Robust damping of interarea oscillations with.pdf

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Robust damping of interarea oscillations withunified power-flow controller

converter 1

B.C. Pal

converter 2

Abstract: An H,-mixed-sensitivity design of a damping device employing a unified-power-flowcontroller (UPFC) is presented. The problem is posed in the linear-matrix-inequality (LMI)framework. The controller design is aimed at providing adequate damping to interarea oscillationsover a range of operating conditions. The results obtained in a two-area four-machine test systemare seen to be very satisfactory both in the frequency domain and through nonlinear simulations.

sh u n t transformer

1 IntroductionThe damping of interarea oscillations in power systems hasbeen a topic of research for decades [l, 21. The complexnature of the interactions among many control loops makesthe damping-control design task challenging. The designmethodology should therefore aim at improving dampingperformance while ensuring the least interaction with othermodes over the full range of system operating conditions.This type of control action has been sought by pole-placement and eigenvalue-sensitivity-based approaches[3,4], but these techniques do not always ensure robustnessin damping performance. Additionally, the amount ofcontrol effort required in maintaining adequate damping isgenerally quite large.In the last few years, the concept of H , control designwhich can guarantee robust performance and robuststability, despite uncertainty in plant parameter variations,has been applied in power systems to damp out low-frequency oscillations [5-7]. Normally, the problem isformulated as a weighted mixed-sensitivity design andsolved by a Riccati approach. The mixed-sensitivity H ,controller design based on the linear-matrix-inequality(LMI) formulation has shown interesting results [8] indamping-controller design since the solvability of a LMI-based formulation applies to singular plant. The numericalnature of the solution provides an improved controller withthe same H , norm as that obtained by the Riccatiapproach because the controller does not suffer from pole-zero cancellation [9]. The selection of weights has becomemuch easier, as no restriction is imposed on the augmentedplant. It is shown [lo] that a controller based on an LMIapproach guarantees higher damping ratios for the inter-area modes than can be achieved by the controller obtainedby the conventional Root-locus approach for the samecontrol effort. The injection of real power available from arelatively small sized superconducting magnetic-energy-storage device in a controlled fashion [8, 111 has beenutilised to ensure damped behaviour of power systems

EE, 2002IEE Proceedi,i(j..vonline no. 20020660doi: O. 1049/ip-gtd:20020660Paper first received Ith Octob er 2001The au th o r is with the Control and Power Group, Department of Electrical andElectronic Engineering, Imperial College of Science, Technology an d M edicine,London SW7 2BT, U K

following disturbances. In this paper, the same concept isextended for a UPFC.2 UPFC ModelThe UPFC is the most versatile FACTS device envisaged sofar [12]. It offers the options of voltage regulation, phaseshifting and line-impedance compensation through controlof its series and shunt converters. The schematic of a UPFCconnected between bus k and bus In is shown in Fig. 1. Thesteady-state model of a UPFC for power-flow studies hasbeen reported in [13-151. The simple power-injection modelsuggested in [14] is used here where the series- and shunt-converter voltages are replaced by nodal power injections asshown in Fig 2.The magnitude and phase angle of the seriesvoltage produced by the converter and the magnitude andphase angle of the AC voltage applied across the shuntconverter can be controlled independently.

r l

In the steady state, the real power flowing through theshunt converter equals the real power exchanged betweenthe series converter and the transmission system. Thisrelationship puts a constraint on the independent control ofthe converters. Nevertheless, the reactive power of the shuntconverter can be controlled independently for bus voltageIEE Proc.-Gener. Trmisiii. Di.ctr.ih., Vol. 149, No. 6, Nooei1iher 2002 733

Authorized licensed use limited to: Imperial College London. Downloaded on January 22, 2009 at 03:24 from IEEE Xplore. Restrictions apply.


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Pk= -rb,VkVm sin(Ukm y ) P , = rbSVkV,sn(0k, + y )Qk= -rbVcos y 0 = rbVkV COS ^^, + y )

1b = - xFig.2 UP FC poiver-injection mode l

G2 2 4

or VAR control and the power flow through the line can becontrolled through r and y . For a scheduled delivery ofpower at the receiving end, r and y will be fixed. The small-signal model is shown in Fig. 3by two first-order blockshaving small time constants of 0.02s each. The primarypurpose of the UPFC is to control power flow in the steadystate. It is found in the study system that, for 400 MW and40 MVAR to be received at bus 6, the required values for rand y are 0.10 and 80 . Without UPFC, 400 MW powercan be received at the cost of additional reactive-powerdemand at bus 6. The damping of interarea oscillationsdoesnot improve much with UPFC working on steady state.Supplementary signals are therefore necessary to damp outinterarea oscillations. A power-system stabiliser (PSS) isrecognised as the most cost-effective option for dampingcontrol, but with slow and DC-type excitation [16] a PSScannot contribute much to the damping process.

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ontrollerwashoutrmin

2nYref

I0Fig.3 Small-signal model of U P F C

area 1

In Figs. 2 and 3, r and y are the UPFC variablesrepresenting the ratio of series transformer voltage to kthbus voltage in p.u. and the angle of the series voltage inradians, respectively. The term h,, is the susceptance of theseries transformer combined with line susceptance hk}?,.3 Study systemFor study purposes, the two-area and four-machine testsystem shown in Fig. 4, investigated by many researchers[3, 5, 81 for interarea mode analysis, is considered. Allgenerators are represented by three damper windings on therotor and the excitation system is of the static DC lA type[3].The transfer of a specified amount of power with threetielines in operation is termed the prefault case. The sameamount of power transfer with one of the tielines out ofservice is termed the post-fault case. The transition fromthe prefault case to the post-fault case is through theopening of one of the tie circuits following a three-phasefault near bus 8 on one of the tielines. A total of 2600 MWconstant-impedance ((21) load is considered at buses 5 and6. Two capacitor banks injecting 200 MVAR each into bus5 and bus 6 are assumed to facilitate 400MW flow fromarea to area 2. For this power flow. the eigenvalue analysisof the system showed three electromechanical modes withdamping ratio/frequency of oscillation to be O.OS/ .OS, 0.09/1.10 and 0.02/0.62Hz respectively. The first two modes arelocal modes of area 1 and area 2, respectively, while thethird mode involved all four machines and so is an interareamode. The focus of this paper is on the damping-controllerdesign for this interarea mode.The UPFC is located in one of the circuits of the tielinewith shunt converter connected to bus 5 and the seriesconverter connected in the line between bus 5 and bus 8.Various locally available signals, e.g. bus voltage, busfrequency, real power in all the lines terminated on a bus,line-current magnitudes, rotor speed etc.. are considered asthe input signals. Observability analysis shows that the linereal power, active line current and line-current magnitudecarry valuable information about the interarea mode. Thetransfer function considered here is the input-outputbehaviour of the system between the linecurr ent magnitudeand the v-input of the UPFC. The magnitude of the linecurrent between bus 5 and bus 9 is treated as an outputsignal because it has the largest observability magnitude.4 LMI-based controller designThe theory of LM1 detailed in [17]. The design problemtreated in this paper consists of finding an internallystabilising controller that satisfies an infinity-norm

area 2

Fig.4 Four-machine test system134 IEE Proc.-Gener. Trarisni. Di ytrih. Vul. 149, No. 6, Noueniher 2002



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constraint. Consider the standard mixed-sensitivity config-uration of Fig. 5. G is the open-loop plant, K is thecontroller to be designed and W , and W, are weights.y,, isthe magnitude of the current in the line between bus 9 andbus 5. y is the deviation in line-current magnitude or error;i v is the current-magnitude reference. z in Fig. 5 is anexogenous output. This design minimises a weighted mix ofthe transfer function S= 1-Gf i - I that ensures disturbanceattenuation and good tracking; KS K(I- GK)- ' handlesthe robustness issues and constrains the controller effort.This mixed-sensitivity (SjKS) design objective can berepresented as

where y is the bound on H , norm

The details of the mixed-sensitivity control design can befound in [IS]. The state-space description of the systemabove can be written asi x + B I w + B ~ u 1 )

y C ~ XD21 w +D 2 2 ~ (3)The controller K can also be described in state-spaceform asAkXk + B,@ (4 )

D22 is dependent on the input-output relationship of theplant. For the small-signal model of the UPFC describedabove with line current as the stabilising feedback signal, theplant becomes strictly proper, resulting in D22 0. OtherFACTS devices with a specific choice of the stabilisingfeedback signal may result in a nonzero 0 2 2 . In those cases,the design can be carried out by considering the plant asstrictly proper (setting Dz2 0) and the resulting controllerK can be modified later to include the effect of 0 2 2 byputting K K ( Z D 2 2 K ) - . Therefore, without loss ofgenerality, 0 2 2 can be set to zero thereby making thederivation simpler.The transfer function between w and z can be describedas

where

c,/= [ c1 + Dl2DXC2, D12ch ]DCi= DII+ Di2DkD21

The objective of the mixed-sensitivity minimisation is to findan internally stabilising controller that minimisesIn an LMI formulation [19], the same

objective is achieved in the suboptimal sense if there existsan X = X T> O such thatI FE:sI_.

A ; X + X A , i B e / XCfi1 BICI -1 DI c / OC c /X D ,I -y2Z

with IC,, sI A C / ) - B c l+ D , / (


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obtained [19, 201:

(13)The variables Yl1 YZ1 nd Y22 re given in terms of newcontroller variables A ,C, D as

A R + R A T + B ~ C C T ~ ; ~ +B ~ D D ~ ~Yll - Y l 1

The LMIs in (12) and (13) can be solved for A , C, D bythe recently the developed interior-point-optimisationalgo-rithm [21]. Once 2, ,b are found, the actual controllervariables A k , Bk, Ck,Dk are recovered from A , C, D bysolving @)- I 1).

The technique described above was applied to thedamping-controller design for the system under study. Toexpedite the design process in the LMI routine [22], theplant was reduced and the controller design was then

performed on the reduced plant. The optimal Hankel-norm-approximation technique [18] was used to obtain aeight-order reduced plant by means of the Robust ControlToolbox in Matlab [23].The standard design practice [18] in H , control design isto choose W,, as a high-gain lowpass filter for output-disturbance rejection. W, should be a highpass filter toreduce the control effort in the high-frequency range. Thereshould also be a lowpass filter to ensure robustness due tovariation in the plant model because of varying operatingconditions. There is therefore a conflict in the nature of W2to ensure robustness and minimise control effort. Thesingular-value response of the weighting functions Wl andW, are displayed in Fig. 6.The controller was designed with the help of the MatlabLMI toolbox [22].The controller was of 12th order, but asthis large-order controller is very awkward to implement inpractice, a simpler second-order controller using modelreduction on the controller was obtained. The reducedsecond-order controller was given by

K ( s ) -4.5 ( s 2 + 3.14) (9)5 Control ler performanceThe damping performance of the LMI controllers wasexamined at different operating conditions with CI loads.Table 1 shows the open-loop and closed-loop damping ofthree modes when 400 MW flows from area 1 to area 2. It is

-30 I I100

Fig. 6 Singular-valu e responseIO 102

frequency, rad/s1

Table 1: Damping ratios in both operating casesMod e Open-loop (prefault) Closed-loop (prefault) Open-loop (postfault) Closed-loop (prefault)

WNEDM-based control WNEDM-based controls f Hz) f Hz) s f Hz) f Hz)

I 0.02 0.62 0.19 0.56 0.003 0.51 0.13 0.452 0.08 1.08 0.08 1.08 0.08 1.08 0.08 1.083 0 09 1.10 0.10 1.10 0.09 1.10 0.10 1.10

136 IEE Proc.-Genrc Trunsin. Distrib Val. 149 No. 6, Noueiiiher 2002



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seen froin the results that the controller improves thedamping of the interarea mode only. The damping of otherlocal modes are untouched which is very desirable to avoidmodal interaction through action of the controller. Thedamping performance of the controller was also checked atvarious power-flow conditions and the results are displayedin Table 2. It is found that, at different power-flow patterns,the damping is again adequate. Table 3 shows dampingratios and frequencies with constant-current (CC), constant-

Table 2: Damping ratios at various values of power flowPower Open-loop Closed-loopflow (area1+area2)

f Hz) s f Hz)00 M W 0.02 0.65 0.20 0.64

200MW 0.02 0.64 0.19 0.59400 M W 0.02 0.62 0.19 0.56

-400 M W 0.02 0.60 0.12 0.58

Table3: Damping ratios and frequency at different loadcharacteristicsLoad type lnterarea mode closed-loop (prefault)

s f Hz)CIccCPCC+CP

0.190.370.360.27

0.560.570.700.54

power (CP) and an equal mix of constant-current constant-power type loads (CC+CP). From the results in Table 3, itis confirmed that the controller maintains robustness indamping to variation in load characteristics.A nonlinear simulation was performed for a largedisturbance. A three-phase fault at bus 8 was applied for70ms, after which the fault was cleared from the faultedline. Fig. 7displays the large disturbance performance ofthe controller examined for up to 20s. A limit of 0.10 wasimposed on the controller output to restrict the series-transformer output voltage to 20 of bus 5 voltage. It isseen that the responses are very satisfactory even withsystem noiilinearities and the imposed operating limits ofthe various dynamic components.A 16-machne 68-bus system [lo] is now being investi-gated. The system has three interarea modes. The effect of aUPFC is being studied with other two FACTS devices:SMES and TCSC. The results will be communicated in afuture paper.6 ConclusionsThe mixed-sensitivity-based H , in the LMI framework isapplied successfully in a simple two-area power system thatsuffers from severe interarea oscillations. A UPFC isemployed as the controlling device. The performance ofthe controllers is seen to be robust over a range of operatingconditions. The performance of the controller is found to besatisfactory at different load characteristics. The controllerdoes not affect the damping of the other local modes. Thelarge-disturbance performance of the controller is also seento be very satisfactory.7 AcknowledgmentThe author thanks Dr. Brian Cory and Dr. Imad. M.Jaiinoukha in the Control and Power Group for theircomments and suggestions.

0 10 15 20 0 5 10 15 20time s time s

0.20

0.15

2 0.10.

0.05-100 1 , , ,

00 5 10 15 20 0 5 10 15 20time s time s

Fig._ _ _ without control_-__ with controlDynmzic rexpome of the system to large disturbances

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Robust damping of interarea oscillations with.pdf