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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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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