are deri derive ved d from from

a mapping from a set of input patterns

  pro propa paga gati ting ng back backwa ward rd the the erro errors rs

(e.g. extracted features) to, a set of 

asso associ ciat ated ed with with the the outp output ut Unit Unitss

output

class

since since the target target values values for hidden

inform informati ation on ) .This .This networ network k can be

units are not given or it is defined to

designed and trained to accomplish a

obta obtain in the the valu values es of the the desi desire red d

wide variety of mappings. This ability

output at hidden layer.

patterns

(

e.g.

comes from the nodes in hidden layer  or layer of the network which learns to respond to features found in input   patte pattern. rn. The featur features es recogn recognize ized d or  extracted by the hidden units ( nodes) corr corres espo pond nd to the the

corr correl elat atio ion n

of 

activity among different input units. As the the netw networ ork k is trai rained ned wit with differ different ent exampl examples, es, the networ network k has the ability to generalize over similar  featur features es found found in differ different ent patter patterns. ns. The The

hidd hidden en uni unit

(node nodes) s)mu musst be

trained to extract a sufficient set of  genera eral

feat eatures

appl pplicab cable

to

Error Backpropagation:-

The back propagation (or backup) algorithm is a generalization of the

Widrow Hoff error correction rule. In the Widrow-Hoff technique an error  which is the difference difference between between what the output is and what it is supposed to be is form formed ed and and the the syna synapt ptic ic strength is changed in proportion to erro errorr time timess the the input nput sign signal al in a direction which reduces the error. The direction of change in weights is such that hat the erro errorr will will redu reduce ce in the direction of the gradient (the direction of most rapid change of the error). This type of learning is also called gradient

search. In

the

case

of 

multil multilaye ayerr networ networks, ks, the proble problem m is

2.1.4 The Application of ANN to STLF & Results:-

much more difficult.

The The

Choice of activation function

The

most

common

mult multil ilay ayer er

activat vation

function used in multilayer perceptron is the sigmoid. The equation of the sigmoid function is

ANNS ANNSTL TLF F feed feed

impl implem ement entss

forw forwar ard d

neur neural al

network which was trained by using   backpropagation training algorithm.  Naturally 24 hours data points leads to 24 input nodes in MLP model. Here 2 hidden layers are considered. MSEB data for the period Oct 94 to June

95

i.e

of 35

weeks

for  

The back propagation algorithm for 

development and implantation of the

network

software was utilized.

using

the

sigmoid

88

activation function is described below .The equation of sigmoid function is Written as

safe safe operat operation ion of electr electrica icall energy energy networ networks. ks. During During the steady steady state state study of an electrical network any one of the possib possible le conting contingenci encies es can have either no effect, or serious effect, or even fatal results for the The algorithm

Backpropagation with

MLP

model

of 

netw networ ork k safe safety ty,, depe depend ndin ing g on a given network operating state.

Arti Artifi fici cial al Neura Neurall Netw Networ ork k (A") (A") is

Load flow analysis can be used

develo developed ped for the proble problem m of short short

as a crisp technique for contingency

Term Load Forecasting (STLF) with

risk

a lead time of at least 24 hours. The

 performing at run time the necessary

 best performance was obtained for the

load oad flow flow anal analy ysis sis stud studiies is a

load load fore foreca cast stin ing g for for the the Tues Tuesda day y

tedious

which

and

operation. operation. An alternative alternative solution is

averag averagee percent percentage age error error of 2.00% 2.00%

the off-line training and the run-time

and 0.20% respectivel respectively. y. This comes

appl appliicat cation

very close to the precision obtained

net networ works. ks.

 by the human forecaster. The turning

describing how artificial neural

of

terms

networks can be used to bypass the

selection of the weights and threshold

traditional load flow cycle, resulting

values play key role in convergence

in significan significantly tly faster faster computation computation

of the network. High values of the

times

weight weightss lead lead to the diverg divergence ence and

anal analys ysis is.. A disc discus ussi sion on over over the the

generally generally small values of the order of 

efficiency

10-2 the yield better results.

techniques is also included.

App2: Power System Contingency

2.2.1 .2.1 What is

Analysis

power system?

gives

the

gain,

the

maxi aximum

momentum

assessment.

and

for

However  

time

of This his

art artifi ificial cial art articl icle

onl online

of

consuming

neur neural al aim aims

at

cont ontinge ngency

the

proposed

conti ntinge ngency in

system contingency is defined Cont Contin inge genc ncy y anal analys ysis is and and risk  risk  assessment are important tasks for the

as a disturbance that can occur in the network and can result in possible

loss loss of part partss of the the netw networ ork k like like

on all operating points found in the

  buses, buses, lines, lines, transforme transformers, rs, or power 

data databa base se and and then then a powe powerr flow flow

unit unitss in any any of the the netw networ ork k area areas. s.

solution

Load Load flow flow analysi analysiss

network. According to the results of 

is an adequ adequate ate

is

  pos possi sibl blee cont contin inge genc ncy y on a give given n

contingency applied of the specific

operating point of the network. It is

oper operat atin ing g point point can can be rank ranked ed as

oft often

“innocent”,

that hat

expe experrienc ienced ed

solution

the

the

case case

flow

on

ans ans for for stud study ying the the eff effect ect of a

the

power

attempted

“violating”,

the

or 

engineers, involved in operation of a

“div “diver ergi ging ng / seri seriou ous” s”.. The The prepre-

given given system system,, can guess guess effect effective ively ly

contingency

operating

point

contingency contingency without without the the support support of   parameters, various operating point numerical

comp omputa utations.

This

indices and metrics, the contingency

intuition of the operators is useful in

and the power flow result are next

suppor supportin ting g the initia initiall select selection ion of a

stored stored in a table table per conting contingenc ency. y.

list of possible contingencies, which

This contingency table constitutes a

then hen wil will be anal analy ysed sed using sing the

set of features and tuples that can be

described here technique.

considere ered

as

suit uitable ble

neura ural

network input layer data elements if  2.2.2. System Architecture

sele select cted ed in any any comb combin inat atio ion n and

A suitable way of studying the effects

after being statistic statistically ally normalized. normalized.

of cont contin inge genc ncie iess on an elec electr tric ical al

The power flow solution classifying

network is through the definition of 

any contin contingenc gency y for any operat operating ing

repr repres esen enta tati tive ve

 point, is the output layer value of the

oper operat atin ing g

poin points ts,,

creati creation on of a releva relevant nt data data base, base, in

neural network.

which which parame parameter terss relati relating ng to these these oper operat atin ing g poin points ts is stor stored ed as thes thesee

  Neu Neura rall netw networ ork k trai traini ning ng is a

have been measured directly through

computer computer intensive intensive work that needs,

network snapshots. Once a number of 

however, to be done only once. As

operating points is simulated, a list of 

soon as the neural network is trained

contin contingenc gencies ies to be studie studied d upon is

for a contin contingenc gency, y, the predic predicti tions ons

formed. Each contingency is applied

about the effects of a contingency on

any any oper operat atin ing g poin pointt can can easi easily ly be

cumu cumullativ ativee

deduce uced.

genera generati tion, on, reacti reactive ve load, load, reacti reactive ve

The

  pre predi dict ctiions ons

efficiency

depe depend ndss

of

on

the

vari variou ouss

act active

load, oad,

act active

genera generati tion, on, appare apparent nt power power etc. etc. In

fact factor orss such such as the the qual qualit ity y and and the the

recent

quantity of the training features, the

reference nces

type, complexity and connectivity of 

aggregates aggregates that yield better better results results

the neural network.

when when appli applied ed,, such such as the the acti active ve

2.2.4 Feature

Neural

Network

Input Selection

bibliogr ography phy in

apparent

ther here

more ore

power

are

elabo aborate

margin

index

(expr (expres esse sed d as the the frac fracti tion on of the the flowing flowing aggregate aggregate apparent apparent power, over

the

agg aggrega egate

MVA

line

transmission limits) and the voltage stability index. The voltage stability index

is

computed

as

“the

sens sensit itiv ivit itie iess of the the tota totall reac reacti tive ve   pow power er gene genera rattion to

a

  pow power er

know known n

cons consum umpt ptiion, on,

‘reactive

power

reac reacttive ive as

dispatch

coefficients’ ”.

  Neu Neura rall

net networ works

can can

be

trai traine ned d with with any any numbe numberr of input input features.

The

neura ural

trai traini ning ng

proc proces esss

can can

network  ork  sele select ctiv ivel ely y

overweight the most salient features A wide wide range range of electr electrica icall networ network  k   parameters can be used for describing the network state. Some of them can  be the network load level expressed as a perc percen enttage age of the maxi maxima mall network load, the number of lines, the cumu cumula lati tive ve rati rating ng of all all lines lines,, the the

and underweight the least significant ones.

However, er,

the

selection

 procedure is time consuming for the training of the neural network, while after the training is complete, it is not not alwa always ys obvi obviou ouss whic which h of the the

input nodes are of greater importance. Furt Further her more more,, the the leas leastt impo import rtan antt input layer nodes may add noise to the neural network network training training process. Bearing this in mind, a pre-selection of the neural network input nodes is of grea greatt use. use. This This can can be achie achieved ved through the use of statistical methods. The statistical methods that apply in the the proc proced edur uree of the the sele select ctio ion n of  features are used in the classification theory. The classification of a set of  training examples by two features in two classes is considered to be better  when when

the the

sub-p ub-pop opul ulat atiions ons

look  look 

different. the simplest test proposed is the the test test of sepa separa rati ting ng two two clas classe sess usi using just ust the the mean means. s. A featu eaturre selection

test

from

Means

where M1 and M2 are the vectors of  feature means for class 1 and class 2, C1 -1 and C2 -1 are the inverse of  the covariance matrix for class 1 and class 2 respectively. For reasons of  simplicity, a combination of bus and line losses only has been considered as

a

constituent

element

of

a

contingency under study. The four  most salient features found were the aggregate reactive power generation, the the

volt voltag agee

stab stabil ilit ity y

inde index, x, the the

aggregate aggregate MVA power flow and the real power margin index. This set of  selected features has been used for  the training and testing of the neural networks subsequently built.

and

Variances is also proposed:

2.2.5 Quality index

The The qual qualit ity y inde index x is a qual qualit itat ativ ivee measure of the classification power  of the neural network. It is an index A and B are of the same feature

that that has has been been calc calcul ulat ated ed for for all all

measured for the classes 1 and 2 n1

simulations and applies on the idea

and n2 are the corresponding number 

that that with within in the the thre threee clas classe sess of 

of cases sig is a significance level. In

cont contiingen ngency cy

[4] the following measure for filtering

diff differ eren ence ce can can be cons consid ider ered ed to

features separating two classes is also

occur

 proposed:

categor gories

of

con contingencies:

“inn “innoc ocen ent” t”

and and

“non “non-i -inn nnoc ocen ent” t”

stat states es,,

between

the

two

major  ajor 

possible

contin contingenc gencies ies.. In order order to comput computee

comput computati ationa onall time time and recour recourses ses

this

requirements.

“quality

index”

(QA)

the

following formula has been used: 2.5.6 Result

Seven ANNs have been trained for  predicting where ai,j is the I-th element of the jth colu column mn of the the conf confus usio ion n matr matrix ix Ai,j. Ai,j. The The conf confus usio ion n matr matrix ix Ai,j Ai,j is a matr atrix

of freq freque uenc ncie iess.

For each each

element element of the matrix matrix ai,j ai,j the i index index refers to predicted values, while the j index refers to real values. The values range from one to three denoting the three possible contingency cases: one in

case

of

nonconvergence

the

severity

of  

contingencies for the network of the islan sland d of Cret Crete, e, the tes testing ting set  performance of these ANNs was in the range of 57% to 96% 96%, this   per perfo form rman ance ce did did not not seem seem to be affe affect cted ed by the the spli splitt betw betwee een n the the trai traini ning ng and and test testin ing g case cases, s, as for  for    both a 70-30 and a 85-15 split the results were simillar.

/

  potentiall potentially y serious serious contingency contingency,, two in

case

of

MVA

and

voltage

viol violat atio ions ns and and thre threee in case case of an innocent contingency. This This techni technique que is involv involves es a tedious training phase, where a set of  neural

networks

is

created,

corr corres espo pond ndiing to a give given n set set of   possible contingencies. The resulting set of ANNs demonstrate satisfactory   predi predicti ctive ve power power in classi classify fying ing the contin contingenc gencies ies correc correctly tly at run time. time. The The run run time time perf perfor orma manc ncee of the the sys system tem is very very good good in terms erms of 

while sensitivity analysis in terms of  the ANN architecture demonstrated that that the the numb number er of hidde hidden n nodes nodes seem to have a serious effect on the performance

of

the

network ork,

sugg sugges esti ting ng use use of more more comp comple lex x ANNs.

The promis promising ing resul results ts of this this study study

Applications,” Proceedings of the

suggest

IEEE, October 1990.

appli plication

of

similar 

techniques in other areas of security

D.C. Park, et al., “Electric Load

asse assess ssme ment nt of powe powerr syst system emss and and

Forecasting Using an artificial

other industrial processes.

 Neural Network,” IEEE Transactions on Power Systems,

4. BIBILIOGRAPHY:

 Neural networks

1.Patrick K. Simpson, Artificial  Neural Systems, Pergamon Press, Elmsford, N. Y., 1990.

Volume 6, Number 2,May 1991,  pages 442-449.

5.Load Forecasting by ANN-IEEE computer applications in power  systems. Duane D. Highley" and Theodore J. Hilmes "

2.”Special Issue on Neural Networks I: Theory and Modeling.”

Contingency analysis:

Proceedings of the IEEE, September  1990.

6.Mitchell T. M., Machine Learning, McGraw-Hill

Load forecasting

Series in Computer Science, 1997,  p.81

3.Jacques de Villiers and Etienne Barnard, ”Backpropagation Neural  Nets with One and Two Hidden Layers,” IEEE Transactions on  Neural Netcuorks, Volume 4, January 1993, pages 13G144.

7 Grainger J. J., W D. Stevenson, Jr., Power System Analysis, McGraw-Hill, 1994, chap. 9 8 Wehenkel L.A., Automatic Learning Techniques in Power Systems, Kluwer Academic

4.“Special Issue on Neural Networks 11: Analysis, Techniques, and

Publ., 1998, (p. 210)

3. Keywords:

Artificial neural networks, contingency analysis, load forecasting, applications of ANN in power system, Artificial intelligence training and testing.

Document By SANTOSH BHARADWAJ REDDY Email: [email protected]

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