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IEEE Transactions on Power Delivery, Vol. 12, No. 4, O ctober 1997 1635IMPROVING POWE R SYSTEM DYNAMICS BY SERIES-CONNECTED FACTS DEVICES

M. Noroozian L. AngquistReactive Power Compensation Division

ABB Power SystemsS-721 64 Vasteris, Sweden

Member Non-Member

AbstractThis paper examines improvement of power systemdynamics by use of unified power flow controller (UPFC),thyristor controlled phase shifting transformer (TCPST) andthyristor con trolled series capacitor (TCSC). M odels suitablefor incorporation in dynamic simulation programs forstudying angle stability are analysed. A. control strategy fordamping of electromechanical power oscillations using anenergy function method is derived. The achieved controllaws are shown to be effective both for damping of largesignal and small signal disturbances and are robust withrespect to loading condition, fault location and networkstructure. Furthermore, the control inputs are easily attainablefrom the locally measurable variables. The effectiveness ofthe controls a re dem onstrated for m odel ]power systems.Keywords: FACTS, series-connected voltage source, UPFC,TCPST, TCSC, power swing, energ,y function , controlstrategy, local variables.

1. INTRODUCTIOIrJ

The power transfer capability of Ilong, inter-regionaltransmission lines is usually limited by both large and smallsignal stability. Such economic factors as the high cost oflong lines and the revenue obtainable from the delivery ofadditional power give strong incentives to explore alleconomically and technically feasible means of raising thestability limit.The fast progress in the field of power electronics hasalready started to influence the power industry. In principle,thyristor-controlled series capa citor (TCSC ) and thyristor-controlled phase shifting transformer (TCPST ) could providefast control of the active power through a transmission line.The possibility of controlling the transmittable power alsoPE-040-PWRD-0-01-1997 A paper recommended and approvedby the IEEE Transmission and Distribution Committee of the IEEEPower Engineering Society for publication in the IEEE Transactionson Power Delivery. Manuscript submitted January 3, 1996; madeavailable for printing January 8 , 1997.

M. Ghandhari G. An d er s o nNon-Member Senior Member

Dept. of Electric Powe r EngineeringRoyal Institute of TechnologyS-10044 Stockholm, Sweden

implies the potential application of these devices fordamping of power system electromechanical oscillations.Both a series capacitor and a phase shifting transformer ex erta voltage in series with the line. For a series capacitor, theinserted voltage lags the line current by 90 degrees. For aphase shifting transformer, the inserted voltage is inquadrature to the source voltage. By the development ofthyristors with current extinguishing capability, all solid stateimplementation of power flow controllers could be realised.The unified power flow controller (UPFC) is a new devicewithin the FACTS family which consists of series and shuntconnected converters.The use of series-connected controllable components forpower flow control in electric power systems is described in[ I ] an d [ 2 ] . In 1966 Kimbark showed that the transientstability of an electric power system can be improved by aswitched series capacitor [3]. Later work has explored thebenefits of the controllable series capacitor for improvingsmall disturbance stability [4]. Recent studies show thatseries reactive compensation is more efficient than shuntreactive compensation for damping of power sw ings [ 5 ] .A question of great importance is the selection of the inputsignals for the FACTS devices in order to damp poweroscillations in an effective and robust manner. This paperdevelops a control strategy for the series-connected FACTSdevices based on energy functions. To do this, a commonstructure model for series-connected devices is developed.The derived control strategy has a basic structure for thethree components and it is based on the variables which caneasily be obtained from locally measurable variables. Theselected control strategy is shown to be very effective forincreasing the stability limit of the studied power systems.This work is in the line with [6] and [7 ] which energyfunction approach are used for power swing damping. Thiswork presents a novel model for series-connected FACTSdevices for incorporation in the energy function. The outlineof this paper is as follows:Section 2 describes the operating principles and m odelling ofseries-connected FACTS devices UPFC, T CPS T and TCS C.Section 3 develops a control strategy for the series-connected FACTS devices based on an energy function.Section 4 demonstrates the performance of the devices fordamping of power oscillations for various fault scenariosthrough numerical examples.

0885-8977/97/$10.00 0 1997 IEEE

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16362. ELLING

In this section, a general model is derived for series-shunt-connected FACTS devices (UPFC , TCPST and TCSC). Thismodel w hich is referred to as the injection model, is valid forload flow and angle stability analysis, i.e., for situationswhere phasor based models are valid. The model is helpfulfor understanding the impact of these components on powersystem. Furthermore, the contribution of UP FC, TCPST andTCSC to the energy func tion can conveniently be identified.

el ~i ng f Series-Shunt-ConnectedDevicesUPFC and TCPST inject a voltage in series with a linethrough a series transformer. The active power involved inthe series injection is taken from the line through a shunttransformer. UPFC generates or absorbs the needed reactivepower locally by the switching operation of its converters,while the reactive power injected in series with the line bythe TCPST, is taken from the line and is circulated throughthe shunt transformer. Fig. 1 shows a general equivalentdiagram o f a series-sh unt-conne cted device (like UPFC andTCPST). -Y 'Y4 V"

Fig. 1: Equivalenit circuit diagra m of UPFC or TCPSTIn Fig. 1, X , is the effective reactance seen from the line sideof the series transformer. For UPFC X , = Xseries,or TCPSTX , = X,,,,,, +n2Xshunt, here X,,,,, is the reactance of seriestransformer, Xshunts the reactance of shunt transformer andn depends on the phase shifter angle [11[8].% is the induced series voltage, and 7, represents a currentsource. is a fictitious voltage behind the series reactance.Fig. 2 shows the phasor diagram of the equivalent circuitdiagram. -

I ,

Fig. 2 : Phasor diagram of the equivalent circuit diagram

The magnitude of is controllable by UPF C and T CPS T. Ifwe define r = ~ ~ ~ ~ / ~ ~ ~ ,hen 0 < r < r,,,. The angle y iscontrollable by UPFC from 0 to 2 7c.For TCPST: y =f 2 .

It is shown in [ l] an d [2] that the equivalent circuit diagramof Fig. 1 can be modelled as the dependent loads injected atnodes i and j. This model is called injection model and thegeneral configuration is show n in Fig. 3 :

Fig.3: Injection model fo r series-shunt connected device sThe expressions for Ps , ,Q sr, ,,Q, are given in Table 1(6q = e i - Q j ) :

UPFC TCPST

Table 1 UPFC and TCPST injection loads (b , = I/ X , )It is see n that ei= -ej which is expected, since UPFC andTCPST do not generate or absorb active power (when lossesare ignored).

2.2 Modelling of TCSCFor studies involving load flow and angular stability analysis,a TCSC can be m odelled as a variable reactance. However,for the purpose of developing a control strategy and h aving asimilar approach with that o f UPFG and TCP ST, it is usefulto have an injection model representation of the TCSC.Namely, the equivalent circuit diagram in Fig. 1 is validwhen 7, is set to zero, p= 4 2 n the phasor diagram of Fig.2 an d X , is considered to be as a part of the transm ission linereactance. The injection model for a TCSC withcompensation degree Kc is given in Table 2 [8].

Table 2: TCSC injection loads

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16373. CONT ROL STRATElGY To make V negative with maximum absolute value,

s i n (O i l + y ) must be kept equal to +_1epending on the signof - ( O b ) . This gives the following control law:

Control law for UPFC :

ddt

This section develops control strategies for damping ofelectromechanical oscillations for series-connected FACTSdevice s. First the model of the con trollers are incorporated inan energy function. Then the time derivative of the energyfunction is determined to yield the control laws.3.1 Energy Function d ;n

if -(e..) 0 then: K , = Kcmi"1 d t 4

The difference between the voltage angles across the series-connected FAC TS devices are used as inp ut signals.3.3 Influence of loading condition and n etwork topologyBased on this control strategy, the inpu t signal is measured ateach sampling time (say 20 ms) and the controllers outputare determined. This control structure is independent of thesystem loading, network topology and fault types.3.4 Influence of Multiple FACTS devicesThe mathematical approach for deriving the developedcontrol strategies can be extended to multiple series-connected FACTS devices if the requirement of the energyfunction are satisfied. S upp ose that there are totally m series-connected FACTS devices in a power system. Each device islocated between the nodes i,,, j, , such that n = 1,2,...,m ., Inthis case the derivative of energ y func tion is extended to:

" dv =Ccjn(einjn)I od t1For example for UPFC, we have:P J = -rbs 6 Vj s i n (e i i + y )

Equation (3) simplifies to:V = -rb,?

A sufficient condition to mak e v negative is that each devicefulfils the controls laws derived above. In this way, eachseries-connected FACTS device will contribute to thedecrease of the total energy without deteriorating the impact(4)

( 5 ) of th e oth er controllers.d tVj s i n ( e i j+y ) - (B i , ) I O

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1638

7 5 -50.

In this section, the developed c ontrol laws are applied for themodel power systems. First, a two machine system isconsidered and the effectiveness of the control strategy forUPFC, TCPST and TCSC is studied. Next, the interaction ofthe controllers with each other is examined in a threemachine system.

UPFC

TcPST

.1 Two ~ a ~ ~ ~ n ~ystems

ymax = 0.14, = 17 MVA, S,o,, = 160 MVASshunt-trans = l7 VA 7 Sseries-trans = 16 0 MVArmax O.18((bmax= 10")

-Sshunt-trans - series-trans = lg3M VA

The power system shown in Fig. 4 is used to study theperformance of the proposed control strategies forUPF CTC PST and TCSC. Two systems are connected via anintertie. Th e lengths of the lines are shown in the figure. Thetotal power flow through the intertie is 2100MW (840 M Wthrough the 200 km line and 1260 MW through the 300 kmline). Th e machines are m odelled with field windings and theinfluence of exciters are included. No damper windings aremodelled.

I 6 [deg.] TCSC

Bus I Bus i ____I_ Busi Bus2

TCSC

a--S=3000+j750 S=41OO+jl025Fig. 4: 500 kV test pow er system

K , is variable from zero to 34%, Mvar = 148

regulation, the ratings of shunt transformer and converter 1will increase). The voltage angles at the two nodes B us i andBus j are taken as input variables. T he difference betw een th etwo machine angles (6 )with different disturbances using theproposed control strategy for the three devices ar e shown andcompared with the case without FACTS devices.

Time [SI

Case i: A three phase fault occurs on point F. The fault iscleared after 80 ms with opening of the faulted line. Fig. 5shows the variation of the angle difference between the twomachines.

15 0

3100 6 [deg.] TCPST j 1 0 0 ~ l d e g . l T CS C'

'0 2 4 6 8 1 0

Fig. 5 : Variation of 6 against time f o r the case iThe series-connected FACTS devices are used in this systemin order: Case ii: A three phase faults occurs near Bu s I and it ise To equalise the loading between the two parallel system.e To improve the damping ofpow er swings.The da ta for the three devices are given in T able 3:

cleared after 80 ms (transient fault). Fig. 6 showssimulation results.I 6 [deg.] UPFC06 [deg.] No FACTS Device0

-10Tim [SI

3010-10

2 4 6 8-30; '2 4 6 8 1 030; '

-10-30 O kim [S I

0 2 4 6 8 1 0

the

3

Table 3: Data fo r FACTS devices Fig. 6: Variation of 6 against time fo r the case iiIt is to be noted that a UPFC can also be used for voltageregulation. However, in this example this feature is no texploited in order to have a basis for comparison between thethree components. (Clearly, in case of provision for voltage

The simulation results show that the proposed controlstrategies can be used to effectively damp the power swings.

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1639SM 2 and SM3) are shown. A three phase fault occurs on thebus connected to TCSC1. The fault is cleared after 100 ms.Fig. 9a, 9b, 9c, 9d show the simulation results.

. .

4.2. Multi-Machine S ystemThe power system in Fig 8 is used to study the influence ofmulti-FACTS devices o n damping of power swings using theproposed control strategy. Two sub-systems are connectedvia an intertie. The total power flow through the intertie is2000 MW. The machines are modelled in detail and theinfluence of exciters are included. The data for thesynchronous machines are given in Appendix 1.

SM 2 ITCSCZI20h

Load 2I50h

.

2000m

TCSCI200h

-4Load 4Load 3Fig. 8: 500 kV test pow er system

61 2 [deg.] TCSC2

Following both large and small disturbances, the systemexhibits power oscillations. To stabilise the power swings,two TCSCs are assumed to be located on the system. TheTCSC s reactances are modelled as: I 6 23 [deg.] TCSC2

where X is the virtual reactance of the TCSC, X,, is thereactance of the TCS C capacitor and Kboost shows the degreeof the voltage boost across the capacitor (In general, thevirtual reactance of a TCSC can be both inductive andcapacitive, however, in this example only the capacitivereactance is used). For this example, the following values areselected:

100-

0 -

Table 4: Data fo r the controllable s,eries capacitors

L 4814

The response of the system a three phase: fault is studied withthe following schemes:a. Both T c s c s act as f i xed capaci tors ( Ikbo,,, = 0 ).b. TC SC l is controlled and TCSC 2 acts us a fixed capacitor.c.TCSC2 is controlled and TCSCl acts as afixed capacitor.d. Both TCSC l and TCSC2 are controlled.In each scheme, the variation of 6, , (angle differencebetween SM1 and SM2) and S,, (angle difference between

Time [SI Time [SI

Fig. 9a: Variation of S,, and S,, against time withf ixedcapacitors

Time [ ] Time [SI

Fig. 9b: Variation of a,, and a,, against time with TCSCI

Time [s] Time [s]-100, 2 4 6 8 Ib 4 2 4 6 8 ILFig. 9c: Variation of 6 ,, and 6, , against time with TCSC 2

122oo/6 12 [deg.] TCSCl+TCSC2 S,, [deg.] TCSCl+TCSC2

T i m [SI Time [SI

Fig. 9d: Variation of 6 , , an d 6,, against time with bothTCSC l and TCSC2

The simulation results show the effectiveness of the controlstrategy. TCSCl has a better damping effect than TCSC2because it is located on the main intertie and has a larger size.It is interesting to note that the introduction of the TCSC2into the system, does not degrade the impact of the TCSClon the damping of power swings. This example shows anoutstanding feature of the proposed control strategy, namely:the controllers do not affect each other adversely.4.3. Experiment on Large SystemsThe proposed control laws has been successfully tested in a300 bus, 60 machine of Nordel system.



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1640AC LE ENTS

The authors wish to thank Mr. Lars Lindquist from ABBPower Systems for his help in simulating the controllablecomponents.BI

This paper has developed a general injection model forseries-connected FACTS devices. The models have beenincorporated in an energy function and the control laws fordamping of electromechanical oscillations are concluded.The conc lusions of this paper can be summarised as follows:The prop osed control strategy based upon locallymeasurable variables can be used fo r series-connectedFACTS devices (UPFC , TCPST and TCSC ) to damppower swings. The pel formance of such a controller isrobust with respect to network structure, fault locationand system loading.Using the proposed control strategies, the series-connected FACTS devices can be used in severallocations. Th e total effect on damping ofpo we r swings islarger than the impact of the individual devices.

EFERENCES[1 ] M . Noroozian and G. Andersson, Power Flow Controlby Use of Controllable Series Components, IEEETransaction on Power Delivery, Vol. 8, No. 3, July 1993, pp.[2] M. Noroozian, et al, Use of UPFC For Optimal PowerFlow Control, In Proceedings of Stockholm Power Tech,Stockholm, June 1995.[3] E.W. Kimbark, Improvement of System Stability bySwitched Series Capacitors, IEEE Transactions on PowerApparatus and Systems, PAS-85(2), Feb. 1966, pp. 180-188.[4 ] A. Olwegird, et . al, Improvement of TransmissionCapacity by Thyristor Control Reactive Power, IEEETransactions on Power Apparatus and Systems, PAS- 100(8),[5] M. Noroozian and 6. Andersson. Damping of PowerSystem Oscillations by Controllable Components. IEEETransaction on Power Delivery, vol 9, No. 4, Oct. 1994, pp,[6] G.D. Galanos, et al, Advanced Static Compensator ForFlexible AC Transmission. IEEE Transactions on PowerSystems, Vol 8, No. 1,Feb. 1993, pp. 113-121.[7] J. F. Gronquist, et al, Power Oscillation DampingControl Strategies For FACTS Devices Using LocallyMeasurable Quantities. Presented at IEEE 1995 Wintermeeting, paper No. 95 WM 185-9 PWRS.[81 M. Noroozian, Exploring Benefits of ControllableComponents in Power Systems, PhD thesis, Royal Instituteof Technology, Sweden, 1994, TRITA-EES -9402.[9] M.A. Pai, Energy Function Analysis For Power SystemStability, Kluwer Academic Publishers.

12-18.

Aug. 1981, pp. 3933-3939.

2046-2054.

Mojtaba Noroozian: (M92) He received his B.SC. inelectrical engineering from Arya-Meh r (sharif) University inTehran, M.Sc. in power systems from University ofManchester, Institute of Technology (UMIST) and Ph.D.from Royal Institute of Technology, Sweden. He has beenwith ASEA (AB B) since 1984. He is now with ABB PowerSystems AB, Reactive Power Com pensation Division.Lennart Angquist:. He received his M.Sc. degree inelectrical engineering from Lund Institute of Technology,Sweden. He joined ASEA in Vasteris, working with motordrives and power electronics for industrial and tractionapplications. Since 1987 he has been with ABB PowerSystems AB, Reactive Power C ompensation Division.Mehrdad Ghandhari: He is a graduate student at the RoyalInstitute of Technology, Sweden. His interest is powersystem dynamics.GSran Andersson: (M86-SM9 1 ) He received his M.Sc.and Ph.D. degree from the University of Lund. In 1980 hejoined ASEA:s HVDC-division and in 1986 he wasappointed professor in Electric Power Systems at the RoyalInstitute of Technology, Stockholm. He is a member of theRoyal Swedish Academy of Engineering Sciences and theRoyal Swedish Academy of Sciences.

I x, I 0.20 I 0.20 I 0.20 I

.. I I I0.03 I 0.08 I 0.08I 0.06 I - I -

Loadmodel: P = P , ( V / V o ) , Q = Q , ( V / y )



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APPENDIX 21641

Rearranging, we have:Th e following d efinition s are valid in this study:nR s the numb er of generators buses. The generator busesare numbered from 1 to ng.

nb s the numb er of non-generator buses. The non-generatorbuses are numbered from ng+1 lo ng 1- nb .

M,is the inertia constant of machine n .a,, an dbo,,,, s the susceptance between Bu s m an d Bu s n .bdl,s transient suscepta nce of the n th machine.

The system equations are written in the centre-of-inertiaframe with the follow ing definitions:

the angle and angular velocity of machine n.

It "with M = C M n , e,=%,-6,,, , n = n R + l , . . , n g + n b

n= l - -6 , = 6 , - 6 , 0, U " -mcol U) , :=U , -o,,,( n = l,2,..,ng)The energy function is selected as:U( W,t V )= v,, (W) v p , ($, V ) v,where V,,(W) is the kinetic energ y of the: system:

an d V p E (, V ) s the potential energy:

n= l n=n,+l

Assume that a series-connected FACTS device is connectedbetween node i an d j in a power system. The energy functionfor the power system is:U(&,& 6,V )= V,,(W> + VP,(& i ,V )+v,Th e time derivative of energy function becomes:

+

=l m=l+n, n = lg+nb ng ng+nbng+nb

x b d n V m E n inZnzn8, + z LnznVmVni n g m n gin= n=lI+n, nz= n=I+n, I+n,

m=l+n,

- I Q . . Q . .-P.O. - p . g . - A V . ---"v.V II I SJ J v,The expressions of V can be recognised as follows:- The expression in the first bracket is the power swingbalance and is equa l to zero .- The second bracket consists the expression for the totalactive powers going out from all load buses and is equal tozero.- The expression in the third row is the total reactive powersgoing out from all load buses and is equal to zero. Thus thetime derivative of the energy function simplifies to:- L Q . . Q . .c = - p . o . - p . o . - " ' v . - " ' yv, J yI IConsequ ently, the time derivative of energy functio n forseries-connected FA CTS dev ices is:

-2 v m v m- vmvn013om, - vmvnos0,,+ v m v n in o,,o,, -V,,V, sin zinznzin-m=l+ng n=l+n,

series connected facts

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