Measurement and evaluation of instantaneous reactive ... - IEEE Xplore

IEEE Transactions on Power Delivery, Vol. 9, No.3, July 1994

1253

MEASUREMENT AND EVALUATION OF INSTANTANEOUS REACTIVE POWER USING NEURAL NETWORKS

T.W.S.Chow and Y.F.Yam

City Polytechnic of tiong Kong, Hong Kong

ABSTRACT

-

accurately.

Overall success depends on accurate, and f a s t

The e r r a t i c disturbance caused by a n electric arc f u r n a c e

convergence

requires a f a s t and a c c u r a t e V A r evaluation algorithm f o r

algorithm 161.

compensation.

This paper describes t h e development of a

novel

using

method

Networks

(ANN)

the to

approach

evaluate

of

the

Artificial

Neural

VAr.

instantaneous

Because

in

the

t h e level of

based algorithm i s capable of operating at a much lower

methods.

sampling rate and delivering a n a c c u r a t e and f a s t response

based

output.

By h a r d w a r e implementation of t h i s algorithm using

instantaneous

neuron

chips,

erratic

the

VAr

fluctuation

can

be

arc

characteristic,

Comparing t o t h e conventional methods, t h i s neural network

the

furnace

there

VAr

instantaneous

has

a

has

been

an

evaluation

highly

interest

fluctuating in

predicting

a r c f u r n a c e disturbances by using s t a t i s t i c a l

This paper describes a novel method, on

artificial

converging

neural

VAr.

a

With

real-time

networks, more

to

accurate

evaluate and

VAr

instantaneous

which i s

fast

evaluation

algorithm, t h e amount of disturbance generated by t h e arc

accurately estimated f o r compensation.

f u r n a c e can b e b e t t e r controlled and suppressed. INTRODUCTION The f i r s t p a r t of t h e paper p r e s e n t s a mathematical model The electric arc f u r n a c e hitherto s t i l l provides

t h e most

that

will be

used

in l a t e r

sections f o r t h e

analysis of

efficient way of producing alloy s t e e l s f r o m s c r a p metals.

conventional

In t h e United States alone, between 1975 and 1981, some 15

instantaneous VAr evaluation algorithm.

million

t h i s paper briefly discusses, and compares t h e limitations

tons

of

newly

installed

arc

furnace

capacity

brought t h e arc f u r n a c e s s h a r e s up t o one t h i r d of total

production

highly

arc

The

Ill.

non-linear

plant;

it

VAr caused by t h e rapid,

furnace,

generates

however,

a very

the is

a

fluctuating

large and e r r a t i c variations in

f u r n a c e c u r r e n t which i s always considered as a disturbance t o t h e electrical-supply an

unacceptable

consequence,

level

causes

network.

fluctuating

of

voltage

severe

light

reactive

fluctuation flicker

plant

s t a t i c VAr compensation system.

and

conventional methods

VAr evaluation.

real-time

and,

to

other

as

a

used

Generator

a

loads

be

capable

real-time

instantaneous

Source Inductance

responsive

I

..................................................

high speed s t a t i c V A r compensators t3-51, a n advancement in

must

novel

Q ".

Induct lve

v PCC

Arc Furnace

compensators alone cannot provide a complete solution f o r

compensator

this

The second p a r t of

approach.

Although t h e innovation in

a n e l e c t r i c arc f u r n a c e compensation.

for

of

ANN and describes t h e formation of a

power electronics technology h a s enabled t h e development of

the

development

instantaneous VAr evaluation method based on t h i s

To o p e r a t e such a

requires

the

The t h i r d p a r t of t h i s paper introduces

t h e Back-propagation

This disturbance causes

connected t o t h e same supply g r i d [21. rapidly

of

methods

A s t h e controller of of

evaluating

the

instantaneous V A r f l o w s into t h e uncompensated supply g r i d

94 WM 255-0 PWRD A paper recommended and approved by the IEEE Power System Instrumentation t Measurements Committee ofthe IEEE Power Engineering Society for presentation at the IEEE/PES 1994 Winter Meeting, New York, New York, January 30 - February 3, 1994. Manuscript submitted October 2, 1992; made available for printing December 29, 1993.

Figure I

Single phase equivalent c i r c u i t f o r a n arc furnace

ARC FURNACE MODEL An a r c f u r n a c e for

the

mathematical

investigation

0885-8977/94/$04.00 Q 1994 IEEE

of

model

i s f i r s t l y established

conventional

VAr

evaluation

.

1254 methods

and

the

later

instantaneous

VAr

evaluation

single

inductive

phase

development

load

of

an

a1gori:hm with

varying

based

ANK

In

Fig.

resistance

400

I

a

1.

fed

through a source impedance of negligible r e s i s t a n c e is used t o represent the

supply

a

typical

grid

electric The

[6].

a r c f u r n a c e connected erratic

fluctuation

of

to 0

the

0 3

0.2

0.1

f u r n a c e resistance caused by t h e melting of metal s c r a p s is Figure 2a = V

*

0.7

0.6

0.8

The system p a r a m e t e r s a r e defined as:

modelled by R L .

v

0.5

0.4

Time ( m s )

*

Variation in a r c f u r n a c e c u r r e n t with t i m e

sin(wt)

By solving t h e following differential equation diL

iLRL

V

- + -= dt

LL

LL

sin(wt)

0

0 2

0 1

03

0 5

0 4

0 6

08

07

Time ( m s )

[

"s

iL =

sin(wt-#2)

+ s i n ( $ -wt 2

e-' 1

1

Figure 2 b

Variation in

with time

v PCC

V +

2 sin(wt I - 6 1

e-A

STATEMENT OF PROBLEMS

ZL I

R L Z (t - t i )

There a r e f o u r conventional methods commonly used f o r t h e

A=-

evaluation

LL

of

VAr

The

161.

instantaneous

can

VAr

be

evaluated by A ) c u r r e n t sampling at voltage c r o s s over, B) v

pcc

= v 5

- iLXs

volt-ampere product, C) p a r a m e t e r cross product .and D) r a t e of

where v

is t h e voltage a t t h e point of common coupling, PCC

t

is t h e time a t which t h e load impedance varies f r o m Z L1

change

performance

of

parameters.

of

each

VAr

..Using evaluation

Eqtns.

(1-31, t h e

algorithms

will

be

discussed and compared.

t o Z L 2 because of t h e change in t h e a r c f u r n a c e r e s i s t a n c e from R

L1

to R

L2

.

Where Z L 1 , ZL2. 9, and #

a r e defined a s

f 01lows:

A)

Current sampling a t voltage Cross Over

The

z

output

of

corresponding

this

to

algorithm

the

inductive

a

quantised of

level

the

load

c u r r e n t given by

L1

I x = I Lm s i n ( x n - 6X ZL2=/

is

component

RL:+

(4)

+ d c component

XL2

where I

zero

i s t h e load c u r r e n t measured a t t h e x t h v PCC

c r o s s over, and I Lm is t h e peak value of t h e load c u r r e n t . To minimise t h e e f f e c t of c u r r e n t harmonics and t r a n s i e n t s , The load VAr over M cycles is

t h e average value is used. then proportional t o

Based on t h e above equations, Fig. 2 a r e t h e simulation of and load c u r r e n t

t h e variation of t h e v

i

due t o R

PCC

In

Fig.

3c.

it

varying a t pseudo-random in t h e range between 50Q t o 2502.

algorithm has a

and t h e frequency of variation ranged f r o m 2 H z t o 100 H z .

seems

to

Apparently, In

l a t e r sections of

of

d i f f e r e n t types of

this

paper,

real-time

analysis and V.4r

evaluation

will all be based on this a r c f u r n a c e model.

development algorithms

cannot

shows

that

noticeable

be

fast,

the

overall

cope

satisfactorily.

with This

it

an

the

output

delay. has

step

a

significant

response

abrupt

algorithm

response

of

this

Although t h e response

change is

not

of in

load

suitable

application of a r c f u r n a c e V A r compensation.

overshoot.

this

algorithm current for

the

1255 B) V A r evaluation by volt-ampere product The integral over one period of t h e product of voltage and

a q u a r t e r of cycle delayed c u r r e n t can be used t o evaluate t h e steady state V A r flow.

-

Q =

-

vp c c (ut) i L [ u ( t - G ) ] d ( u t )

O

(6)

-T

where T i s t h e period of supply.

This Volt-Ampere Product

algorithm can be implemented by t h e voltage and c u r r e n t samples as given by

pr

- .

QL,Pn-

where

i

'pcc,x

L,x-n/4

x=P+1

Q L , P n corresponds t o

volt-ampere

(7)

n

the

running

average of

product and n i s t h e number of

the

samples per

cycle of supply voltage.

The integral properties of t h i s algorithm h a s a n e f f e c t of reducing

t h e bandwidth

o r d e r harmonics. Fig.

3d

is

approximation

V A r flowing

fundamental

in attenuating

am

aac

ai

am

ao6

aiz

ai4

ais

ai8

Qz

higher

The output of t h i s algorithm shown in closer

a

and r e s u l t s

f

in t h e

to

the

network

steady

because of

state the

reduced bandwidth.

The output response of t h i s algorithm

i s slightly sluggish.

This may not be acceptable t o a f a s t

iI

response compensation system.

C) VAr evaluation by p a r a m e t e r c r o s s product The reactive power flow in t h e system may a l s o be evaluated by

obtaining

the

differential

cross

product

of

the

alternately delayed voltage and c u r r e n t p a r a m e t e r s as given by Q

L

1 =-(P 2

2

- P )

(8)

1

where (9)

P

1

= v

pcc

( u t ) iL[u(t

-

-I_)]

" nc=

(8)

(10)

Figure 3a & 3b 3c 3d 3e 3f

This can be represented by d i s c r e t e p a r a m e t e r samples and implemented as follows, V

pcc,x-n/4

=

1

L,x 2

- v

pcc,x

i

L.x-n/4

(11)

To implement t h i s technique as a running average and hence reduce t h e distortion

due t o isolated voltage and c u r r e n t

spikes, we have P+N

where P r e p r e s e n t s t h e running average summation point and

N V

pcc,x-n/4

i

L,x n

-

v

pcc.x

i

- Camputer simulation of V ~ C Cand 1, The output of algorithm A - The output of algorithm B (N=25) - The output of algorithm C (N=25) - The output of algorithm D (N=25)

-

is the

number

of

samples

representing t h e summation

period. L.x-n/4

(12) Fig. 3e shows t h a t t h e response of t h i s algorithm converges much f a s t e r t h a n t h e previous two, but i t h a s a significant overshoot and undershoot.

1256 D)

V A r evaluation as a function of t h e r a t e of change of

sampling point, N , a very high sampling frequency, l / ~ , i s

parameters.

required.

The s t e a d y s t a t e value of VAr-flow in t h e electrical supply

evaluation

network’can be evaluated by t h e function shown below

networks,

In l a t e r section, t h e development of a new V A r algorithm, will

be

based

on

thoroughly

back-propagation

described.

neural

a special

With

t r a i n i n g procedure, t h e output of t h i s neural network based

(13) where

k

is

the

desired

integration

interval

and

is

Q,

(14) c a n be simplified t o

By using

delivering

a

higher

accuracy

without

the

BACK-PROPAGATION N E U R A L NETWORKS

A

neural

2

mLm

sin6

t h e voltage

(15)

and

current

samples,

Eqtn.

(14) i s

known

is

network

processing

1 Q=-VI L

of

requirement of operating a t a higher sampling frequency.

defined by

and Q

algorithm can be very close t o t h e instantaneous V A r and i s capable

a

structure

parallel,

consisting

neurons

as

unidirectional

signal

distributed

interconnected channels

information

processing

ot

called

elements

together

with

connections.

Each

neuron h a s a single output connection t h a t branches into as

given as

many

collateral

connection

connections

carries

the

desired.

as

same

Each

signal.

The

collateral

strength

of

connection between neurons is represented by a value called a weight. (16)

Each neuron can have its local memory, which

r e p r e s e n t s t h e s t a t e of neuron.

The neuron output depends

only upon t h e c u r r e n t values of t h e input signals arriving where T i s t h e sampling period.

a t t h e neuron

via

impinging connections

s t o r e d in t h e neuron’s local memory. aver t h e integration

i s t h e running average of Q

QLpN

L.X

period k.

characteristics

of

each

neuron

and upon values

The input t o output

are

described

by

the

activation function and local memory of each neuron. P+N

(17)

Neural net models a r e specified by t h e net topology, node characteristics,

k = Nr

w a s used. where P r e p r e s e n t s t h e running average summation point and

N

is t h e

number

and

or

training

learning

rules.

of

samples

representing

the

summation

arranged

point.

This network

i s made up of

in t h r e e or more layers.

s e t s of

shows t h a t

t h e response

of

this

algorithm

is

capable of providing a very good balance in response time and

damping.

Because of

i t s differential -property,

h a s a n e f f e c t on increasing

r e s u l t s in higher o r d e r harmonics amplification. t h i s algorithm amplification,

h a s t h e drawback it

can

generally

this

t h e bandwidth

and

Although

of

high frequency noise

be

compensated

by

neurons

These a r e a n input

network,

the

output

of

neurons

in

a

t r a n s m i t t e d t o neurons in t h e upper layers.

algorithm

our

layer, an output layer and one or more hidden layers. this

Figure 3f

In

application, a neural network of a f e e d f o r w a r d a r c h i t e c t u r e

the

feedforward

network

does

‘ n e u r o n s in t h e same layer.

not

are

A neuron of

interact

Except

In

layer with

f o r t h e input

other layer

neurons, t h e net input t o each neuron i s t h e sum of t h e weighted

outputs

of

the

neurons

in

the

prior

layer.

Therefore, t h e net input t o neuron j , i s described by

(18)

the

system low-pass f i l t e r . w . . i s t h e weight of connection f r o m neuron i t o neuron j , J I

In

accordance

with

the

above

analysis,

selected f o r t h e development of From Eqtn. (17), t h e evaluated Q instantaneous

VAr

by

algorithm

D

0,

is

a n ANN based algorithm. L.PN

can be assumed as a n

reducing t h e integration

interval

k.

very

small

integration

interval,

k.

In o r d e r t o achieve a and

a

very

large

is j

The output of

neuron j i s then obtained by t h e operation of a nonlinear function on t h e net input. o

I t is also noticed t h a t t h e evaluation accuracy i s a f f e c t e d

by t h e number of sampling point N.

i s t h e output of neuron i in t h e previous layer, (3

t h e local memory (threshold) of neuron j .

The

J

function

=

This can be described a s

f(net.1

(19)

J

f(net )

is t h e

nonlinear

activation

J

of t h e neurons, given by t h e sigmoidal function:

function

1257 1

f(x1 =

(20)

OUTPUT b Y E R

1 + exp(-x)

neural networks is mainly due t o

The learning ability of its

capability

training modify

to

adjust

algorithm the

network.

the

devised

weights

weights.

by

of

Back-propagation

multilayer

..........

I71 i s used t o

Rumelhart

feedforward

0

HIDDEN LAYER

neural

In our application, i t i s appropriate t o consider

back-propagation

neural

networks

as

a

method

to

solve

The output of a

nonlinear function approximation problems.

INPUT IAYER

f e e d f o r w a r d neural network can be considered a s a function f ( x , W ) of input vector x and weight matrix W. feedforward function

is

network

used

c R"+

f(x) : A

Rm.

(x y 1, ( x 2 , y 2 ) ,

examples

1'

to

1

Assume a

approximate In

the

a

...,( xk .y k 1, ...

of

the

yk = f ( x ) a r e presented t o t h e neural network.

can approximate

network weights

W

the

function

bounded

training

by

Back-propagation neural network f o r VAr

Figure 4

stage,

evaluation

mapping

The neural

adjusting

its

so t h a t t h e error E can be reduced, where E i s

defined as

The learning capability

of

is exploited t o develop a

ANN

special training procedure such t h a t the modified algorithm is capable

of

delivering

a

better

performance

than

the

conventional approaches. E =

1 (y 1 -

2

&x i I)',

(21)

X ~ E A

The network The weights are updated

in t h e gradient descent direction

of E, i.e.

where Aw

=

JI

-

r)

aE

F,

where w JI

E Ji

w

(221

and t h e positive constant n determines t h e learning wJ,, r a t e of t h e neural network. The larger t h e constant q is, t h e f a s t e r t h e change in t h e weights is. may

lead

feedforward function,

to

oscillation

neural

in

weight

However, a large space.

For

a

network with sigmoidal activation aE has been determined 171. aw

t h e evaluation of

Ji

In

order

to

speed

process without

up

the

convergence

of

the

training

leading t o oscillation, Rumelhart suggested

t o modify t h e training algorithm in Eqtn. (22) t o include momentum t e r m , such t h a t

are

generated

using

where n labels t h e iteration in t h e learning process and a

the

is explained

procedure pairs of v

reduces

weight

This momentum t e r m provides a damping e f f e c t and the

amount

of

oscillations

neural

during

the

training

process.

INSTANTANEOUS V A r EVALUATION VIA ANN

5.

special

L ,PN'

training

In this. example,

101

A-sampling frequency of 5000 Hz is

evaluated Q,, P I 0 0

The V A r , Q,,,,,,

is

the algorithm D.

from these samples by

This

shown in Fig. 5 is used a s a t a r g e t value f o r the

network training.

Instead of

using t h e 101 p a i r s of v PCC

and

samples a s inputs t o t h e neural

i

shows t h a t only 5 pairs of v

and i

network,

Fig.

5

a r e sub-sampled from

PCC

the

same sample t r a i n

a s the

101 s e t s

for

t h e network

this arrangement,

the output of

the trained network is equal t o Q L.Pl00

+ c,

where c is the

network

training

error

always

inherited

this

been

With

from

the

investigation,

kept

below

network error

in

The

required f o r a 50 Hz line frequency.

time will be much longer.

space.

the

PCC

and c u r r e n t variation.

i s a constant which determines t h e e f f e c t of past weight movement

model.

in Fig.

changes on t h e

of

Before

and i L a r e sampled f r o m one cycle of voltage

Throughout

direction

The network

4.

network can %e applied f o r V A r evaluation, a large number

inputs (i.e. m=5).

(231

current

in Fig.

of training patterns, which include t h e v p c c , i L and Q

i s t h e amount of change f o r t h e weight component

JI

is shown

instantaneous V A r .

the 'corresponding Aw

n

topology

m pairs of v p c c ( x ) and i L ( x ) , and t h e output is

inputs a r e

this

2%.

is preferred

network

Apparently,

but

a

procedure. error very

has small

its corresponding training

This method has t w o advantages. because

the

202

to

10.

Secondly, t h e sampling frequency can be much lower.

In

this

is

Firstly,

the

number

of

network input

neural

network

only 250 Hz. in

Fig.5,

size

neuron

data

is is

approach,

much

smaller

reduced

the

from

sampling

frequency

Although the d a t a a r e sampled f r o m one cycle can

be

collected

from

a

fraction

of

the

that

the

The back-propagation neural network i s applied t o model t h e

cycle

Eqtns (16) & (17) f o r t h e evaluation of instantaneous VAr.

evaluated result can be closer t o the instantaneous VAr.

to

reduce

the

integration

period

k,

so

1258

pCc(1)

-

Conventional calculation using 101 sets of inputs per cycle 5 0' vpe, and IL aamplea M used to (raln

--- -- --

Conventional calculation using 5 sets of inputs per cycle

network'

the neur.l

......................

For nalwork

T

Output using neural network model and 5 sets of inputs per cycle

XI06

I .6

101 w(. of vpec and IL rampler targets c%looc M uaed to wduat. V*r for UaInIng the

neurd network

1

It

Figure 5 Neural network t r a i n i n g mechanism RESULTS Figure

4

a

shows

three-layer

employed f o r t h i s application. neurons f o r 5 p a i r s of v

back-propagation

network

The input layer contains 10 and iL samples.

The output

0.2' 0

50

100

150

200

PCC

250

300

350

400

450

I 500

Tmie (s)

layer h a s one neuron, which gives t h e instantaneous VAr. The number of neurons in t h e hidden layer w a s chosen t o be 50. The learning r a t e

1)

and momentum t e r m a w e r e chosen t o

Figure 6 Output comparison based on samples collected i n one cycle

be 0.2. I t w a s found t h a t t h e network worked well with In t h i s t h i s number of hidden neurons and parameters. investigation,

all

simulations

were

carried

out

using

a

33MHz 80386 PC AT with 80387 coprocessor. Each t r a i n i n g set contains numerous patterns. consists of a QL,p,oo

Each p a t t e r n

and 5 p a i r s of corresponding v PCC

and iL samples. The t r a i n i n g s e t w a s generated so t h a t t h e values of Q L , P 1 O Ow e r e evenly distributed in t h e r a n g e of

V A r variation.

After having been trained, t h e network w a s

applied t o evaluate t h e V A r using inputs samples d i f f e r e n t

8-

f r o m t h a t f o r training.

7-

very

capable of

i t w a s found t h a t t h e network i s

generating Q

L.PlO0

f r o m any 5 sets of

inputs.

.

9.

P

3 ,-

1

g58 4-

Very promising r e s u l t s have been obtained and are shown in Fig. 6.

In t h e s e simulations, t h e v

and iL samples f o r PCC

each the

w e r e collected in one cycle as discussed in

QL.Pl00

last

section.

Using

the

algorithm

D, t h e

mean

percentage e r r o r between t h e evaluated V A r based on 101

sets and 5 sets d a t a sub-sampled f r o m t h e s a m e 101 sets

3-

:i

1

1

'0

.

300

100

400

of

500

600

700

900

800

Time (s)

c u r r e n t and voltage samples w a s found t o be about 20 %. This

illustrates

insufficient training

to

iterations,

evaluate VAr. output

that represent

of

sub-sampled

the

five one

samples cycle.

neural

network

per

cycle

After is

is

applied

neural

network

using

5 sets of

data

f r o m t h e same sample t r a i n as t h e 101 sets.

The mean percentage e r r o r between t h e output of

Output comparison based on samples collected in

114 cycle

to

The dotted line in Figure 6 r e p r e s e n t s t h e

trained

Figure 7

100,000

neural

In Fig. 7, t h e voltage and c u r r e n t samples f o r each Q L,P100 in one-quarter of a cycle and t h e neural

w e r e collected network iterations.

was trained

with

the

same number

of

training

A sampling frequency of 20,000 Hz i s required.

network and t h e evaluated V A r based on 101 sets of c u r r e n t

With

and voltage samples i s below 2%.

response t o t h e changing V A r is f a s t e r .

a f a s t e r sampling frequency and

t h e same

N, t h e

Fig. 7 shows t h a t

1259 t h e t r a i n e d neural nktwork can deliver a n a c c u r a t e VAr with sampling frequency of 1000 Hz.

Conventional calculation using 101 sets of input p e r cycle

The mean percentage e r r o r

between t h e evaluated VAr using 101 sets and 5 sub-sampled

sets of d a t a i s about 2 %.

_____________Output using neural network model a n d 5 sets of inputs p e r cycle

The mean percentage e r r o r

XI08

between

the

output

of

neural

network

model

and

the

evaluated VAr using 101 s e t s of samples i s less t h a n 2%. Figure 7 a l s o shows t h a t using 5 samples t o r e p r e s e n t 1/4 cycle i s more acceptable in conventional approach.

The e f f e c t of t r a i n i n g i t e r a t i o n s on network performance i s illustrated

in

8.

Fig.

When

the

number

of

training

i t e r a t i o n s is 5,000, Fig. S a shows t h a t t h e VAr generated from

t h e output

neuron

cannot

converge t o t h e i r t a r g e t

In addition, a f t e r a change in f u r n a c e resistance,

values.

zt

t h e mean values of VAr do not converge t o t h e t a r g e t value.

0

Figure. 8 b shows t h e comparison between VAr output by t h e

200

100

300

400

neural network a f t e r 100.000 i t e r a t i o n s and t h a t evaluated by conventional approach using 101 sets of samples. error

and

fluctuation

between

t h e VAr

output

relationship

between

error

i t e r a t i o n s is shown in Fig. 9. training

iterations,

it

and

number

of

500

600

BOO

io0

900

1000

Time (ms)

The

from the

neural network and the t a r g e t values i s negligible.

i

F

Output comparison after t h e network h a s been

Figure 8 b

t r a i n e d .for 100,000 i t e r a t i o n s

The

training

By increasing t h e number of

is possible

t o further

reduce

the

e r r o r in t h e network output.

DISCUSSIONS

Eqtn. (17) can only evaluate t h e VAr a t a c e r t a i n i n s t a n t a f t e r t h e voltage and c u r r e n t samples are captured. evaluated VAr lags t h e sampling process.

The

By reducing t h e 0

'

.

.

I

0

.

4

3

' 6

5

*

I

*

7

0

8

10 1104

Training Iterations

Conventional calculation using 101 sets of i n p u t s p e r cycle Figure 9 Output using n e u r a l network model a n d 5 sets of inputs p e r cycle

.-_---I------

'

*

2

Variation in error w i t h d i f f e r e n t number of iterations

portion of each cycle taken f o r samples, t h e evaluated VAr will approach t o t h e t r u e VAr flowing in t h e power supply network.

In t h e

present

investigation,

although

w e r e only taken in one-quarter of a cycle. i s possible 1/400 the

t o reduce t h e portion of

cycle. same

In addition, accuracy

t h e cycle down t o

t h e new algorithm can deliver

as

conventional

methods

substantially less voltage and c u r r e n t samples.

4 0

Y 100

200

300

400

500

800

with

Thus, t h e

evaluation system can be operated at a lower sampling rate.

700

800

900

1000

Time (ms) Figure 8a

samples

In p r a c t i c e i t

The ,long computational

time required by s e r i a l computers

can

hardware

be

eliminated

by

chips

implementation

using

Output comparison a f t e r t h e network h a s been

technology

allows 8

t r a i n e d for 5,000 i t e r a t i o n s

number

synapses can be expanded

of

neuron

.

algorithm

neurons

with

Recently,

of the

8 synapses each

this VLSI

(the

by adding e x t e r n a l

1260 h a r d w a r e s ) t o be f a b r i c a t e d in a single MD1220 Neural Bit

S.E.Haque

Slice.

capacitor-thyristor

This neuron chip h a s an equivalent processing power

of 55 MIPS [SI.

and

N.H.Malik,

"Operation

controlled

reactor

a

of

fixed

(FC-TCR) power

f a c t o r compensator," IEEE Trans. on Power Apparatus

The compensation system constructed by

these neuron chips can evaluate t h e instantaneous V A r with

and Systems, Vol. PAS-104, No. 6, pp. 1385-1390,

negligible processing time a f t e r t h e weights obtained f r o m

1985.

the

learning

chips.

process

a r e download

This performance

can

t o the

never

be

of

RAM

achieved

these by

S . Etminan and R .

the

compensators." this

study,

has

it

Sotudeh, "Fast converging reactive

power measurement techniques f o r high speed s t a t i c V A r

conventional methods.

In

June

also

been

demonstrated

that

the

Proc. of 22th

UPEC 87,

pp. 7081-

7084, Sunderland, U.K. 1987.

neural network model using only 5 s e t s of input can deliver a n equivalent that

the

enhanced

by

training. decreased training

accuracy of

performance

101 input

of

this

selecting

sets.

This suggests

algorithm

appropriate

can

sets

be

of

D.

further

input

Rumelhart,

"Learning

for

E.

G.

internal

propagat;on,"

Hinton.

and

R.

J.

representations

Parallel

Distributed

Williams,

by

error

Processing,

D.

The e r r o r of t h e network output is found t o be

Rumelhart and J . McClelland (Eds.), vol. 1, M I T P r e s s ,

by

1986.

increasing

set.

In

the

number

addition,

Fig.

of

9

patterns

illustrates

in

the

the error

can substantially be decreased by increasing t h e number of

Neural Network Devices,

Micro Devices, 1990.

iterations. Tommy W

CONCLUSIONS

S

Chow obtained

his B.Sc

( f i r s t c l a s s honors)

d e g r e e and Ph.D f r o m t h e University of Sunderland, England. By

introducing

approximating t o estimate

back-propagation

t h e VAr the

neural

evaluation

network

function,

instantaneous V A r

for

is possible

it

as t h a t

a s accurately

obtained by conventional methods operating at a very high sampling r a t e .

The methodology developed in t h i s paper is

successful and r e s u l t s

a r e promising.

He

had

been

working

on

current

Supercomputing Homopolar Machines.

collection

system

L e c t u r e r in t h e Electronic Engineering Department Polytechnic of Hong Kong.

of

He i s now a Senior of City

His c u r r e n t r e s e a r c h activities

are Artificial Neural Networks and i t application.

The neural network

model and training mechanism developed in t h i s paper a r e

Y

very flexible and versatile t o provide any specified output

Polytechnic of Hong Kong.

requirement.

r e s e a r c h a s s i s t a n t in t h e Electronic Engineering Department

accuracy

Because of

properties

e r r a t i c fluctuation

of of

the f a s t this

VAr

ANN

convergence based

generated

by

G.J.McManus,

121

"Electric

limitations

electric

and

networks, system identification and adaptive control.

IEEE

"Flicker Trans.

on

No.9, pp.

2627-2631, September 1985.

P. T. Ho and S . K. Tso, " S o f t w a r e control of s t a t i c reactive

current

compensation,"

IEE

Proc.

vol.

135

pt.c, NO. 6 , pp. 518-527, NOV 1988.

141

R.Sotudeh and

J.Holmes,

compensation,"

Proc.

Dundee t i . K , April 1984.

"High of

19th

speed UPEC.

from

of t h e s a m e college.

electric

Power Apparatus and Systems. Vol. PAS-104,

131

(Hons) degree

reactive pp.

power

329-332,

City

He i s now a M.Phil s t u d e n t and

arc

an

D.J.Ward,

utilities."

B.Eng

the

f u r n a c e succeeds i n technology

J.F.Buch of

his

high

Iron Age, Mp.7 t o hlp.18, Feb 1980.

R.C.Seebald,

obtained

and

REFERENCES

and profit,"

Yam

algorithm,

furnace can be accurately estimated f o r compensation.

111

F

His research i n t e r e s t s a r e in neural