Transactions on Energy Conversion, Vol. 5, No.1, March 1990
IEEE
23
IMPROVED PGIER
R.J. Fleming
SMIEEE
SYSTEM STABILIZERS
M. M. Gupta
SMIEEE
Jun Sun
Non-member
Power Systems Research Group
University of Saskatchewan
This paper
proposes
three
novel
Abstract
approaches to improve a conventional power system
stabilizer (PSS) in a single machine to infinite bus
system.
These
improved
stabilizers
use
the
conventional PSS in the usual manner plus modification
of the terminal
voltage feedback signal to the
excitation system as a function of the accelerating
power on the unit.
This nonlinear action increases
the power system stability greatly.
Also, since these
improved stabilizers are based on the conventional
stabilizers they are simple to implement.
X'
d
d-axis transient reactance of machine
X'
q
q-axis transient reactance of machine
T '
do
d-axis transient open circuit time constant
General
s
Laplace operator
over a letter indicates derivative
Keywords - Power system stabilizer (PSS), improved
PSS, accelerating power, power system stability.
1
INTRODUCTION
A single machine to infinite bus system is shown
in Figure 1.1.
NOMENCLATURE
(p.u., except as indicated)
System V ariables
o
torque angle (degree)
W
rotor speed (rad./sec. )
Fig. 1.1
field voltage
accelerating power
are:
electrical power
A single machine to infinite bus system
The swing equations of this system in Figure 1.1
Ii= w
(1)
mechanical power
(2)
infinite bus voltage
V
reference input voltage
ref
V
s
stabilizer output
V
terminal voltage
t
R
System Parameters
D
damping coefficient
H
inertia constant of the machine (secs. )
K
A
gain of excitation system
T
A
time constant of excitation system
r 9+jX
£ transmission line impedance
d-axis synchronous reactance of machine
q-axis synchronous reactance of machine
89
SM
633-9
Ee
A paper recommended and approved by
the IEEE Energy Development and
Committee of
Long
Beach,
the IEEE/PES
California,
submitted January 27,
June 21,
Power
Generation
the IEEE Power Engineering
presentation at
1989.
July
1989;
When the mechanical power P is not in equilibrium
m
W
with the electric power P (o) and damping power
e
o
during and following disturbances, the rotor speed w
suffers electromechanical oscillations.
The oscilla­
tions of concern to stability are in the 0.2 to 2.5 Hz
frequency range [3]. usually, the damping coefficient
D is small and these oscillations are strong and
lightly damped.
This causes the rise of periodic
variations in electrical quantities and, possibly, the
initiation
of torsional shaft
oscillations in a
multistage turbo-generator unit.
The most extreme
result is dynamic instability due to negative damping.
Even in stable situations, insufficient damping of
these oscillations limits the ability to transmit
power out of the plant [2,41.
Society
for
1989 Summer Meeting,
9 - 14, 1989. 'bnuscript
made available
for printing
A proper stabilizing signal derived from the
speed control loop and introduced into the excitation
system can increase the damping torque of the machine
at these oscillation frequencies; therefore, consider­
able attention and efforts have been directed toward
using the excitation control systems to improve power
system stability.
Three novel approaches to improve conventional
Based on the
stabilizers are proposed in this paper.
conventional stabilizer, these improved stabilizers
introduce an auxiliary stabilizing signal,
(6P ) ,
a
which is a function of accelerating power into the
terminal voltage feedback loop and make this feedback
nonlinear.
These improved stabilizers increase the
power system stability greatly, while they are simple
to implement.
0885-8969/90/0300-0023$01.00 © 1990 IEEE
24
COOVENTIONlIL STABILIZER
2
Limiter
Figme 2.1 is a block diagram of a conventional
It
application.
(PSS)
stabilizer
system
power
includes an output amplitude limited static exciter
and an output limited stabilizer (PSS) with a transfer
function G(s) •
Vt
+
Vs
r
I
I
I
Limiter
__
- - - - ------,
PSS
improved
�
I
I
i---:----w
E
f
1----1---
I
r----'--- �a=[Pe-Pm)
1---- stabilizing
signal
Limiter
PSS
2.1
Fig.
Block diagram of a PSS
example system to which the
applied as
are
Figure 2.1.
The da.ta for the
controllers shown in
follows.
Base MVA
D
=
Xd
x�,
=
100
MVA,
Xd
8.0 (p.u.),
H
Xq
=
0.136 (p.u.), r
P
(MW)
o
90.00
q
4.30 (secs.)
1.164 (p.u.)
=
0.146 (p.u.), T
d
The operating
Table I.
Table I.
=
X
�
=
=
Fig. 3.
�
point
�
of
;
=
machine
is
in
shown
The Operating point of the machine
Q
o
(MVAR)
V
00
(p.u.)
to
1.05
37.62
terminal voltage
force the
to
chosen
be
should
feedback 50 that the field voltage � will go down to
f
make electrical power go down to balance mechanical
When �
power as soon as possible.
K(� )
< 0,
a
a
should be negative to reduce the terminal voltage
feedback in order to increase electrical power as soon
as possible.
According to the above principle, K(AP ) has been
a
PSS(A),
chosen in three ways to improve performance:
PSS(B), and PSS(C) respectively.
3.84 (secs.)
0.009 (p.u.)
the
Block diagram of improved stabilizer
(deg.)
4 0.73
3.1
Stabilizer PSS(A)
in
Figure 3.1.1 shows K as a function of AP
a
graphical form.
In this case, K switches between
positive and negative values according to the sign of
The effect is somewhat similar to bang-bang
AP
a'
A small dead zone bound can be considered
control.
- 0, as indicated by the dashed lines in
around AP
a
Figure 3.1.1.
The key point of designing a PSS is to determine
the best transfer function G(s) to provide the damping
By using rotor speed 00 as a stabilizing
needed.
signal and using the phase compensation method [5] of
design, G(s) for the machine was obtained as shown in
K
0.0035
(3) •
G(s)
4 s
(1 + 4 s)
x
0.15 (S
(1
2
+
+
9.88 S + 97.56)
0.05 s)
2
3
IMPROVED STABILIZER
improved
the
between
difference
only
The
stabilizer and the basic stabilizer is that the
stabilizing signal �P is introduced into the terminal
a
voltage feedback loop, where �
is the difference
a
between electrical power and mechanical power and can
Figure 3 is the block
be measured approximately [6].
diagram of the improved stabilizer where the feedback
from terminal voltage V is a function of � '
a
t
Because K(�P ) is a function of � ' the terminal
a
a
voltage feedback becomes nonlinear feedback.
The principle of designing K(� ) is as follows:
a
> P ' positive K(� )
> 0, this means P
�
a
a
e
m
When
I
10.001
,
(3)
The first term in (3) is a reset term that is used
to "wash out" the compensation effect with a time
constant of 4 secs.
The second term is a lead
compensation pair that can be used to compensate the
system phase lag [1,3].
IT,----­
/>'P
0.0035
Fig.
3.1. 1
a
K(/>,P ) for improved PSS(A)
a
Nonlinear computer simulations were carried out
for both small and large disturbances to study the
A 10 MW mechanical power
performance of this system.
step change and a 0.02 p.u. voltage reference step
change are considered as small disturbances and a
three-phase short circuit of 0.1 secs. duration on the
infinite bus as a large disturbance.
the
program,
simulation
nonlinear
the
In
resistances of the system components were included,
saturation was represented in both axes as a function
of the total air gap flux for a round rotor machine,
one damping winding in the q-axis was included, and
included
representation
machine
rotor
round
the
transient saliency.
Figures 3.1.2, 3.1.3 and 3.1.4 are the responses
comparing the improved PSS(A) with the conventional
PSS and no PSS (only terminal voltage feedback) for
disturbances
large
and
small
of
cases
the
respectively.
25
The maximum overshoot Mp and settling time Ts (for
boun d) of rotor speed i n the case of a 10 MW
mec hanical power step change are listed in Table II.
1%
Rotor Speed OVershoot and Settling Time
Table II.
ROTOR SPEED Ul
OVershoot
Settling time
Ts (sees.)
Mp (p.u.)
EXCITATION CONTROL
No PSS
0.3280
0.2239
0.2064
PSS
Improved PSS(A)
3.3
Improved PSS(C)
Figure
3.3.1
f unc ti on
K (6P )
a
slope
The osci ll ati on frequency without the PSS is about
The improved PSS(A) damps t he oscillation
Hz.
much more than the PSS.
O.0035
for
an
overshoot
the
decreases
PSS(A)
imp ro ved
This means that
somewhat further than the PSS.
the improved PSS(A) is not so sensitive to large
power disturbances. This can also be shown in the
responses of large di stur ban ce s .
3.
However, the settl ing time decreases from 1.350
(sees.) to 0.525 (sees.). This indica tes that the
improved PSS(A) is quite effective for small power
disturbances.
Improved PSS(B)
Figure 3.2.1 shows K as a linear function of aP .
a
K
0.15
-:l---- lip a
-----"V"+ ::::.� -::
O OO
O. 15
�
"
lIP
a
�l�----:O�.�OO
I
----------�
The
2.
slope
the
by
2.1
3.2
is
improved PSS(C) whic h is the combi nation of improved
PSS(A) when liP is small and improve d PSS(B) when aP
a
a
is large.
2.525
1.350
0.525
can be obtained
The fo ll owing conclusions
comparing the improved PSS(A) with the basic PSS.
1.
From these results, it is found that the improved
PSS(B) decreases overshoot significantly, however, the
settling time is almost the same as f or the PSS. This
me an s the improved PSS(B) is effective for large power
power
small
to
sensitive
not
but
disturbances
the
of
combination
a
Therefore,
disturban ce s.
advantages of PSS(A) and PSS(B), giving PSS(C) is
developed below.
1-0.0035
Fig. 3.3.1
K(llP ) for impr oved PSS(C)
a
It can be predicted that the improved PSS(C) must
be effective for lar ge as well as small power distur­
ban ces and it must decrease both the overshoot as well
as the set tl in g time.
These advantages are cl early
shown in Figures 3.3.2, 3.3.3 and 3.3.4 and Table IV.
Table IV is given to compare maximum overshoot and
settling time (for 1% bound) of rotor speed Ul in the
Also,
case of a 10 MW mechanical power step c ha nge.
it is found that the improved PSS(C) does not have a
significan t effect on the static deviation of terminal
voltage in the case of step change.
Table IV.
Rotor Speed Overshoot an d Set tling Time
ROTOR SPEED Ul
Fig. 3.2.1
K(llP ) for improved PSS(B)
a
The dashed line in Fig. 3.2.1 represents the small
By using this function of
= O.
a
K, i t is clear that the larger absolute values of llP
a
w ill have more effect on terminal voltage feedback,
therefore, improved PSS(B) must have more effect on
large disturbances.
error bound around llP
Figures 3.2.2, 3.2.3 and 3.2.4 are the responses
comparing the improved PSS(B) with the PSS in the
cases of small and large disturbances respecti vel y.
Table
is
III
given
to
compare maximum
overshoot
and settling time (for 1% bound) of rotor speed
the case of 10 MW me chani cal power step change.
Table III.
w
in
Rotor Speed OVershoot and Settling Time
ROTOR SPEED Ul
OVershoot
EXCITATION CONTROL
PSS
Improved PSS(B)
Mp (p .u . )
0.2239
0.1665
Overshoot
Mp (p.u.)
EXCITATION CONTROL
PSS
0.2239
0.1664
Improved PSS(C)
4
Settling time
Ts (secs.)
1.350
0.600
CONCLUSIONS
From the simulation results, it is concluded that
these three kinds of improved stabilizers can improve
power system stability much more than the conventional
PSS which has been used widely in power systems since
While the impro ve d PSS is based on
the 1970's.
conventional PSS and only a llP stabilizing signal i s
a
introduced into the terminal voltage feedback loop, i t
Comparing
is simple to imple men t the improved PSS.
the three kinds of improved stabilizers, the improved
PSS(C) is the best one since it is e f fec tive for both
small and large dist urb ance s, and is also effective to
improve both overshoot and settling time of rotor
speed deviations.
Settling time
Ts (sec s. )
1.350
1.225
------ ---- ------
--
26
0.35
.-:-
0.10
�
�
.,;
.,g,
0.15
g
0 0'
--:
0.10
."
:
�
0.00
o
f:
0 25
020
0.05
,
1.5
1.062
'3'
2
2.5
3
time (sees.
)
35
•
.. 5
S'
ri.
0>
c
10.8
(I
0.
5
�
�
$!
::
..,9;
"
.2
"0
>
g
1.5
2
2.5
3
time (sees . )
3.5
..
..5
1.0415
5
MW
+--H:±W�""_----­
-0.1
-03
0.'
05
1.S
2
2.5
3
time (sees.
)
3.5
..
".S
-0.
1.065
.!
... .
5
5
time (sees.)
1
-0.1
"U
%
�
-0.2
eo -O.l
I
0.5
o
1.5
r
2
I
2.5
,
3 3.5
time (secs.)
1 . 07
L065
g
J
05
1
1.5
1
2'S
�3�5
time (secs.)
Fig. 3.2. .3 Responses for the ca se
of
0.02 p
voltage reference step cha ng
e
2.50
1
)
3.5
4.5
..
5
1.0'�
1.050
5
./5
2
t ime (s ecs.
1.070
�
a
I.�
5
1.060
.,g
u
o
I
o.!)
1.'s.
� 2:5 .3
t ime (s ee s. )
Fig. .3.3.3 Responses
fo r
'
.5 5
the case of 0.02
vol ta ge reference step change
30
-0
...?.. 0.0+++'9____________
."
II
.
-1.0
p
e
- - +0 -'0'. , -',
�
1.0
�
"
0.9
g
"0
�
O.G
0.5
I
2.5
i
5i
,VS
time (sees.)
rig. 3.1.4 Respons es for the cose of 0 th ree
phase shod circuit of 0.1 (sec .
1.5
liS
duration on infinite bus
PSS(A)
PSS
no PSS
)
� 2iS i
time (sees. )
.,
'"
I
2
1
,
.2
-:
o
o.s
(sees. )
1.0
3'5
_
0.
T7s-2.-�2r:s-;,-4., ��
5 .-.';_;
�
time (sees. )
:;- 1.0
3o.g
.
0>
.£ 0.8
�
0.7
0.6
O.s.
4'5
0.15
c
.
-1.0
-2. 0
0
-3.
e
-30
--,'-; -,'-�,r.5--�' --'3��5 -'--":5--'
time
�
-!'!.
.,;
1. o.o+++'9r--g-
-2.0
o
0.5
� o.o +-�--==_---
2.0
- 3.0
o
time (secs.)
0.'
u
�
g
:-
-
5 -,
'� --,", ,r' --,r,--3,--,l:5� -,-.�-
0.2
:\
- T­
. . .... .
0
Fig. 3.3.2 Responses for the cose of 10 MW
mec han i ca l power step chonge
mechanical power step change
3.0·
-2.0
0"
1.0.15
..2
voltage reference step chenge
�
a.
';;' 0.9
t1>
.2 0.8
� 0.1
c
-4
1.050
1.065
time (sees.)
"
.�
3.5
1.052
�
1.060
1.050
-1.0
"0
3
lOSe.
"0
,
45
g. o.o+++b-t-�""'::"=-�---
-•.
1.0SI5
.2
C
� 2iS � 3�5
1.060
-.------.
�
1.0
0
2.5
5
s-
.�
1.'S
1.051
+-�--.--.-,__-,-,__,___,--.__,
1.5 2 2.5 J l.S. • ..s.
o 0.5
time (s ee s. )
0
g
'.0
o
2
- --.-----
3
-0.4
Fi g. 3.1.3 Responses for the case of 0.02 p.l'
e
.�- ==
..�-�
- =�- - .=-. -=.-�---=.-.=
.
-.
---,
,---
-----,. - .--o
0.5
1
1.5
1.075
�
0.5
-0.1.5
.E
�
g
.�
-
+-..:..2�·;;--'"'-·=�--
-0.10
�
"
� 1. 70
(I
e
5
-0.2
s-
'.0
�
U
-0.1
�
5
1.070
1050
�
time (s:ecs.)
•
U
o.o+-"'=�=___________
:' .
�
L
eo
-0.1
11.055
"0
,
0'
LOSD
"0
U
S
02
0.1
o.o
0.00
-0.05
Fig. 3.2.2 ResponsE's for the case of 10 �W
meehanical po w er step change
1. 7
s-
,
3.1.2 Responses for the cose of 10
0.'
�
�
2
1.052
+-�--.--.-.--,--'_-r-.-.__'
rig.
;
U
,
�
]
�
u
2
"0
�
o
1.051
t1>
1.056
g
��==----
1.060
---;;
0.05
..
+--.-.--,--,----.--.,-0:--.-.-,
-o
0.10
u
"
1.062
1.05�
l?
-0.15
5
1.060
.2,
.
.
0.00
-0.1(1
0.5
!,:,
0.15
1*
+-I'+�f=li+',,-",""''''�----
0. 30
0.30
�
�
0,25
0.20
0.35
0. 35
--:-
"0
C
'§
5
�
0
rig.
-
1 J'S
e (sees.)
3.2.4 Re spons e s tor the case of a three
phase short circuit of 0.1 (sec.)
--05
;
15
j
�--�
'
2 .!l-
ti m
du rat ion on infinite bLoS
PSS(8)
PSS
0.7
0.6
0.5
0.4.
o
05
---,-- I
1
1 5
:1
I
2.5
,�-�
.3
time (s ees. )
.3 5
..
- -T
".5
rig. 3.3.4 Responses for tne case of a three
phas e short
circuit of
durati on on inf inite bus
0.1 (se.:.)
PSS(C)
PSS
27
REFERENCES
[1]
Anderson, P.M.
and Fouad, A.A., Power System
Iowa State
Control and Stability, Chapter 8,
Un1versity Press, Ames, Iowa, 1977.
[2]
Fleming,
R.J.,
"Machine
Interactions
Mu1timachine Generating Plants", proceedings
CEA Meeting, Toronto, March 25, 1970.
[3]
Larsen, E.V. and Swann, D.A., "Applying Power
System Stabilizers", IEEE PAS-100, No. 6, pp.
3017-3046, June 1981.
[4]
Watson, W. and Coultes, M.E., "Static Exciter
Stabilizing
Signals
on
Large
Generators
Mechanical Problems", IEEE Winter Meeting, pp.
204-211, New York, Jan. 30 - Feb. 4, 1972.
[5]
Li,
L. ,
"The
Application
of
Power
System
Stabilizers in a Multimachine Generating Plant",
E.E.,
M.Sc.
Thesis,
Dept.
of
Univ.
of
Saskatchewan, 1986.
[6]
Bayne,J.P., Lee,D.C., Watson,W., "A Power System
stabiliser Stabilising Signal For
Thermal Units
Based on Derivation Of Accelerating Power", IEEE
Trans. PA5-96, Vol. 77, N, Nov;t>ec 1977, pp.
in
of
1777-1783.
Ronald
J.
Fleming
(SMIEEE,
P.Eng.)
was
born in
Saskatchewan, Canada, in 1930.
He received his
education in Saskatchewan, completing his ph.D. in
1968 in electrical engineering. He served as process
instrument engineer with Atomic Energy of Canada Ltd.
for two years and has been active as a consultant and
research contractor in the area of electric power
system control for several years.
He has been on the
faculty of the Department of Electrical Engineering at
the University of saskatchewan since 1958, teaching
and doing research in the area of power system
modelinq and control.
He has been participatinq in
the research activities of the Power Systems Research
Group and was Head of the Electrical Engineering
Department from 1984 to 1988.
He is currently a
professor in the Electrical Engineering Department.
Madan M. Gupta rec�ived the B.Eng. (Honors) in 1961,
M.Sc.
1n
1962,
both
in
electronics­
and
the
colllltli
ll1 cations engineering, from BITS Pilani, India.
He received the ph.D. degree for his studies in
adaptive control systems in 1967 from the University
of Warwick, U.K.
From 1962 to 1964, he
electrical-colllltli
ll1 cations
served as a
engineering
lecturer in
at
the
He joined the faculty
University of Roorkee, India.
of the College of Engineering at the University of
Saskatchewan in 1967 as a sessional lecturer, becoming
a full professor in July 1978.
His present research
interests are in the areas on non-invasive methods in
medical
diagnosis,
medical
imaging,
intelligent
robotic
systems,
cognitive
information,
neural
networks, and computer vision.
He is co-author with A. Kaufmann, of the books
Introduction
to
Fuzzy
Arithmetic:
'1heory and
Applications (Van Nostrand Reinhold, 1985) and Fuzzy
Mathematical Models in
Engineel'ing and Jlllanagement
Science (NOl'th-Holland, in press) and is the editor of
the
books
Fuzzy
Automata
and Decision
Processes
(1977), lIdvances in Fuzzy Set 'ltteary and Applications
(1979), Appl'oximate Reasoning in Decision Analysis
(1982), Fuzzy Information, Knowledge Representation,
and Decision Analysis (1983), Appl'oximate Reasoning in
Expert Systems (1985), Fuzzy <DIpJting (1988), Fuzzy
Logic in Knowledge-based Systems Decision and Control
(1988), all with North-Holland, and .Adaptive Methods
for Control Systems Design (IEEE Press, 1986).
He is
the subject editor for the Encyclopedia of Systems and
Control
(Pergamon
Press,
Oxford,
1987) and has
authored or co-authored over 200 research papers.
He
is an advisory editor for the International Journal of
Fuzzy Sets and Systems (IFSA) and other journals in the
field.
His recent research interest lies in the theory
and design of new sensors, new devices and intelligent
systems using biological and cognitive processes as a
basic (for possible applications in health sciences,
space
exploration,
manufacturing
processes
and
robotics) .
Jun Sun was born in Shanghai, China, on May 2, 1946.
She graduated in electrical engineering from Tsinghua
University, Beijing, China, and received the M.Sc.
degree
in
electrical
engineering
from
Chongqing
University, Chongqing, China, and the M.Sc. degree in
electrical
engineering
Saskatchewan, Saskatoon,
1987 respectively.
from
the
canada, in
University
1968,
of
1982 and
From 1968 to 1979 she was with the North-East
Power Company, China, working in the Power Plant
In 1982
Electrical Adjustment and Test Department.
she
joined
the
faculty
of
Chongqing univers�ty,
Chongqing, China, and was a lecturer of electr�cal
In 1985 she joined th� EI�ctr1cal
engineering.
of
Engineering
Department
of
the
un1ve�s1ty
.
Saskatchewan, Saskatoon, canada, and now 1 S work1ng
towards a ph.D. degree in the area of excitation
control of power systems.