Formula for the effect of a static VAr compensator on synchronising torque coefficient

A.A. El-Emary

Indexing terms: Static VAr compensator, Synchronising torque coefficient

Abstract: A static VAr compensator (SVC), constructed by a fixed capacitor (FC) and a thyristor controlled reactor (TCR), is designed and implemented to improve the damping of a synchronous generator, as well as controlling the system voltage. The SVC is placed at the generator bus terminal, with the speed and voltage deviation as the feedback signals. In the paper a formula has been developed showing the effect of SVC on synchronising torque coefficient, such that damping is improved and the system voltage is controlled. A simplified analysis of the effect of SVC on the stability of a machine connected to an infinite bus, as well as a simplified 21 bus real system, is presented. Results from digital simulation show that the SVC can greatly enhance the damping of the system oscillation caused by disturbance. Also, the voltage profile of the generator is controlled by the SVC.

List of symbols

A = system matrix 1” = control matrix X = state vector 0 = angular velocity 6 = torque angle V, = terminal voltage T, = electromagnetic torque Tio Eja = exciter field voltage E& K,, T, = exciter gain and time constant Kp, KI = gains of the PI controller K,, T, = thyristors gain and time constant M , D = inertia constant and damping coefficient Kl-K6 = constants of the linearised model of synchronous

V, = infinite busbar voltage P, Q 0 IEE, 1996 IEE Proceedings onhne no. 19960544 Paper first received 13th Dember 1994 and in revised form 12th April 1996 The author is with the Electrical Power and Machines Department, Faculty of Engineering, Cairo University, Giza, Cairo, Egypt

= d-axis transient open circuit time constant

= voltage proportional to direct axis flux linkages

machine

= generator active and reactive power

A = linearised incremental quantity B = inductive susceptance of SVC Bc = capacitive susceptance of SVC Vref = reference input voltage Re, Xe = resistance and reactance of transmission line 1, = SVC current Tw = washout time constant of the PI controller I = unit matrix nsvc = number of SVC located at generator terminal

ng = number of generators Xd, Xq Xi = d-axis transient reactance S = Laplace operator GI + JB, = terminal load admittance

1 Introduction

(5 nd

= d-axis and q-axis reactance

Extensive growth of electric power systems and the development of high voltage long distance transmission systems, separating generation from load, have accen- tuated the importance of increasing the dynamic and transient stability limits of synchronous machines. Essentially, the problem is one of improving the dynamic and transient performance of the machine by suitable control methods. Different methods for improving the machine oscillation using stabilisation of synchronous machines through output feedback con- trol have been developed [l-51. In this approach the linearised equations of the machine are considered, and a control law consisting of constant feedback coeffi- cients of the systems state variable are derived. Also, several papers have discussed the effect of excitation and a power system stabiliser (PSS) on damping machine oscillation [6-9].

Over the last decade, SVCs have become a popular means of providing fast-acting reactive support in power systems. These devices are used for voltage sup- port, minimisation of reactive power and system losses and for improving stability limits. Attention is focused on the utilisation of SVC to improve system damping and control voltage [lo-1 81. These approaches discuss various supplementary signals for improving system stability, include deviation in the rotor velocity, and the bus voltage.

The purpose of this paper is to present a new for- mula for the effect of a static VAr compensator upon a synchronising torque coefficient. Also, the coefficient change of the SVC, called the effectiveness factor, is introduced. The proposed method using SVC modifies the machine parameters, such that synchronising

IEE Pvoc -Gener Tvansm Distrib , Vol 143, No 6, November 1996 582

improved by the proposed method.

at its terminal. Model 2, is a simplified transmission network of the uni-

TcRt I n TFC - 2 7 2

. I Model 1, study system

Figl.2 Model 2, interconnectedpower system of UPS of Lower Egypt

I I I

A6 .

I -"rei

incremental model of synchronous machine with volt-

linearised incremental model of a synchronous connected to an infinite bus through a trans-

n line and the model for the voltage regulator, ix parameters IC-& which

are functions of machine ers and system impedances as well as of the g conditions [19]. For the multimachine sys-

, the linearised model of this sys-

143, No. 6, November 1996

Fig.4 SVC model

2.2 Static VAr compensator (SVC) In this paper a thyristor controlled reactor with fixed capacitor (TCR + FC) is used as the SVC. Fig. 4 shows the schematic diagram of one phase of the three-phase SVC and its control block diagram [12, 131. The SVC unit is connected to the generator terminal as shown in Fig. 1. The primary function of the SVC is to control the reactive power and stabilise the system voltage. The auxiliary stabilising signal U is added to the input of the SVC controller and fed into the excitation system to damp the machine oscillation. The steady-state oper- ating point of the SVC is given by [ 151:

Eqn. 1 is linearised about an operating point giving:

To derive a general relation corresponding to single and multimachine systems, assume that the SVC is located at the terminal bus of the synchronous genera- tor. Furthermore, the input signal AVi to the main con- trol circuit of the SVC [15] is given by:

I, = BV, (1)

AI, BoAVt + VtoAB (2)

AK = -AV, - GIAL + U ( 3 )

3 Proposed method

In this Section, a mathematical procedure of the pro- posed method corresponding to multimachine power system is derived. The system model is formed using the matrix approach. To form this model, including the effect of the SVC, the A , matrix is incorporated in the mathematical calculations. Rearranging eqns. 2 and 3 in matrix form, we obtain:

P I S 1 = [Bol [Aol~~V, l + ~ ~ o l ~ V t o l [ A o l T [ ~ B l (4)

0

1 0

... 0 1

. . .

0

...

... 0 :J If nsvc = ng (i.e. SVC located at all generator termi- nals) the A. matrix is unity diagonal matrix, and if A. = 0 (i.e. no SVC located at generator terminals).

I ' I W I 5 Synchronous machine model with new controller purmneters

Eqn. 20 represents a new formula of the developed electromagnetic torque. The first term represents the synchronising torque coefficient, which must be posi- tive to ensure system stability. The second term repre-

584

sents the degree to which a change in SVC susceptance can cause a relative acceleration of the machines. This term may be defined as the effectiveness factor of the SVC. Raising this factor gives more system stability. Fig. 5 shows the final basic model of machine contain- ing the effect of SVC compensation.

In the following studies, the output signals AV,, U are fed back to the corresponding input of the SVC controller gain [9], and incorporated in each machine, shown in Fig. 5, which can be modelled by an equiva- lent second-order differential equation.

The state equation of the system can be expressed as follows:

where X = [A6 Awl*, the state vector AB is the control signal, and

x = AX + FAB

A = [ * 0 377 31 .=[*I 0

4 Test examples

To demonstrate the damping effect of the proposed SVC scheme, implementation test results of the system with and without SVC are compared. The following studies have been carried out.

4.7 Case study I The study system shown in Fig. 1 consists of a syn- chronous generator supplying power to an infinite bus through a transmission line. The system data is given in the Appendix .

0.2

U e a

- 0 .I W

0

-0.1 L Fig.6 4- B = 0.6

Time response ofrotor angle deviation

~ B = 0.8 _ _ _ _ without SVC

I 0.2

0

Fig.7 -e- B = 0.6 __ B = 0.8 _ _ _ _ without SVC

Time response of voltage deviation

IEE Proc-Gener. Transm. Distrib.. Vol. 143, No. 6, November 1996

de rol Fii

6) (ii) PO of 0.8

mc

4.1

Th reg

sys

su5

Eg

c F a W

Fig - _ _ -a

U 0 L

2

Fic ~

_ _ -a

1 ass tor shc

(9 (ii) effi ger of (iii sv loc

chr ow

IEE

le time response of the rotor angle A6 and voltage ation AVt for a 0.1 assumed pulse disturbance in r speed w is shown in Figs. 6 and 7. From these res the following observations are noted: le original system without SVC is unstable; he system becomes stable when the SVC is incor- .led into the system. It is shown that more damping itor angle and terminal voltage can be achieved at U SVC susceptance as compared with 0.6pu SVC Zptance, due to a higher effectiveness factor and a z positive synchronising torque.

Case study 2 proposed method was applied to the 21-bus system :senting the 220kV power network of Lower Jt, as shown in Fig. 2. The line and bus data of this :m are given in [20].

0

-0.1

__----

-0.31

3 - SVC located at bus 8 - SVC located at bus 7

without SVC

Rotor angle deviation at generator 3

t

0 . 2 c 3 ~ SVC located at bus 8 - SVC located at bus 7

without SVC

Rotor angle deviation at generator 6

le time response of the rotor angle A6 for a 0.1 ned pulse disturbance in rotor speed w of genera- , is shown in Figs. 8 and 9. From these curves, it is m that: Le original system without SVC is more oscillatory he rotor angle deviation of generator 3 is more tively damped if the SVC is located at terminal of rator 7 than if the SVC is installed at the terminal merator 8 ncreased damping of generator 6 is achieved if the is installed at generator 7 compared with the SVC ed at generator 8. Improved damping is achieved, g to the higher effectiveness factor and the syn- nising torque being more positive.

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5 Conclusion

In this paper, a formula for electromagnetic torque has been developed, showing the effect of SVC susceptance upon the synchronising torque coefficient. Also, the effectiveness factor, which represents the degree to which a change in SVC susceptance can cause a relative acceleration of the machines, is introduced. This for- mula gives insight into the effect of SVC compensation upon system dynamic performance. Significant damp- ing improvements can be achieved at a higher effective- ness factor and a more positive synchronising torque coefficient.

Analysis of the test results shows that a proposed method presented in this paper utilising the SVC is capable of improving machine damping oscillation and controlling system voltage under abnormal conditions.

6 References

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3

1973, PAS-92, pp. 204-21 1

I \ ,, pp. 1386y-1393 GHANDAKLY, A., and KRONEGGER, P.: ‘Digital controller 8 design method for synchronous generator excitation and stabilizer systems’, ZEEE Trans., 1987, PWRS-2, (3), pp. 633-650

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11 MANSOUR, Y., XU, W., ALVARADO, F., and RINZIN, C.: ‘SVC placement using critical modes of voltage instability’, ZEEE Trans., 1994, PS-9, (2), pp. 757-763

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13 CHENG, C.H., and HSO, Y.Y.: ‘Application of a power system stabilizer and a static VAr controller to a multimachine power system’, ZEE Proc. C, 1990, 137, (l), pp. 8-12

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(2), pp. 655-661

(2), pp. 458465 17 LERCH. E.. POUCH. D.. and XU. L.: ‘Advanced SVC control

for damping power system’ oscillations’, ZEEE Trans., 1991, PAS- 6, (2), pp. 524-531

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7 Appendix Excitation:

7. I System data Initial operating point: All system data are in per unit value, except that M and time constants are in seconds 10-19. Generator:

K , = 300 T, = 0.05

P = O . 9 Q z O . 6 V t = 1 Line and load: Re = -0.034 X e = 0.997 Gi = 0.249 BI = 0.262 svc: Xd = 0.973 X , = 0.55 XA = 0.19 D = 0.025

Ti, = 7.76 M = 7 GI = 0.15 Kr = 2.5 T, 1 B = 0.6

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