Damping function of unified power flow controller

H .F. Wa ng

Abstract: The paper presents the establishment of a linearised Phillips-Heffron model of a power system installed with an unified power flow controller (UPFC). On the basis of the linearised model, the damping function of the UPFC is investigated. Basic issues on the design of the UPFC damping controller are discussed, regarding the effectiveness and robustness of the damping function of the UPFC, among which the selection of effective and robust input control signals of the UPFC to superimpose its damping function is specially addressed. An example power system is presented.

1 Introduction

The unified power flow controller (UPFC) was pro- posed [l] to achieve the flexible AC transmission sys- tems (FACTS). It is a multiple-functional FACTS controller with primary duty to be power flow control [2]. The secondary functions of the UPFC can be volt- age control, transient stability improvement, oscillation damping etc. Recently, there has been a growing inter- est in studying the UPFC, its modelling [3, 41, its basic function to control the power flow [5] and its capability to increase system transient stability [6]. In [2] and [3], the damping function of the UPFC is demonstrated by examples. However, so far there has been no research reported which devotes itself to investigation into the basic issues on the damping function of the UPFC.

Therefore, in this paper, the linearised Phillips-Hef- fron model of a power system installed with an UPFC is first established, which is of the same configuration as that of the unified model for static var compensator (SVC), thyristor-controlled series compensator (TCSC) and thyristor-controlled phase shifter (TCPS) presented in [7]. On the basis of the linearised model established, the phase compensation method [8] is applied for the design of the UPFC damping controller: (i) to select the operating condition of the power sys- tem where an effective and robust UPFC damping con- troller can be designed; (ii) to choose the most effective and robust input con- trol signal of the UPFC on which the damping func- tion of the UPFC is superimposed; (iii) to set the parameters of the UPFC damping con- troller. 0 IEE, 1999 ZEE Proceedings online no. 19990064 DOL 10.1049/ip-gtd: 19990064 Paper first received 18th May 1998 and in revised form 1st September 1998 The author is with the Department of Electrical and Electronic Engineer- ing, University of Bath, Bath BA2 7AY, UK

The discussions above are demonstrated by an example power system. Although the damping function of the UPFC is investigated for single-machine infinite-bus power systems in this paper, some basic issues are raised and studied. Insight and comprehension on these issues are provided, which will guide further investiga- tion into the UPFC damping function in more compli- cated power systems.

I I L - - - - - - - - - - - - - A UPFC

Fig. 1 UPFC installed in single-niuchine in$nite-bus power system

2 with UPFC

Linearised model of power systems installed

Fig. 1 is a single-machine infinite-bus power system installed with an UPFC, which consists of an excitation transformer (ET), a boosting transformer (BT), two three-phase GTO based voltage source converters (VSCs) and a DC link capacitor. In Fig. 1, mE, mE and SE, SE are the amplitude modulation ratio and phase angle of the control signal of each VSC, respectively, which are the input control signals to the UPFC. If the general pulse width modulation (PWM) (or optimised pulse patterns or space-vector modulation approach) is adopted for the GTO-based VSC, the three-phase dynamic differential equations of the UPFC are [3]:

-3 0

IEE Proc.-Gener. Transm. Distrib.; Vol. 146, No. I , January 1999 81

cos(wt + S E + l200)] [q ZEc

t %[cOs(wt + 6B) cos(wt + 6B - 120") 2 c d c

cos(& + 6 B + 120")] [ ZBc

By applying Park's transformation and ignoring the resistance and transients of the transformers of the UPFC, the equations above become:

1 1

wc 2 [:E::] [:E - /E] [:E:] + [ mEsi;6Evd,

mo cos 6 ~ v d , 2

(1) The nonlinear dynamic model of the power system of Fig. 1 is [7]:

s = wow W = (P, - Pe - D w ) / M &; = ( -E, + E f d ) / G o

From eqns. 1, 5 and 6 we can obtain:

82 IEE Pro?.-Gener. Transm. Distrih., Vol. 146, No. 1, January 1999

WO D M

-_

0

0 0

0 0 0

(13) where AmE, AmB, AdE, ASB are the linearisation of the input control signals of the UPFC. The linearised dynamic model of eqn. 13 can be shown by Fig. 2, where only one input control signal is demonstrated, with U being e (Au = Am,), b (Au = AmB), Se (Au = AS,) or Sh (Au = ASB). It can be seen that the configuration of the Phillips-Heffron model is exactly the same as that installed with SVC, TCSC and TCPS presented in VI.

Ab *

Fig. 2 PhillipsHeffion model of power system instulled with UPFC

Also from eqn. 13 it can be seen that there are four choices of input control signals of the UPFC to super- impose on the damping function of the UPFC, InE, nzB, SE and 6,. Therefore, in designing the damping control- ler of the UPFC, besides setting its parameters, the selection of the input control signal of the UPFC to superimpose on the damping function of the UPFC is also important.

IEE Proc.-Gener. Transm. Disfrib., Vol. 146, No. I . January 1999

3 UPFC damping control

The linearised model of the power system installed with the UPFC of eqn. 13 can be expressed by Fig. 3 [9], where H(s) is the transfer function of the UPFC damp- ing controller. From Fig. 3 we can obtain the electric torque provided by the UPFC damping controller to the electromechanical oscillation loop of the generator to be:

. 1

I elect romechan icol osc i Ita t i on Loo D

I

Kc(s) 0 K o k 1 0 I i +

qql - Fig. 3 Closed-loop system instulled with UPFC dumping controller

An ideal UPFC damping controller should contribute a pure positive damping torque to the electromechanical oscillation loop with ATupFc = DupFcAw, that is:

which results in:

D U P F G = [ K c (A0 ) 11-0 (A0 ) + DU P FC K I L (A0 )] (A0 ) = F ( X o ) H ( X o )

(16) F(&), which is named as the forward path of the UPFC damping controller, has a decisive influence on the effectiveness of the UPFC damping controller. Since F(&) varies with power system operating condi- tions and choices of input control signals of the UPFC, it can be used for the selection of power system operat- ing condition at which the UPFC damping controller is designed, and of the input control signal of the UPFC to be superimposed by the UPFC damping function. If we assume the set of the operating conditions of the power system is Q(p), F(&) can be denoted as the func- tion of system operating condition p and input control signal of the UPFC uk, F(&, p, uk). The criterion of the selection can be:

h s e l e c t e d = min F(Xo, h, U k ) , h E R ( h )

U s e l e c t e d = %~xF(XO> P s e l e c t e d , U ~ C )

(17) P

Uk E { ~ E > ~ B , ~ E I ~ B } (18a)

min F(&, P , w) Uselected

1 83

uk E {mE,mBr6Ei6B} 7 E (18b)

(i) Eqn. 17 requires that the operating condition, where the UPFC damping control is least effective, is selected for the design of the controller, since once the UPFC damping controller is designed at the least effective operating condition, its effectiveness at other operating conditions is guaranteed. Thus the robustness of the damping controller is achieved. (ii) For the efficient operation of the UPFC damping function. the required damping should be provided at minimum control cost. This can be achieved by apply- ing the criterion of eqn. 18a so that the most effective input co:itrol signal is selected. (iii) A good design of damping controller requires that it provides a steady damping over all the range of power system operating conditions. If the damping contribution from the controller increases greatly, on the one hand, with the variations of power system operatin,$ conditions, the damping function could be over-strong at some operating conditions, which would pose much unwanted influence on other modes in the power system. On the other hand, a sharp drop in the damping contribution from the controller with the changes of power system operating conditions results in poor robustness. Therefore, the criterion of eqn. 186 requires that, when the input control signal of the UPFC is selected, the damping contribution by the UPFC damping controller changes as little as possible with the variations of power system operating condi- tions so that a smooth damping function of the UPFC over Q(j.1) is obtained. However, this criterion should be applied jointly with that of eqn. 18a, since failing to meet the requirement of the effectiveness is not a proper sclection.

A set of similar criteria to eqns. 17 and 18 to select the effective and robust installing locations and feed- back signals of FACTS-based stabilisers are proposed for a multimachine power system [lo]. The author is working to generalise eqns. 17 and 18 for the study of damping function of UPFC installed in multimachine power systems, where an effectiveness function will be proposetl to replace F(&, p, uk) in eqns. 17 and 18.

Furthermore, from eqn. 16 we can see that the phase compensation method can be used to set the parame- ters of the UPFC damping controller. Without loss of generalily, we can assume:

ST, Ku (1 + sTz)(1 + ST^) 1 + ST, 1 + STU (1 + ~T1)(1 + ST^)

H ( s ) = ~~

H(X0) = HLO, F(X0) = F L p (19)

By setting:

the required amount damping torque DuPFc can be provided by the UPFC damping controller. According to eqn. 20, parameters of the controller can be set.

4 Example

A single-machine infinite-bus power system installed with an UPFC is shown by Fig. 4, parameters of which are given in Appendix 7. The system may operate with

84

single or two transmission lines connecting the genera- tor and the infinite-bus bar with the load condition to be Pe0 = 0.1 - 1.2pu, V,, = l.Opu, Vho = 1.Opu. So, the set of system operating conditions is:

n(P) = { b :vtO = 1.0 pu, VbO = 1.0 pu, P,O = 0.1 pu - 1.2 pu, single line, two lines}

X L

damping controller

Fig. 4 Single-muchine infinite-bus power system installed with UPFC

The UPFC is installed for the purpose of multiple con- trol functions, one of which will be the suppression of a low-frequency oscillation occurring in the system, since it is found that the damping of the responsible electro- mechanical oscillation mode is negative or very poor over Q ( p ) , as shown in Fig. 5. From Fig. 5 it can be seen that, at the operating condition,

CL1 = {VtO = 1.0 pu, V b O = 1.0 pu, PeO 1.2 pur single line}

0.0051-

; -0.01t single Line\

-0.015

2 -0.02 L

-0.03

-a -0.035

-0.OLI I

\ I

0.2 0.L 0.6 0.8 1 .o 1.2 Peo, p.u.

Fig.5 Dumping of oscillation mode over Q(p)

the oscillation mode is of poorest damping. Therefore, pl could be selected as the operating condition at which the UPFC damping controller is designed. However, the results of calculation of the forward path, F(&), over Q ( p ) as shown by Figs. 6 and 7, show that, for all the candidate input control signals to be superimposed by the UPFC damping controller, uk E {mE, mB, aB, aB}, pl is not the suitable operating condition to design the controller, since as predicted by the computation of F(&) (Fig. 6), at p, the UPFC damping controller is more effective to damp the oscillation, so that once it is designed at pl, its effectiveness at other operating con- ditions cannot be ensured (i.e. the robustness of the damping controller may not be achieved). With Uk = a,, we have F(&) = 0 over Q ( p ) . Therefore, the oscilla- tion mode is not controllable if the input control signal is chosen to be 6,. In the following, 6, will not be included in the discussion.

IEE Proc.-Gener. Transm. Distrib.. Vol. 146, No. I . January 1999

0.3-

0.25

0.2

n . I5

of eqn. 18a lead to the selection of the input control signal for the UPFC damping controller as uk = mB. (iii) The results of applying the criteria of eqn. 18b are: - ( a ) with ~k = WZE,

maxF(Xo,P,uk) - minF(Xo,P,uk) = 25.73 - minF(Xo,P,uk)

(b) with uk = SE, -

Peo, pu Fig.6 Vuriution of magnitude of F(&j over S ( p j

o,05-

35r

maxF(Xo,P,%) - m i n F ( X o , P , m ) = o.73 uk:mElsingle line) Uk' 6E (single line) uk=mE( two line)

\

\ min F(X0, I*, Uk) Therefore, with uk = nzB, the UPFC damping controller

0--- I f provides the smoothest damping to the oscillation

l5 t uk:mgltwo line)

0.2 0.4 0.6 0.8 1.0 1.2 Peo, pu

Fig.7 Variation ofphase ofF(&,j over S ( p )

(i) According to the criteria of eqn. 17, it can be seen that the operating condition to be selected for the design of the UPFC damping controller is:

1 .Opu, Pe0 = 0.1 pu, two lines};

P,, = 0.1 pu, single lines}. (ii) At p2 and p,Telecled, the most effective input control signal is uk = mB as indicated by Fig. 6. So the criteria

(a) with uk = mE and SE, p2 { V I , 1 l.opU, vho 1

(b) with Uk = nZg, pssylected = { VI, = l.opU, vho = l.opU,

P s e l e c t e d = {KO = 1.0 PU, KO = 1.0 PU, P,o = 0.1 pu, single lines}

Then the phase compensation method outlined by eqns. 19 and 20 is used to set the parameters of the UPFC damping controller at ,uselected with US&ted = mB. The results are:

Use lec t ed = m B

h'u = 6.38, Tu = 0.01 S, T, = 10.0 S, 7'1 = 0.9 S,

T2 = 0.89 S, T3 = 0.9 S, T4 = 0.70 s The oscillation mode is moved by the UPFC damping controller to 4 = -0.5405 2 j5.2517 with a satisfactory damping of 0.1.

To verify and confirm the correctness of the selection of the operating condition and the input control signal of the UPFC above, the phase compensation method is used to design the UPFC damping controller with sev- eral other selections as shown by Table 1, where pl = { V,, = l.Opu, V,, = l.Opu, PeO = 1.2pu, single lines} at which the oscillation mode is of the poorest damping when the power system installed no UPFC damping controller, p2 = { Vto = l.Opu, Vbo = l.Opu, Peo = 0.1 pu, two lines} which is selected for uk = mE and uk = 13,. Other parameters of the UPFC damping controller in Table 1 are Tu = 0.01s, T , = 10.0s, T, = 0.9s, T3 = 0.9s. From Table 1 we can see that, as predicted by Fig. 6, to achieve an effective design of the UPFC damping controller, u , ~ , ~ ~ ~ ~ ~ , ~ = mB requires lowest gain value (i.e. minimum control cost). From the last col- umn of Table 1, it can be seen that, for all cases, the damping of system oscillation is improved effectively.

However, when the robustness of the UPFC damping controller, its effectiveness at the operating conditions

Table 1: Results of the UPFC damping controller designed with five other selections

Oscillation mode t o be assigned by the controller

Operating Input control Parameters of the UPFC damping condition signal controller

1-11 A, = -0.4781 + j4.5187

cI1 A, = -0.4765 * 14.6642

Pl uk= mB Ku = 10.52, T2 = 0.70s. T4 = 0.57s A, = -0.4620 j4.5496

uk= m,

U I = dE

K, = 88.01, T2 = 0.48s, T, = 0. 41 s

K, = 24.63, T2 = 0.82s, T, = 0.65s

P2 uk= mE K, = 227.3, T, = 0.32~, T4 = 0.45s & = -0.5864 2 j5.5692

1-12 U, = 6, Ku= 68.92, T, = 0.74s, T, = 0.60s A, = -0.6629 * j6.1094

1EE Proc -Gmer Transm DrJtrib , Val 146, No 1 January 1999 85

Table 2: Results of examining the robustness of the UPFC damping controller

E“ 0.08- 0.06 0.01 0.02

0 -

Condition under wich the UPFC damping controller is design

Oscillation mode at p2 Oscillation mode at k,

with uk = m, at v , A0 = -0.0292 f j6.0006 with uk = 6, at pl

with uk = mB at p1

with uk = m, at p2

A, = -0.2863 2 j6.0517 A, = -0.4541 f j6.0933

A, = 0.0671 f j1.3910* with uk = & a t p2 A, = - 1.4493 j4.6211

with Uselected = mB at k e l e c t e d & = -0.4389 2 j4.4659

- - -

I

other than that where it is designed, is examined, shown by Table 2 of the results of eigenvalue compu- tation, it can be seen that the UPFC damping control- ler set at ,uselected with.u,,lected = mB is most efficient and maintains both effectiveness and robustness.

without UPFC damping controller

30C 25C 200

150 100 50

0

uk=mg with increased gain 200

150 100 50

0

I 2.0 1.0 6.0 8.0 10.0 t , s

Fig. 8 Nonlineur simulution with UPFC dumping controller designed

“,6%inear siinulation at p, (one of two lines is switched off after clearance of fault)

0.16r. ,

/;k=mB with increased gain

0 .I

of eqns. 1 and 2. The oscillation is started by a three- phase to-earth short circuit, which occurred at 1.0 sec- ond of the simulation and which is cleared after 100ms.

Uk’ m g uk=mg with increased

gain

3 -

I 4 I

0 2.0 1.0 6.0 8.0 10.0 t,s

Fig. 1 1

Nonlrneur siniulution ut pyelecred

Nonlinear simulation with UPFC dumping controller designed ut P,+lted

t , s Fig. 9 ut PI Input control signal of mB

Nonlinear simulation with UPFC dumping controller designed

z- 1 3 e 2 i OL 1

0 2.0 1.0 6.0 8.0 10.0 t , s

Fig. 10 at PI Nonlineur simulation at p2

Nonlinear simulation with UPFC damping controller designed

Figs. 8--14 are the results of nonlinear simulation of the power system, where the power system and the UPFC are modelled by nonlinear differential equations

86

oi:i:[ 0.01L F u k = m g with increased gain

0.008

0.006- 1 uk=mg 0.001 - 0.002-

J 0 A A 0 n j

0 2.0 4.0 6.0 8.0 10.0 t . s

Fig. 12

Input control signal of mB

Nonlineur simulation with UPFC damping controller designed ut Pxlrc tcd

without UPFC 10 9 8 7

2 6 9 5 “ 1

3 2 1

01 4

0 2.0 L.0 6.0 8.0 10.0 t,s

Fig. 13 designed ut

Nonlineur simulation ut 112 with the UPFC damping controller

(i) From Fig. 8 it can be seen that the UPFC damping controller designed at p1 with uk = mE and uk = SE can suppress the oscillation effectively when the power sys- tem operates at p l . However, with uk = mB, the effec- tiveness of the damping controller is not the same as that indicated by eigenvalue assignment. This is caused by the limitation of the input control signal on mB (0 s

IEE Proc.-Gener. Trunsm. DiJlrib.. Vol. 146, No. I . Junuury 1999

mB 5 1) as shown by Fig. 9. The damping controller does not achieve its damping effect as expected by the eigenvalue assignment as shown by the last column in Table 1. However, with an increased gain value K , = 24.63 (same as that with uk = SE), the damping control- ler with uk = mB can damp the oscillation effectively as shown by Figs. 8 and 9.

uk= mE 20

0 I

t , s 0 2.0 1.0 6.0 8.0 10.0

Nonlinear simulution ut p, Fig. 14 For uk = m,, the controller designed at , u ~ ~ , , ~ ~ , ~ ~ , , otherwise, designed at p2

(ii) When the power system operates at p2, Fig. 10 shows that the effectiveness of the UPFC damping con- troller designed at pl is not maintained, as indicated by the results of eigenvalue computation presented in the second column of Table 2. Therefore, the robustness of the damping controller is not achieved. (iii) Figs. 11 and 12 show that the limitation on mB also causes the difference between the results of eigenvalue computation and nonlinear simulation on the effective- ness of the UPFC damping controller designed at p,ye- lected with U,,[,,ted = mB. However, with increased gain value to be KU = 16.0, the oscillation is well damped. (iv) From Fig. 13 it can be seen that the UPFC damp- ing controller designed at p2 with uk = mE and uk = SE can suppress the oscillation effectively when the power system operates at p2 as indicated by the results of eigenvalue computation presented in the last column of Table 1 . However, when the power system operates at pl, the damping function of the controller with uk = mE is over-strong, which moves one pair of eigenvalues of the power system onto the right side of the complex plane as indicated by * in Table 2. This is also con- firmed by the nonlinear simulation presented by Fig. 14. (v) Fig. 14 demonstrates that, at p,, the UPFC damp- ing controller with an increased gain value designed at

with USe,,lected = mB can damp the oscillation as effectively that designed at p2 with uk = SE, but less control cost (lower gain value) is needed. Therefore, p,yelectrd and uselected = mB are still the correct selection.

5 Conclusions

The major contributions of this paper are: (i) the establishment of the Phillips-Heffron model of a single-machine infinite-bus power system installed with

an UPFC, which adds the UPFC, one of the most important FACTS controllers, into the category of the unified model presented in [7]; (ii) proposal of three criteria to select the operating condition of the power system to ensure the robust design of the UPFC damping controller and the input control signal to be superimposed by the UPFC damp- ing function to achieve the maximum efficiency of the damping controller. (iii) application of the phase compensation method to set the parameters of the UPFC damping controller.

6

1

2

3

4

5

6

7

8

9

References

GYUGYO, L.: ‘A unified power flow control concept for flexible AC transmission systems’, IEE Proc. C, 1992, 4, (139), pp. 323- 33 1 GYUGYO, L., RIETMAN, T.R., EDRIS, A., SCHAUDER, C.D., TORGERSON, D.R., and WILLIAMS, S.L.: ‘The unified power flow controller: a new approach to power transmission control’, IEEE Trans., 1995, PWER-2, (lo), pp. 1085-1097 NABAVI-NIAKI, A., and IRAVAM, M.R.: ‘Steady-state and dynamic models of unified power flow controller (UPFC) for power system studies’, IEEE Trans., 1996, P W R W , ( ] I ) , pp. 1937-1943 PAPIC, I., ZUNKO, P., POVH, D., and WEINHOLD, M.: ‘Basic control of unified power flow controller’, IEEE Trans., 1997, P W R M , (12), pp. 17361739 SMITH, K.S., RAN, L., and PENMAN, J.: ‘Dynamic modelling of a unified power flow controller’, IEE Proc. C, 1997, 1, (144),

LIMYINGCHAROEN, S., ANNAKAGE, U.D., and PAHALA- WATHTHA, N.C.: ‘Effects of unified power flow controllers on transient stability’, ZEE Proc. C, 1998, 2, (145), pp. 182-188 WANG, H.F., and SWIFT, F.J.: ‘An unified model for the anal- ysis of FACTS devices in damping power system oscillations. Part I: Single-machine infinite-bus power systems’, IEEE Truns., 1997,

WANG, H.F., LI, M., and SWIFT, F.J.: ‘FACTS-based stabi- lizer designed by the phase compensation method. Part I and 11’. Proceedings of APSCOM-97, Hong Kong, 1997, pp. 638-649 LARSEN, E.V., SANCHEZ-GASCA, J.J., and CHOW, J.H.: ‘Concept for design of FACTS controllers to damp power swings’, IEEE Trans., 1995. PWRS-2, (lo), pp. 948-956

pp. 7-12

PD-2, (12), pp. 941-946

10 WANG, H.F.: ‘Selection of robust installiig locations and feed- back signals of FACTS-based stabilizers in multi-machine power systems’, IEEE Trans., 1998, PWRS, (PE-066-PWRS-0-05) (in press)

7 Appendix

The parameters of the example single-machine infinite- bus power system (in pu except where indicated):

H = 4.0 s, D = 0.0, = 5.044 s, xd = 1.0,

x q = 0.6, X& = 0.3, ICT = 0.1, ZL = 0.3, K A = 10.0, TA = 0.01 S, Vdco = 10 kV,

C D ( S ) = ~ K d c (voltage controller of 1 4- S T d c

DC link capacitor), K d c = 2.0 PU, T d c = 0.01 s

IEE Proc.-Gener. Trunsiii. Distrib., Vol. 146, No. I , Junuury 1999