Advanced SVC control for damping power system oscillations ...longya/ECE844/SVC-control.pdf · 524 IEEE Transactions on Power Systems, Vd.6, No. 2, May 1991 ADVANCED SVC CONTROL FOR

524 IEEE Transactions on Power Systems, Vd.6, No. 2, May 1991

ADVANCED SVC CONTROL FOR DAMPING POWER SYSTEM OSCILLATIONS

E. Lerch D. Povh, Senior Member, IEEE

Siemens AG Erlangen Fed. Rep. of Germany

L. x u

Zhejiang University P. R. China

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 ta t ic 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

In 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 by t h e IEEE Power System Engineering Committee of t h e IEEE Power Engineering Society f o r p re sen ta t ion a t the IEEE/PES 1990 Summer Meeting, Minneapolis, Minnesota, Ju ly 15-19, 1990. 7990; made ava i l ab le f o r p r i n t i n g June 21, 1990.

A paper recommended and approved

Xanuscript submitted January 29,

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. In 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 instal- lation of SVC which is adequate for improvement of power system damping.

2. Estimation of Machine Phase Angles Using

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 the 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 op- posite phase.

Local State Variables

0885-8950/91/05004521.~1991 IEEE

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 the 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 the 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 as reference.

The voltage angle difference between Vj and & is then

(2 )

If E_k is defined as the voltage behind the transient machine reactance x'dk which can be taken into account in Y'k, 6kj gives an estimate for the phase angle of the gener- d 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 an 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 are 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.

Fig. 1 Definitions for estimated phase angle 6 (reference node I ) ki

In the case of more complex systems i t is possible to provide adaptive matching of the equivalent reactance; deter- mination and matching of the equivalent reactances is also possible on-line by using extended Kalman filter [51.

2.1 Effect of SVC on Oscillation Behaviour of

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 the voltage a t the SVC and alteration of the 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 as a function of the rate of change of the phase angle (change in generator speed) [8 ] . The effect of SVC on the 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 the SVC is estimated on the basis of these theoretical con- siderations in order to control the SVC.

Generators

2.2 Control Concept Employing a Local Phase

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 gy means of shunt reactors. Under steady state conditions 815 MW are fed to power system 1. A control range of + 200 Mvar was selected for the SVC. the steady state condxions are given in Fig. 2 .

Angle Signal

fault location voltage control

6000 MVA 500 kV

H=7s

815 MW 815 MW

f200 Mvar 1300 MW

2000 Mvar 500 Mvar

4441 MW 2449 Mvar

5200 MW

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

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

SVC-sig.

V-control sig. TCR and TSC

voltage control firing circuit

bang-bang

linear control 8 -control Sig. filtering - or /and

- - $.

- - measured at SVC-node

- j = SVCl6ode

- -

Fig. 3 Concept of SVC damping control

program [6], whereby the maximum damping is calculated taking into account the whole non-linear system. The mea- suring equipment for Pjk, &, v . in (1) was modelled as 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 an identification procedure, however, minimize the overall time behaviour of AP1.2. Consequently the higher frequency signals of the SVC are additionally evaluated in the proce- dures and suppressed by matching the parameters.

The optimizatiodidentification procedure 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 as variable susceptance.

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 (AP1-2 1 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 un- stable. 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)

As shown from Fig. 4, the change of local frequency characteristic (Af at SVC node) is not suitable to be taken as input signal for the damping controller because of difficulty to filter out the low frequency signal of generator oscillation.

without SVC in operatlon

' af chan e in frequency at ~ 3 c - n d e

8 - controlled SVC

AV - A h h r -

at SVC-node

0. 1.5 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 1 pu. 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& de- pendent 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 as an example the unfavourable phase angle ( A a) of the voltage signal for power system oscillation damping compared with the optimum phase angle signal.

7 .

1 0 t200 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

QSvcWvar) +

527

-

SVC-sig.

-

6 -controlled V-controlled - - ~-

- _ _

I I

AV V-controlled - - - - - V V V V k

at SVC-node

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.

Meanwhile bang-bang control has some disadvantages: -

- Optimization is mathematically complicated. Reali- sation 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.

AV A AP. V v at SVC-node

Sestim 0. 1.5 3.0 4.5 6.0 7.5,,,,9.0

Fig. 7 Transmitted power increased to 925 MW ( system condition according to Fig. 2 )

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 modifica- tion 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. <*? G Js) linear controller t

G, (s ) = 600 * * I 1.

1+0.01 S 1i0.026 s t 0.01 s2 -- I

1 2 3

1t0.317 s 0.075 s 1tO.0093 S 1+0.075 s

G,(s) = 0.292 * - 1- - -- Fig. 8 Combined bang-bang and linear SVC controller

4 5 6

a) - c) referred to Fig. 3

First a suitable set of initial values for parameters of bang- bang 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

SVC-sig. :

.25 pu

blocked A /

vdta e control in oseration

\v

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& ti 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.

0 KQ in(pu) I(a QsvCWar) ZlZg

5 =Z2 Qsvc additiona! parameter 2 266 068 for optimization 5 2188 0.38

Tab. 1 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

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, that a linear control concept might result in a better system damping.

3. 3-Generator Systems

To verify the effectiveness of the proposed controller, fur- ther digital simulations are 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

4000 MVA, 3000 MVA and 2000 MVA and the inertia con- stants 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 as those used above.

A SVC with rating of + 400 MVar is installed a t the middle bus between G1 and G2. The same SVC-control has been used as in the two area example because simulation has shown that larger changes in controller structure or controller parameters are not necessary.

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 as in the two generator system. Simulation results show, that the proposed controller is also effective in damping the oscillations in the enlarged system.

System I differs not very much from the original two area system, if one considers G1 and G3 as an 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 as a subsystem, conditions are as in system I. So the results are also similar to that 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 as G1 and G2. It is obvious that 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 that 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. 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

300 km

12 sec

Fig. 10 3 areas-system with bang-bang and linear SVC control

Fl = 549 MW ' - - 300 km

I 300 km

A V at SVC

12 sec 800 MW APG3

~ 8 -contolled SVC operation SVC not in operation - _ _ _ _

Definitions

inertia of machine mechanical machine constant machine phase angle damping coefficient active electrical power generated active power turbine power

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

weighting factors for voltage- and reactive power influence SVC damping controller gain

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. PAS- 102, 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. PAS-

S. Yokokawa, Y Ueki, H. Tanaka, e. a.: "Multivariable adaptive control for thermal

100, NO. 8, August 1981, pp. 3930-3939

generator" IEEE TRANS on Energy Conversion, Vol. 3, No. 3, September 1988, pp. 479-486

B. Kulicke, H.-J. Hinrichs: "Parameteridentifikation und Ordnungsreduk- tion 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

Appendix: S ingle Generator Sytem with SVC

The classical machine equation for a single generator system with a SVC and a fixed frequency power system as depicted in Fig. A1 is taken as a starting point. I

M - + D - + P = P m d26 d 6

dt2 * If UG = Unet = 1 pu, UG can be written as

& = cos6 + j s i n 6

For gsvc it follows that

lJsvc = Usvc (cos 6/2 + j sin 8/21

The power flow in the system is given by

The active power transmitted between generator and power system is found from (3) to be

P = (UsvJX) 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) ysvc

If equations (A7) and (A8) are linearized following rela- tionships are found for the steady state operating point (Usvc-0 = u o , 60) .

and

A us, ysvc (A10)

KSVC' y-,x svc "svc -0

Fig. A1 Basic diagram of one generator - SVC - system

53 1

For A Usvc it follows that

U,sin 6 d 2

Ysvc X + 2 (2 U , - COS^ J2’ A UsVC = - A6

Linearization of equation (1) results in

d2A6 dA6

dt2 dt M - + D - + A P = A P m

( A l l )

(A121

Alteration of active power is found from (5)

A P = [ C l l X ) ~ i n 6 ~ / 2 ] AlJ,,+ [(UJ2X)cos6,12] A6 (A131

Equation (A131 shows that i t is possible to increase damping of the system if Usvc is altered linearly as a function of the rate of change of the machine phase angle, that is

d A6 [ ( l~X)s in60121AUsvc= 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 are 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. Cur- rently 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, Baden, Switzer land): 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. dynamic voltage control 2. system stabilization 3. power oscillation damping 4. small signal damping 5 reactive power control (slow)

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].

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.

The authors' comments are appreciated.

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.

0

4 , , , , , , , , , , , , , I I I ' I d I I I I I I I I I I I I I I 4 .J -qoo 0

TIME IN SECONDS

Figure A. Response to pulse disturbance

200% U00

4 L

PULSE OlSlURBlNtE U Y

: : - -zoo n

c

+ , , , , I I I 1 I I I I I I I I I I 2d I I I I ! - U 0 0 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 the 1st harmonic is ul( t )=Ul~in(2xf~t+0~) with 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. I t interacts strongly with another mode, at a frequency ranging

533

from 0.63 Hz to at 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 an 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 in 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 87TH0187-5-

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. 105-1 15.


PWR, pp. 79-92.

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 shifting transformer [l]. From local voltage and 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.

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 xz = 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

and in the second example (System V-b)

Machine 3 is coupled tighter to machine 1 than it is to machine 2. Therefore the angle of the Thevenin 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.

61 = - 30" 8 2 = -10" 83 = 0

81 = - 10" 82 = -30" 83 = 0

G3 ;G2

I

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


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.

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We appreciate the authors' comment on the use of bus- voltage 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 SVC 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 PI- controller is implemented.

Manuscript received August 17, 1990.

We would like to thank all the discussers for their interest in this paper and their comments and questions.

A. Hammad and M. Haeusler

In Fi . 5 of our paper we have shown the increase of system oscilfation dam ing by increasing the SVC-rating. However, the increase or the SVC-rating leads to a larger reactive power oscillation and voltage oscillation. In Tab. 1 we have shown how to combine the damping of active power oscillation and the limitation of voltage deviation during power oscillation by using different target functions to limit the reactive power oscillation.

We agree with the discussers that an intelligent coordination of various SVC control demands is necessary. We wanted to 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 to 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 to be admitted that in principle, the damping effect of single input Time Optimal Control to multi-mode oscillation is limited, regard- less 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 speci- fic systems. To improve this new control strategy, multi-input Time Optimal Control has sti l l to 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 to have better observability of 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. Digi- ta l filters in combination with intelligent supervision to re-

duce the risk of adverse interaction can help to 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 = 550 MW

I I 300 km 1'

____...____.___ ,..300" -.-- 1 3 phase short circuit at line 2-3 cleared by opening line 2-3

SVC in operation

S2., exactly calculated - S2., estimated at SVC-node - - - - - - - v "

' V 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 to 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 amplitude 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 %e- quency change was calculated by using the derivative of the

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voltage phase angle at the SVC-node. The mode of inter- system 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 to be used to find the swing mode of the system.

For these reasons the use of derivative of voltage phase angle can be complicated.

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. There- fore 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.

PI-, = 785 Mw

,

Fig. 2 Derivative of SVC-node voltage for different load flow situations Manuscript received October 2 6 , 1990.

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