多区域互联电力系统的自适应滑模负载频率控制.pdf

本文研究了一类计及电动汽车的电力系统中的负荷频率控制问题.首先,文章将电动汽车模型与传统的负载频率控制模型相结合,在未知扰动波动范围的条件下设计了自适应滑模控制律.其次,本文分别考虑了电网调频中的匹配扰动和不匹配扰动问题,并利用李亚普诺夫稳定性理论导出了匹配和不匹配条件下的系统稳定的充分条件.最后,通过两个区域电力系统的仿真结果表明,电动汽车作为电源和负载都可以提高电网的频率稳定性,所设计的控制器可以有效地调节电网的频率波动.关键词:电力系统;自适应滑模控制;电动汽车;负荷频率控制引用格式:王志鹏,陈向勇,刘华伟,等.多区域互联电力系统的自适应滑模负载频率控制.控制理论与应用,2023,40(7):1252 1260DOI:10.7641/CTA.2023.20341Adaptive sliding mode load frequency control formulti-area interconnected power systemsWANG Zhi-peng1,2,CHEN Xiang-yong1,2,LIU Hua-wei1,2,LIU Xue-qiang3,QIU Jian-long1,2(1.School of Automation and Electrical Engineering,Linyi University,Linyi Shandong 276005,China;2.Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong,Linyi Shandong 276005,China;3.Linyi Power Supply Company,State Grid Shandong Electric Power Company,Linyi Shandong 276005,China.)Abstract:This paper studies the load frequency control(LFC)of power system with electric vehicle(EV).Firstly,combining the EV model with the traditional load frequency control model,an adaptive sliding mode control law is de-signed under unknown disturbance fluctuation range.Secondly,the matched and unmatched disturbances in power networkfrequency modulation are considered,and the sufficient conditions for system stability under matched and unmatched con-ditions are derived using Lyapunov stability theory.Finally,the simulation results of two regional power systems show thatelectric vehicles can improve the frequency stability of the power grid as both power source and load,and the designedcontroller can effectively adjust the frequency fluctuation of the power grid.Key words:power system;adaptive sliding mode control;electric vehicles;load frequency controlCitation:WANG Zhipeng,CHEN Xiangyong,LIU Huawei,et al.Adaptive sliding mode load frequency control formulti-area interconnected power systems.Control Theory&Applications,2023,40(7):1252 12601IntroductionPower systems aim to be environmentally friendly,resulting in a rapid integration of new energy sourcesandsystems12.Inthefuture,fuelvehicleswilleven-tually be replaced by electric vehicles due to the grow-ing popularity and demand of electric vehicles(EVs)in the market.EVs convert chemical energy to electricenergy,and their response speed is fast 3.EVs par-ticipating in load frequency control(LFC)of tradition-al power systems can improve the stability of load fre-quency.With the maturity of the vehicle-to-grid(V2G)technology,it can be used as a distributed power supplyand load 4.In the V2G technology,EVs are regardedas power sources,providing measurement to the grid,and realizing a two-way flow of energy between theEVs and the grid.Owing to the uncertainty of new en-ergy and the limitations of new energy generation tech-nology,it is necessary to use energy storage equipmen-Received 3 May 2022;accepted 21 April 2023.Corresponding author.E-mail:.Recommened by Associate Editor:LI Shi-hua.Supported by the National Natural Science Foundation of China(62173175,61877033)and the Natural Science Foundation of Shandong Province(ZR2019BF045,ZR2019MF021,ZR2019QF004).No.7WANG Zhi-peng et al:Adaptive sliding mode load frequency control for multi-area interconnected power systems1253t to store the electricity generated by the new energy,and EVs have been used as energy storage equipmentto store the electricity,significantly lowering the con-struction and operating cost of the power grid.In thefuture,EVs in power grid frequency control will be in-evitable 5.With the promotion of low-carbon environmentalprotection and the green pollution-free concept,an in-creasing number of scholars and engineers have studiedtheloadfrequencyofacombinednewenergyandpowersystem.In this study,the LFC of power grid with EVsand the uncertain mismatch of the power grid was in-vestigated.In 6,the design of reliable LFC for uncer-tain multi-area delayed power systems was studied.As-suming that the parameter uncertainty is random,a setof lines were generated by constructing an appropriateLyapunov Krasovskii functional and combined it withWirtingers inequality to guarantee the stability andextended dissipation of multi-area power systems.Insome studies,various control methods and algorithmsfor frequency regulation of power system have beenproposed,such as fuzzy proportional integral deriva-tive(PID)control,particle swarm optimization(PSO),adaptive control algorithm,reinforcement learning al-gorithm and so on due to the uncertainty and random-ness of new energy sources.With the new energy wasconnected to the traditional power system,the operationof the power system will face great challenges.In 7,an adaptive fuzzy PID controller with filter based onPSO was proposed by using a new wind power gen-eration model.Differential evolution optimization wasused to optimize the controller parameters,it signifi-cantly increased the cost of the system.According tothe characteristics of new energy uncertainty,a non-linear dynamic recognition learning model was devel-oped.Recent studies have also shown that combiningonline reinforcement and model predictive control canimprove the learning ability of model and provide real-time control.However,the reward function must exact-lymatchthedesiredfunction,whichaddstothedifficul-ty of its implementation 8.In 9,a scheme based onload control was proposed to control systems that do nothavesufficientcontinuouscontrollableloadsbyline-by-line method.From 10,the traditional automatic gen-eration control system model was improved by a fuzzyproportional integral(PI)approach to adaptively adjustthe PI control parameters of the controller.A decentral-ized fuzzy logic approach was proposed for wind pow-er interconnected systems to reduce the frequency de-viation and power of the connected lines 11.In 12,an adaptive control law and parameter update algorithmwere established to interconnect LFC regions based onfuzzy logic.However,the design of fuzzy control lack-s systematicness and has no definite goal.From 13,LFCwasusedtostabilizethefrequencywithinthespec-ified range in the three-area power system.The problemof the LFC for power systems with communication de-lays was solved by a dynamic output feedback schemein 14.In the case of actuator failures and communi-cation delays,the LFC of multiarea power systems wasdiscussed based on an event-triggered mechanism and afault-tolerant strategy in 15.Sliding mode control(SMC)is a control approachinpowergridsthatchangestheswitchingcharacteristicsof the system structure.Compared with the abovemeth-ods,it has the characteristics of fast response and no pa-rameter interference.This property enables the systemto perform a small,high-frequency motion along thestate trajectory without interference externally and fromthe system parameters.SMC improves the robustnessof the system.SMC can be divided into the followingthree steps:1)the existence of sliding modes;2)a pointoutside the switching plane reaches the switching planein a finite time;3)to ensure the stability of sliding modemovement.In 16,an LFC method for single area pow-er system based on sliding mode control was presented.For an uncertain multi-area interconnected power sys-tem,appropriate switching surfaces were constructedfor each area,and controllers were designed based onSMC in 17.In 18,through sliding mode control,thefrequency deviation of power plants in the power gridwith integrated electric vehicles is adjusted.SMC caneffectively reduce the ripple of the input current in ahybrid system of photovoltaic and wind energy in 19.In 20,a tube-based model predictive control(MPC)was given to change the response of aggregated EVs.A control signal is generated to minimize the frequen-cy bias error while taking into account various opera-tions and physical constraints.In 21,an appropriatediscrete-time integral switching surface was designedto make multi-region interconnected system more ro-bust based on event triggered SMC.For fuzzy singu-lar perturbation system,a novel sliding mode methodwas presented in 22,which made the matched uncer-tain disturbances fully compensated.Furthermore,animproved adaptive fuzzy SMC law was constructed toadapt to the unknown upper bound of matching uncer-tainty.In 23,an adaptive fuzzy sliding mode track-ing controller was designed by combining integral SMCwith adaptive control technology in the unmanned shipsystem to ensure the sliding mode tracking under theinfluence of all uncertainties.In 24,a new slidingmode controller was designed to minimize frequencybias by controlling the speed regulator of the generatorset based on the observer.Inspired by the discussions,This paper will investi-gate the adaptive sliding mode LFC problem for multi-area interconnected power systems with EVs.The maincontributions are listed as:1)Combining electric vehicle and traditional power1254Control Theory&ApplicationsVol.40system model,it is more in line with the actual require-ments of energy utilization,and the designed control s-trategy is more flexible to frequency regulation.2)The stability criterion of power system undermatched disturbance and mismatched disturbance arederived respectively,which further improves the robust-ness of the system.3)The upper bound of the external disturbance con-sidered is unknown,and its influence is effectively es-timated and compensated by using the adaptive controlmethod.2Model description2.1Model of EVsA regional interconnection model is establishedbased on the traditional power system LFC model com-bined with EVs.Fig.1 shows an overview of the model.Specifically,an equivalence model of EVs is expressedby a transfer functionGev(s)=Kev1+sTev,(1)whereKevis the gain andTevis the time constant.?ev+11?evSOC?10%evFig.1 Equivalent model of EVThestateof charge(SOC)rangesfrom 10%to90%,and EVs can be safely charged and discharged.utisthe input power,andPevis the output power of EVs.WhenPev 0,EVs are in the discharge state,sup-plying power to the power system for the transmissionof electric energy.WhenPev 0,EVs demand elec-tric energy from the power system as loads are in thecharging state.WhenPev=0,EVs are in a static s-tate,indicating that they are not discharging or chargingat the moment.t06t16tm,10%SOC6SOCtm690%SOC,(2)wheret0,tmare the time when EVs connect to the pow-er grid and leaves the power grid,respectively.t1is thetime to participate in frequency regulation.SOCtmisthe state when EVs leave.Pev=1Tevut1TevPev.(3)It can be seen from the value ofPevthat posi-tive and negative represent different states of EVs as aload and power source.This is the biggest differencebetween EVs and other loads.2.2LFC model of power systemPower systems can be composed of a multi-areapower grid.To ensure the power systems safe and sta-ble operation,each area must be connected to each oth-er to coordinate and control the load frequency.Whenthe system is stable,linearization can be conducted inthe minimum range of stable points.The LFC modelis composed of thermal power units and EVs.Fig.2shows the established LFC model of the EV intercon-nected power system.?1?EV control loop?11?+11?+11?ev?+11?ev?ev?ps?+1?ps?21?L?2Generator control loop?+?+?2?1Fig.2 Multi-area power grid model with EVsAs shown in Fig.2,i=j=1,2,N,Nisthe number of areas;fiis the frequency deviation ofthe system;Ptiis the output power deviation of a syn-chronous generator in a thermal power unit;Xtiis thedeviation of the position of the regulating valve of thegovernor of the thermal power unit;Peviis the outputpower deviation of the EVs;Teviis the time constantof EVs;Keviis the charging/discharging coefficient ofEVs;PLiisthefrequencydeviationofthedisturbanceload;Biis the regional frequency offset coefficient;Riis the coefficient of adjustment;uiis the signal that thecontroller gives to EVs;Tiis the steam turbine timeNo.7WANG Zhi-peng et al:Adaptive sliding mode load frequency control for multi-area interconnected power systems1255constant;Ttiis the time constant of the governor;Ptieis the power offset of the power line;Tpsiis the timeconstantofthesystem;Kpsiisthegain;iandjaretheangle deviations of different areas,respectively;Eiisfrequency deviation of different areas;a1anda2are thedistribution coefficient;andTijis the power synchro-nization factor of the contact line between areas.Based on the model in 25 and the EVs established,the model of the following units is expressed asfi=KpsiTpsifi+KpsiTpsiPti+KpsiTpsiPeviKpsiTpsiPLi12KpsiTpsiGij(i j),(4)Pti=1TiPti+1Tixti,(5)xti=1TtiRifi1Ttixti+1Ttiuia1TtiEi,(6)Pevi=KeviTeviPevi+a2KeviTeviEi,(7)Ei=KiBifi+12Gij(i j),(8)i=2fi,(9)wherefi,Pti,xti,Pevi,Ei,iare the cha-nges of frequency,power output,governor valve posi-tion,integral control and rotor angle deviation,respec-tively;Tpsi,Ti,Tti,Teviare the time constants of pow-er system,turbine,governor,respectively;isNj=1,j=i;Kpsi,Kiare the power system gain,speed regulationcofficient;Tijis connected gain betweeniandj.Thenwe get the following matrix form:xi(t)=Aixi(t)+Biui(t)+Gijxj(t)+FiPLi,(10)wherexi=fiPtixtiPeviEiiT,xiRniis the dimensions of system matries andAiis the coefficient matrix,Biis the input matrix andFiis the perturbation matrix,andAi=KpsiTpsiKpsiTpsi0KpsiTpsi0A1601Ti1Ti0001TtiRi01Ttia1Tti00000KeviTevia2KeviTevi0KiBi0000A56200000,Gij=0 0 0 0Kpsi2TpsiTij0 0 0 000 0 0 000 0 0 000 0 0 0Ki2Tij0 0 0 00,Bi=0 0 1Tti0 0 0T,Fi=KpsiTpsi0 0 0 0 0T,whereA16=12KpsiTpsiTijandA56=Ki2Tij.Then the system model with parameter uncertainty is asfollows:xi(t)=(Ai+Ai)xi(t)+(Bi+Bi)ui(t)+Gijxj(t)+(Fi+Fi)PLi,(11)whereAi,Bi,Fiare uncertain parameters andnorm-bounded.We definehi(t)=Aixi(t)+Biui(t)+(Fi+Fi)PLi,we have xi(t)=Aixi(t)+Biui(t)+Gijxj(t)+hi(t),(12)and the equivalent form of system is expressed as x(t)=Ax(t)+Bu(t)+h(t),(13)wherex(t)=x1(t)xN(t)T,u(t)=u1(t)uN(t)T,h(t)=h1(t)hN(t)TandA=A1G12G1NG21A2G2N.GN1GN2AN,B=diagB1,B2,BN.3Main results3.1Matched conditionThissectionconsidersthematchingoperationofthepower grid under ideal conditions.We make the follow-ing assumptions to prove that the system is stable.Assumption 1AandBare fully controllable,and we defineh(t)=Bh(t).Assumption 2The unknown disturbanceh(t)isbounded,h(t)6q.First,the sliding surface is selected ass=Cx(t)wt0C(A BH)x()d,(14)whereCandHare constant matrices,and meet the fol-lowing requirements:1)CBis a nonsingular matrix;2)A BH 0.Whens=0and s=0are satisfied,Eq.(13)reaches sliding surface.1256Control Theory&ApplicationsVol.40By combining Eqs.(13)(14),we can get s=C x(t)C(A BH)x(t)=CAx(t)+Bu(t)+h(t)C(A BH)x(t)=CBu(t)+Ch(t)+CBHx(t).(15)When Assumption 1 is satisfied,the equivalent con-troller is derived asueq1(t)=(CB)1CBh(t)+CBHx(t)=h(t)Hx(t).(16)Substituting Eq.(16)into Eq.(13),we obtained x(t)=B(CB)1(CBh(t)+CBHx(t)+Ax(t)+h(t),(17)then one has x(t)=(A BH)x(t).(18)According toA BH 0.Proof Define