AUTOMATIC VOLTAGE REGULATOR AND FUZZY LOGIC POWER SYSTEM STABILIZER

8/16/2019 AUTOMATIC VOLTAGE REGULATOR AND FUZZY LOGIC POWER SYSTEM STABILIZER

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IEE 2nd Internationa l Conference on Advances n Power System Control, Operation and Management, December

1993,

Hang Kong

DESIGN AN D IMPLEMENTATION OF A PC-BASED

AUTOMAT IC VOLTAGE REGULATOR AND FUZZY

LOGIC PO W ER SYSTEM STABILIZER

Ju an Shi L.H.Herron A.Kalam

Save Energy Research

Group

D e p a r t m e n t

of

Electr ical and Electronic Engineer ing

Victoria University

of

Technology

P.O.Box 14428, MM C, Melbourne

Victor ia

3000.

Austral ia

Abstract

This p aper descr ibes th e design and im-

pleme nta t ion of au to mat ic vo l tage regu-

lator (AVR) and fuzzy logic power sys-

tem s tab i lize r (F LPS S) for s ing le ma-

chine inf inite bus power syste m. Th e

AVR was designed using z-domain an-

a ly t ica l des ign met hod. Th e proposed

FLPSS employes two nonlinear fuzzy

membersh ip func t ions t o improve i ts per -

formance. Th e design and digital s im-

ulation studies are carr ied out using

MATRIXx-a large control system design

and s imula t ion sof tware package . Th e

des ign is implemented

in a

Power Sys-

t e m La b o r a to r y

w i t h

an IBM-486 com-

pute r ac t ing as the rea l t ime contro l le r .

Both s im ula t ion and im plemen ta t ion re-

su l ts show tha t the proposed PC-based

AVR and FLPSS are very effective.

Keywords: Voltage control, fuzzy logic applica-

tions

1

Introduction

Currently, the availability of powerful PC has led

to their increasing use in all aspects of power con-

trol engineering.

In future years, they are ex-

pected t o play an even greater role in power system

control schemes, because of their ability in com-

bin ing var ious tasks , on- l ine upda t ing of da ta an d

providing a logical or quick decision. Th us , the ap-

plication of a PC-based control in power system is

being increasingly used

for

mo n i to r in g , d a t a a c-

quisition and on-line control.

The success of excitation control in improving

power sy s tem dy namic per formance in cer ta in s i t -

ua t ions has led to grea te r expec ta t ions as to the

capability of such control

[3].

Because of the sm all

e f fec t ive t ime cons tan ts in t he exc i ta t ion sys tem

control ioop, it was assumed that,

a

large control

effort could be expended through excitation con-

trol

with a relatively sm all input of control en-

e rgy. B ut the exc i ta t ion sys tem in troduces a large

phase lag a t low sys tem f requencies jus t above the

na tura l f r equency of the exc i ta t ion sys tem. Thus

i t can be assumed tha t the vol tage regula tor in

the exc i ta t ion sys tem in troduces nega t ive damp-

' ing [1 ,2].The appl ica tion

of

a power system sta-

bilizer PSS) is to generate a supp lemen tary s ta -

bilizing signal, which is applied to the excitation

control loop of

a

genera ting un i t , to in troduce a

pos i tive d ampin g torque .

In addition to performing the pr imary control

functions traditionally offered by the analog con-

trols , the PC-based controls have

a

far greater

deal of f lexibility and ability to im plement sophis-

ticated control algorithms.

This paper presents a n effective and efficient

Autom atic Voltage Regula tor (AVR) and Fuzzy

Logic Power System Stabilizer (FLPSS) design

which can be easily implemented by computer fa-

cility with high accuracy.

Th e complete system has been simulated using a

MATRIXx

software package on Sun w orkstation.

The d ig i ta l AVR and FL PSS are implemented

us-

ing an on-line 486 PC. Both s im ula t ion and imple-

mentation results for s ingle machine inf inite bus

sys tem show tha t the proposed PC-based AVR

and FLP SS are very effective.

Th e system configuration for the single machine

infinite bus system is shown in Figure

1.

Figure

1:

One-machine inf inite bus system

2 Design

of

AVR

2.1 Mathematicle model

Th e full model for s ingle machine inf inite bu s sys-

tem is

a

7th order model .

A machine model cho-

sen for power system dy nam ic studies depends not

only on the na ture

of

the problem, but a lso on

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the comp uta t iona l f ac il i t ies and contro l techniques

available.

A

simplif ied f irs t order approximation

voltage loop of the machine is given by:

Where K i s th e D C g a in a n d Ti, is the open circuit

d-axis time constant of the generator respectively.

These param eter va lues have been exper imenta lly

de te rmined accord ing to th e IEEE test procedure

on a 5kVA, 240V synchronous mach ine. There-

fore , the t r ans fe r func t ion be tween the te rmina l

voltage and the f ield voltage can be represented

as

:

0.2622

G u ( s )= 1 + 0.2126s

T he exciter is modeled using f ield dr ive unit an d

the t ime cons tan t of the uni t is found to be very

small compared to t he s ign if ican t t ime cons tan t of

the sys tem under s tudy and is therefore, neglec ted .

Th e transfer function of the f ield dr ive unit is :

G F D U ( ~ )A

(3)

where

A

is the ga in

of

the f ield dr ive unit and is

found to be 25 in th is case . T he three phase l ine

vol tages a re t rans formed to a proportional DC sig-

na l which is measured by the A/ D converte r. Th e

sensor circuit, which rectifies, filters and reduces

the te rmina l vo l tage to 5V for compar ison , whose

transfer function is found experimentally and is

given by:

~

B

1

+

rs

G,(S)=

4)

Again th e t im e cons tan t of the sensor circui t

T

is neglected

as

i t

is

very sm all compared t o the

ma c h ine t ime c o n s ta n t . Th e se n so r DC g a in

B

is found to be 0 .0042. To design a digital con-

tro lle r the sys tem trans fe r func t ion m us t be t r ans -

formed f rom s -domain to t he z -domain . For a sys -

tem trans fe r func t ion

G p ( s ) ,

he z-domain transfer

function

G p ( z ) ,

an b e obta ined b y us ing the fol-

lowing equa t ion :

where

G p ( s )

n this case is equal to:

K

1

+

T ,s

Gp(s)=

A

(5)

2.2 AVR

Design

Further consider the single voltage-regulator loop

as

follows:

For a sys tem trans fe r func t ion Gp(s) , h e z -

doma in t r ansfe r func t ion

G ( z ) ,

an be obta ined

as in equa t ion

(7).

On dealing with the low frequency which is of the

order

of

a

fraction of 1Hz

to a

few

Hz

for large

Figure 2: The voltage regulator

loop

sca le power sys tem , the sampl ing t ime has been

chosen as 25ms . The n the open- loop pulse han sfe r

function becomes GAVR(Z)G(Z) .ext define the

desired closed-loop pulse transfer function as F z ) :

O.O29z-'

G z )

= A *

1

- O. 8 8 9 ~- '

9)

From the g iven sys tem trans fe r func t ion the out-

put sequence of the system can be expected to

satisfy the transient cr iter ia.

I t is r equired t ha t

the system exhibit a f inite settling time with zero

s teady-s ta te e r ror.

F 2 ) =

a,

+ q z - 1 + . . .+ U N Z - N

(10)

To f ind the pulse transfer function G A V R ( Z )h a t

will satisfy equation

(8 ) ,

it can be seen that

The physical reliazability condition is that the

control s ignal must be less tha n 1 0 due to t he lim-

i ta t ion of the D 24onverter.

I f th e desired set ting tim e for a unit s tep inpu t is

0.3 sec,the out pu t sequences are desired as follows:

F ( z )

=

3 5 . 2 ~ ~ ~3 1 . 3 1 8 ~ ~ ~2 7 . 8 1 6 ~ ~

2 4 . 7 4 4 ~ - ~2 2 . 0 0 8 ~ ~ ~1 9 . 5 6 ~ - ~

1 7 . 4 8

+ 1 5 . 4 5 6 ~ ~ ~13.752z-'+

1 2 . 2 1 6 ~ - l o

+

1 0 . 8 4 8 ~ - ~ ' 9 . 6 7 2 ~ - (1 2)

B F z ) =

0.14672-1

+

0 . 1 3 0 4 ~ - ~ 0 . 1 1 6 0 ~ - ~

0 . 1 0 3 1 ~ - ~0 . 0 9 1 7 ~ - ~0 . 0 8 1 5 ~ - ~0 . 0 7 2 5 ~ - ~ +

0 . 0 6 4 4 ~ - ~ + 0 . 0 5 7 3 z - ~ + 0 . 0 5 0 9 ~ - ~ ~ + 0 . 0 4 5 3 z ~ ~ ~ +

0 . 0 4 0 2 ~ - ' ~

Thus the controller transfer function can be

rewritten

as

* A (13)

.0586 1.2345z-12

1 B F Z )

AVR(Z)

Figures 3 a n d 4 show the te rmina l vo l tage per -

formance corresponding t o different sudden load

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changes. Th e solid l ine shows the termi nal volt-

age per formance wi th the des igned AVR. The dot -

ted l ine shows the terminal vol tage wi thout the

AVR. I t is obvious th at t he sys tem equipped wi th

the des igned AVR kept the outpu t constant under

dis turbance condi t ions .

Figure 3: Termina l vol tage cor responding to sud-

den inductive load change (casel)

2

*

Figure 4: Termina l voltage cor responding to

sud-

den inductive load change (case2)

3

3.1

T h e

Fuzzy Logic Power System

Stabilizer

FLP

SS)

Introduction

most widely used conventional PSS is the

lead- lag compe nsator where the gain se t t ings are

fixed

at

certain values which are determined un-

der par t icular ope rat ing condi t ions . T he des ign of

the conventional

PSS

is based on a l inear approx-

imation of the nonlinear power plant .

Since the

operating point of a power system drifts as a re-

sult of continuous load changes or unpredictable

major di s turbances such

as

a three-phase fault ,

the fixed gain conventional PSS can no t adap t t he

stabil izer parameters in real t ime based on on-l ine

measurem ents. Al 'though general para met ers can

be decided for a conventional

PSS

according to

a part icular range of operating condit ion, the de-

s ign procedure appe ars to be very complex. A

self-tuning PSS has been empl oyed t o ad ap t t he

s tabi l izer to mainta in good dynam ic performance

over a wide range

of

operating condit ions.

Although the self-tuning PSS has offered bette r

dynamic per formance th an the f ixed gain

PSS,

i t

suffers from

a

major drawback of requiring model

identification in real-time which is very time con-

sum ing, especial ly

for

a microcomputer with l im-

i ted comp utat ional capaci ty .

The re are unc ertainties in the electric power sys-

tem and because of this there always exist i inmod-

elled dynamics in the power system. As a result ,

the

PSS

does not always perform effectively in the

real electrical power system.

To

overcome these problems and to cope

with the changing enviroment in power system,

FLPSS is developed without real-t ime identif ica-

t ion. FLPSS can be easily constructed using a P C

with

A / D

a n d

D/A

interfaces. The operating con-

dit ions of the synchronous machine are expressed

by the q uantit,ies of speed d eviatio n an d accelera-

t ion in the phase plane.

3.2 FLPSS Design

Synchronous generator condit ion can be expressed

with the quanti t ies of speed deviation and accel-

erat ion in the phase plane. Th e phase plane is

divided into t ,wo sectors. Th e stabil izing signal

iJ, t) is given by:

Us t)

=

U S ( k ) , (14)

for kAT

5

t 5

( k + 1)AT

n a discrete form , where

k indicates the t im e

kAT,

a n d

AT

represents the

sample interval . Th e generator condi tion a t th e

t i me

t

=

kAT is

given by the point

p ( k )

in the

phase plane.

Th e origin in the p hase plane is the desired equi-

l ibrium po int . ll the control effort should be di-

rected

to

moving the current condit ion

p ( k )

to-

wards th e origin as quickly as possible.

The accelerat ing control of the study unit

is

achieved by applying a negative stabilizing signal

to the exci ta t ion loop, as the electrical output of

the study unit can be decreased by the negative

stabil izing signal . Correspondingly, decelerating

control is achieved by applying

a

positive stabiliz-

ing signal to the exc itat ion loop with th e increased

electrical output through the posit ive stabil izing

signal .

Two fuzzy nonlinear membership functions,

N { B i ( k ) }

a n d

P { ( k ) } ,

re defined for the pro-

posed

FLPSS

as shown in Figure

5

to represent

both the sectors

A

a n d

B

respectively. Th e te rm

Bi (k) indicates the phase angle of the point

p i ( k ) .

By using these membership functions, the stabi-

lizing signal is computed as follows:

G k

N i

(IC)} i Jm m - {Qi k) Jmaz]

N{B i k ) }+

P{Qa k))

J k)

=

(16)

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for

D k ) >_ D ,

G k)

= 1.0, (20)

D ( k )

I

P k ) I 21)

T h e t e r m

G k)

indicates the gain factor at t he

t i me

t

= kAT, a n d G ( k ) s given by

a

nonlinear

function.

The maximum value of the s tabi l iz ing s ignal

U,,, depends on the generat ing uni t . Dis tance

pa r ame t e r

D ,

and angles a a n d p can be adjusted

to thei r opt im al values according to a per formance

index which is defined

as

follows:

M

J =

[ t k A ~ k ) ] ’

( 2 2 )

k = l

T h e i ndex

J

is specified to investigate the t ime

opt imal i ty of the s tudy u ni t . According to the val -

ues of the performance index, the optimal set t ings

of the adjus table parame ters can be determined.

T h e f unct ion P { e i ( k ) } can be expressed as fol-

lows:

0

for 0 5 8, 5

00

2 [ V I 2

0

(23)

for o

+

180 + a 5 8i

5

360

Where a l l the angles in the above equat ion are

in degrees.

00

+

a / 2 a n d

00

+ 180+ 01/2 a r e t he

crossover points.

4

Simulation Study

Th e s imulat ion s tudy resul ts presented here were

ob t a i ned on

a

5kVA synchronous generator driven

by a dc motor an d represented by a thi rd order

l inear ized m odel wi th param eters as shown in the

Appen dix. Th e generator was init ia lly loaded a t

0.9 power fac tor. Since the power system oscil-

la t ing f requency corresponding to a disturbance

is approximately 1.5Hz, the digi ta l AVR an d the

stabilizer were designed with

a

controller sampling

time of 25 ms.

,T he per formance of the proposed FLPSS un-

der a step change in reference voltage

is

shown

in Figures 6 and 7. Th e per formance of the pro-

posed FLP SS has been com pared with a conven-

tional PSS when

a

0 . 1 ~ ~

tep increase and de-

crease in reference voltage V,,f have been applied.

The dotted l ine shows the system response with-

out PSS. The d ot ted l ine with much smal ler mag-

nitude is the system response with a conventional

PSS an d th e solid l ine is the system response with

the FLPSS. The resul t s show that the proposed

FLPSS

gave an overall improved performance.

5

Implementation Study

In orde r to verify the design for the fuzzy logic con-

troller as well as the simulation results, the fuzzy

controller was implemented and tested on

a

one-

machine infinite bus system.

After th e system is run u p to speed, the genera-

tor

was synchronized and connected to an infinite

bus.

In al l the tests, the steady st ate was defined

with an electrical power of 1625W at 0.9 power

factor. Th e tests were examined after

a

sudden

load change. Different load has been applied to

test the robustness of the system response.

Figures 8-13 show the rotor angle and speed

deviation corresponding t o different sudd en load

change s respectively. Figures 8,lO a n d 12 show the

system response w ithout P SS. Figures 9,11 and 13

are the resul t s wi th a FLPS S. To veri fy th e ro-

bustness of the system performance, different op-

eratin g loading conditions have been applied an d

similar result has been obta ined . Figure 12 and 13

are the results under another operating condit ion.

Th e s tudy shows that the sys tem wi th a F L P S S

increase the system damping dramatically.

6 Conclusions

In thi s paper a digi ta l automa t ic voltage regulator

(AVR) and fuzzy power system stabil izer (FL PSS)

have been designed for single machine infinite bus

power sys tem. Th e AVR and FLP SS have been

implemented using the on-l ine

I BM PC as

the real

t ime controller . T he simulation results show tha t

the proposed FLPSS provided bet ter dynam ic per -

formance under di s turbance condi t ions than the

conventional PSS. The design of the FLPSS does

not requi re mathe mat ical m odel representa t ion

of

the synchronous machine and power plant and

is quicker and easier to implement than the self-

tuning PSS which requires real-t ime model iden-

t i f icat ion. Both s imulat ion and impleme ntat ion

resul t s show that the digi ta l AVR mainta ins the

terminal voltage values under various loading con-

di t ions and FL PSS increases th e sys tem da mpin g

dramatically. The studies also show that the pro-

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posed AVR and FLPSS is effective over different

operat ing condi t ions .

References

L A R S E N ,E .V . ,S W A N N ,D .A . : A pp ly i ng

Power System Stabi l i sers” .

EEE Trans. ,PAS-

100, 1981,

p p .

3017-3046.

A N D E R S N ,P FO UA D A .A. , “Pow r

System Control and Stability”. Iowa S tate

Universi ty Press, Ames, Iowa, 1977.

DEMELLO F.P. CONCORDIA C.:Concepts

of Synchronous Machine Stabil i ty

as

Affected

by E xc i t a t i on C on t r o l ” , I E E E Trans., PAS-

88,1969,

p p

316-329.

HSU ,Y Y. L I O U ,K .L . :“Design of Self-tuning

PID Power System Stabi l i ser for Synchronous

G e n e r a t o r ” . IEEE Trans . , EC-2, 1987,

p p

-343-348.

H I Y A MA ,T : “Appl icat ion of Rule-Based Sta-

bil ising Controller to Electrical Power Sys-

t e m ” . I E E Proc. C, Vol. 136, No.3,1989,pp.

H IYA31

A ,T

SA M ES €1I hl A ,T

‘

Fuzzy Logic

Control Scheme for On-line Stabil isat ion of

Multimachine Power System.” Fuzzy

Seis and

Systems 39 1991), pp.181-194

ZIMMERMANN,H.J . :Fuzzy Set Theory and

Its Applications. Kluwer-Nijhoff Publishing

Company, 1985.

1 75-181.

I /I\,, ~

/I\

0 ’

/ I

9 5 t l O 1’80 2 7 5 3 0 5 350 ’’

Figure 5: Membership funct ions

APPENDIX

One-machine inf ini te bus sy s tem generator un i t

L w m -

d a t a :

x; = 0 . 4 7 9 ~ ~

x q

=

0 . 4 8 9 ~ ~

Ti,

=

0.345s

H

=

0.764s

Wb = 314r ad / sec

R,

=

0 . 0 2 ~ ~

x = 0.5pu

x d = 1.027pu

Figure 6:

change in reference voltage

Rotor angle cor responding to s tep

Figure

7 :

Speed deviat ion cor responding to s tep

change in reference voltage

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6/6

10

-20

-25

I

d

2 4 6 8 IO 12 14

16

I8 20

t lm

m sccmda

-301

Figure 8: Rotor angle cor responding to sudden

load change (wi thout PSS)

tor sngle auh uaypss

2 0 7 -

I

-=I ,

2 4 6 8 IO

12

14 16 18 20

30

Figure 9: Rotor angle cor responding to sudden

load change (wi th FLPSS)

0

Figure

11:

Speed deviation corresponding to sud-

den load change (with FLPSS)

15Li

20

2

4

8

IO

I2

14

16 8

Figure

12:

Rotor angle cor responding to sudden

load change (wi thout

PSS)

4 ,

U

j

0

4 6 8 IO I2 14

16

18 20

tunc

m

ccmds

Figure

10:

Speed deviation corresponding t o sud-

den load change (wi thou t PSS)

Figure 13: . Rotor angle cor responding to sudden

load change (with FLPSS)

298

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AUTOMATIC VOLTAGE REGULATOR AND FUZZY LOGIC POWER SYSTEM STABILIZER