524
IEEETransactionson Power Systems,Vd.6, No.2, May 1991
ADVANCED SVC CONTROL FOR DAMPING POWER SYSTEM OSCILLATIONS
E. Lerch
D. Povh, Senior Member, IEEE
SiemensAG Erlangen
Fed. Rep. of Germany
Keywords:
Static Var Compensation, power oscillations, damping,
local phase angle, estimation.
Abstract
Dynamic reactive power compensation is used to a n increasing extent to improve voltage and reactive power
conditions in ac s stems. Additional tasks can also be
performed by the i t a t i c Var Compensators (SVC) to increase the transmission capacity as result of employment of
SVCs for power oscillation damping. This is of particular
importance in the case of weakly coupled power systems.
A new SVC control for damping of power system oscillations has been developed. To increase system damping SVC
uses phase angle signal estimated from the measurement
of voltage and power at the SVC location. By means of a n
optimization and identification procedure optimized design
of the damping control with various control concepts can be
determined taking into account non-linear power systems.
As a result of this method it is possible to increase power
system damping considerably, in particular in critical situations close to the stability limit, using only locally measured state variables at the SVC thus leading to increased
transmission capability of the power system.
1.
Introduction
I n recent years SVC has been employed to a n increasing
extent since dynamic reactive-power control gives considerable advantages for power system operation. Besides
to the voltage control as a main task SVC may also be
employed for additional tasks resulting in improvement of
the transmission capability.
90 3 1 L60-6 PWRS
A paper recommended and approved
by t h e IEEE Power System Engineering Committee of t h e
IEEE Power Engineering S o c i e t y f o r p r e s e n t a t i o n a t t h e
IEEE/PES 1990 Summer Meeting, Minneapolis, Minnesota,
J u l y 15-19, 1990. Xanuscript submitted January 29,
7990; made a v a i l a b l e f o r p r i n t i n g June 21, 1990.
L. x u
Zhejiang University
P. R. China
An important aspect when using SVCs is damping of power
oscillations. Damping of power system oscillations plays a n
important role not only in increasing the transmission
capability but also for stabilization of power system conditions after critical faults, particularly in weakly coupled
systems. In this paper the use of SVCs for damping critical
power system oscillations on the basis of local state variables is described.
To achieve this objective i t is necessary to improve the SVC
control concept by introducing signals which reflect power
system oscillations. The normally used SVC voltage control
is not in a position to effectively damp these oscillations. In
some critical cases the voltage control can even amplify
oscillations. The optimum variable would be the phase
angle difference of systems which oscillate with respect to
each other. I n absence of a telecommunication link this
variable is not available. However, a n estimation of phase
angle difference can be carried out at the point of installation of SVC which is adequate for improvement of power
system damping.
2.
Estimation of Machine Phase Angles Using
Local State Variables
Voltage and frequency and in addition active and reactive
g w e r and currents in the incoming lines to the node of the
VC are locally available as measured variables. The use
of these local state variables only is a n objective to calculate the phase angle difference and to use this signal for
reduction of power system oscillations. The realization of
this new method became easier through the development of
digital SVC control which is able to calculate the estimated
phase angle difference.
In a number of publications various concepts for damping
of oscillations b means of frequency correction signals
have been descriged [ l , 21. This method can also be derived
from equation (A14) in t h e appendix. The frequency is an
adequate control variable for example in a relatively small
system, oscillating against a relatively large system whose
frequency is hard1 affected b the power oscillations I7 1.
The use of a localry measuref frequency is suitable only
when the power system oscillation frequency can be clearly
filtered. In the case of loosely coupled power systems this
requirement is not always satisfied so that filtering of the
oscillation signal from the influenced frequency is complicated [3]. Another often used control signal is the measured
value dPldt [41.
For large phase angle values close to the synchronization
limit erroneous signals can be generated since the phase
angle deviation and the active power flow may be of opposite phase.
0885-8950/91/05004521.~1991IEEE
525
A new method will be described using local measurement
of voltage, active power and reactive power flow to derive a
signal for the phase angle of t h e generators with respect to
the SVC (reference node). A good estimation is, however,
only possible if the desired phase angle is observable in the
power flow a t the location of t h e SVC.
If the SVC is considered a t the node j in a power system
with a generator or subsystem k the complex voltage drop
&
E can be derived from Fig. 1.
--I
where 5 = Vj is taken a s reference.
The voltage angle difference between Vj and & is then
(2)
If E_k is defined a s the voltage behind the transient machine reactance x'dk which can be taken into account in
Y'k, 6kj gives a n estimate for the phase angle of the generd o r a t the node k with respect to the load angle a t node j.
As a result of power system reduction to a two generator
system taking the SVC node into account, the coupling admittance Y.k can be calculated for a n actual power system
condition.$he phase angle difference between the systems
is obtained by elimination of the reference angle of the SVC
node. By means of this difference signal the oscillation of
the two power systems with respect to each other can be
estimated. Fig. 7 depicts a comparison between estimated
and exactly calculated load angle difference of both generator systems. The rough estimation is sufficient to approximate the phase angle difference. No attempt was made to
improve matching since the phase angle of both signals is
in close agreement and this is essential to give the proper
signal for damping control. In a multi-generator system the
phase angle differences of individual systems with respect
to each other can be selectively calculated if these a r e
coupled via the SVC node (measurable and observable).
In order to check the sensitivity of feedback with respect to
the equivalent reactance load switching was performed in
both power systems by opening and closing one of the
double circuit lines of the studied system (Fig. 2 ) . The
equivalent reactance of the unfaulty power system was
adequate for estimation of the phase angle within this
power system configuration.
2.1
Effect of SVC on Oscillation Behaviour of
Generators
On the basis of a single generator system connected to a
fixed frequency power system described in the appendix it
can be shown that there is a direct correlation between
alteration of t h e voltage a t the SVC and alteration of t h e
phase angle of the generator. Therefore, damping of the
system oscillations cannot be directly influenced by the
voltage control of the SVC. However, it is possible to increase damping if the voltage of the SVC is controlled
linearly a s a function of the rate of change of the phase
angle (change in generator speed) [ 8 ] . The effect of SVC on
t h e improvement of damping conditions, however, decreases with the increased power system short-circuit
capacity. However, in case of high short circuit capacity the
SVC location is also not suitable for voltage control.
The phase angle of generators seen from the location of t h e
SVC is estimated on the basis of these theoretical considerations in order to control the SVC.
2.2
Control Concept Employing a Local Phase
Angle Signal
The configuration depicted in Fig. 2 was investigated in
order to demonstrate the basic effectiveness and robustness
of the new local damping signal.
The 600 km long 500 kV double circuit line connects two
power systems with a total capacity of 6600 MW.
Approximate1 40 % of the charging capacity of the line is
compensated g y means of shunt reactors. Under steady
state conditions 815 MW a r e fed to power system 1. A
control range of
200 Mvar was selected for the SVC. t h e
steady state condxions are given in Fig. 2 .
+
fault location
815 MW
voltage control
6000 MVA
500 kV
H=7s
4441 MW
2449 Mvar
f200 Mvar
5200 MW
2000 Mvar
1300 MW
500 Mvar
line data
r=0.028 aKm, x=0.26 alKm, c=14 nF/km
Fig. 2 Single line diagram and pre-fault conditions for two area system
Fig. 1 Definitions for estimated phase angle 6
ki
(reference node I)
In the case of more complex systems i t is possible to provide
adaptive matching of the equivalent reactance; determination and matching of the equivalent reactances is also
possible on-line by using extended Kalman filter [51.
The effectiveness of SVC for damping oscillations is limited
by the maximum rating of the SVC. Maximum damping is
thus achieved employing bang-bang control with correct
phase angle of the signal thus utilizing the maximum SVC
rating [41. Fig. 3 depicts a SVC control employing a
damping signal. Additional filters are required in order to
filter out interference signals from the relevant frequency
range of oscillation from 0.3 to approximately 2 Hz. The
transfer function to filter out harmonic content in the
estimated phase angle signal from ( 2 1
was employed for bang-bang control. Parameters can be
determined by a optimization procedure in the NETOMAC
526
As shown from Fig. 4, the change of local frequency characteristic (Af at SVC node) is not suitable to be taken a s
input signal for the damping controller because of difficulty
to filter out the low frequency signal of generator oscillation.
V-control sig.
voltage control
filtering
-
TCR and TSC
firing circuit
without SVC in operatlon
bang-bang
or /and
linear control 8 -control Sig.
'af atchan~ 3 ec -innfrequency
de
8 - controlled SVC
- $.
measured at
SVC-node
SVC-sig.
-
j = SVCl6ode
AV
Fig. 3 Concept of SVC damping control
-
-
-
h h r -
A
at SVC-node
program [6], whereby the maximum damping is calculated
taking into account the whole non-linear system. The measuring equipment for Pjk, &, v . in (1) was modelled a s a
first order time delay with 2d ms helay time.
If the target function of oscillation damping for optimization procedure is minimized
z=
p P - z d r +min
(4)
where a bang-bang system is designed according to (3)and
represents the change in active-power flow between system
1 and system 2 at the SVC node, the parameters of the
transfer function Gl(s) can be obtained.
The parameters of Gl(s) are, however, not optimal with regard to higher frequency content of the bang-bang oscillation. Parameters, determined by means of a n identification procedure, however, minimize the overall time behaviour of AP1.2. Consequently the higher frequency signals of the SVC are additionally evaluated in the procedures and suppressed by matching the parameters.
The optimizatiodidentificationprocedure is a special mode
of NETOMAC program which calculate a large number of
alternatives using various parameters and determines
automatically the optimum parameter set according to a
target function.
The system dynamics were simulated with the NETOMAC
program including the control concept depicted in Fig. 3
whereby the SVC was modelled a s variable susceptance.
1.5
0.
3.0
4.5
6.0
7.5sec~9.0
Fig. 4 System oscillation without SVC and with
6 - controlled SVC in operation
The influence of the SVC rating on the reduction of oscillations can be seen from Fig. 5 where the damping near the
instability of the system in absence of a n SVC (Fig. 4) is
defined as 1pu. SVC ratings of k 100 to k 500 Mvar have
been taken into account.
Voltage control of SVC is not able to damp power s stem
oscillations. The transmitted active power is sole& dependent on the phase angle difference of the two power systems and the SVC used to maintain a constant voltage increases the synchronizing torque and SVC in voltage control mode acts to increase stability limit. This influence
goes, however, hand in hand with a reduction of power system damping Fig. 6 shows a s a n example the unfavourable
phase angle (A a) of the voltage signal for power system oscillation damping compared with the optimum phase angle
signal.
7 .
Fig. 4 depicts optimized employment of the SVC for oscillation damping with the SVC capacity of f200 Mvar.
Parameters of Gl(s) are shown later in Fig. 8. System reaction without SVC is also shown. A three-phase fault in the
vicinity of system 2 of 70 ms duration was assumed to be
the cause of power system oscillation.
Power oscillations of approximately 0.5 Hz and amplitudes
in excess of 500 MW (AP1-21 occur a t the transmitted power
of approximately 815 MW (P2-1)after the fault in case SVC
is not in operation. The system is operating a t its limits.
Oscillations are weakly damped. At transmitted power in
excess of 905MW the power system would become unstable. If damping is defined over the area under AP1-2 in
accordance with equation ( 4 ) without and with SVC,damping due to the damping control is increased by 78 8 I Fig. 5)
1
0
t200
QSvcWvar)
t500
+
Fig. 5 Damping of system oscillations as function of
SVC-rating based on the case without SVC ( Z, )
system conditions according to Fig. 2
527
6 -controlled
- -
-
V-controlled
~-
SVC-sig.
- _ _
I
I
AV
A
V
-V-V-V-V-k
V-controlled
AV
AP.
v
at SVC-node
at SVC-node
1.5
0.
Sestim
6.0
4.5
3.0
7.5,,9.0
Fig. 7 Transmitted power increased to 925 MW
( system condition according to Fig. 2 )
0.
1.5
3.0
4.5
6.0
7.5sec,9.0
Fig. 6 SVC operation with voltage and phase angle control
( system condition according to Fig.2 )
Under the selected load conditions system damping may
also be increased by the classical correcting signal dP/dt;
however, if the transmitted active power is increased close
to the stability limit, e. g. to 925 MW, the robustness of the
new signals becomes apparent (Fig. 7) especially in the
region of initial oscillation (phase angle difference in excess of 90"). In the case of classical dP/dt control there could
be a faulty control order in the time interval A t depending
on the saddle in the power flow. Using the same parameters for filtering and control a dP/dt controlled damping
results in up to 10 % less system damping in this case
depending on the prefault transmitted power. Comparison
of the estimated phase angle 8estim with the actual value
82.1 (Fig. 7) demonstrates the robustness of the selected
correction signal a t this critical load situation close to the
stability limit. The phase of actual value and estimated
value are practically equivalent.
As shown here the estimated signal contains the sudden
changes in the SVC-voltage. The assum tion of constant
SVC-voltage simplifies equations (1)a n 8 (2) and reduces
the calculation accuracy, but with the advantage that the
filtering transfer function can be neglected. Com arison of
the damping effects of both signals with and wit1out SVC
in this way shows that the filtering transfer function reduces the damping up to 15 % depending on the washout
time constant Tw from(3).
In many cases linear control is very effective to solve dynamic stability problem caused by small disturbances. But for
the transient stability problem there is much larger control
area needed. Damping of power system oscillations by
means of bang-bang feedback results therefore in optimum
utilization of the available SVC rating. To get the same
damping effect, bang-bang control needs less investment.
In later stage of transient process when oscillatioh is
not anymore severe, bang-bang control may have
adverse effect (high frequency oscillation).
To tackle the above mentioned problem, control modification has been introduced. In the first stage of the transient
process bang-bang control alone is effective. Later, when
oscillation has been already damped a normal linear
controller including a PD-block and a differentiation block
is introduced.
<*?
K=600.
t
G Js) linear controller
--*
---
G , ( s ) = 600
1
G,(s) = 0.292 *
4
Fig. 8
1.
*
I
1+0.01 S
1i0.026 s
2
t
0.01
s2
I
3
0.075 s
1t0.317 s
-1
1tO.0093 S
1+0.075 s
5
6
Combined bang-bang and linear SVC controller
a) - c) referred to Fig. 3
Meanwhile bang-bang control has some disadvantages:
-
-
Optimization is mathematically complicated. Realisation is more difficult than for linear controller.
High non-linearity of the signal introduces large
amount of harmonic components in system voltage
and current and may result in difficulties for correct
SVC control action.
First a suitable set of initial values for parameters of bangbang control is selected. Then a set of parameters is optimized which makes the controller to have optimum dynamic behaviour during the transient process caused by
large disturbance. The bang-bang controller is switched to
the normal linear control when system oscillation amplitude is reduced to certain limit. The modified control con-
528
4000 MVA, 3000 MVA and 2000 MVA and the inertia constants being 5 s, 5 s and 3.5 s, respectively. Each rtiachine
has a voltage controller with PSS. All the other machine
parameters are just the same a s those used above.
A SVC with rating of
A
/
\v
vdta e control
.25 pu
in oseration
For comparison, the fault of same type and same duration
is also applied close to bus 2 in all studied network configurations. The damping control signal is the same phase
angle difference between G1 and G2 a s in the two generator system. Simulation results show, t h a t the proposed
controller is also effective in damping the oscillations in
the enlarged system.
Fig. 9 Combined bang-bang and linear SVC controller
( system condition according to Fig. 2 )
Damping of power system oscillations improves pro or
tionally with the large SVC rating. However, this lea&
increasing reactive power oscillations and thus to voltage
deviations during the phenomenon. Optimized design
between the damping effect and the limitation of voltage
deviations is possible. The results for various target
functions and parameters are collected in Table 1, which
take active and reactive power oscillations and voltage
deviations into account. Low value for Kv and KQ means
preference for damping effect and high value preference for
the limitation of voltage deviation and reactive power
oscillation during damping control action.
ti
0
KQ in(pu)
I(a QsvCWar) ZlZg
5 =Z2
Tab. 1
Qsvcadditiona!
parameter
for optimization
5
2 266
2188
068
0.38
Optimized system parameters
Z : ref. for evaluation of damping , expressed in equ. (4)
AP1-2, A Q ~ -in~pu, based on 200 MVA , AQsVc in kV / MVA
System I differs not very much from the original two area
system, if one considers G1 and G3 as a n equivalent generator. The introduction of G3 produces additional oscillation
modes between the generators, but it's influence is not so
significant because of its location and relatively smaller
rating. Therefore we get similar result as for the two area
system.
In system I11 the distance between kl and G3 is eitendea
to 300 km. The connection between G1 and SVC is changed
from double line to a single line and new single line is
added between SVC and G3.
Considering G1 and G3 a s a subsystem, conditions are a s in
system I. So the results are also similar to t h a t of system I
with a certain difference in the transient process of G3.
In the radial system 11, the coupling between G1 and G3 becomes weaker by deleting the direct line between them.
Consequently, the swing mode between both generators becomes less important, while the other 2 swing modes, i. e.,
the swing between G1 and G2 are effectively controlled by
SVC. As seen from the reduced time to damp out the oscillation G3 increases the synchronizing torque in the system.
In the system IV, there is a direct connection between G2
and G3. G3 has to the SVC location the same position a s G1
and G2. It is obvious t h a t the power flow through this line
can hardly be controlled by the SVC. Only small damping
by the PSS of G3 is seen in the oscillogram. Therefore the
oscillation in this system lasts much longer t h a t in other
test systems. But the considerable damping effect can still
be observed in this case.
A fault on the line 2-3, cleared by disconnecting this line
(changing the system structure), was also calculated and
damped out without problems.
4.
In the investigated cases the used turbine governor show a
fast reaction, sensitive to the SVC-control. Slow turbine
governors will be less affected by SVC bang-bang control.
When turbine governor has fast control behaviour one can
observe the effect, t h a t a linear control concept might
result in a better system damping.
3.
+
400 MVar is installed a t the
middle bus between G1 and G2. The same SVC-control has
been used a s in the two area example because simulation
has shown t h a t larger changes in controller structure or
controller parameters are not necessary.
blocked
SVC-sig. :
3-Generator Systems
To verify the effectiveness of the proposed controller, further digital simulations a r e performed for various 3-generator systems of different network structures and different
operation conditions.
All 4 systems, as shown in Fig. 10, are developed from the
above used two area system by connecting a new generator
G3 with the ratings of generators G1. G2, G3 being
Conclusion
A new method is described which defines the phase angle of
generators on the basis of voltage and power measurement
a t the location of SVC. This state variables are employed
for improvement of damping of power system oscillations
by SVC. The new SVC control can optimally damp active
power oscillations. The new damping signal is shown to be
robust in particular in vicinity of the stability limit and
has the advantage that no error signals occur at large
differences of the phase angle.
The estimated phase angle can be utilized for various control concepts. On the basis of a bang-bang control combined
with a linear controller the optimized control loop design
was demonstrated in a fully non-linear system with different objectives. By means of parameter identification procedure optimum feedback can be determined. As a result of
freedom with regard to the optimization criteria varying
technical optimization factors can be taken into account.
Tests on a simulator are planned, but not yet realized.
529
System I
System I1
System 111
System IV
800 MW,
800 MW,
P21= 734 MW
Fl
-
300 km
300 km
=
549 MW
'
300 km
I
12sec
A V at SVC
800 MW
12sec
APG3
Fig. 10 3 areas-system with bang-bang and linear SVC control
8 -contolled SVC operation
- _ _ _ _ SVC not in operation
~
Definitions
Appendix: S ingle Generator Sytem with SVC
inertia of machine
mechanical machine constant
machine phase angle
damping coefficient
active electrical power
generated active power
turbine power
The classical machine equation for a single generator system with a SVC and a fixed frequency power system I as
depicted in Fig. A1 is taken as a starting point.
voltage behind transient reactance
voltage drop
admittance node j-k
shunt admittance node j
active power flow node. k
reactive power flow nodi j-k
complex number
If UG = Unet = 1 pu, UG can be written as
weighting factors for voltageand reactive power influence
SVC damping controller gain
The power flow in the system is given by
M -d26
+D-+P
d 6= P m
dt2
*
& = cos6 + j s i n 6
For gsvc it follows that
lJsvc = U s v c (cos 6/2 + j sin 8/21
operating point
linearized or change in
References
E. V. Larsen, H. H. Chow:
"SVC control design concepts for system
dynamic performance"
Sympos. on Appl. of static VAR systems
IEEE PES, San Francisco, July 1987, pp. 36-53
J . R. Smith, D. A. Pierre, I. Sadighi, M. H.
Nehrir
"A supplementary adaptive var unit controller
for power system damping"
IEEE TRANS on Power Systems, Vol. 4, No. 3,
August 1989, pp. 1017-1023
A. G. Phadke, M. G. Adamiak, J. S. Thorp:
"A new measurement technique for tracking
voltage phasors, local system frequency, and
rate of change of frequency"
IEEE TRANS on Power App. Syst., Vol. PAS102, No. 5, May 1983, pp. 1025-1039
A. Olwegard, K. Walve, G. Waglund, H. Frank,
S. Torseng:
"Improvement of transmission capacity by
thyristor controlled reactive power"
IEEE TRANS on Power App. Syst., Vol. PAS100, NO.8, August 1981, pp. 3930-3939
S. Yokokawa, Y Ueki, H. Tanaka, e. a.:
"Multivariable adaptive control for thermal
generator"
IEEE TRANS on Energy Conversion, Vol. 3,
No. 3, September 1988, pp. 479-486
The active power transmitted between generator
and power system is found from (3) to be
P = ( U s v J X ) sin 6/2
From the difference of,the reactive power flows
QSVC-net- QG-svc it can be found for SVC that
as per figure A1
Qsvc = (usvc-o -
US"C)
If equations (A7) and (A8) are linearized following relationships are found for the steady state operating point
(Usvc-0 = u o , 60).
and
A us,
B. Kulicke, H.-J. Hinrichs:
"Parameteridentifikation und Ordnungsreduktion mit Hilfe des Simulationsprogrammes
NETOMAC"
etz-Archiv, Bd. 10 (1988) H. 7, pp. 207-213
W. Bayer, N. Sudja:
"Use of Static Compensators to provide fast
stand-by reactive power for a 500 kV remote
transmission line"
6. Cepsi Conference, Jakarta Indonesia, 1986
W. Bayer, P. Sihombing:
"Aspects of damping of power oscillations by
power modulation"
7. Cepsi Conference, Brisbane Australia, 1988
ysvc
KSVC'
ysvc
(A10)
y-,x
svc
"svc -0
Fig. A1 Basic diagram of one generator - SVC - system
53 1
For A U s v c it follows that
U,sin 6 d 2
A UsVC = -
Ysvc X
+ 2 ( 2 U , - COS^ J2’
A6
(All)
Linearization of equation (1)results in
d2A6
dA6
M-+D-+AP=APm
dt2
(A121
dt
Alteration of active power is found from (5)
A P = [ C l l X ) ~ i n 6 ~ AlJ,,+
/2]
[(UJ2X)cos6,12] A6
(A131
Equation (A131 shows that i t is possible to increase
damping of the system if U s v c is altered linearly a s a
function of t h e rate of change of the machine phase angle,
that is
d A6
[ ( l ~ X ) s i n 6 0 1 2 1 A U s v c =K dt
(A141
Edwin N. Lerch was born in Germany
in 1953. He received Dip1.-Ing. degree
from the university of Wuppertal 1979
and complete his Ph. D. in 1984 in
electrical engineering. Since 1985 he is
a member of the high-voltage transmission engineering and system planning department a t Siemens, Erlangen
in the industrial power system and
machines group. He is working on
power system stability, dynamics of
multimachine systems, control, optimization and identification problems in electrical power systems. He is member
of the ETGIGMA group 3 ”network control” since this year.
Dugan Povh was born in Beogradl
Yugoslavia in 1935. He received
Dip1.-Ing. degree from University
Ljubljana/Yugoslavia in 1959, Dr.-Ing.
degree from TH Darmstadt/Germany
in 1972 and is also Professor a t the
University of Ljubljana. He is active in
a number of committees and working
groups of CIGRE and IEEE.
His areas of interest a r e system
analysis, network planning, insulation
mission systems and development of HVDC a i d static var
compensator technique. Prof. Dr. DuEan Povh is the head of
the department on system planning in the Siemens Power
Transmission and Distribution Group.
Liwen Xu was born in Hangzhou
P. R. China on May 25, 1956. He received his B Sc. from Huazhong
University of Science and Technology
and M. Sc. from Zhejiang University,
both in electrical engineering. Currently he is working toward the Ph D.
degree a t Zhejiang University under
the supervision of Prof. Zhengxiang
Han. At present he is visiting Siemens
and works on the SVC control. His
main interest is in the field of power system stability
control.
532
DISCUSSION
A. Hammad and M. Haeusler (ABB Power Systems,
B a d e n , S w i t z e r l a n d ) : The authors are to be commended
for an interesting paper.
Static VAr compensators - in the form of thyristor
controlled reactors and/or thyristor switched capacitors
have been in use in transmission networks since the early
1970's [A] . Controls of a typical multi-task SVC comprise the
following [B]:
1.
2.
3.
4.
5
dynamic voltage control
system stabilization
power oscillation damping
small signal damping
reactive power control (slow)
0
4
, , , , ,
, , , , , , , ,
I
I
I
'Id
I
I
I
I
I
I
I
I
I
I
I
I
I
I
.J
-qoo
4
0
Local measurements at the location of SVC are sufficient
for estimating the phase angle across the transmission
system. The deviation of the estimated phase angle across
the transmission system is a robust control technique for
damping power oscillations. Combining a bang-bang
control strategy with a linear (smooth) control proved to
be an efficient method for rapid damping [C]. In fact,
several SVC installations around the world since 1985
employ such controls [D].
TIME IN SECONDS
Figure A. Response to pulse disturbance
200%
U00
L
4
In practical SVC controls, however, large system voltage
excursions like those shown in Fig. 7 in the paper, on
account of the SVC control action, are not allowed.
Intelligent coordination among the various SVC controls,
rather than a simple summation, is usually employed.
PULSE
U
Y
OlSlURBlNtE
:
:
--zoo n
The authors' comments are appreciated.
c
REFERENCES
[A]
CIGRE Working Group 31-01, "Static Shunt Devices
for Reactive Power Control", CERE paper 31-08, 1974.
[B] A. Hammad, "Applications Jf Static VAr Compensators
in Utility Power Systems", IEEE PES Special Publication on
Application of Static VAr Systems for System Dynamic
Performance, No. 87 TH0187-5-PVJR. pp. 28-35.
[C]
A. Hammad, "Analysis of Power System Stability
Enhancement by Static VAr Compensators", IEEE Trans. on
Power Systems, Vol. PWRS-1. No. 4, Nov. 1986, pp. 222-227.
[Dl
A. Hammad, M. Haeusler, P. Enstedt, B. Roesle, "Static
VAr Compensators for Maximizing Power Transfer and
Stabilization of HV ac Transmission", IEEE/CSEE Joint
Conference on HV Transmission Systems in China, Oct. 1987,
paper No. 87 JC-17, pp. 108-114.
Manuscript received August 4 , 1990.
JOHN F. HAUER (Bonneville Power Administration,
Portland, Oregon): The authors have presented very
interesting results and insights concerning the damping of
large-scale oscillations. I have some reservations as to how
broadly these apply to more complex power systems, however.
Similar work at BPA, dealing with an SVC on the Pacific AC
Intertie damping transient oscillations in the western North
American power system, lead to somewhat different
conclusions [1,2]. The accompanying figures illustrate basic
concepts for sizing and tuning transient dampers that differ
markedly from those for ambient dampers. These represent a
limiting condition underlying the authors' method, which is
approached as filter bandwidth tends to zero.
+
, , , ,
I
I
I
1
I
I
I
I
I
I
I
I
I
I
2d
I
I
I
I
!-U00
0
TIME IN SECONDS
Figure B. Transient damping via 39 Mvar pulse train
Transient oscillations commonly involve just one critical
mode. This suggests a time-optimal "output cancelation"
strategy, in which the damper produces opposing oscillations
until the oscillatory term in the system output y(t) is reduced
to an acceptable level (at time t=T). The figures show this for
a 5-mode linear model having a negligably damped mode
near fc=0.714 Hz. The bang-bang control u(t) has a level of
U=39.27 Mvar, for which t h e 1st harmonic is
u l ( t ) = U l ~ i n ( 2 x f ~ t +with
0 ~ ) U1=4U/n=50.00 Mvar. System
response using ul(t) as the control signal is not graphically
distinguishable from that of Figure B.
The amplitude of the canceling response will, for zero
damping, increase linearly with time. This provides initial
guidelines for trades between the SVC modulation limit U
and the "quenching time" T, for assumed oscillation levels.
Exact control timing requires knowledge of the oscillation
frequency fc, the phase BC of the associated modal component
yc(t) in y(t), and the phase component $(fc) of the (suitably
defined) frequency response function Ur?=I L$(f)
relating yc(t) to ul(t). Then 8u=ec-$(fc)+1800. It appears
possible to determine these on-line, using a phase-locked l00p
[ l ] or a moving-horizon strategy drawing upon the signal
decomposition and identification methods of [31. Extensions
would be needed for multi-modal oscillations. The authors
develop this information implicitly, using narrow filters
developed through off-line studies.
The mode of concern on the western system ranges in
frequency from roughly 0.75 Hz to 0.69 Hz or lower. It
interacts strongly with another mode, at a frequency ranging
533
from 0.63 Hz to a t least 0.65 Hz. System dynamics change
significantly with operating conditions, and with the critical
resource loss that triggers oscillations. This is especially true
of system response to control action, which often exhibits
pathological phase characteristics. In addition to these and
other complications, accuracy of the models that predict
transient oscillations is suspect.
I share the authors' view that the key to transient damping
lies in bang-bang control, controller supervision, and reliable
controller input(s). The supervision should also coordinate
damper action with open-loop remedial action schemes, and
it may require some degree of self-tuning or parameter
sheduling. While locally estimated angle difference has been
examined at BPA as a controller input, AC Intertie
complexity and system variablity argue that the controller
should be provided with a n ample reserve of directly
measured dynamic information.
My chief concern is with the filters. Their tuning must be
sharp enough to focus contro!ler action u p m the critical
mode(s) and to avoid adverse interactions with nearby modes,
but broad enough to accomodate uncertainties i n system
dynamics. Very sharp filters may require supervision to
avoid oscillatory response to step inputs, and may produce
adverse interactions. Would the authors please compare the
frequency response of Gl(s) against that of the power system,
for systems I11 and IV? How would they deal with the
variable, bi-modal situation described above? Finally, how
would they validate or refine their controller settings in the
field?
J.F. Hauer,"Reactive Power Control as a Means for Enhanced
lnterarea Damping in the Western U S . Power System--A
Frequency-Domain Perspective Considering Robustness
Needs," Appllcatlon of Static Var Systems for System
Dynamic Performance, IEEE Publication 87TH0187-5PWR, pp. 79-92.
John Hauer [2] has pointed out that there can be a
problem in multi-mode systems. We appreciate the fact
that the authors have used a three machine system
which does have two modes.
We would suggest an
additional three machine topology be considered
(System V) and the control algorithm be tested for two
equilibrium conditions.
We suggest that the algorithm
will enhance stability of both modes for one of the
cases, and detract from stability of one mode for the
other case. System V is shown in figure 1. Let
XI = 0.5
= 1.0
x4 = 1.0
x3 = 0.5
Hi = Hz
H3 = 00
In the first example (System V-a), let the injected
powers be such that the equilibrium values of the
machine angles are
61 = - 30"
8 2 = -10"
83 = 0
and in the second example (System V-b)
81 = - 10"
82 = -30"
83 = 0
Machine 3 is coupled tighter to machine 1 than it is
Therefore the angle of the Thevenin
to machine 2.
voltage of machines 1 an 2 combined will be closer to
the angle of machine 1 than it is to machine 2. Then
in case V-a, if machines 1 and 2 swing apart, the
angle between machine 3 and the Thevenin voltage of
the other two machines will increase, causing the SVC
to raise the voltage.
This will enhance the power
flow between machines 1 and 2, which is exactly what
we want it to do. However, in System V-b, if machines
1 and 2 separate, the angle between machine 3 and the
Thevenin voltage decreases, causing the SVC to drop
the voltage which will decrease the power flow between
machines 1 and 2, letting them swing apart faster.
xz
G3
;G2
I
J.F. Hauer,"Robust Damping Controls for Large Power
Systems," IEEE Control Systems Magazine, pp. 12-19,
January 1989.
J.F. Hauer,"The Use of Prony Analysis to Determine Modal
Content and Equivalent Models for Measured Power System
Response," Elgenanalysls and Frequency Domain
Methods for System Dynamlc Performance. IEEE
Publication 90TH0292-3-PWR. pp. 105-115.
Manuscript received August 4 , 1990.
BAKER and T. KAKAR, Washington State University,
Pullman WA:
We agree with the use of local
measurements to estimate the angle (and angle rate)
between areas to control a SVC on an intertie
connecting the areas.
We have successfully used this
same idea in the control algorithm for a phase
From local voltage and
shifting transformer [l].
current magnitudes, phase angles between the currents
and the voltage, and the Thevenin's impedances between
the node where the SVC is located and the connected
areas, the angle between the Thevenin Voltages of the
two connected areas can be found.
The authors are
certainly correct in saying there is more useful
information in this angle difference (and angle rate)
than in local frequency.
Their point is also well
made that for small angles, the power (and power rate)
comes close to conveying the same information.
For
this reason, the use of the rate of change of power as
a feedback signal in SVC's has proven satisfactory for
many systems where distances are very short with
respect to a wavelength.
System V
Figure 1
The authors should be commended for their work in
developing this algorithm.
We feel that the problem
cited can be mitigated.
REFERENCES
[l] R. Baker, G. Guth, W. Egli and P. Eglin, "Control
Algorithm for a Static Phase Shifting Transformer to
Enhance Transient and Dynamic Stability of Large Power
Systems," IEEE Transactions on Power Apuaratus
Systems, Vol. PAS-101, No. 9, pp. 3532-3542, Sept.
1982
[2] J. F. Hauer, "Reactive Power Control as a Means
for Enhanced Inter-area Damping in the the Western
U.S. Power System--A Frequency Domain Perspective
Considering Robustness Needs," in Applications of
Static Var S stems for Svstem D namic Performance,
IEEE Pub 87TYHO187-5-PWR. pp. 79-;2, 1987
Manuscript received August 4 , 1990.
G. ANDERSON and T. SMED, Dep. of Electric Power Systems,
Royal Institute of Technology, Stockholm, Sweden.
The authors are congratulated on presenting a
comprehensive analysis of an important issue in a well
written paper. Their physical insight in the discussed
phenomena has guided their analysis which we believe is
the correct and most powerful approach.
534
We appreciate the authors' comment on the use of busvoltage as an input for damping purposes based on the
following reasoning:
The damping action i s achieved by modulating the
reactive power output from the S V C in an appropriate
phase with regard to the power oscillations, and the task
o f the controller i s therefore to determine this
(appropriate) phase from the chosen input signal. Our
experience indicates that the derivative of the bus voltage
magnitude is a reliable indicator o f the appropriate phase
o f the reactive power modulation for damping purposes.
This observation will explain the instable behavior shown
with pure V-control in figure 6 o f the paper, when a PIcontroller is implemented.
duce the risk of adverse interaction can help t o overcome
the problem.
In Fig. 10 of our paper we have given the results for four system configurations. We control the phase an le difference
depending on the optimization procedure. On?y in system IV
we find need for larger adaptation of parameters to the system configuration. The system is operating well also, when
opening line 2 - 3 after the fault, as shown in Fi . 1. This
shows, that the design of the parameters IS robust ayso in the
case of system parameter changes, but in our example there
is no strong interaction between the swing modes.
PZ-1 =
Manuscript received August 17, 1990.
550 MW
I 300 km 1'
I
We would like to thank all the discussers for their interest in
this paper and their comments and questions.
,.300"
3 phase short circuit at line 2-3
cleared by opening line 2-3
In Fi . 5 of our paper we have shown the increase of system
oscilfation dam ing by increasing the SVC-rating. However,
the increase o r t h e SVC-rating leads t o a larger reactive
power oscillation and voltage oscillation. In Tab. 1 we have
shown how t o combine the damping of active power oscillation and the limitation of voltage deviation during power
oscillation by using different target functions t o limit the reactive power oscillation.
We agree with the discussers that an intelligent coordination of various SVC control demands is necessary. We wanted
t o show the principle reaction dependin on new local
measured phase angle control. Using intejigent control it
will be possible to use different phase angle signals to adapt
the SVCdamping to the different modes of oscillation in a
multi-area system. But the main target should be, to make
the control as robust as possible to increase system security.
In our example the system is operating close to (and behind)
the system stability limits (calculated without SVC). The
transient overvoltage appears for some seconds. The question is t o access whether the system instability or the system
overvoltage is more dangerous for the system.
R. Baker and T. Kakar
The discussers presented a challenging question on damping
of oscillations in multi-mode system, which we have also
realized a t the beginning of our work. It has t o be admitted
that in principle, the damping effect of single input Time
Optimal Control to multi-mode oscillation is limited, regardless of whether i t s being SVC control or being any other control like braking resistor, excitation and governor control.
Sometimes it may even be uncontrollable regarding to specific systems. To improve this new control strategy, multi-input
Time Optimal Control has still t o be developed, which is just
our next work. In terms of the example presented by Mr. R.
Baker and T. Kakar there do exist the problem of getting the
signal correctly reflecting the oscillation between G1 and G2.
But in case of that network structure we would rather locate
the SVC to the connecting bus of XI, X2 and X3 t o have
better observabilityof the whole system oscillation modes.
J. F. Hauer
The discusser describes a complicated bi-modal oscillation
situation where the swing frequencies depend on system
conditions. In such a situation the control concept can only
be adaptive. In addition, tunin of the filters to the critical
mode is complicated because oathe modal interaction. Digital filters in combination with intelligent supervision to re-
1
____...____.___
-.--
A. Hammad and M. Haeusler
SVC in operation
v
'
V
-
"
S2., exactly calculated
S2., estimated at SVC-node -
U
"
------
without SVC
Fig. 1 Change in topology after the three phase short circuit
To answer the question of controller setting in the field: The
first step of system investigation is calculation of eigenvalues
to find the modes of oscillation. In addition a digital model
of the system is created to identif a (reduced) equivalent
d namic system structure by matiematical identification.
T i i s equivalent model will be used in a hardware system simulator also to test the control of the real SVC-controller
and adapt, if necessary, the control behaviour. Finally, in the
field we make tests limited by the requirements of the
system operation. It will be also necessary t o observe the
control behaviour over a longer period to prove the correct
control performance.
G.Anderson and T. Smed
As shown in Fig. 6 of the paper the change of voltage ampli-
tude cannot be used for power oscillation damping. The
damping information can be found using the derivative of
the voltage phase angle. This signal can be interpreted as
local frequency change. Coupling a relative small system
with a large one shows transient frequency changes without
offset from the basic frequency in case of power system
oscillation.
A coupling of two systems as in the paper shown in Fi . 2
shows a local frequency change depicted in Fig. 4. This %equency change was calculated by using the derivative of the
535
PI-, = 785
voltage phase angle at the SVC-node. The mode of intersystem oscillation must be filtered out of this signal, because
both systems are drifting slowly from the basic frequency
(zero-line). Therefore at least a 6th order filter has t o be
used to find the swing mode of the system.
Mw
For these reasons the use of derivative of voltage phase
angle can be complicated.
,
Fig. 2 Derivative of SVC-nodevoltage for different load flow
situations
The derivative of the bus voltage magnitude can also be
used as damping signal. But in Fig. 2 we have shown the
change in voltage at SVC-node, the change in power flow
between the two areas and the dVsvcIdt-values for a power
transportation of 785 MW and 850 MW to area two. It can
be depicted that increasing the flow between the areas
results in saddle-points in the voltage characteristic. Therefore the dVsvc/dt-measurements can produce error-signals.
Designing a bang-bang control will increase the problems
because of additional harmonics especially near the vicinity
of stability limits.
Manuscript received October 2 6 , 1990.