IEEE Transactions on Power Delivery, Vol. 11, No. 1, January 1996
ROBUST,
M.
NEAR TIME-OPTIMAL
OSCILLATIONS
Royal
CONTROL
WITH
FUZZY
Senior
K.
Member
Institute
Dept.
minimum
presents
switching
a fuzzy
logic
to damp
controller
power
for series
system
electrome-
lished from observation
of the dynamicrd behaviour of a
simple power system and the general engineering knowledge about the system dynamics.
The performance
of
the controller
is shown to be robust and comparable
to
of a minimum-time
optimal
Eng. and Computer
controller.
time
theory
Analytical
WA USA
has been
approach
solutions
els. Furthermore,
a large
Science
State University
Pullman,
chanical oscillations.
A set of control
rules are constructed
and inference is provided
by fuzzy logic reasoning. The knowledge base for the controller
is estab-
that
of Elec.
Sweden
control
paper
Tomsovic
Washington
of Technology
Abstract
reactance
SYSTEM
Member
Power Systems
S-1OO 44 Stockholm,
This
OF POWER
LOGIC
G. Andersson
Noroozian
Member
Electric
393
proposed
are limited
numerical
computational
[3].
The
has many practical
to a few simple
solutions
effort
generally
bance
Small
stability,
disturbance
switched
based contpolier,
fuzzy
1.
stability,
reactance,
logic,
large
optimal
distur-
control,
rule
able as a prototype
compared.
Fuzzy
logic
fuzzy
theory
against
and are presently
to get attention.
turbance
both
INTRODUCTION
large disturbance
stability
In 1966, Kimbark
ity
of an electric
switched
might
limit
power
stability
that
system
series capacitor.
and small
the transmission
[1] showed
the transient
stabil-
can be improved
In recent
years,
dis-
capacity.
by a
progress
in
the field of high power electronics has led to the development of thyristor
switches which can be used for switching of series capacitors
(reactors).
By controlling
the
reactance of a transmission
line, damping of electromechanical power system oscillations
can be enhanced [2].
The application
of optimal
system state to its initial
in many
industrial
application
The control
was motivated
processes[4].
in the system
of
algorithms
implemented
Fuzzy logic
by a need to consider
can be
controller
uncertainties
and
For example,
the
model.
fuzziness might be concerned with the system description, i.e. when one cannot specify accurate dependencies
between input (control) and state and output variables.
Power systems transmitting
high power over long distances are often subject to stability
problems.
In this
respect,
limited
which other methods
(FL C) was the first
controller
approximations
robustness
modrequire
to certain class of problems.
As has been pointed out
in [3], the optimal control approach might be most suit-
based on fuzzy logic have been successfully
Keywords:
optimal
drawbacks.
control
steady-state
theory
to move the
operating
point
in
In particular,
useful when
conventional
of fuzzy logic for improving
is proposed.
A general
the power
review
power systems can be found
This paper presents a FLC
electromechanical
system
stability
of fuzzy logic methods
in
in [6].
for damping
oscillations
which
of power system
can provide
robust
control characteristics
with respect to line loadlng and
fault type. The power systems studied in this paper are
quite simple, but by studying
simple systems the basic characteristics
of the controller
can be analyzed and
conclusions drawn which give insight for larger systems.
Further,
nomena
95 WM 237-8 PWRD A paper recommended and approved
by the IEEE Transmission
and Distribution
Conunittee
of the IEEE Power Engineering
Society
for presentation at the 1995 IEEE/PES Winter Meeting,
January 29,
to February
2, 1995, New York, IU.
Manuscript
submitted
July 20, 1994; made available
for
printing
January 11, 1995.
the fuzzy logic methodology
appears very
the process is too complex for analysis by
quantitative
techniques.
In [5], application
since all the essential
studied
dynamics
here are modelled,
for the phe-
general
conclusions
can be extracted
from the results presented in the paper. This means that the proposed control method can
be implemented
in more
complex,
i.e.
systems, to damp tieline oscillations.
extension of the work reported in [7].
realistic
This
paper
power
is an
The paper is organized as follows: In section 2, the dynamics of a simple power system is analyzed and a multimachine test system is deseribed. Section !3 presents the
proposed
fuzzy logic controller.
proposed
approach
simulations
The performance
is demonstrated
and discussed in Section
0885-8977/96/$05.00 @ 1995 IEEE
through
4.
of the
numerical
394
2.
DYNAMICS
OF A SIMPLE
SYSTEM
POWER
reactance
with
A model
Fig.
of a single
1.
This
system
dynamic
switched
machine.
We
at the
to
assume
and
a reduced
the
of the
bus
The
Under
of
plane
U–
dashed
lines
and
to
so~d
~ X
– u. In
and U-
U+
lines,
Fig.
2, the
are sketched
respectively.
in
the
of the
(classical
model)
behind
the
Lb, the voltage
is E.
steady
& X + u and
corresponding
essential
influence
voltage
machine
is V.
is shown
the
phase
model
machine.
reactance
infinite
system
illustrate
on the speed-angle
synchronous
transient
power
is used
phenomena
react ante
of the
machine
system
U+
trajectories
state
condition,
Pm
Figure
1: Model
oj a simple
power
system
Figure
2:
(The
the mechanical
and
b =
mission
tor
power
Pm equals
O. If a three
line,
the
is reduced
Pm, there
to zero.
is then,
leads
to instability,
critical
clearing
transient
phase
electrical
the
fault
occurs
power
Assuming
time.
conditions
The
can
of the
a constant
power
the
fault
system
power
on the
output
an accelerating
unless
electrical
P.,
X
= 0.5,
difference
The
where
straints,
which
point.
that
The
Pm–—
the
switching
dynamics
under
the
at one of them.
the
The
– DW
(2)
e(6, w) = arctan(~)
speed
reactance
machine
swing
can be minimized,
steady-state
time.
operating
This
is an
maximum
control
consists
+ u)
which
nature.
is usually
complex
problem
is applicable
or
shows
The
not
that,
is reached
control
of maintaining
(X
intervals,
such
condition
optimal
principle
boundary
control
(X
that
the
system
– u)
during
real
● The
origin
if the
fault
must
take
lengths
trajectories
initial
trajectories
+ kr
actance.
solving
are
so-called
the
polar
optimal
tl~.
The
coordinates
O <0<
ing
for
the simple
differential
states
obtained
6(0)
and
system
equations
w(0).
corresponding
can be con(1)
Two
to
and
(2)
families
of
the
transfer
the
or
place
along
However,
we must
forces.
two
F. The
switching
by
realistic
switching
A OB.
the
amplitude
action
re-
a physical
constrained
can achieve
for
The
control
with
system
action
switching
curve
affected
a particular
two
1,
when
inspection
second
switching
are
consider
with
Close
as we are concerned
Thus
k =
and
observations:
within
the
(4)
when
quadrant,
quadrant.
than
OB
quadrant,
third
can be reached
2m
a limited
time
range
of disturbances.
o The
systems.
second
A O and
optimality
time
the
is less severe
of
control
approach
for
in
2, reveals
system,
the optimal
formal
feasible
[3].
Trajectories
by
the
is terminate-d
is uOPt =
in
con-
operating
(3)
fourth
structed
state
curve,
it
be represented
following
with
final
form
switching
below
of Fig.
Phase
the
w can
the
and
k = 2, (6, w) is in the
or more
1.(),
s(f5, &J) = (62 + d)+
)
angle
is of bang-bang
phase
U–
constant
time
=
(s, $) aa
tion
The
=
OB
damping
its
system
V
desired
trajectory
D:
of optimal
2.1
Above
is Uqt
6 and
A O and
an optimal
lies
appropriate
control
and
Ii = O, [6, w) lies in the first
at
1.10,
the
the
(6, w)
optimal
simple
=
satisfy
when
Pontryagin’s
control
OB
through
pass
reactance
original
reactance
A O and
transient
the
the
E
D = 6, U = 0.2).
X:
minimal
and
P = 0.8,
is,
curve
conti-ol
by
sin 6
X*7L
machine
w: control
in
are:
EV
6: machine
Ideally,
for
p.u.
segments
before
(1)
& = w:
in
= 0.03,
segments
input
power
i=w
(
M
is cleared
be described
trajectories
data
transgenera-
states
w=;
Phase
system
optimal
switching
time
of (S, 6J). For example,
to
point
F in
the
occur
near
360°
and
must
occur
near
270°.
Based
on (the
servations,
multi-machine
general
a set
test
phase
if the
system.
plane,
fault
insights
of control
is determined
for a severe
the
is very
developed
rules
were
by the posi-
fault
correspond-
switching
small,
by
must
switching
these
developed
obfor
a
395
Multi-Machine
2.2
Test
The power system
performance
of the proposed
connected
with
via an intertie.
field
cluded.
shown in Fig.
windings
the stability,
windings
are modelled.
the line is sectionalized.
L and reactance
are in-
To improve
Each section
has
jaL.
Lz
I
B
BU86
BU85
I
60
In general,
(6)
d(k)
–
(7)
it could be possible
a new operating
point
different
choice of such a new operating
of this paper.
transformed
Bw4
Btd?
=
ew (k) = W. – w(k)
are
are modelled
of exciters
eb(k)
the
Two sub-systems
The machines
and the influence
No damper
a length
3 is used to study
FLC.
the errors e6 (k) and ew(h) at sample k are
bance),
System
one. The
the scope
is outside
eb (k) and ew (k) should
The quantities
be
O(k)) accord-
(S(k),
are the
ing to (3) and (4). These transformed
quantities
controller
input.
The controller
output is the status of
Bwl
the three switches
in Fig.
3.2
Description
Fuzzy
State
disturbance.
linguistic
3: 500 kV test poweT
the system to
point
to the polar coordinate
1, i.e. Co, Cl, C2.
The fuzzy set classifications
Figure
to control
from the initial
system
Al:
zero
AA:
large
are based on the severity
Five fuzzy partitions
variable
is associated
(Z), Az:
(L),
small
A5:
The membership
(S),
are considered
with
As:
of
and a
each set as follows:
medium
(M),
veTy iaTge (VL)
functions
for these fuzzy sets are shown
in Fig. 4.
A small or large disturbance
causes the two subsystems
to swing
which
against
each other
might
result
in in-
stability.
To stabilize the power swings, a switched reactance (+j ~)
is assumed on the midpoint
of the line. In
the normal
condition
equal to j#L.
the total
reactance
of the intertie
This Value can be varied from j(~L
is
– ~)
to j(z~ + ~)
by switching the controlled
reactance. In
the multi-machine
system, b is the swing angle between
the centers of inertia
for the two subsystems.
ment and estimation
of this angle are feasible
recent advances in the synchronized
[8] or by measuring
tion
the voltage
of the switched
trolled
reactance
reactance
with
to bring
where
10ms).
[iqm)
+
T
the con-
the
is
sectors l?l,
for
S
is divided
into
l?2, B3, B4, B5, ~G and B7 (Fig.
degree of membership
is associated
seven
5) and a
to each angle (0).
operating
point, i.e. to the same 6
even when e.g. a line section is lost
u
– 6((k – I) T)]
To gain
partitions
the system
in connection
with a fault.
The angular frequency
computed at the kth sampling time from:
w =
4: fizzy
In the same way the phase plane
at the loca-
[9]. By varying
Figure
the
measu?’ement
and current
it is thus possible
back to the initial
as before the fault,
phasor
Measure-
is
(5)
sampling
time
further
flexibility
(In
this
example
T
to the scheme,
=
line
switching could also be considered as control actions, as
suggested in [10]. This possibility y has not been explored
in this paper but might be a useful complement
controlled
reactance scheme employed here.
3.
FUZZY
LOGIC
CONTROLLER
to the
Figure
(FLc)
It should
The proposed
3.1
Input
FLC
and
is described
Output
in the following:
Variables
that
pa?’tiiions
the scaling
foT 6
of the fumy
sets is
accomplished
through
the information
from phase trajectories and the switching
curve. A heuristic
try and
error
If 60 and W. are the states of the initial operating point
(which are known from estimation
prior to a distur-
be noted
5: Fuzzy
procedure
is needed
to find
an appropriate
fuzzy
partitioning
for a desired response. In practice the scaling can be realized by the use of fuzzy chips [11].
396
3.3
Design
Control
of Rule
rules
are constructed
oft he dynamical
ing
curve.
Table
4.
Base
based
behaviour
The
rule
on the
of the system
base consists
observations
One
fault
and the switch-
of 35 rules
as shown
in
1.
As
A4
A3
AZ
Al
RESULTS
Machine
Infinite
Bus System:
occurs near the generator in Fig.
cleared
after
trajectory
s
SIMULATION
80 ms.
for
FLC
with
with
dashed lines.
the fault
place
on the
OPT
O) after
other
of ii against
phase
fault
with
solid
the
point
and
the
system
stitchings.
at point
for
switching
FLC.
to the
off)
takes
point
S is
S’ is close
to it.
The
pre-fauh
Fig.
F
(reactor
The
The
S1l.
case
at point
is switched
S
is
transient
(OPT)
second
and
two
switching
system
is switched
capacitor
OPT
line
conducts
The
the
S for
switching
(point
The capacitor
on and
The
line and for uncontrolled
is cleared.
at point
A three
1.
the
controller
dotted
for
is switched
6 shows
time-optimal
line,
when
Fig.
-
equilibrium
FLC
undergoes
7 shows
the
an-
variation
time.
150
w [deg./s]
Table
1: Rule
-table
1C9
F
----
---.-- -------------
--.:~:-:..Uncontrolled
----
-
--=
-,-.
,,..
..:.’
.
.:
y
50
-
Logical
Logical
Inference
inference
grades
for
the
consists
of
g membership
determining
output.
The
rules
then
u(k)
are
OPT
/,
,,
o-
controller
-50
of the
form:
c)
.,50A
Xi:
If S(k)
is AP and
O(k)
is Bq,
15
?0
for
Xi
two
(rule
i ).
inputs
/J(xi)
The
S(k)
Cn
The
and
are
the
grade
value
for
the
of Xi
6:
Transient
for
the
40
6
3, -
(n=
[d+
/’,
Uncontrolled
,- \
/
‘,
/’
‘,
.
O, 1, 2) is
~=~,~,J~,.e.
. .
,’
,\
=
=
P(C2)
where
w,
X&(xi)
7?Z2
ml,
3.5
Defuzzification
The
final
state
‘,
-
,0
‘,
;
*5
-
*O
-
FLC
“t
‘,
,’
‘,
//”
\
J
,,
\
output
switches
be employed
(in this
must
of rides
corresponding
+ml
+mz
be a discrete
value
A decision procedure
to determine
the control
states.
in order
Figure
(11)
4,...
case w
= 35).
one machine
For example,
if
= 0.3 and fi(cz)
= 0.8, then the
be C2 (switch on the capacitor).
that fuzzy set partitioning
of S and
of the rule base, are constructed
for
the base system loading.
For other loading conditions
the controller is tuned by scaling the fuzzy partitions
for
controller
with
guarantees
respect
the robust
to loading
performance
conditions.
Variation
of 6 against
System:
3 is given
-time
The data for the system
in the Appendix.
Machine
FLC is present. The uncontrolled
response is shown with
of the OPT was not feasible
dashed lines (The simulation
output.
This
[s]
indi-
degree is selected
S [12].
Time
.’
must
value
in this
It is to be noted
O and organization
,’
‘.
.Wfl is the reference machine.
The loading of the intertie is 2000 MW. The response of the system to different disturbances
are shown with solid line when the
value jL(C. ) defined in
the largest membership
P(CO) = 0.2, K(cl)
output signal would
,’
\
,/
7:
Multi-Machiie
shown in Fig.
suggested by the membership
(9-11).
The value of C. with
as the crisp
,’
(lo)
Stage
control
the
2,3,
mz are the number
to each switching
cating
i =
‘,
,’
(9)
z = 10,14,15,...
w
‘\
/’
‘.-,
p(c~)
w plane
1,
25
C.
[
40
35
in 6-
trajectory
(8)
output
30
sets
&Bg(8(k))}
=Zl!&?Q
P(co)
fumy
is
= min@Ap(S(k))!
membership
corresponding
membership
f?(k)
25
20
is Cn.
Figure
where AP, 13q and
\
\.,,,, \
!!,
!4,
FL G
o
,,,
t,,,
,,,
,,,
.:.\.
.
‘.’,.
,.....
-,.30
-’-----.--__._____===!::~s’~’;:;deg ~
,,,2
3.4
...
. .
\.
,/”
of the
case,
between
Case
but
FLC
i:
cleared
OPT
case).
The
A three
after
and
Case
Intertie
half
local
of the load
simulates
variations
phase
80 ms.
inter-area
ii:
it is reasonable
and
a small
will
to expect
remain
following
fault
Figs.
modes
loading
on
9 show
against
time
decreased
to
at BUSJ is disconnected
disturbance).
of S2 and
difference
to
that
of
cases are considered:
occurs
8 and
the
similar
Figs.
63 – 62 against
BUS6
it
is
of
(3 stitchings).
1500 MW.
for
One
100 ms (This
10 and
time
and
the variations
11 show
(3 stitchings).
the
397
Case
A three
iii:
sections
between
is cleared
after
phase fault
occurs on one of the line
BUS4 and BUS5 near Bus5.
100 ms by opening
The fault
the faulted
line.
‘OO-.]
‘,
i 50
1’
In
/’
100
this case only the capacitor
is switched
which
/“
preserves
-\
/’
the initial
equilibrium
point.
Figs.
12 and 13 show the
variations
of 62 and 63 ~ 62 against
number of stitchings
is 3.
time.
The
50
1
/’
,
,’
~
1’
,!,.
,’ ~~
total
o
Time
Case iii
-50
0,23
4se7
Figure
12: Variation
6-
[s]
L?o,o
of inter-area
mode
against
time
/“;
6-
0
“ii
‘l;
.50
Time
Case i
;
2345
Figure
8: Variation
-06
[s]
.7ss
inter-area
of
t
20
mode
against
1
time
4
.i6e7
Figure
The
13: Variation
simulation
power
system
ample,
in the
control,
other
the
of local
mode
against
62 [deg.]
/,
5 -8
there
-:
the
stable
of the
small
ex-
without
the
case.
disturbance
cases
modes
the
In
has
impact
is not
of
negative
It is worthwhile
the
relatively
influence
some
the
example
was selected
is still
all
the
oscillation
in this
of the
For
in the controlled
are also damped.
modes
of the
performance
is unstable
following
In
time
significantly.
the system
damping
that,
controller.
remaining
inherent
damping
low for a better
controller.
oscillations
However,
small
ent damping
effect
-7.5
I
That
after
the
preis why
Case
,,
,2s4
Figure
contributed
Time
ii
the
are
in power
by the
realistic
action
damped
system
power
systems,
of
by
the
these
inher-
or by the damping
system
stabilizers.
10: Variation
of inter-aTea
[s]
1
5e7s
5.
9?0
mode
against
i es
controller
;\,
1.55
-,,,,:;
,!
using fuzzy
logic for control
to damp power oscillations
of
was proposed.
The rule base of the controller was constructed
based on
the dynamical
behaviour of a simple system. Numerical
W-J
–??
:1
,,
CONCLUSIONS
time
A rule-based
%
oscillations
sources
line reactance
, .’3
in
j
~:
.sO
simulations
show that
the performance
of the controller
is effective. for damping of both large disturbances
and
The response of the controller
is
small disturbances.
, 45,.4
,,,
--
,.*
that
against
1
k
the
,.25
show
improved
on the local
local
sentation
:
mode
it becomes
of the system
;,
,,
-e
the
local
considerably.
control
and
time
of
been
Case iii,
the
to mention
-6
-5
9: Variation
results
has
while
cases
improved
Figure
Time [s]
s9>0
Case iii
‘O*ZS
62 [deg.]
6$!–
-i
‘
r
;;
,,
‘j
ii
Ca8e
~ Time
ii
[s]
I
0,23
4567
S9<0
comparable
with that of a minimal
time optimum
controller for a single machine system in view of damping
time and number of switching actions. The performance
of the controller
is robust with respect to line loading
and fault type. The structure of the controller
is easy to
understand
Figure
11: VaTiation
of local
mode
against
time
and easy to implement
and is attractive
from
an engineering
point of view. Other questions, such as
the optimal placement of controllable devices need further
work to be answered.
398
BIOGRAPHY
ACKNOWLEDGEMENTS
The
ABB
authors
wish
to
Corporate
lating
thank
ABB
Research
discussions
with
for
Mr.
Power
project
M.
Systems
support.
Chamia
and
Stimu-
are
Mojtaba
Noroozian
gratefully
acknowledged.
the Royal Institute
Kimbark.
by Switched
on
Power
Improvement
180–188,
of System
Series Capacitors.
Apparatus
Feb.
and
IEEE
Stability
Ph.D.
~.
sion
Capacity
IEEE
PAS-85
N.
System
IEEE
(2): PP.
D.K.
PAS-89
H.J.
Optimal
and
May/June
Set
of
G&an
Andersson
M.A.
Hassan
and
Sys-
1970.
Theory
and
Its
Ap-
[6]
O.P.
Test
Results
Self-Tuned
PSS.
IEEE
8(2): pp.
K. Tomsovic.
of IEE
M.
Noroozian,
[8]
G.
System
In Proceedings
System
vanced
Virginia
Tech
Power
of Fuzzy
K.
Fourth
Symposium
Systems,
January
Technology
VA,
on
Wide
at
AdArea
the
on Computers
Arlington,
of
pages
1993.
in
Presented
Conference
Fuzzy
with
Perspective
Control,
E. Lerch,
trol
for
D.
Povh
Damping
‘Zhm.aciions
May
[10] S.
and
L.XU.
Power
cm Pow..
Third
IEEE
H.
October
Advanced
Transactions
on
November
1511-1517,
197.5 and
Engineering
Sciences and the Royal
Swedish
Kevh
Tomsovic
1960.
He received
University,
B.S.
Houghton,
from
1987
fessor
(M’87)
the
in
University
was
born
from
1982,
in
SVC
Con-
Oscillations.
IEEE
System.,
6(2): pp.
524–535,
Stabilizing
Power
Switching.
Systems,
8(4): pp.
and
the
M.S.
State
[12]
M.
and
Noroozian.
Components
Institute
Fuzzy
Systems,
Ezpioring
in Power
of Technology,
l(l):
pp.
Benejis
Systems.
1994.
and
Seattle,
He is currently
at Washington
LA,
in
Technological
of Washington,
respectively.
- Generator
data
Equivalent
gen.
Ph.D.
in
1984
an assistant
pro-
University.
B
(PbaJe = 1000
MVA)
Silfl
S&f,%’
SM3
thermal
hydro
hydro
s.
5500
H
4s
4s
4s
xd
1.00 p.u.
0.60 p.U.
0.30 p,u.
1.00 p.u.
0.60 p.U.
0.30 p.u.
TjO
2.00 p.u.
1.90 p.u.
0.25 p.U.
6.0 p.U.
5.0 p.in.
5.0 p.u.
D
6 P.U./p.U.
6 p. U./p.U.
6 p.U./p.U.
0.10 p.u.
0.10 p.u.
0.10 p.u.
1.00 p.u.
1.00 p.u.
1.00 p.u.
Ke
K.
K.
Xq
x;
Transformer
Terminal
Exciter
volt.
MVA
1800
= 30
T. = 0.05
lines
L = 350 km,
(double
z = 0.20 fl/km
L2 = 50km
z = 0.34$1/km,
b==5E-6
S/km
S1 =
S
T.
MVA
=
27–42,
of
PhD
1800
10
= 0.05
S
MVA
=
Te =
10
0.05
circuit)
(compensated
L3 =
line)
100 km, z = 0.34t2/km,
(p.u.)
6 + jl.2,
S4 = 1.0+
(The
1993.
T. Miki, et. al. Silicon Implementation
for a Novel
of InHigh-Speed Fuzzy Inference Engine. Journal
telligent
Academy
Slidell,
Michigan
voltage
S2 =
0.1 + jO.010,
S3 =
1993.
Controllable
thesis,
TRITA-EES-9402.
Royal
0.1 + jO.010,
jo.2
dependency
of the
loads
is assumed
linear).
[11]
1980,
ASEA:S
1993.
System
Glavitch.
in
HVDC- division
and in 1986 he was appointed professor in Electric Power
Systems at the Royal Institute
of Technology,
Stockholm. He is a member of the Royal Swedish Academy of
- Loads
and
of Lund
1980 he joined
in Electric
1991.
Chen
university
In
Type
Tomsovic.
Design
to Power
Application
Engineering.
Set The-
Transactions
and
Control
of the
the
- Transmission
[9]
was born in Malm6,
APPENDIX
1993.
Measurement
and
a
June 1993.
Australiaj
An
Monitoring
Energy
Systems.
Application
Melbourne,
Hauer.
Based
on
Andersson
Expert
J.F.
Logic
Status
Damping
Logic.
406-411,
a Fuzzy
221–228,
113-10(2),
and
!i%ansactions
to Power
Japan,
Power
Implementation
for
Current
ory Applications
[7]
Malik.
from
degrees
1985.
Laboratory
Conversion,
(M’86-SM’91)
respectively.
and
[5]
with
of Sciences.
Control.
Apparatus
(5): PP. 975-984,
Fuzzy
Sys-
1981.
Improvement
Power
Kluwer-Nijhoff,
Power.
and
August
Using
on
Zimmerman.
plications.
Reactive
Reitan.
Stability
Transmis-
Apparaius
3939–3933,
Transactions
tems,
[4]
and
of
Control
on Power
(8):pp.
Ramaro
Power
Improvement
al.
by Thyristor
PAS-100
and graduated
Sweden, in 1951. He received his IvI.S. degree and Ph.D.
l%ansactions
tems,
[3]
et.
of Technology
in 1981. In
his study at
Transactions
Systems,
1966.
Olwegi%d,
in 1955.
degree in June 1994.
degree
[2]
was born in Iran,
M.S. degree in power systems from UMIST
1984 he joined ASEA. In 1990, he continued
REFERENCES
[1] E.W.
(M’92)
He received his B.S. degree in electrical engineering from
Arya-Mehr
(Sharif)
University
in Tehran in 1979 and
r
‘ ‘w
Figure
14: Exciter
model
to be
S
399
Discussion
Carson W. Taylor, Bonneville
Power Administration,
Portland Oregon: This is an interesting
paper. Fuzzy logic
phase-plane
control techniques
are attractive
for series
capacitor bang-bang switching, or for single insertion,
The possibility
of thyristor-switched
series capacitors and
the availability
of microprocessor
controllers
has revived
interest in bang-bang switching,
Because of the unfortunate earlier submission dates of manuscripts,
the authors
were probably not aware of the Kosterev and Kolodziej
paper [A]. I invite the authors to compare their approach
and results with those of Kosterev and Kolodziej.
With regard to estimation
of angle difference,
apparent
impedance measurement
[B-E] is another approach. This
may have technical and cost advantages for damping of low
frequency
interarea
oscillations.
The BPA-developed
RRdot phase-plane
controller
could be adapted for series
capacitor insertion or other special stability control.
The control proposed in the paper must be modified to allow
anew post-disturbance
operating angle. One method would
be to suspend control once speed difference is within
a
deadband. The final post-disturbance
state with weakened
transmission
should be with the series capacitor inserted.
Comments?
Power System - a R, Rdot Relay Application
for Generation Trip on N-NE
Intertie,’
CIGRE, paper 34-105,
1990.
E. C. W. Taylor, discussion of IEEE Committee
Report
‘Synchronized
Sampling and Phasor Measurements
for
Relaying
and Control:
IEEE Thansaetions
on Power
Delivery, Vol. 9, No. 1, pp. 442-452, January 1994.
Manuscript received March 1, 1995.
M.
Noroozian,
G.
Andersson
paper and the discussion
Case iii is the most practical simulation
case in the paper.
Could the authors also provide results for a single insertion
(one instead of three stitchings),
as is used today with
mechanical switches [1]?
+ The
authors
have fOU1ld the paper
●
Clearly
the final weakened post disturbance
new and unknown
and R. L. Cresap, “A New Out-of-Step
of Change of Apparent
Resistance
IEEE
!#-ansactions
switched
post-disturbance
on
Power
Apparatus
Vol. PAS-lO2, No. 3, pp. 631-639, March
Relay with Rate
Augmentation,”
and
and
state should
on. To allow
operating
for a
point,
idea to use the speed only as input to “identify”
the
this new
operating point is probably useful. However, it must be
combined with some other criteria to identify situations
where (0 is small and the angle difference is large. For
these situations
a switching
should
be done. One
possibility might be to use the acceleration of 0), i.e. h.
of the rule
loading.
tuned
For
other
on-line
loading
by
S(k)andt3(k)are
controller
controller
of S and Q and organisation
base, are constricted
for
input
the
satisfactory
simulations
fuzzy
and
set
S.
u(k)is
of the fuzzy
is
If
the
logic
F’{(xS(k),fie(k)}
defined by the rule base and
scaling.
results
for different
the controller
variables
output, the general function
can be expressed as:
showed
the base system
conditions
scaling
the
cx and ~ are appropriate
c. C. W. Taylor, J, M. Haner, L. A. Hill, W. A,” lllittelstadt,
by Kosterev
future work.
where F denotes the mapping
Series
A. D, N, Kosterev and W. J, Kolodziej, “BangBang
Capacitor
Transient
Stability
Control,”
IEEE/PES
paper 94 SM 536-3 PWRS.
B. J. M. Haner, T. D. Laughlin,
and C. W. Taylor, “Experience with the R-Rdot Out-of-Step Relay,” IEEE lYansactions on Power Delivery, Vol. PWRD-1, No. 2, pp. 3539, April 1986.
The
the introduction
of the apparent impedance measurement
method developed by BPA which will be considered in
u(k) =
References:
Tomsovic:
Kolodziej an interesting approach toward solving the nonlinear control problem. The authors want also to thank for
. The fuzzy set partitioning
In the Western North American interconnection,
we have
had good experience with single insertion of series capacitors, with manual bypass some minutes later. Single insertion and the use of power system stabilizers
seems to be
very effective (cost effective).
If there was need, three
mechanical
stitchings
(insert,
bypass, insert)
may be
possible for low frequency interarea
oscillation
stabilization.
K.
and comments.
be with the series capacitor
Regarding
robustness,
the authors
state: “For other
loading conditions
the controller
is tuned by scaling the
fizzy partitions
for S [12].” This is a critical issue. Can the
authors describe their tuning
methods, and the on-line
implementation?
and
authors wish to thank the discusser for the interest in this
The
following
scaling
based on a large number
of
loading conditions:
ct=l-o.3(P-Pm*),
where Pb~,, is the base loading
p=l
and P is the present loading
of the intertie. This implies that the adaptation of the
controller is done by contraction or expansion of the fuzzy
partitions
(scaling of c+, C/z,c+and di in Fig, 4).
Syeteme,
1983.
D. J. G. Tannuri, L. C. Zanetta Jr., J. Da C, Patrao Neto,
J. Oliveria, C. Simoes, M. C. Bertolucci,
E, Montalvao,
D. Mirandella,
and J. A. de Almeida, “Discrete Supplementary
Control
for the Stability
of Eletronorte’s
.
The
simulation
switching;
capacitor
variation
for
case
iii
i.e., after the opening
is switched
is
repeated
of the faulted
on and it remains
with
line,
connected.
one
the
The
of 8Z against time is shown in Fig. 15. It should
400
be noted that no additional damping is modelled in these
simulations. In a real case, the oscillations should be more
damped.
30
25
20
15
10
5
0
-5
.10
Fig. 15: Variation
Oj-inter-urea
Manuscript received April 19, 1995.
vwde against time