A Robust STATCOM Controller For Power System Dynamic .
A Robust STATCOM Controller for Power System Dynamic PerformanceEnhancementA, H. M.A.RahimS, A,A1-BaiyatF. M.KandlawalaDepartment of Electrical EngineeringK.F.University of Petroleum and MineralsDhahrrm, Saudi Arabia.Abstract: A robust controller for providing damping to powersystem transients through STATCOM devices is presented. Methodof multiplicative uncertainty has been employed to model thevariations of the operating points m the system. The design iscarried out applying robustness criteria for stability andperformance. A loop-shaping method has been employed to select asuitable open-loop transfer function, from which the robustcontroller is constructed. The proposed controller has been testedthrough a number of disturbances including three-phase faults. Therobust controller designed has been demonstrated to provideextremely good damping characteristics over a good range ofoperating conditions.Keywords: STATCOM, FACTS devices, robust control, dampingcontrol, loop-shaping method.1.INTRODUCTIONIt is well established that reactive compensation oftransmissionlines through rapidly variable solid state,thyristor switches of the FACTS devices improve both thetransient as well as dynamic performances of a power system[1]. These devices dynamically control the power flowthrough a variable reactive admittance to the transmissionnetwork and, therefore,generally change the systemadmittance.Controllablesynchronousvoltage sources,known as static compensators, are a recent introduction inpower systems for dynamic compensation and for real timecontrol of power flow. The static compensator (STATCOM)provides shunt compensation in a similar way to the static varcompensators (SVC) but utilizes a voltage source converterrather shunt capacitors and reactors [2]. The basic principleof operation of a STATCOM is the generation of acontrollable AC voltage source behind a transformer leakagereactance by a voltage source converter connected to a DCcapacitor. The voltage difference across the reactancereactive power exchanges between theproduces activeSTATCOM and the power system [3]. It has been reportedthat STATCOMcan offer a number of performanceadvantages for reactive power control applications over theconventional approaches because of its greater reactivecurrent output capability at depressed voltage, fasterstability, lower harmonics, andresponse, better controlsmaller size, etc. [4].i ndTwo basic controls are implemented in a STATCOM. Thefirst is the AC voltage regulation of the power system, whichis realized by controlling the reactive power interchangebetween the STATCOM and the power system. The other isthe control of the DC voltage across the capacitor throughwhich the active power injection from the STATCOM to thepower system is controlled [3,5]. The STATCOM is normallydesigned to provide fast voltage control and to enhancedamping of inter-area oscillations. A typical method to meetthese requirementsis to superimpose a supplementarydamping controller upon the automatic voltage control loop[4].The effect of stabilizingcontrolson STATCOMcontrollers have been investigated in several recent reporting[3-6]. PI controllers have been found to provide stabilizingcontrols when the AC and DC regulators were designedindependently. However, joint operations of the two havebeen reported to lead to system instability because of theinteraction of the two controllers [3,6]. While superimposingthe damping controller on the AC regulator can circumventthe negative interaction problem, the fixed parameter PIcontrollers have been found invalid, or even to providenegative damping for certain system parameters and loadingconditions [4].This article investigates the effect of a damping controllerin the voltage regulator loop of the STATCOM. A robustcontroller is designed for a single machine infinite bus systemwith a STATCOM, The variations of the operating conditionshave been taken into consideration by modeling them asmultiplicativeunstructureduncertainty.A loop-shapingtechnique [7] has been employed to design the controllers.Two robust controllers, one in the speed feedback and theother in the voltage feedback loop have been investigated. Itwas observed that a robust controller in the speed loop with echanical oscillations, and keeps the bus voltagevariations to significantly small levels, for a wide range ofoperating conditions.2. THE POWER SYSTEM MODELA single machine infinite bus system with a STATCOMconnected through a step-down transformer is shown inFig. 1. The robust controller is designed considering a worstcase dynamic model with the following assumptions [4].a.0-7803-7173-9/01/ 10.00 2001 IEEENo detailed exciter and governor dynamicmodels; constant generator voltage e behindreactance x,J’;damping is neglected; mechanicalpower input Pm is constant.8870-7803-7031-7/01/ 10.00 (C) 2001 IEEE
b.STATCOM is a reactive current source withtime delay. Inductive current generated bySTATCOM is assumed positive.a,IAdAmo-tv.v,& -’‘( v,x,x,tAP.!2HS Dc.a21,alssalKCvTs lD- IL--l-JIFig.2 Block diagram of the linearized system,Fig. 1 Single Machine System with STATCOMThe system is then described by the following equations:3. ROBUST CONTROL DESIGNA/i UIoAaIAti. *[DAO-APCIAIS [–AI (1) CAUIwhere, b is the load angle,w is the angular speed, 2H is theinertia constant, D is the damping constant. The deliveredelectrical power P. is expressed ase; VMPe —sinx; x,O JV*x ‘ – Xqsin 20(2)2 (x: x, )(xq x, )The direct and quadrature axes components of bus voltage V are written as (x, -xj)J’,cosd e .x, 1,X2(L Xj)cose(3)w —x1 x2 xdv (xl xq)L sin ,yx, (x, xq)sin )lILI—(4)x, -t X2 X,l0 is the phase difference between quadrature axis of thegenerator and V.,, and is related as, tan 6 V d/V .By linearizing equations (2),(3), and (4), the variations inpower output and STATCOM bus voltages are written asA robust STATCOM controller is designed for a range ofoperating points by considering perturbationsaround anominal plant. These perturbationsare modeledasmultiplicative uncertainties in the robust design procedure.This section gives a brief theory of the uncertainty model, therobust stability criterion, a graphical design technique termedloop shaping, which is employed to design the robustcontroller. Finally, the algorithm for the control design ispresented.3.1 Uncertain@ ModelingSuppose that the nominal plant transfer fimction of a plantis P and consider that the perturbed transfer function becauseof variations of parameters al, a2, a , a4 in Fig.2 (for variousoperating conditions) can be expressed in the formP (l DW,)P(7)Here, W2 is a fixed stable transfer function, the weight, and Dis a variable transfer function satis@ingmultiplicativeIIDII 1. In theuncertainty model (7), DW2 is the normalizedplant perturbation away from 1. If IIDIIK 1, then(8)APe a1A6 azAI (5)AVM a3A8 a4AI ’where, a@PJLXi.,a7 8P@I,, a3 Nm/M,and a@VJ81s.The STATCOM controller output is written as,Au -Cv AVm COAO3.2 Robust Stability and Performance(6)C, and Cw are the controllers in the voltage and speed loop,respectively. The linearized system block diagram is given inFig.2.0-7803-7173-9/01/ 10.00 2001 IEEESO, Iw, (j@)] provides the uncertainty profile and in thefrequency plane is the upper boundary of all the normalizedplant transfer fimctions away from 1.Consider a multi-input control system given in Fig.3.Suppose that the plant transfer function P belongs to a set P.A controller C provides robust stability iff it provides internalstability for every plant in the set P.8880-7803-7031-7/01/ 10.00 (C) 2001 IEEE
Obtain the db-magnitude plot for the nominal as wellas perturbed plant transfer functions.Construct W, satisfying constraint (8).Select Wj as a monotonically decreasing, real, rationaland stable function.Choose L such that it satisfies conditions (1 O) and(1 1). The transition at crossover frequency should notbeat a slope steeper than –20dbldecade.Check for the nominal and robust performance criteriagiven in the theorems in section 3.2.Test for internal stability by direct simulation of thefor pre-selectedclosed loop transferfunctiondisturbances or inputs.Repeat steps 4 through 6 until satisfactory L and C areobtained. Note that a robust controller may not existfor all nominal conditions, and if it does, it may not beunique.1.xT“AcPFig.3 Unity feedback plant with controller.‘L2.3.4.5.Theorems:C providesmultiplicativerobust stability z llWzT\lm 1, forur!certain@. Also,condition for robust performancenominal performanceconditionnecessary6.and suJ7kientis WIS W1’f 1. Theis givenas7.W,SII 1 [7].IIIn the above, WI is a real, rational, stable and minimum phasefunction. T is the input-output transfer function, complementof the sensitivity function S, and is given as1(9)S – —l Ll f’cThe proofs of the above theorems are given in reference [7],4. IMPLEMENTATIONT l–As shown in Fig.2, the STATCON can be controlledthrough two control functions C. and Cv in the speed andvoltage feedback loops, respectively. In this study, the robustdamping control design was carried out independently foreach loop. The effect of employing control in both the loopssimultaneously was then investigated.3.3 The Loop Shaping TechniqueLoop shaping is a graphical procedure to design a propercontroller C satisfying robust stability and performancecriteria given in sec.3 .2. The basic idea of the method is toconstruct the loop transfer function, L PC to satisfy therobust performance criterion approximately, and then toobtain the controller from the relationship C L/P. Internalstability of the plants and properness of C constitute theconstraints of the method. Condition on L is such that PCshould not have any pole zero cancellation. A necessary4. I Robust Speed Controller DesignThe robustthe system inof the systemin the absencecontroller design procedure starts by arrangingthe form as shown in Fig.3. The block diagramwithout considering the voltage feedback, andof any input is shown in Fig.4.condition for robustness is that either or both IWI1,IW1\ mustbe less than 1[8]. If we select a monotonically decreasing W,satisfying the other constraints on it, it can be shown that atlow frequency the open-loop transfer function L shouldsatisfy,1(lo),L] 1 ;21while, for high frequency,1-IW,IILI 1(11)Iw,l pv,lAt high frequent y ILI should roll-off at least as quickly asIF’I does. This ensures properness of C. The general featuresof open loop transferfunctionis that the gain at lowfrequency should be large enough, and ILI should not dropoff too quickly near the crossover frequency to avoid internalinstability.The nominal operating point for the design was computedfor delivered power of 0.8 per unit at unity power factor. Offnominal power outputs between 0.2- 1.2 p.u and power factorsranging between 0.8 lag –0.8 lead were considered. Thepower system data is given in the Appendix. The dbmagnitude vs. frequency response for the nominal andperturbed plants is plotted in Fig.5. The nominal planttransfer function for the selected operating point is computedas1.0435s(12)P (s 50)(s’ 60.66)FromFig.5,thequantity (ja)/ P(jco) – 1perturbed plant is constructed and the uncertaintyfitted to the function3.4 The AlgorithmThe control design procedure for robust stability and robustperformance can be summarized in the following steps.0-7803-7173-9/01/ 10.00 2001 IEEEFig 4 Collapsed block diagram for robust speed feedback system.w, (s) 0.8s2 2.24s 39.2S28890-7803-7031-7/01/ 10.00 (C) 2001 IEEE 0.98s 49foreachprofile is(13)
A Butterworth filter satisfies all the properties for Wl(s)and is written as,w, (s) K f:S3 2s2fc 2sf:for the nominal operating condition is shown in Fig.8. Therotor angle variations for a number of operating conditionsare plotted in Fig. 9.(14) f;For K l and fC O.1 in W, and for a choice of the open looptransfer fimction L as,L(s) 208.75(s 1)(s 2)(15)(s .01)(s 50)(s2 60.66)gives the desired controller transfer fimction,5cm(s) 200(s 1)(s 2)-150(16)S(s ,7 Robust and nominal performance criteria,-200[0.12 0.2uoaor%I110Frequency100100010000(rad/see) Fig.5 Nominal and perturbed plant transfer functions.A-0,2-0.4The db-magnitude plot relating WI, Wz and L, which wasemployed to arrive at the controller, is shown in Fig. 6. Theplots for the nominal performance and robust performancecriteria are shown in Fig.7. Notice that nominal performancecriterion has been very much satisfied, while the robustperformance criterion exceeds 1 for a very small frequencyrange. This peaking in frequency is for the worst-case designof the controller for damping D O. Though, in reality, someclamping is present, the procedure shows that the performancecriterion may not be satisfied for all possible conditions. Thisis, of course, expected in the power system problem.50I-0.610I1I23Fig.8 Generator speed variation of with robust controller in the speed loop.80Po l ,2,pf O.81eadkIPo l, pf quency10“’’”l100J1000Po 0.6,pf 0.81ag1-010111123I4Time(sec.)Fig.9 Load angle with the robust controller for various conditions.(radkec)Fig. 6 Loop shaping plots relating W,, WZand LThe robust STATCON speed controller was tested byapplying an input torque pulse of 100 /0 of 0.05 sec. durationto the generator shaft. The speed variation of the generator0-7803-7173-9/01/ 10.00 2001 IEEEIt can be observed that good damping properties can beobtained with the robust speed controller over a wide range ofoperating conditions. While, the controller can be designed toprovide still more damping, the steady state error and peakovershoot in the bus voltages may be excessive in this case8900-7803-7031-7/01/ 10.00 (C) 2001 IEEE
characteristics. All these case studies are for a 100 /0 inputtorque pulse for 0.05 sec. duration.4.2 Robust Controller Design in the Voltage LoopThe block diagram corresponding to Fig. 4 with the voltageloop controller is shown in Fig. 10., 1](, 12P@g8IwlleadbP l,1.“,0,95la80-”-Apm-cq I!l .“ A0“ r/j wdPo O8P,, [),5[1:)51“ p., upfe,*U,bII.Fig. 10 Collapsed block diagram with voltage controller.(17)(s 50)(s2 60.7316)Because of the sign of P, the nominal plant is in a positivefeedback loop. Such a system does not fall in the category ofinternal stability [7] and robustness criterion cannot beapplied as such. However, by forcing Cv to take the oppositepolarity, a robust controller was designed following similarprocedure as in sec. 4.1. The controller does providereasonable amount of damping over a range of operatingconditions, but is not as effective as the speed controller Cm.It is to be notecl that earlier studies also revealed that theSTATCON voltage control loop does not provide enoughdamping [4,6]. PI controller design is often unsatisfactory,and may even lead to unstable situations [6]. This can beattributed to the fact that there is a pair of poles and a pair ofzeroes in P on the imaginary axis, which are in closeproximity. These pole-zero pairs are responsible for theoscillatory nature of response in that voltage loop which is adesirable for voltage regulation purpose. In the followingsection, a robust design for a controller in the speed loop ispresented which retains a nominal voltage feedback CV 1.4.3 Coordinated Robust Speed ControllerThe nominal plant transfer with robust controller in thespeed loop and including the voltage feedback can beexpressed as,1.043s2(18)P(s) —(S 58.6249)(s2 1.694s 10.69)Note the positive feedback situation disappears allowing aproper robust design. Continuing with the same designprocedure employed in sec. 4.1, a choice of the open looptransfer function,“ o12345Time(sec.)Fig, 11 Generator power angle for various loading conditions“4 i .21-3g0.83al”.z0.6p“,(),9sIda.PO I.295lG”d. 1%.1.()p,,,()95PO (18.“.unf;5lagsb. Po l. I P,, Fig. 12. Bus voltage variations for various loading conditions.4.4 Fault StudiesThe coordinated robust controller designed through thelinear system modeling was then applied to the nonlinearpower system model. The set of nonlinear equations (2), (3),and (4) were employed to solve the power output and busvoltage of the STATCON. Note that these nonlinearequations have to solved at each integration step iteratively.For a self-clearing three-phase fault for 0.1 second on theremote bus, the generator torque and bus voltage are shownin Figs. 13 and 14, respectively. Two loading conditions areconsidered - (a) nominal power output of 0.8pu at 0.99leading power factor, (b) steady state pre-fault output of1.lpu at 0.95 lagging power factor. The transient profile ofload angle and bus voltage, with fault on the overloadedmachine, show that the control design is extremely robust.(19)5. CONCLUSIONSA novel method of designing robust damping controlstrategies for STATCON controller in a power system isproposed, The controller designed was tested for a number ofdisturbance conditions including symmetrical three-phasefaults. The robust design has been found to be very effectivefor a range of operating conditions of the power system. Theoperating conditions for which the controller provides goodperformance depends on the spectrum of perturbed plants100(s 7)(s2 2s 1)(s2 1.694s 10.69)(20)c(s) —S2(S .01)(S2 5s 49)provides excellent damping control over a wide range ofoperating conditions. The load angle and bus voltagevariations for 5 widely varying loading conditions are shownin Figs. 11 and 12, respectively. As can be observed, therobust controller provides very good overall damping0-7803-7173-9/01/ 10.00 2001 IEEEII 65.505)104.35(s 7)(s2 2s 1)L(s) —(S .01)(s 58.6249)(s2 5s 49)with the resulting control function,Iv20The nominal plant transfer function for this formulation is 10.31885(s2IP() l,o p., 095 l“gc,8910-7803-7031-7/01/ 10.00 (C) 2001 IEEE
[5] H.F.Wang and F.Li, “Design of STATCOM Multivariable SampledRegulator”, Int. Conf. on Electric Utility Deregulation and Power Tech.2000, City University, London, April 2000.[6] H.F.Wang, “Phillips-Heffron Model of Power Systems Installed withSTATCOM and Applications”, IEE Proc. Gen. Trans. and Distr., Vol. 146,no 5, pp.521-527, September 1999.[7] J.C.Doyle, B.A. Francis, A.R.Tannenbaum, “Feedback Control Theory”,MacMillan Publishing Co, New York, 1992.[8] W.S.Levine, “The Control Handbook, CRC Press and IEEE Press, 1996.selected in the design process. The robust design is muchsuperior to the ccmventional PI and similar other controllers,where the controller coefficients normally need to be retunedfor various operating conditions. The graphical loop-shapingmethod is simple and straightforward to implement.100,1I8.APPENDIXa Po O8, 0993leadb Po ] 1,095 lagThe power system data are as follows:H 3 sec., D O, XI 0,3, X2 0,3, x ’ 0.3, xd l.O, x 0.6,K l ,T O.02, lS. O.a20I(JL ——— o12435Time(sec.)Fig. 13 Generator angle variations following fault for 2 different operatinga Po O8 p“, O993 leadb Po l. I pu, 0.95 lago12345Time(sec.)Fig. 14 Terminal voltage characteristics corresponding to Fig. 15.6. ACKNOWLEDGEMENTThe authors wish to acknowledge the facilities provided atthe King Fahd University of Petroleum and Minerals,Dhahran, Saudi Arabia.Abu H. M.A.Rahim (S’69, M72, SM83)did his B.SC. in Electrical Engineeringfrom the Bangladesh University ofEngineering and Technology (BUET),Dhaka in 1966 and Ph.D. from theUniversity ofAlberta, Edmonton,Canada in 1972. After a brief postdoctoral work at the University ofAlberta, he rejoined the Faculty inBUET, Dhaka. Dr. Rahim was a VisitingFellow at the University of Strathclyde,Glasgow (U.K.) in 1978. He worked atthe University of Bahrain between 198895. He worked at the University ofPetroleum and Minerals during the period 1978-88. He rejoined KFUPM in 1995, where presently he is aProfessor. Dr. Rahim’s main fields of interest are Power System Sta
A Robust STATCOM Controller for Power System Dynamic Performance Enhancement A, H. M.A.Rahim S,A,A1-Baiyat F.M.Kandlawala Department of Electrical Engineering K.F.University of Petroleum and Minerals Dhahrrm,Saudi Arabia. Abstract: A robust controller for providing damping to power system transients through STATCOM devices is presented. Method
Power Quality Enhancement in STATCOM connected Distribution 909. 3. Overview of D-STATCOM with proposed control algorithm In the paper, the GSA method is proposed for enhancing the performance of D-STATCOM. Figure 1 portrays a schematic diagram of a three-phase VSC based DSTATCOM linked to a
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106 Swapnil R. Borakhade and Archana G. Thosar Figure 1: Single-line diagram of a STATCOM. The voltage source-converter or inverter (VSC or VSI) is the building block of a STATCOM and other FACTS devices. A very simple inverter produces a square voltage waveform as it
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