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Control System for a PWM-Based STATCOM Pablo García-González and Aurelio García-Cerrada,Member,IEEEAbstract—The always-increasing switching frequency of modern solid-state power switches,together with the application of multi-converter topologies,make it possible to use Pulse Width Modulation(PWM)in high power applications of STATCOMs (STATic Synchronous COMpensators).This paper investigates the control system for a PWM-based STATCOM.First of all,a discrete-time model of the STATCOM is derived to take into account the discrete-time implementation of the controller.Secondly,the control algorithm is detailed.It en-sures decoupled control of the real and reactive power exchanged between the power converter and the electric-energy system.This is necessary to control the d.c.capacitor voltage during transients of the exchanged reactive power.Finally,the control of the capacitor voltage is explained in detail.The controller is tailored to keep the capacitor voltage almost constant in spite of the fast control of the reactive power.This helps to reduce the capacitor size significantly.The main contributions will be illustrated using a15kV A laboratory prototype.Index Terms—Pulse width modulated power converters,reactive power control,static var vompensators.I.I NTRODUCTIONR EACTIVE power compensation is an important issue in the control of electric energy systems.Reactive power in-creases the transmission system losses,reduces the power trans-mission capability of transmission lines and can cause large amplitude variations in the receiving-end voltage.Moreover, rapid changes of the reactive power consumption of loads can cause voltage-amplitude oscillations(for instance,arc furnaces cause flicker).In addition,voltage variations can change the real power demand in the electric system,resulting in power oscil-lations[1].Reactive power compensation has been traditionally handled with devices such as:Thyristor-Controlled Reactors(TCR)and Thyristor-Switched Capacitors[2].However,if high dynamic performance is required,reactive power compensation must be handled with faster devices such as the STATCOM.Moreover, the reactive power compensation of TCRs and TSCs depend on the Point-of-Common-Coupling(PCC)voltage while the com-pensation of the STATCOM is independent of that voltage[3]. Previous research efforts focus mainly on the control and per-formance of STATCOMs based on square wave multipulse-con-verters[4]–[6]and[3].However,the increasing switching fre-quency of modern solid-state power switches,together with the application of multi-converter topologies make reliable to use PWM in high-power applications[7]–[9].Manuscript received March31,1999;revised February23,2000.The authors are with E.T.S.de Ingeniería(ICAI),Universidad Pontificia Comillas de Madrid,c/Alberto Aguilera23,28015Madrid,Spain(e-mail: pablo@dea.ixai.upco.es;aurelio@iit.upco.es).Publisher Item Identifier S0885-8977(00)10318-8.Fig.1.Configuration of a STATCOM(left)and simplified model(right).p andq are the instantaneous real and reactive power exchanged by the STATCOM inPCC.p is the power consumed in the filter+transformer inductance.p are the real and instantaneousreactive power exchanged by the converter with the a.c.system.This paper investigates in detail the control system for aPWM-based STATCOM.The controller fundamentals werealready presented in[4]giving neither implementation detailsnor results.A few years later,reference[5]shows goodtransient performance of the reactive-power controller of aSTATCOM but it also shows undesirable variations of thed.c.-link voltage.Here,implementation details and validationin a prototype are the main objectives.It was soon clear thatthe d.c-link voltage control deserved more attention than thatpaid in the literature.First of all,the STATCOM configurationand an equivalent linear model are presented.Secondly,thecontrol system is explained in detail taking into account its dis-crete-time implementation.The controller is tailored to achievefast control of the instantaneous reactive power exchanged bythe STATCOM and to maintain the converter d.c.-link voltageconstant.It is shown that decoupled real and reactive powercontrol is necessary.Finally,a prototype is described and themain contributions are illustrated with experimental results.Good transient performance of the reactive-power controller isshown together with almost-constant d.c.-link voltage duringtransients.II.S YSTEM C ONFIGURATION AND M ODELINGFig.1depicts a STATCOM applied to an electric energysystem.Its components are the shunt converter()and the connection filter.The shunt converter can be modeled as a controllable voltage source().All other variables are explained in the figure caption for clarity andwill be referred later.Therefore,the STATCOM behaves asa current controller.Note that the energy exchanged by theSTATCOM is limited by the capacitor stored energy.Hence,only reactive power can be exchanged in steady state.0885–8977/00$10.00©2000IEEEThe instantaneous three-phase variables of the STATCOM can be described in state-space frombyandis the angular speed of the reference frameandand(2)The Park’s transformation selected here keeps invariant the instantaneous power expression.In addition,since-axis layson the space vector of the connection point voltage(is the angular speed of the spacevectoris equal to the system frequency in rad/s.As shownlater,)and the instanta-neous reactive power((4)Therefore,are proportional to and ,respectively and the control of the power injected into the electric energy system reduces to the control of and .The control inputsin(1)can be set arbitrarilysince can always bemeasuredwhere(5)and–and.Since the controller must be implemented in a micropro-cessor,it is useful to derive a discrete-time version of the model in (1).It is going to be assumedthat(7)(8)andis not strictly constant in practice,the discrete-timemodel is only an approximation.However,variation only of themodulusofand the model will be correct.Variationsofdue to system har-monics must be filtered in the measurement system.These is-sues have not been a problem in the prototype tested here or in the previous simulation work [13].Equation (6)gives the value of the state variables()at timeinstant.However,the controller will need most of the sampling interval to calculate the required system input from reference values and measurements.Therefore,it is reasonable,to assume that the system input attime.Thediscrete-time model for (1)must be writtenas:(9)As shown in Appendix A,the one-sampling-interval delay reflected in (9),can be easily taken into account when designing the controller.The discrete-time model (9)takes into account the effects of the digital performance of the control algorithms.As shown in (7)–(9)there are cross-coupling termsbetween axis variables in the state()matrices.Coupling in the input matrix cannot be seen in the continuous-time model and it is inherent to the discretization process.However,this problem may be easily overcome by arranging the system asfollows:(10)whereaffects only through a simplefirst-order transfer functionwhile affects only.Hence,de-coupled control of and is now very simpleusingand as control inputs obtained with independent control laws.The converter outputvoltagesand must be calculated from therequired valuesofand using (11)becauseand integral controllaws have been applied to ensure zero tracking error in steady state and to increase the robustness of the closed-loop system.The design of the control laws can be reduced to the design of two state feedback proportional control laws using the aug-mented systems derived in Appendix A [see (18)].Note that perfect decoupling is only possibleifand are known [see (11)].These variables are not availableatinstant.Each prediction is done with the previous measurements and the control inputs.Summarizing,•The reference valueforis given by the d.c.-link voltagecontroller.Fig.3.Block diagram of the feedforward–feedback control system for the converter d.c.-link voltage.•The STATCOM controllers give the requiredvaluesofand [see (19)of Appendix A].•The required converter output voltages are calculated from (11),using the current prediction in (12)and (13).B.Control of the Capacitor VoltageIf capacitor-voltage variations are bounded the converter output voltage can behave as an independent voltage source.Capacitor-voltage variations can be naturally kept small in-creasing the capacitor value but this makes the device more expensive.Adequate transient performance of the voltage controller should make it possible to minimize the capacitor value but this problem has not been taken into account in the literature.Fig.3depicts the capacitor-voltage controller.The simplest version is the one drawn with a solid line and it is the one proposed in the literature[4].models the real-power consumption of the filter (see Ap-pendix B).The filter power consumption consist of a)the losses in the filter resistance(in Fig.1)varies.Therefore,system losses.However,when there is a change inthe instantaneous reactive power reference(insteady state due to the feedback controller.The performance of the closed-loop controller can be im-proved if theperturbationestimationsof().Transferfunctionscan be easily obtained with the model of the STATCOM andthe control law developed in Section III.The nonlinear func-tion(-andandandandin Fig.1)has been built with threesingle-phase transformers DY connected (380/220V ,2.9kV A each transformer).The primary is connected to the converter and the secondary to the electric system.5)The filter has been built with three inductances connected between the secondary of the transformer and the point of coupling to the electric energy system.The inductance is 39mH with1.25follows its reference closely with no error insteady statewhilewithinthe(1)]disturbanceestimation and without [VVA 15kV A prototype has been used to validate the system model and the controller design.The converter PWM has been implemented with a reasonably-low switching frequency to have realistic results.The experimental results show thatthe overall-system model(convertercontroller)describes the prototype performance accurately.The converter d.c.-link capacitor can be kept small if fast capacitor-voltage control is achieved.The proposed controller uses a model for the connection filter power consumption to en-sure fast d.c.-link voltage control.A closed-loop controller is also proposed to guaranty long-term voltage tracking in spite of modeling errors and neglected converter losses.The paper has dealt with transient performance only.Har-monic injection is now been investigated in the prototype.A PPENDIX AD ERIV ATION OF THE A UGMENTED S YSTEM WITH PROPORTIONALintegral control law is going to be appliedto ensure zero tracking error in steady state and to increase the robustness of the control law.A discrete-time integral control law can be written as[12]:is the reference valueandbyintegralcontrol law of system (9)reduces to the design of the state-feedback control laws for (18)and the reactive power system.The control law for the real power(.Notethatandand,(24)Using the Backward Rectangular Rule approximation of the numerical integration [12],the discrete-time modelresults,and[6]L.Gyugyi,N.G.Hingorani,P.R.Nannery,and N.Tai,“Advanced staticvar compensator using gate turn-off thyristors for utility applications,”, Cigre paper23-302,1992.[7]J.Kuang and B.T.Ooi,“Series connected voltage-source converter mod-ules for force-commutated svc and dc-transmission,”Trans.on Power Delivery,vol.9,no.2,pp.977–983,1994.[8] B.Mwinyiwiwa,B.-T.Ooi,and Z.Wolanski,“UPFC using multicon-verter operated by phase-shifted triangle carrier spwm strategy,”IEEE Trans.on Industry Applications,vol.34,no.3,pp.495–500,May/June 1998.[9] B.Mwinyiwiwa,Z.Wolanski,and B.-T.Ooi,“Current equalization inSPWM FACTS controllers at lowest switching rates,”in IEEE Power Electronics Specialists Conference(PESC),vol.1,1997,pp.325–330.[10]P.C.Krause,Analysis of Electric Machinery.New York,NY:Mc-Graw-Hill Inc.,1986.[11]H.Akagi,Y.Kanazawa,and A.Nabae,“Instantaneous reactive powercompensators comprising switching devices without energy storage components,”IEEE Trans.on Industry Applications,vol.IA-20,no.3, pp.625–630,May/June1984.[12]G.F.Franklin and J.D.Powell,Digital Control of Dinamic Sys-tems.Reading,MA:Addison-Wesley,1980.[13] A.García-Cerrada,P.García-González,R.Collantes,T.Gómez,andJ.Anzola,“Comparison of thyristor-controlled reactors and voltage-source inverters for compensation of flicker caused by arc furnaces,”IEEE Trans.on Power Delivery,2000,to be published.[14]J.Holtz,“Pulsewidth modulation for electronic power convertion,”Pro-ceedings of the IEEE,vol.82,no.8,pp.1194–1214,Aug.1994.Pablo García-González(M.Sc.1992,Unversidad Pontificia Comillas)From Oct.1993to March1995 he was with Valenciana de Cementos where he was a Project Engineer involved in control applications. He is currently working toward his Ph.D.at the Department of Electronics and Control Engineering of Universidad Pontificia Comillas(UPCO).His research interests include power electronics applica-tions in electric energysystems.Aurelio García-Cerrada(M.Sc,1986,Univer-sidad Politécnica de Madrid,Spain),(Ph.D.1991 University of Birmingham,UK).He is currently a Member of the Staff of the Electronics and Control Engineering Department and the Inst.de Investi-gación Tecnológica(IIT)at Universidad Pontificia Comillas in Madrid.His research interests include power systems,monitoring and control and power electronics and its applications.。