Effects of unified power flow controllers on transient stability

S. Limyingcharoen U. D. Ann a kkag e N.C. Pahalawaththa

Indexing terms: Unified power flow controllers, In-phase voltage control, Quadrature voltage control, Shunt compensation, Transient stability

Abstract: The paper investigates the mechanism of the three control methods of unified power flow controllers, namely in-phase voltage control, quadrature voltage control and shunt compensation, in improving transient stability of power systems and examines the utilisation of the voltampere ratings by the three control methods. The study is based on a single machine infinite bus system with a unified power flow controller connected in series with the transmission lines. The potential of the three control methods in transient stability enhancement is identified. Analytical results indicate that significant reduction in the transient swing can be obtained with any of the above methods by using a simple proportional feedback of rotor angle deviation. The analysis of the transient energy function shows that the transient stability margin can also be substantially improved with in-phase voltage control and quadrature voltage control, however, to a smaller extent with shunt compensation. The analysis is verified by transient stability simulation. The simulation results show that the quadrature voltage control, apart from being more effective in reducing the transient swing than the in-phase voltage control, incurs a substantially smaller real power flow in the excitation converter. This makes a larger voltampere capability of the excitation converter available for shunt compensation.

1 lntroduction

Flexible AC transmission systems (FACTS) offer an alternative solution to transmission expansion by increasing the utilisation of the existing facilities towards their thermal limits. FACTS technology can also provide the ability to direct the power flow through a designated route El].

With increased power transfer, transient and dynamic stability is increasingly important for secure

0 IEE, 1998 IEE Proceedings online no. 19981698 Paper first received 10th December 1996 and in revised form 23rd September 1997 The authors are with the Department of Electrical and Electronic Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand

operation. Fast responding FACTS can be used to enhance the stability.

A unified power flow controller (UPFC) is a type of FACTS controller and has a basic structure shown in Fig. 1. It is capable of both supplying to or absorbing from the power system through the excitation converter and transformer a controllable amount of reactive power and inserting a voltage of controllable magni- tude and phase angle in series with the transmission system through the booster converter and transformer [2]. The inserted series voltage can be resolved into in-phase and quadrature components with respect to the sending end voltage, providing two control aspects. The in-phase component causes the magnitude of the receiving end voltage to change and the quadrature component causes the phase angle to change. The func- tion of supplying or absorbing reactive power is essen- tially the same as that of a static var compensator (SVC) or a static condenser (STATCON). The ability to change the phase angle of the voltage is similar to that of a thyristor controlled phase angle regulator (TCPAR).

In a power system installed with UPFC, the three control aspects become available: in-phase voltage con- trol, quadrature voltage control and shunt compensa- tion. Although these three controls can be used independently for stability improvement, they are sub- ject to the same operating limits of the device. The in-phase and quadrature voltage controls compete with each other for the available voltampere (VA) rating of the booster converter and cause real power flow in the DC link. The DC link power flow in turn competes with shunt compensation for the available VA rating of the excitation converter. Therefore, it is very important to quantify the effectiveness of these three control methods and coordinate the three control actions in the best possible way to utilise the available ratings of the UPFC.

Studies reported in the literature [3-61 have shown that SVCs, TCPARs and UPFCs can be used to enhance the transient stability of the power system, but not much attention has been given to comparing the three methods for their ability to improve the transient stability. In addition, the extent to which the in-phase voltage control of UPFC affects the stability of power systems has not been reported.

The purpose of this paper is to examine the mecha- nisms of controlled shunt compensation, in-phase volt- age control and quadrature voltage control of the UPFC in improving transient stability of power sys- tems and consider the utilisation of the VA ratings of the UPFC by the three different methods.

182 IEE Proc-Gener. Tmnsm. Distrib., Vol. 145, No. 2, March 1998

exciter transformer

L

1 12 exciter booster

converter DC bus converter booster t rans former

exciter f ir ing signals booster firing signals

I converter firing control I

Fig. 1 UPFC basic components

2 Transient swing analysis

The effectiveness of each UPFC control method in improving transient swing is studied in this Section. A single machine-infinite bus (SMIB) system shown in Fig. 2 is used in the study. The system data are given in the Appendix (Section 7.1).

I transmission Line 1 I

generator I I transformer I transmission Line 2

I infinite

bus ‘ f fault

Fig.2 Single mchine-inznite bus system

I L - - - - - - - - - - - l UPFC

Fig.3 SMIB circuit model

In the analysis, the components of the SMIB system are represented by their circuit models as in Fig. 3. The UPFC is represented by the combination of a variable shunt susceptance, a shunt current source and a con- trollable series voltage source [2, 61, as shown in the UPFC block in the diagram. The variable shunt sus- ceptance, b,, reflects the reactive compensation ability of the excitation converter. The controllable series volt- age source, V,, represents the booster converter which inserts variable in-phase and quadrature voltage com- ponents in series with the line voltage. The shunt cur- rent source, I,, absorbs the same amount of real power, P,, as is injected into the network by the controllable voltage source. This represents the DC power flow between the excitation converter and the booster con- verter.

Neglecting the resistances, the transmission line is represented by a series reactance, xL and the trans- former by a leakage reactance, xp

For the purpose of analysis given in this Section and in Section 3, the synchronous generator is represented by the classical model. The rotor dynamics of the gen- erator is governed by

= w - w o d6 d t -

where PMo is the mechanical power and is assumed to be unchanged during the period of analysis. The gener- ator output P, is a function of 6 and the UPFC con- trol variable, U, where U is defined as:

for controlled shunt compensation: U = bs for in-phase voltage control: U = a for quadrature voltage control: U = b

The generator output increases with increasing rotor angle even without the UPFC control action, and this action opposes the widening of the rotor angle. The transient stability can be enhanced by providing addi- tional synchronising power (and hence synchronising torque) which is in phase with the rotor angle deviation [7]. In order to provide the SMIB system with this additional synchronising power, a linear control strat- egy based on the deviation of the rotor angle is used and can be expressed as:

where au = klas (3)

as = s - S O (4)

a u = u - U , ( 5 ) where kl is the controller gain, So the initial rotor angle and u0 the reference setting.

The angle deviation signal can be obtained by inte- grating the rotor speed deviation of the generator. Ap alternative method is to calculate the rotor angle, 6, using

IEE Proc.-Gener. Tuansm. Distrib., Vol. 145, No. 2, March 199X 183

where 6’ is the phase angle of the terminal voltage, V,, with respect to that of the infinite bus, I , is the genera- tor current, $ is the generator’s power factor angle and xq is the quadrature axis synchronous reactance.

The generator’s terminal voltage phase angle with respect to a common reference can be measured using the synchronised phasor measurement technique described in [8].

In order to provide a reference for the comparison, each control method operates within the same VA rat- ing which is the rating of the UPFC converters. In addition, the operation of the excitation converter is also limited by its rated current and that of the booster converter by its rated voltage. The UPFC ratings are given in the Appendix (Section 7.2). The controller gain is chosen such that a rotor angle deviation of 15 degrees will cause the control to change from the mini- mum value to the maximum value.

The system is subjected to a three-phase fault on one of the transmission lines for 0.10s, after which the fault is cleared by removing the faulted line.

=! a L a z a

\

1.0

0.5

0 0 LO 80 120 160

fl

1.0

2

6 i a

n

0.5

0 0 LO 80 120 160

rotor angle, deg. b

Transient power-angle characteristics of SMIB system with dif- Fig. 4 p e n t UPFC control methods a Uncontrolled case h Controlled shunt compensation (i) prefault, (ii) postfault, (iii) during fault

As the fault location is close to the UPFC, the volt- age at the excitation transformer will be very low dur- ing the fault, thus reducing the effectiveness of shunt compensation. In addition, the high magnitude of the fault current which passes through the booster trans- former will make it necessary to reduce the inserted series voltage to keep the converter VA within the

184

limit. Therefore, the effect of the UPFC is very limited during the fault, and thus the UPFC controller is assumed to be active only after the fault is cleared. This assumption simplifies the analysis.

The equal-area criterion is applied to determine the maximum rotor angle during the transient period. The transient power angle curves for uncontrolled and con- trolled cases are shown in Figs. 4 and 5 . The presence of the dependent current source, I,, in the UPFC model in Fig. 3 makes the network nonlinear. For in-phase voltage control and quadrature voltage control, P , cannot be expressed explicitly and thus an iterative technique is used to compute PG numerically. Note that the abrupt changes in the slope of the curves of the controlled cases are due to control saturation. Also note that the power angle curve in the case of quadra- ture voltage control (Fig. 5b) does not pass through the origin due to the phase shift introduced by the con- troller.

1.0 * Q

a i

2 Q

0.5

0 0 LO 80 120 160

ro to r angle,deg. b

Fig. 5 j’erent UPFC control methods a In-phase voltage control b Quadrature voltage control (i) prefault, (ii) postfault, (iii) during fault

Transient power-angle characteristics of SMIB system with dif-

The prefault operating condition is given by point a. When the fault occurs the generator output is suddenly reduced to point b and the operating point starts to move along the curve bc due to acceleration. As the faulted line is removed, the operating point moves from point c to point d and then along the curve dhe to reach the maximum swing at e. The operating point follows the path ehf for the backswing.

IEE Proc.-Gener. Transm. Distrih., Vol. 145, No. 2, March 1998

Comparison of the uncontrolled case with the con- trolled cases shows that by activating the UPFC con- trol actions after clearing the fault, the generator power can be substantially increased. Therefore, the maximum rotor angle (i.e. the angle for which the area A3 is equal to the area AI + A2), is much smaller. In addi- tion, the acceleration area A2 is reduced, thus requiring a smaller area A3 and hence a flirther reduction in the maximum swing.

It is noted that the reduction in the area A2 is partic- ularly prominent for quadrature voltage control, in which case there is no accelerating area A2 due to the effect of phase shift. This results in a significant improvement of the first swing transient.

Following the peak of the first swing, the rotor will decelerate. When it decelerates past the point where the control leaves the maximum limit (point X on the curve), the control action will reduce the electrical power, thereby reducing the deceleration. The maxi- mum backward rotor deviation, with respect to the postfault equilibrium (point h), will be smaller for the controlled cases than that for the uncontrolled case. This results in reducing the peak to peak swing and this effect is significant in the case of quadrature voltage control. The reason is that the rate of reduction of the generator output with decreasing 6 is further increased by the effect of phase shift.

3 Stability margin

The transient stability of the SMIB system can be ana- lysed using the transient energy function which is defined as [9]:

1 2

V ( 6 , w ) = - M ( w - P M O ( S - S S E P )

6

+ 1 PG(Q,U(Q))dQ (7) 6 S E P

where M = 2 H I q and SsEp is the rotor angle at the postfault stable equilibrium point.

The first term is the kinetic energy, and the sum of the second and the third terms is the potential energy.

ro tor angle, deg. Fig.6 Potential energy profiles o j SMIB system with clqjerent UPFC control methods (I) prefault, (ii) quad. voltage, (iii) in phase voltage, (iv) prefault SEP, (v) dur- ing fault, (vi) fault clearing, (vii) shunt comp., (viii) uncontrolled

The potential energy components of the transient energy are shown in Fig. 6, and are used to depict the states of the system during the transient condition. The stable equilibrium point (SEP) and unstable equilib-

IEE Proc -Genu Tranym Di\tirb Vu1 145 Nu 2 Mulch 1998

rium point (UEP) correspond to the local minimum and local maximum of each particular potential energy profile, respectively.

During the acceleration period the SMIB system acquires some transient energy with respect to the post- fault SEP. As losses are neglected, the transient energy is constant when evaluated along the postfault trajec- tory [9]. The kinetic energy component of the transient energy is converted to potential energy as the speed deviation decreases during the deceleration period, and at the maximum rotor angle the kinetic energy is com- pletely converted to potential energy. The acquired transient energy during the acceleration period is, therefore, equal to the potential energy of the prefault operating point with respect to the potential energy of the postfault SEP.

In order to compare the transient stability margins, the prefault potential energy is taken as a reference level. The transient stability limit, which is determined by the maximum kinetic energy that the system can absorb after fault clearance, corresponds to the nearest UEP. Therefore, the transient energy at the UEP is the critical energy and can be obtained from eqn. 7 as

I4 = V ( 6 U E P , 0) 6 U E P

= - P M o ( b E P - S S E P ) + hi,, PG(&,

(8) For the system to be transient stable, the critical energy must be greater than or equal to the transient energy acquired during the acceleration period. The transient stability margin is the difference between the critical energy and the transient energy acquired by the system during the acceleration period. To improve the stability margin the controller must be capable of either increas- ing the critical energy or reducing the acquired tran- sient energy.

Fig. 6 shows that the critical energy of the nearest UEP is increased when the UPFC is controlled.

Table 1 compares the critical energy, the acquired transient energy and the transient stability margin of the SMIB system for the uncontrolled case and the three UPFC control methods.

Table 1: Transient energy of SMIB system

Transient Critical Stability energy energy margin

Uncontrolled case 0.1590 0.1687 0.0097

In-phase voltage control 0.1536 0.3088 0.1552

Quadrature voltage control 0.1607 0.2979 0.1372

Controlled shunt compensation 0.1545 0.2538 0.0993

With in phase voltage control, the critical energy can be raised markedly resulting in a significant improve- ment in the stability margin compared with that of the uncontrolled case.

With quadrature voltage control, the critical energy is raised to a slightly smaller extent compared with that of in phase voltage control. The improvement in the stability margin is slightly less.

With controlled shunt compensation the increase in critical energy is the smallest, however, still substantial.

For the SMIB system the transient energy can be related to the equal area criterion [lo]. It should be noted that the reduction of the acquired transient

185

energy is equivalent to the reduction in the area A1 + A2 in Figs. 4 and 5. The consequence is that the area A3 is reduced leaving a larger area A4 as the stability margin. It is therefore desirable to coordinate the con- trol methods so that the area A2 is minimised and at the same time the combined area A3 + A4 is maxim- ised.

All three control actions result in a reduction in the area A2, quadrature voltage control being able to totally eliminate the area A2 attributing to its phase shifting effect. They also result in different degrees of increase in the generator output at large angle devia- tions, leading to an increase in the combined area A3 + A4. This contributes to an improvement in the tran- sient stability margin.

It should be noted, however, that the transient energy for the quadrature voltage control is higher than that for the other cases due to the loss of the decelerating area corresponding to area A2' in Fig. 56.

When fault clearing is delayed, area A1 will be extended towards higher power angles. This results in an increased area A2' at the expense of area A3 + A4. Therefore, as the system gains its transient energy dur- ing fault it also loses its opportunity to convert the transient energy to potential energy. The resulting effect is a reduction in the stability margin with delayed fault clearing. This reduction is larger for quadrature voltage control than for the other control methods, as shown in Fig. 7.

0.OL 0.06 0.08 0.10 0.12 0.11 fault clearing time,s

Fig. 7 Eflect of dalayed fault clearing on stability margin (i) quad. voltage, (ii) shunt comp., (iit) uncontrolled, (iv) in-phase voltage

Although this is a drawback for quadrature voltage control, the results of the analysis suggest that, in order to improve the first swing transient, quadrature voltage control should be coordinated with the other control methods such that a satisfactory stability margin is also maintained at these operating conditions. Investigation of the control coordination is, however, beyond the scope of this paper.

4 Simulation results

model is given in the Appendix (Section 7.2). The UPFC ratings were specified such that the restrictions on control action due to VA rating do not influence the comparison of the three control methods. The DC bus nominal voltage and DC capacitor were chosen so that during the transient periods EDc did not fall to a value below which the converter would lose its current con- trol capability [14]. The PI controller for the DC bus was tuned to rapidly restore the DC bus power balance following a step change in the booster voltage.

The comparison of the swing curves in Fig. 8a agrees with the result of the analysis using the equal-area cri- terion, that the quadrature voltage control offers the best transient swing improvement. The in-phase voltage control is less effective than the quadrature voltage control in reducing the transient swing. The effective- ness of the shunt compensation is the lowest, but is nevertheless substantial. For each control case the con- trol action was restricted so as not to exceed the ratings of the UPFC. Fig. 8b shows the VA of the booster converter resulting from in phase voltage control, the VA of the booster converter resulting from quadrature voltage control and the VAR supplied by the exciter converter resulting from shunt compensation.

.._.''_'._. . I uncontrolled

0 1 a

2

i-exciter MVAR ! j (shunt comp.1 !

I 5 L

I

0 1 2 time,s

b Transient slinulation results with dflerenr UPFC control methods Fig. 8

a Swing curves b MVA and MVAR flow through converters

In order to verify the above analysis, transient stability simulations were carried out using the above control strategy. A more detailed third order generator model [ l l ] with IEEE type DC1 exciter [I21 was used in the transient simulations. The parameters of the generator and exciter were adapted from [13]. The dynamics of the DC bus of the UPFC was also incorporated and its

186

time,s Transient simulation results with real power jlow into exciter con- Fig. 9

verter

Fig. 9 shows that, apart from being more effective than the in-phase voltage control and shunt compensa- tion, the quadrature voltage control incurs a substan- tially smaller magnitude of real power flow in the

IEE Proc -Gener Transm Dutrib , Vol 145, No 2 March 1998

excitation converter, leaving a larger VA capability available for shunt compensation.

As previously pointed out, the in-phase and the quadrature voltage controls compete with each other for the rating of the booster converter and cause the DC power flow between the converters. The DC power flow in turn reduces the available VA for shunt com- pensation, thus for optimum performance of the UPFC the three control actions, must be properly coordi- nated. Therefore, further investigation is essential in order to determine how the required coordination can be achieved.

In order to verify the analysis on transient stability margin, a series of successive simulations has been car- ried out for extended fault clearing. Table 2 shows the critical clearing time for each of the three control meth- ods. The critical clearing times obtained from the simu- lations agree with those obtained by extrapolating the curves in Fig. 7 towards the zero stability margin, although the analytical results are on the conservative side.

Table 2: Loading limit and critical fault clearing

Critical clearing time ( s )

Uncontrolled case 0.1 1

In-phase voltage control 0.15

Quadrature voltage control 0.14 Controlled shunt comoensation 0.14

5 Conclusions

The effectiveness of three different control aspects of UPFC, namely in phase voltage control, quadrature voltage control and shunt compensation, has been studied using an SMIB system. The study reveals that quadrature voltage control is very effective in reducing the transient swing of the rotor power angle. In-phase voltage control can also effectively reduce the first swing transient. However, quadrature voltage control causes a significantly smaller real power flow through the excitation converter than that resulting from in- phase voltage control, thus leaving a larger VA rating of the excitation converter available for shunt compen- sation. The effectiveness of controlled shunt compensa- tion is less than that for the other methods.

The transient stability margin can be improved by either increasing the critical energy or reducing the aquired transient energy during the acceleration period. The in-phase and quadrature voltage controls are par- ticularly effective in increasing the critical energy. How- ever, at a delayed fault clearing, the effect of the phase shift of the quadrature voltage control can result in a greater reduction in the stability margin than that for other methods.

The results of the above analysis will be useful in the coordination of UPFC controllers, so that the maxi- mum effectiveness is achieved for transient swing reduction and improvement of stability margin. The effectiveness of UPFC controls in damping small signal oscillations was reported by the authors in [15]. Although this issue has not been addressed in this paper, it must also be considered in control coordina- tion in addition to transient stability.

For a multimachine power system the above concepts can be applied to investigate the effects of UPFC on

IEE Pror.-Cener. Tvansm. Distvih., Vol. 145, No. 2, March 1998

the critical machine (or group of machines) in terms of individual machine energy functions which have been successfully used for analysing power system transient stability [16, 171. The authors are presently investigat- ing the application of the concepts to multimachine power systems.

6 References

1 HINGORANI, N.G.: ‘Future role of power electronics in power systems’, Electra, 1995, (162), pp. 33-35

2 GYUGYI, L., SCHAUDER, C.D., WILLIAMS, S.L., RIET- MAN, T.R., TORGERSON, D.R., and EDRIS, A.: ‘The unified power flow controller: a new approach to power transmission control’, ZEEE Trans. Power Deliv., 1995, 10, (2), pp. 1085-1093

3 ARNOLD, C.P., DUKE, R.M., and ARRILLAGA, J.: ‘Tran- sient stability improvement using thyristor controlled quadrature voltage injection’, IEEE Trans. Power Appur. Syst., 1981, 100, (3), pp. 1382-1388

4 O’BRIEN, M., and LEDWICH, G.: ‘Static reactive-power com- pensator controls for improved system stability’, IEE Proc. C,

5 EDRIS, A.: ‘Enhancement of first-swing stability using a high- speed phase shifter’, IEEE Trans. Power Syst., 1991, 6 , ( 3 ) , pp. 11 13-1 I18

6 MIHALIC, R., ZUNKO, P., and POVH, D.: ‘Improvement of transient stability using unified power flow controller’, IEEE Trans. Power Deliv., 1996, 11, (l), pp. 485-492

7 KUNDUR, P.: ‘Power system stability and control’ (McGraw- Hill, 1994), pp. 1103-127

8 ‘Synchronized sampling and phasor measurements for relaying and control’, IEEE Trans. Power Dfliv., 1994, 9, (l), pp. 442452 (IEEE Power system relaying committee working group H-7)

9 PAI, M.A.: ‘Power system stability’ (North Holland, 1981), pp. 105-1 08

10 PAI, M.A.: ‘Energy function analysis for power system stability’ (Kluwer Academic, 1989), pp. 14-18

11 YU, Y.: ‘Electric power system dynamics’ (Academic Press, 1983), pp. 41-44

12 ‘Excitation system models for power system stability studies’, IEEE Trans. Power Appar. Syst., 1981, 100, (2), pp. 494-509 (IEEE committee report)

13 ANDERSON, P.M., and FOUAD, A.A.: ‘Power system control and stability’ (Iowa State University Press, 1977), pp. 436-437

14 GREEN, A.W., BOYS, J.T., and GATES, G.F.: ‘3-phase voltage source reversible rectifier’, IEE Proc. B, 1988, 135, (6). pp. 362- 370

15 LIMYINGCHAROEN, S., ANNAKKAGE, U.D., and PAHALAWATHTHA, N.C.: ‘Stability enhancement of power systems by FACTS controllers’. Proceedings of third New Zea- land conference of postgraduate students in engineering and tech- nology students, Christchurch, New Zealand, 1-2 July 1996, pp. 70-75

16 MICHEL. A.N.. FOUAD. A.A.. and VITTAL. V.: ‘Power svs-

1987, 134, (I) , pp. 38-42

tem transient stability using individual machine energy functions’, IEEE Trans., 1983, CAS20, (5) , pp. 266-276

17 HAQUE, M.H.: ‘Hvbrid method of determining the transient sta- bility margin of a power system’, ZEE Proc., G&r. Trunsm. Dis- trib., 1996, 143, (l), pp. 27-32

7 Appendix

7.1 Parameters of SMIB system The parameters of the SMIB system are given in Table 3. The location of the fault is at 95 percent of the line length from the infinite bus.

Table 3: Parameters of SMIB system

Parameter Value Unit Parameter Value Unit

H 3.120 MJ/MVA TE 0.950 s

xd 1.014 p.u. SE.max 1.308

xs 0.600 p.u. sE,0.75 0.484

x‘d 0.314 p.u. €FDmax 3.870 p.u.

T b o 6.550 p.u. €FDmin -3.870 P.U.

KA 400 K F 0.050

TA 0.050 TF 0.350 s

vRm i n -4.120 P.U. xt 0.070 p.u.

KE -0.243 X / 0.650 p.u.

vRmax 4.120 p.u. K D 2.000

~

187

7.2 Dynamic model of UPFC The DC bus dynamics:

1

of control signals are: b, = a. = bo = 0.

E [IVl 11, - Be{(. + jb)KI,”}] (9)

A PI controller in Fig. 10 is used to maintain the DC bus power balance by regulating the DC bus voltage, E,c. Eb,, is the reference setting of EDc. The parame- ters for UPFC are: xB = 0.07p.u., EDC,R = 31.113kV,

d E D c - -

dt EDCCDC

= SSOOpF, K p 10, KI = 20. The reference setting Fig. 10 DC bus control

188 IEE Puoc.-Cener. Transm. Distrib , Vol. 145, No. 2, March 1558