Kothari D.P., Nagrath I.J. Modern Power Systems Analysis

The

solution

for

a

new

set

of

values

for

b

can

be

easily

obtained

by using

a

table

of

factors

prepared

by

a

careful

examination

of

eqs.

1c-l)

to

(c-g).

we

can

write

the

table

of

factors

F

as

below

for

the

example

in

hand.

fn

fzt

The

row

elements

of

F

below

the

diagonal

are

the

multipliers

of

the

normalized

rows

required

for

the

elimination

of

the

row

element,

e.g.

fzz

=

*,

the

multiplier

of

normalized

row

2

l&q.

(c-6)l

to

eliminate

the

element

(3,2),

i'e-

(])x2.

The

diagonal

elements

of F

are

the

mulripliers

needed

to normalize

the

rows

after

the

row

elimination

has

been

completed,

e.g.

.fzz

=

!

,

the

factor

by

which

tow

2

of

Eq.

(C-4)

must

be

multiplied

to

normalize

the

row.

The

elements

of

F

above

the

diagonal

can

be

immecliately

written

down

by

inspection

of

Eq.

(C-8).

These

are

needed

for

the

back

substitution

process.

In rapidly

solving

Eq.

(C-1)

by

use

of the

table

of

factors

F,

succesiive

steps

appear

as

columns (left

to

right)

in

Table

C.l

below:

Table

C.l

-

5

-

(;X;):i

and

for heading

3, 3

lt

=

fszlz

=

(+x+)

=

I

In fact,

operation

(C-10)

represents

row

normalization

and

(C-11)

represents

elimination

and back substitution

procedures.

Optimal

Ordering

In

power

system

studies, the matrix

A

is

quite

sparse

so that the

number

of

non-

zero

operations and

non-zero storage

required

in

Gauss

elimination

is

very

sensitive to

the sequence in

which the

rows

are

processed.

The row

sequence

that leads

to the least number

of non-zero

operations is

not, in

general,

the

same

as the

one which

yields

least

storage requirement.

It

is believed

that

the

absolute

optimum sequence

of

ordering

the rows

of a

large network

matrix

(this

is equivalent

to renumbering

of buses)

is

too complicated

and

time

consuming

to be of any

practical

value.

Therefore,

some

simple

yet

effective

schemes

have

been evolved

to achieve

near optimal

ordering

with

respect

to

both the

criteria.

Some of the

schemes of near

optimal

ordering

the

sparse

matrices,

which are

fully symmetrical

or

at least

symmetric

in the

pattern

of

non-zero

off-diagonal

terms, are

described

below

[4].

Scheme I

Number the matrix

rows in

the order

of

the fewest

non-zero

terms

in each

row.

If more

than

one unnumbered

row

has

the same

number

of non-zero

terms.

number these in

anv order.

Scheme

2

Number the rows

in the

order

of the fewest

non-zero

terms

in a

row

at each

step

of elimination. This

scheme

requires updating

the

count

of non-zero

terms

after

each step.

Scheme 3

Number the rows

in

order of the fewest

non-zero

off-diagonal

terms generated

in the renraining

rows

at each step

of elimination.

This

scheme

also

involves

an

updating

procedure.

I he chotce

ot scheme

ts a

trade-otf

between

speed

of

execution

and

the

number

of times the result

is to be

used.

For

Newton's

method

of load

flow

solution, scheme 2

seems to be the

best.

The

efficiency

of

scheme

3 is not

sufficiently established

to offset the

increased

time

required

for its

execution.

ft,

ftz

fu

fzz

32

rl3

').ra

L

nll

LTT

(c-e)

1,3

5/2

I

x

I

1

The

heading

row

(i,

j)

of

Table

C-1

represents

the

successive

elimination

and

back

substitution

steps.

Thus,

represents

normalization

of

row

1

represents

elimination

of

element (2,

l)

h

6

9

t4

l,

I

3

9

T4

2,

1

2,2

3, I

3,2

3333

3

3t2

3/2

3t2

14

t4

5

5t4

1,2

aa

3

3t)

1

2,3

a

J

3

1

7,7

2,L

2,2

represents

nonnalization

of

row

2

3,

L;

3,2

represent

elimination

of

elements (3,

1)

an,J

(3,2)

respectively

3.

3

represents

normalization

of

row

3

2,3

represents

elimination

of element

(2,3)

by

back

substitution

r,

3;

7,

2

reprelent

elimination

of

elements (1,

3)

and

(r,

z)

respectively

by

back

substitution.

The

solution

vector

at any

stage

of

development

is

denoted

by

Ut

lz

y3Jr

=

y

The

modification

of

solution

vector

fiom

column

to

column (left

to right)

is

carried

out

for

the

headin g

(i,

j)

as per

the

operations

defined

below:

!i=

fiiji

ttj=i

(c-

10)

(c-11)

!i=

!r-

fi/i

lt

i

+ i

Thus

for

heading

3,

z

lt= lt- fn)z

Mffi#

Modern

po

t-

Scheme I is useful for

problems

requiring

only a single solution with

nq

iteration.

Compact Storage

Schemes

The usefulness of

the Newton's method

depends largely upon conserving

computer storage

ucmg the nu

oI non-zero computatlons.'l'o ettect

these ideas on the computer,

elimination

of

lower

triangle elements is carried

out a row at a time using

the concept

of compact working row. The non-zero

modified upper triangle

elements and

mismatches are stored in a compact and

convenient

way.

Back substitution

progresses

backwards

through

the compact

upper

triangle

table. A

properly

programmed

compact storage scheme results

in

considerable saving

of

computer

time during matrix

operations.

Naturally, there are as many compact working

rows

and upper triangle

storage

schemes as there are

programmers.

One

possible

scheme

for a

general

matrix stores the non-zero

elements of successive rows in a linear array. The

column

location

of these non-zero elements and the location

where

the

starts

(row

index)

is

stored

separately. The details of this and

various

other

schemes

are

given

in

[2].

REFERE

N CES

Singh, L.P., Advanced Power

System Analysis and Dynamics, 2nd edn., Wiley

Eastern, New Delhi, 1986.

Agarwal, S.K.,

'Optimal

Power Flow Studies', Ph.D. Thesi.r, B.I.T.S.r

Pilani,

r970.

Tinney,

W.F. and J.W. Walker,

"Direct

Solutions

of

Sparse

Network Equations by

Optintally Ordered

Triangular Factorizations", Proc.

IEEE,

Nov. 1967,.55:

1801.

Tinney,

W.F.

and C.E. Hart,

"Power

Flow Solution by Newton's Method",

IEEE

Trans., Nov. 1967, No. ll, PAS-86: 1449.

AppBNDrx

I)

Expressions to

be

used in evaluating

the elements

of

the

Jacobian

matrix

of

a

power

system are derived below:

From Eq.

(6.25b)

fr*rr

k:r

A\

exp

(-

i6,)L

lY,/ exp

(i?il

lVll exp

(7dn)

(D-l)

k:r

Differentiating

partially

with respect

to

6*

(m

*

i)

+-

i+

=

Tvil

exp

(-r4) (Yi^l

exp

Q0,^)

tv^t exp

(j5^))

06^

-

a6^

P,

-

jiQ,=

t',

l.

=

lvil

3.

4.

--

j(ei

-

jf)

(a^

+

jb^)

(D-2)

where

Y,^= G,*

+

jB,^

Vi= €i+

jfi '

(a^

*

jb*)

=

(c*

*

jBi)

@^

+

jf^)

Although the

polar

form

of the NR

method is

being

used,

rectangular

complex arithmetic is employed

for numerical

evaluation

as it is

faster.

From Eq.

(D-2),

we

can

write

#=(aJi-b^e)=Hi^

#=

-

(a^ei+

b,f,)=

Ji^

tvrOtlcIt

I rOWgf

For

the

case

of

m

=

i.

we have

*

-i*

=

-

jtvitexp

(-

j6,)i

ty,ni exp

(j4)

tV1,t exp

Qfi)

06,

"

06,

k:l

+

jlV,l

exp

(-

j6

)

(tytil

exp

Q?,,)tV;t

exp

(id))

lr'

q-""

I f.lr.$

=

l%l

exp

(-

j6,)ilY,pl

exp

(i0*)

lvpl

exp

(7d')

k:l

+ lV,lzlY,,l exp

(7d,,)

=

\Ft-

lQ)

+

it*

(D-s)

=

-

j(Pi

-

jQ)

+

jlV,l'(G,,

+

jB,,)

From

Eq.

(D.3),

we

can write

(D-3)

#

=

-

Qli-

Bii

lv;12

=

H"

ao.

;t

=

Pi-

G'itvil2

=

J'

Now

differentiate

Eq.

(D-1)

partially

with

respect

to

lV^l

(m

r i). We

have

a4

0Q,

--

=

lvil exp

(-

j6)

(lYi*l

exp

(j0,^)

exp

Qd^))

alv)

"

alv^l

'

L

Multiplying

by

lV^l on

both

sides,

aPt

I

AO.

atv^tv^t-iffiw^t

-

lvil exp

(-

j6)

lY,^l

exp

(j1i)'tV*l

exp

(i6^)

=

(ei-

jf,)

(a^

+

jb*)

(D-4)

It

follows

from

Eq.

(D-4)

that

!!rr*t=

a^e,+

b,fi=

Ni^

a

lv^l

-!,?:

,tv^l

=

a,,fi

-

b^e,

=

L,^

alv.l

Now

for

the

case

of m

=

i. we

have

aPt

-

j-P.-

exp

e

jilf

tyat exp

(j0*)

tvet

exp

(jQ,)

alvil

"7lvil

,..

o:,

+

lV,l

exp

(-

j6)

lyi exp

Q0,,)

exp

(/4)

Multiplying

by

lV,l on

both

sides

an

Ao'

--t

lv,l-i

"",

lv,l

alvil

'

"

awil

It follows from

Eq.

(D-5)

that

oPi-

'

av,l

\v'l

=

Pt *

GiilViP

=

Nii

,et_

,=Lt

avil

lvil

=

Qi

-

Biilvil

The above results are'summattzed

below:

Case

7

Case

2

m* i

Hi^= Li*= aJ,- b*e,

Ni*=-

Ji*=

d*€i+

b"ft

Yi*=

Gt^

+

jBt*

Vi=

ei+

jfi

(a*

*

jb^)

=

(Gi^

+

jBi^)

@*

+

jk)

m= i

H,=-

Qi-

Biilvilz

Nii= P,+

G,,lV,lz

Jii

-

Pi- Giilvr

Lii=

Qr-

Biilvilz

(D-6)

(D-7)

(D-8)

REFERE

N CES

Tinney, W.F. and

C.E. Hart "Power

Flow Solution by

Newton's

Method",

IEEE

Trans., Nov 1967, No. 11, PAS-86: 1449.

Van

Ness, J.E., "Iteration Methods for Digital Load

Flow

Studies", Trans.

AIEE,

Aug

1959,

78A:

583.

AppBNDrx

E

The

Kuhn-Tucker

theorem makes it

possible

to

solve

the

general

non-linear

programming problem

with

several variables wherein

the

variables

are also

constrained

to satisfy certain

equality and

inequality constraints.

We can state

the minimization

problem

with inequality

constraints

for the

control

variables as

nln

/

(x'

u)

subject to equality

constraints

g(x,u,P)=o

and

to the inequality constraints

u-u^u1

0

u^1-- u

<

0

The

Kuhn-Tucker

theorem

[]

gives

the necessary conditions

for the minimum,

assuming

convexity

for the functions

(E-1)-(E-4),

as

A.C

=

0

(gradient

with respect to u, x, ))

(E-5)

where .C

is the

Lagrangian formed as

-C=f(x,

u)+

)Tg(x,u,p)+

of*u*{,

-u^u*)+

oT*,n1r-in-z)

and

(E-6)

(E-7)

Equations

(E-7)

are known

as exclusion equations.

The multipliers

a,rr*

and @,rri,, ?re

the

dual variables

associated

with the

upper and lower limits on control

variables. They are auxiliary

variables

similar

to

the

Lagrangian multipliers ) for the equality constraints

case.

If z,

violares

a limit,

it can either

be upper or

lower limit and

not both

simultaneously.

Thus,

either

inequality

constraint

(E-3)

or

(E-4)

is active

at

a

time,

that is, either

ei.^^ of

oi.min

exists, but

never both.

Equation

(E-5)

can

be

written as

AL

0x

Ax

\*o-0

(E-e)

In Eq.

(E-9),

oL

=

0f

+rq)'

du

0u

'\aul

It

is evident

that

a computed

from

Eq.

(E-9)

at any

feasible solution,

with

)

from

Eq.

(E-8)

is identical

with

negative

gradient,

i.e.

di= Qi.^u*

tf Ui- ui,*o

) 0

ai=

-

Ai,-io

if ,r,

,t,

-

ui

)

0

aL,.

#=g(x,u,p)=o

OA

d

=

-

K

=

negative

of

gradient with respect to u

if ur,

,n;o

< ui < ui,

^

tf u,=

ui,^*

tf u,

-

ili,

^in

(E-10)

(E-11)

(E-12)

(E-l)

(E-2)

(E-3)

(E-4)

At

the optimum,

state

that

a must

also satisfy

the exclusion

equations

(E-7),

which

,\

ff ,i,

,rt,

<

ui

< ui,

,n"*

lf

u,

=

ui,

,iru*

Qi=-

Q,rnin

S

0

lf ui=

4i,

*in

which

can be

rewritten

in

ternts of

the

gradient

using Eq.

(E-11)

as

follows:

ox

=o

0u,

of,.o

0u,

of,

ro

out

REFERE

N CE

1. Kuhn,

H.W.

and A.W.

Tucker,

"Nonlinear

Programming", Proceedings

of the

Second.Berkeley

Symposium

on Mathematical

Statistics

and

Probability, Univer-

sity of California

Press,

Berkeley,

1951.

di= 0

di=

di,

-*

2

0

AppnNDrx

F

In

developed

countries

the

focus

is shifting

in

the

power

sector

from

the creation

of

additional

capacity

to

better

capacity

utilization

through

more

effective

management

and

efficient

technology.

This

applies

equally

to

developing

countries

where

this

focus

will

result

in

reduction

in

need

for

capacity

addition.

Immediate

and

near

future priorities

now

are

better plant

management,

higher

availability,

improved

load

management,

reduced

transmission

losses,

revamps

of

distribution

system,

improved

billing

and

collection,

energy

efficiency,

energy

audit

and

energy

management.

All

this

would

enable

an

electric

power

system

to

generate,

transmit

and

distribute

electric

energy

at the

lowest

possible

economic

and

ecological

cost.

These

objectives

can

only

be met

by use

of information

technology

(IT)

enabled

services

in

power

systems

management

and

control.

Emphasis

is

therefore,

being

laid

on computer

control

and

information

transmission

and

exchange.

The

operations

involved

in

power

systems

require

geographically

dispersed

and

functionally

complex

monitoring

and

control

system.

The

monitory

and

supervisory

control

that

is

constantly

developing

and

undergoing

improvement

in

its

control

capability

is

schematically

presented

in

Fig. F.1

which

is easily

seen

to

be

distributed

in

nature.

Starting

from

the

top,

control

system

functions

EMS

Energy

Management

System

-

It exercises

overall

control

over

the

total

system.

scADA

Supervisory

control

and

Data

Acquisition

system

-

It

covers

generation

anci

transmission

system.

DAC

Distribution

Automation

and

Control

System

-

It

oversees

the

distribution

system

including

connected

loads.

Automation,

monitoring

and

real-time

control

have

always

been

a

part

of

scADA

system.

with

enhanced

emphasis

on

IT in power

systems,

scADA

has

been

receiving

a lot

of attention

lately.

Fig.

F.l

Real time

monitoring

and

controlling

of

an

electric

power

system.

SCADA

refers

to

a system

that

enables

an

electricity

utitity

ro remotely

monitor,

coordinate,

control

and

operate

transmission

and

distribution

compo-

nents,

equipment

and

devices

in

a real-time

mode

from

a remote

location

with

acquisition

of

data

for analysis

and

planning

from one

con[ol

location.

Thus,

the

purpose

of

SCADA

is to

allow

operators

to

observe

and

control

the

power

system.

The

specific

tasks

of

SCADA

are:

o

Data

acquisition,

which provides

measurements

and

status

information

to

operators.

.

Trending plots

and

measurements

on

selected

time

scales.

.

Supervisory

control,

which

enables

operators

to

remotely

co:rtrcl

devices

such

as

circuit

breakers

and

relays.

Capability

of SCADA

system

is

to

allow

operators

ro

control

circuit

breakers

ancl

disconnect switches

and

change

transformer

taps

and

phase-shifter

position

remotely.

It

also

allows

operators

to

monitor

the generation

and

high-voltage

transmission

systems

and

to take

action

to

ccrrect

overloads

or

out-of-limit

voltages.

It monitors

all

status points

such

as

switchgear

position

(open

or

closed),

substation

loads

and voltages,

capacitor

banks,

tie-line

flows

and

interchange

schedules.

It

detects

through

telemetry

the

failures

and

errors

in

bilateral

communication

links

between

the

digital

computer

and

the

remote

equipment.

The most

critical

functions,

mentioned

above,

are

scanned

every few

seconds.

Other

noncritical

operations,

such

as

the

recording

of

the load,

foiecasting

of

load,

unit

start-ups

and

shut-downs

are

carried

out

on

an hourlv

basis.

Most low-priority

programs

(those

run

less

frequently)

may

be

executed

on

demand

by the

operator

for

study purposes

or to

initialize

thepower

system.

An

operator

may

also

change

the

digital

computer

code

in

the

execution

if

a

parameter

changes

in

the system.

For

example,

the

MWmin

capability

of

a

generating

unit

may

change

if

one

of its

throttle

values

is

temporarily

removed

for

maintenance,

so the unit's

share

of

regulating power

must

accordingly

be

decreased

by the

code.

The

computer

software

compilers

and

data

handlers

are

designed

to

be versatile

and readily

accept

operator

inputs.

DAC

is

a lower

level

version

of SCADA

applicable

in

distribution

system

(including

loads),

which

of

course

draws

power

from

the transmission/

subtransmission

levels.

Obviously

then

there

is no

clear

cut

demarcation

between

DAC

and

SCADA.

In a

distribution

network,

computerisation

can

help

manage

load,

maintain

quality,

detect

theft

and

tampering

and thus

reduce

system

losses.

Cornputeri-

sation

also

helps in

centralisation

of data collection.

At a

central

load dispatch

'centre,

data

such

as

culTent,

voltage,

power

factor and

breaker

status

are

telemetered

and

displayed.

This

gives

the operator

an

overall

view

of the

entire

distribution

network.

This

enables

him

to have

effective

control

on the

entire

network

and

issue

instructions

for

optimising

flow in

the event

of

feeder

overload

or voltage

deviation.

This is carried

out through

switching

inlout

of

shunt

capacitors,

synchronous

condensers

and load

management.

This

would

help

in achieving

better

voltage

profile,

loss

reduction,

improved

reliability,

quick

detection

of fault

and restoration

of service.

At a

systems

level,

SCADA

can

provide

status

and

measurements

for

distribution

feeders

at

the substation.

Dictribution

automation

equipment

can

monitor

selectionalising

devices

like switches,

intemrpters

and

fuses. It

can also

operate

switches

for

circuit reconfuration,

control

voltage,

read

customers'

meters,

implement

time-of-day

pricing

and

switch

customer

equipment

to

manage

load.

This

equipment

significantly

improves

the functionality

of

distribution

control

centres.

SCADA

can

be used

extensively

fbr

compilation

of extensive

data and

management

of distribution

systems.

Pilferage points

too can

be zeroed

in

on,

as

the flow

of

power

can be closely

scrutinised.

Here again,

trippings

due

to

human

effors can

be avoided.

Modern

metering

systems

using electronic

meters,

automatic

meter

readers

(AMRs),

remote

meteripg

and

spot

billing

can

go

a

long

way

in helping

electric

utility. These

systbms

can

bring in

additional

revenues

and also

reduce

the time

lag

between

billing and

collection.

Distribution

automation

through

SCADA

systems directly

leads to increased

reliability

of power

for

consumers

and lower

operating

costs

for the

utility. It

results

in

fbrecasting

accurarte

clenrand

and supply

management,

taster

restora-

tion

of

power

in

case of

a tailure

and ahernative

routing

of

power

in

an

emergency,

A kt'y l'cilturcl

rll'thcstr

$ystcllls

is

lhc rurlolcl

contnrl

lircility

llrlt lllows lnstcr

execution

of

decisions.

Manual

errors

and oversights

are eliminated.

Besides

on

line

and

rcal-time

inlbnnution,

the

systenr

provides

periodic

reports

that help

in

the

analysis

of

performance

of

the

power

system.

Distributi'on

automation

combines

distribution

network

monitoring functions

with

geographical

mapping,

f^.-fe l^^-r.l^-^ --l r 1 t |

!t',

t.'

rilur!

luL;aLtuil,

ailu

su

un, 1.() tmprove

availaDtlty.

tr

aISo

lntegrates

load

management,

load

despatch

and

intelligent

metering.

Data

Acquisition

Systems

and Man-Machine

Interface

The

use

of computers

nowadays

encompasses

all

phases

of

power

system

operation:

planning,

forecasting,

scheduling,

security

assessment,

and control.

I

An energy

control centre manages

these

tasks

and

provides

optimal

operation

of the

system.

A typical control

centre

can

perform

the

following

functions:

(i)

Short,

medium

and

long-term

load

forecasting

(LF)

(ii)

System

planning

(SP)

(iii)

Unit commitment

(UC)

and maintenance

scheduling (MS)

(v)

State

estimation

(SE)

(vi)

Economic

dispatch

(ED)

(vii)

Load

frequency

control

(LFC)

The

above monitoring

and

control

functions

are

performed

in

the hierarchical

order

classified according

to

time scales.

The

functions perfotmed

in the

control

centre

are based

on

the

availability

of

a large

information

base and

require

extensive

software

for

data acquisition

and

processing.

At the

generation

level,

the

philosophy

of

'distributed

conffol'

has

dramatically

reduced

the cabling

cost

within

a

plant

and

has the

potential

of

replacing

traditional

control

rooms

with

distributed

CRT/keyboard

stations.

Data

acquisition

systems

provide

a supporting

role to

the

application

software

in a control

centre.

The

data acquisition

system

(DAS)

collects

raw

data from

selected

points

in

the

power

system

and converts

these

data into

engineering

units.

The data

are checked

for limit

violations

and

status

changes

and

are

sent to the data

base for

processing

by

the

application

software.

The

real-time

data base provides

structured

information

so

that application

programs

needing

the information

have

direct

and efficient

access

to

it.

,

The

Man-Machine

interface provides

a link

between

the

operator

and

the

software/lrardware

used to control/monitor

the

power

system.

The

interface

generally

is a colour

graphic

display

system.

The

control processors

interface

with the

control interface

of the

display

system.

The

DAS

and

Man-Machine

interface

support the following

functions:

(i)

Load/Generation

Dispatching

(ii)

Display

and

CRT control

(iii)

Datt Base

Maintcnancc

(iv)

Alarrn

Handling

(v)

Supervisory

control

(viI

l)rograrnnring

lbnctions

(vii)

DaLa

logging

(viii)

Event

logging

(ix)

Real-time Network

Analysis

With the introduction

of higher

size

generating

units,

the

monitoring

rrtzrtrirarnanf<' horra frnia rrh i- ^o.rro- *l^^+. ^l-^ I- ^-l^- a^:-.--^-.^ rL- -r--^

rvyurrvruvrrro

rrqvw

6vuw

up

ur

y\ryvvr

pr4rrLD

(rrD(J.

Ill uluttt

tu

lrrrpl'uvc

ule

Ixant

performance,

now

all the utilities

have

installed

DAS

in

their

generating

units

of sizes

200

MW and above.

The

DAS in

a thermal power

station

collects

the

following-

inputs from

various locations

in

the

plant

and

converts

thern

into

engineering'units.

l,@E+l

Modern

Po@is

I

Analog

Inputs

(i)

Pressures,

flows,

electrical

parameters,

etc.

(ii)

Analog

input

of

0-10

V

DC

(iii)

Thermocouple

inputs

(iv)

RTD

input

Digital

Inpurs:

(i)

Contract

outputs

(ii)

Valve

position,

pressure

and

limit

switches

All

these

process

inputs

are

brought

from

the

field

through

cables

to

the

terminals.

The

computer

processes

the

information

and

,uppli",

to

the

Man-

Machine

interface

to

perform

the

following

functions.

(i)

Display

on

CRT

screen

(ii)

Graphic

disptay

of

plant

sub-systems

(iii)

Data

logging

(iv)

Alarm generation

(v)

Event

logging

(vi)

Trending

of

analogue

variables

(vii)

Performance

calculation

(viii)

Generation

of

control

signals

Some

of

the

above

functions

are

briefly

discussed

as

follows.

The

DAS

software

contains

programs

to

calculate periodically

the

efficiency

of

various

equipment

like

boiler,

turbine,

generator,

condenser,

fans,

heaters,

etc.

| -^^

a aDJt,

"

power

system

engineers

who

are

adopting

the

low-cost

and

relatively

powerful

computing

devices

in implementing

their

distributed

DAS

and

control

systems.

Computer

control

brings

in powerful

algorithms

with

the

following

advan-

and

so

in raw

materials

and

modifiability, (iv)

effectiveness.

paurly

ururzauon

rn generailon,

(u)

savings

in

energy

due

to

increased

operational

efficiency,

(iii)

flexibiliiy

reduction

in

human

drudgery,

(v)

improved

operator

Intelligent

database

processors

will

become

more

cornmon

in

power

systems

since

the search,

retrieval

and

updating

activity

can

be

speeded

up.

New

functional

concepts

from

the

field

of

Artificial

Intelligence

(AI)

will

be

integrated

with power

system

monitoring,

automatic

restoration

of power

networks,

and

real-time

control.

Personal

computers'(PCs)

are

being

used

in

a

wide

range

of power

system

operations

including

power

station

control,

loacl

management,

SCAOe

systems,

protection,

operator

training,

maintenance

functions,

administrative

data

processing,

generator

excitation

control

and

control

of

distribution

networks.

IT

enabled

systems

thus

not

only

monitor

and

control

the grid,

but

also

improve

operational

efficiencies

and play

a key part

in

maintaining

the

security

of

the

power

system.

RFFERE N

CES

I.

Power

Line

Maga7ine,yol.7,

No.

l,

October

2002,

pp

65_71.

2.

A.K'

Mahalanabis,

D.P.

Kothari

and

S.I.

Ahson,

Computer

Aided

power

System

Analysis

and

Control,

TMH,

New

Delhi,

199g.

3. IEEE

Tutorial

course,

Fundamentals

of

supervisory

control

system,

l9gr.

4.

IEEE

Tutorial

course,

Energy

control

centre

Design,

19g3.

AppBNDrx

G

MATLAB

has been

developed by

MathWorks

Inc. It is

a

powerful

software

package

used

for

high

performance

scientific

numerical

computation, data

analysis

and visualization.

MATLAB

stands

for

MATrix LABoratory.

The

combination

of analysis

capabilities,

flexibility,

reliability

and

powerful

graphics

makes

MATLAB

the main

software

package

for

power

system

engineers.

This is

because unlike

other

programming

languages

where

you

have

to declare

rnatrices

and operate

on them

with their

indices, MATLAB provides

matrix

as one of the

basic elements.

It

provides

basic operations,

as we will see

later,like

addition,

subtraction,

multiplication

by use of simple

mathematical

operators.

Also, we

need not

declare the

type and size

of any variable in

advance.

It is dynamically

decided

depending

on what value

we assign

to it. But

MATLAB

is

case sensitive

and so

we have

to be careful about

the case of

variables

while

using them in

our

prograrns.

MATLAB

gives

an interactive

environment

with

hundreds of reliable

and

accurate

builrin

functions.

These

functions

help in

providing

the

solutions to a

variety

of mathematical problems

including

matrix algebra,

linear systems,

differential

equations,

optimization,

non-linear

systems and many

other types

of

scientific

and

technical computations.

The

most important

feature of

MATLAB

is

its

programming

capability,

which supports

both

types of

programming-

object

oriented

and structured

programming

and is very easy

to learn

and use

and allows

user

developed functions.

It facilitates

access to FORTRAN

and

C

codes

by means

of external

interfaces.

There

are several

optional toolboxes

for

simulating specializeel

problems

of

rJifferent

areas anrd

er-tensions

to link up

NIATLAB

and

other

programs.

SIMULINK is a

program

build

on top of

MATLAB

environment,

which

along with

its specialized products,

enhances the

power

of MATLAB

for

scientific

simulations

and visualizations.

For a detailed

description

of commands,

capabilities,

MATLAB

functions

and

many other

useful features,

the

reader

is referred to

MATLAB

lJser's

Guide/lvlanual.

F;;ff$:

You

can

start

MATLAB

by double

clicking

on

MATLAB

icon

on

your

Desktop

of

your

computer

or by

clicking

on

Start

Menu

followed

by

'programs'

and

then

ciicking

appropriate

program

group

such

as

'MATLAB

Release

12,.

you

will

visualize

a screen

shown

in Fis.

G.1.

Flg.

G.l

The

command

prompt (characterised

by

the

symbol

>>)'is

the

one after

which

you

type

the

commands.

The

main

menu

contains

the

submenus

such

as

Eile,

Edit,

Help,

etc. If you

want

to

start

a

new program

file

in

MATLAB

(denoted

by

.m

extension)

one

can

click

on

File

followed

by

new

and

select

the

desired

M'file.

This

will

open

up

a

MATLAB

File

Editor/Debugger

window

where you

can

enter

your

program

and

save

it for

later

use.

You

can

run this

program

by

typing

its

name

in

front

of command

prompt.

Let

us

now

learn

some

basic

commands.

Matrix

Initialization

A

matrix

can be

initialized

by

typing

its

name

followed

by

=

sign

and

an

opening

square

bracket

after

which

the

user

supplies

the values

and

closes

the

square

brackets.

Each

element

is separated

from

the

other

by

one

or more

spaces

or tabs.

Each

row

of matrix

is

separated

from

the

other

by

pressing

Enter

key

at

the

end

of each

row

or

by giving

semicolon

at

its

"na.

potiowing

examples

illustrate

this.

7 2

-9

-3

2

-51

The

above

operation

can

also

be

achieved

by

typing

Click

on this

to

change

the

cunent

Kothari D.P., Nagrath I.J. Modern Power Systems Analysis

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