Sliding mode control of an active power filter with photovoltaic maximum power tracking

Nomenclature directandquadratureaxesexpressedinthestationaryreferenceframe directandquadratureaxesexpressedinthesynchronousrotatingreferenceframe Lg gridfilterinductance Rg gridfilterresistance Slidingmodecontrolofanactivepowerfilterwithphotovoltaicmaximumpowertracking JoséAntonioCortajarenaa,⁎ [email protected] OscarBarambonesb PatxiAlkortaa JonCortajarenac aEngineeringSchoolofGipuzkoa(Eibar),UniversityoftheBasqueCountry,Otaola29,20600Eibar,Spain bEngineeringSchoolofVitoria,UniversityoftheBasqueCountry,NievesCano12,01006Vitoria,Spain cEngineeringSchoolofGipuzkoa,UniversityoftheBasqueCountry,EuropaPlaza,1,20018Donostia,Spain ⁎Correspondingauthor. Abstract Nowadays,theincreaseinsolarenergyinstallationsasasourceofenergyisgrowingconsiderably.Theconnectiontothegridoftheseinstallationsgenerallyinjectsallthepowerobtainedfromthepanelasactivepower, makingzerothereactivepower.Thesamepowerinjectionsystemcanbeusedtoachieveaunitpowerfactoriftheactivefilterfeatureisintegratedinit.Inthispaper,anactivepowerfilter(APF)thatcancontrolboth,the MPP (maximum power point) of a photovoltaic system (PV) and the power factor of a nonlinear load connected to the grid using a three phase DC/AC power inverter with new sliding mode controllers is presented. Perturbation–observation(P&O)istheusedMPPTalgorithmandthreeSlidingModeControllers(SMC)areusedtoregulatetheDCvoltageofthePVandthecurrentdandqcomponentsoftheactivefilterusingthePQ theory.WithaSMC,noexactknowledgeofthemodelparametersisrequiredanditoffersgoodbehavioragainstunmodeleddynamics,insensitivitytoparametervariationsandgoodrejectionofexternaldisturbances.The spacevectorpulsewidemodulation(SVPWM)of7and5segmentsisimplementedinordertochecktheefficiencyandgridcurrentripple.Severalexperimentaltestshavebeencarriedindifferentconditions,concludingthat thepresentedsystemprovidesanefficientmaximumpowertrackingandagoodpowerfiltercharacteristic. Keywords:Activepowerfilter;Slidingmodecontroller;MPPTcontrol;PQtheory;Efficiency α , β d , q This is the accepted manuscript of the article that appeared in final form in International Journal of Electrical Power and Energy Systems 110 : 747-758 (2019), which has been published in final form at https://doi.org/10.1016/ j.ijepes.2019.03.070. © 2019 Elsevier under CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/) gridvoltagevectorangle gridvoltagefrequency ig gridcurrent iPV solarpanelcurrent iF inverteroutputcurrent iF_MPPT inverteroutputcurrentduetotheMPPT iF_APF inverteroutputcurrentduetotheAPF iinv_DC DC/ACinverteraverageinputcurrent vg gridvoltage vC invertercapacitorvoltage vPV solarpanelvoltage vinv DC/ACinvertervoltagemainharmonic P activepower Q reactivepower θe ωe fPWM invertercommutationfrequency VOC PVopencircuitvoltage ISC PVshortcircuitcurrent VMP PVmaximumpowerpointvoltage IMP PVmaximumpowerpointcurrent PMP PVmaximumpowerpointpower d(t) SMCuncertaintyterms S(t) SMCslidingvariable β SMCswitchinggain λ voltagecontrollerSMCconstantgain KSMC currentcontrollerSMCconstantgain V Lyapunovfunction 1Introduction Themostabundantpermanentenergyresourceonearthissolarenergyanditsavailabilityintheformofradiationishighinmanypartsoftheworld. TheGermanAdvisoryCouncilonGlobalChange(WBGU)conductedananalysisofenergyneedsandresourcesinthefutureuntilthe2050sand2100s.Thisstudyhighlightstheimportantcontributionofsolarenergytothe long-termglobalenergyneeds.Thisscenarioisbasedontherecognitionthatitisessentialtomoveenergysystemstowardssustainabilitythroughouttheworld.Theadvancementoftechnologyandresearchinthedevelopmentof systemsbasedonphotovoltaicpanels,moreeconomicalandwithbettercharacteristics,predictsanincreaseininstallationsworldwideinthecomingyears[1]. Theenergygeneratedbyphotovoltaicpanelsismainlydependentonthelevelofsolarradiationthataffectsthephotovoltaicpanelsandtheirtemperature.Therefore,whenvariationsoftheseparametersoccur,thesystemmust locatethemaximumpowerworkingpoint.Inordertodothis,oneofthesearchtechniquesforthemaximumpowerpointofthephotovoltaicpanelmustbeused[2,3]. Mostgrid-connectedphotovoltaicsystemschemesuseatwo-stageenergyconversiontopology[4–6].ThefirststageisaBoostconvertertoraisethepanelvoltageabovethegridpeakvoltage.Thisconverterimplementsthe MPPTalgorithm.Theobjectiveofthesecondconverter,DC/AC,istoinjecttheenergysuppliedbythepreviousconverterintotheelectricalgrid. AnexperimentalstudyispresentedinAQuantitativeComparisonofCentralInvertersandStringInvertersinUtility-ScaleSolarSystemsinNorthAmerica[7]. By using a higher DC voltage level, the DC/DC stage can be eliminated. Some of the benefits of increase the DC/AC input voltage are the components reduction, including overcurrent protection devices, combiners, disconnects,etc.;lowerlaborcosts;lesscopperintheDCcollectionsystem;lessexpensiveinverters(lesscopper,lowercurrentvaluesforcomponents);andlowertotalcostperwatt.Theconclusionsarethatthecentralinverteris1% moreefficientthanthestringinverterssolution. Thus,inaccordancewiththetendencytoincreasetheinverter'sinputvoltage[8],theseries-parallelorcentralizedtopologywillbeusedinthepresentedapplication,asshowninFig.1. Thelocalloadsofthephotovoltaicsystemcanbeespeciallynonlinear,suchastherectifier-filterstagesofthepowersuppliesofmosthouseholdappliances[9].Theseloadsworsenthepowerfactorbyincreasinglossesin transformersandcablesfundamentallyandleadstopowerqualityproblemsthatmayaffectotherloadsconnectedatthesamepointofcommoncoupling[10].Shuntactivepowerfiltershavebeenstudiedanddevelopedasaneffective solutiontothisproblem[11–13]. ThecontroloftheMPPTinphotovoltaicsystemsandtheactivepowerfiltercharacteristiccanbecombinedinonesystem.In[14]theinverterDCvoltageisfixedforthePVpanelbutnoMPPTisimplementedandthecurrentis controlledwithhysteresiscontrollers,changingtheswitchingfrequencyandthereforetherippleofthecurrentandincreasingthecomplexityofinputfilters.In[15]thePVMPPTisobtainedandthePIaretheusedcurrentcontrollers. Thesecontrollershavetobeadjustedwithahighbandwidthinordertotrackcorrectlythechangingreferenceandthiscanmakethesystemunstable.In[16]theMPPTisimplementedbutthecurrentisregulatedwithahysteresis controllerwiththedisadvantageofprovidinganonconstantswitchingfrequencyandthereforeachangingcurrentripple.In[17]aDC/DCfirststageisincludedbeforetheDC/ACconverterreducingtheoverallefficiencyandPI controllerswithfastdynamicareusedtoregulatethecurrent.In[18]whereonlypresentssimulationresults,theMPPTisimplementedandtheusedcontrollerisahysteresiscontroller.Thehysteresisbandismodulateasafunctionof Vdc,theslopeofreferencecurrentandthefilterinductancevalue.Errorsintheparametersproducevariationinthehysteresisbandandthereforeintheswitchingfrequency.In[19]thegridcurrentsareregulatedusinghysteresis currentcontrollerstogeneratetheinvertergatingpulseschangingtheswitchingfrequencyandthereforetherippleofthecurrent. Inthispaper,thedesign,implementationandperformanceanalysisofathreephasesactivepowerfilterwithPVMPPTcharacteristicsispresented.Theproposednewcontrolschemecanregulatenotonlythemaximumpower ofaPVbutalsothepowerfactorofanonlinearloadcouldberegulated,usuallytoaunitypowerfactor.Itshouldbenotedthatachievingaunitypowerfactorthelossesintheelectriclinesarereduced. ThemainhardwarefeaturecomparedtoothersystemsistheeliminationofthevoltageboostingstageandthustheBoostconverterstageisnotnecessary,anddirectlytheinverterinputvoltageisregulatedwithaslidingmode controllertogetfromthePVthemaximumpower.TheimplementedMPPTalgorithmistheperturbationandobserve(P&O)andtoavoidthemeasurementofthePVpanelcurrenttheinverteroutputpowerismeasuredandusedinthe MPPTalgorithm. Fig.1Activepowerfiltertopology,measuredsignalsandSMCcontrollers. Some methods of adjustment of conventional controllers such as PI (proportional-integral) or PR (proportional-resonant) require accurate information of the plant model to ensure stability [20]. In this context, the most appropriateoptionistoconsidersometypeofrobustcontrolschemesuchastheslidemodecontrolinitiallydevelopedbyUtkin[21]andsuccessfullyappliedtovarioustypesofcontrolstructures[22–24].In[25]anovelterminal slidingmodecontrolmethodformaximumpowertrackingofphotovoltaicpowersystemsispresentedbutonlyforaBoostconverterwitharesistiveload.In[26]aslidingmodecontroldirectpowercontrollerbasedactiveandreactive powercontrollerforthree-phasegrid-tiedphotovoltaicsystemwithaBooststageisproposed.In[27]asystemconnectedtoaPVpanelconsistingoftwocascadeddc–dcboostconvertersundersliding-modecontrolarestudiedinaDC grid.In[28]anoveluncertaintyanddisturbanceestimatorbasedslidingmodecontrolapproachisappliedtoDC–DCpowerconvertersandin[29]anadaptiveslidingmodecontrolalgorithmisdevelopedforgridsynchronizationofa photovoltaicsystem. Aftertheexternalloopresponsibleforregulatingthepanelvoltage,twonewinternalSMCregulatorsareresponsibleforregulatingtheactivepowerfiltercurrentbycontrollingthecurrentdandqcomponents.Theproposed currentdandqreferencesoftheactivefilterpartaregeneratedusingthePQtheory. The stability demonstration of the proposed controllers will be carried out using the Lyapunov stability theory showing that the presented SMC controllers can overcome the system uncertainties, like grid inductance, measurementsmallerrorsandnoise,andgridvoltagetolerances.So,theperformanceandrobustnessoftheproposednewSMCsisvalidateinsimulationandinarealplatforminsuitableandadverseconditions.TheSMCisalso comparedexperimentallywithaconventionalPIcontrollerinordertoshowtheperformanceoftheproposedcontrolscheme. Finally,twospacevectorpulsewidemodulation(SVPWM)techniquesaretested,the7and5segmentsSVPWM,inordertochecktheefficiencyofthesystemandthecurrentripple. Alltheexperimentsaredevelopedonarealplatform. 2Systemmodel ThegridtoinverterequationthatdefinedthesystemofFig.1inthestationaryreferencesystemis, Thesystemwillbecontrolledinthed-qsynchronousrotatingreferenceframesotheequationsobtainedfrom(1)areasfollows: Theactiveandreactivepowersaredeterminedinthestationaryreferencesystemas, 2.1InverterDCvoltagecontrol The MPPT algorithm adjusts the inverter DC voltage according to the perturbation and observe method. However, the MPP voltage level must be higher than the minimum inverter DC voltage required to maintain the regulation, that is, the inverter input voltage should be higher than the grid peak voltage plus the voltage drop in the inductances. If the PV panel is unable to reach this voltage level due to reduced irradiance or increased temperature,theactivepowerfilterwillgettheenergyfromthegridtokeepthevoltageleveltothefixedminimum,workinginthiswayasaconventionalactivepowerfilter.Thiswillbedemonstratedinthesectiononexperimental results. MakingapowerbalanceafterconsideringtheDC/ACinverterandthefilterinductanceasidealandtherotatingreferenceframelinkedtothegridvoltage( vgq = 0),theinvertercapacitorcurrentisexpressedas, FromEq.(5)itisobtained: (1) (2) (3) (4) (5) where vgd isthegridvoltagepeakvalueandistheoreticallyconstant.Eq.(6)canberewrittenafterconsideringsystemuncertaintiesas: wheretheterm d(t) representsthesystemuncertainties,likecapacitortolerances,measurementsmallerrors,andgridvoltagetolerances. Letusdefinethevoltagetrackingerrorasfollows: Takingthederivativeofthepreviousequationwithrespecttotimeyields: Whereitisconsideredthatthereferencevoltageisaquasi-constantsignalbecausewiththeMPPTalgorithmthechangeisslowforthecontrolperiod. TocompensatethesystemuncertaintiesanSMCschemeisproposedwiththeslidingvariable S(t) definedas: Then,theslidingsurfaceisdefinedas: Theslidingsurface(11)isselectedwithanintegralterminordertoavoidthetimederivativeoftheerrorsignalbecausethisderivativewillincreasethenoisesignalratio inarealimplementation. Finally,theslidingmodevoltagecontrollerisdesignedas: Theproposedcontrolsignal(12)presentsthreetermsandinordertoobtainagoodtrackingofthevoltagetrajectory,thegain λ mustbechosestrictlypositiveandtheswitchinggain β mustbechose β≥|d(t)| foralltime.The stabilitydemonstrationoftheproposedcontrolleriscarriedoutusingtheLyapunovstabilitytheoryandcanbefoundin[30]. 2.2Inverteractivepowerfiltercontrol Theinstantaneousreactivepower(IRP)p–qtheoryistheusedalgorithmtogeneratethecurrentreferencesignalsinthecontroloftheinverterasactivepowerfilter.Thisalgorithm,undertheconditionthattheloadissupplied withasinusoidalsymmetricalvoltage,showsthatthereferencesignalsgenerationwiththeIRPp–qtheoryalgorithmprovidescorrectresultsandtheinstantaneousvaluesofactiveandreactivepowerare[31], istheaveragepartoftheactivepowerabsorbedbytheloadandmustbesuppliedbythegridand/orbythePVpanels. istheaveragepartofthereactivepowerabsorbedbytheloadandmustbesuppliedbytheactive powerfilterinordertogetaunitypowerfactorinthegrid. and arethealternatingcomponentoftheactiveandreactivepowersrespectivelytobesuppliedbytheactivepowerfilter. Using(4)andtakinginconsiderationthecurrentsenseoftheinverter,theinvertercurrentcomponentsreferencesrelatedwiththeloadinstantaneousactiveandreactivepowersareobtainedas, (6) (7) (8) (9) (10) (11) (12) (13)         (14) WiththeParktransformationthereferencesintherotatingsynchronousreferencesystemaredetermined, 2.3CurrentSMCs Thecomponentsofthereferencecurrentaretherefore, Oncethecurrentreferencesareobtained,thecontrollerstoregulatethecurrentdandqcomponentswillbedesigned.SlidingModeControllersareusedtotrackthereferencecurrentcorrectlyandproviderobustnesswhen therealparametersdifferslightlyfromthemodelandtherearesystemuncertainties. ConsideringEqs.(2)and(3),thederivativesofthecomponentsofthecurrentare, wheretheterms and representthesystemuncertaintieslikefiltertolerances,measurementsmallerrors,andgridvoltagetolerances. Thecurrentcomponentstrackingerrorsaredefinedas, Takingthederivativeofthepreviousequationwithrespecttotime, TocompensatethesystemuncertaintiestheproposedSMCschemewiththeslidingvariable and are, Finally,theslidingmodecurrentcomponentscontrollersaredesignedas: Now,thestabilitydemonstrationoftheproposedcontrollerwillbecarriedoutusingtheLyapunovstabilitytheory.LetusdefinethefollowingLyapunovfunction: (15) (16) (17) (18) (19)  dd ( t ) dq ( t ) (20) (21) (22)  Sd ( t ) Sq ( t ) (23) (24) (25) (26) (27) TakingthetimederivativeoftheLyapunovfunction,andusingEqs.(21),(23)and(25)itisobtained: where isdefinedas, Therefore, UsingtheLyapunov'sdirectmethod,since isclearlypositive-definite, isnegativedefiniteand tendstoinfinityas tendstoinfinity,thentheequilibriumattheorigin isgloballyasymptoticallystable. Therefore, tendstozeroasthetimetendstoinfinityandalso tenstozero.Moreover,alltrajectoriesstartingofftheslidingsurface mustreachitinfinitetimeandthenwillremainonthissurface.So, Solvingthepreviousequation,itcanbeconcludedthatthetrackingerror convergestozeroexponentially. Fortheqcurrentcomponent,thesameanalysiscanbedoneusingthenextLyapunovfunction, 3Activepowerfiltercontrolstructure Fig.2showsinadeeperwaythestructureofthegrid-tiedthree-phaseinverterofFig.1workingasactivepowerfilterwiththePVmaximumpowerpointtrackingcharacteristic.Themainparametersvaluesofthesystemare showninTable1. Table1Parametersofthesystem. Parameter Value Gridvoltage, 380 V Gridfrequency, 2π50rad/s  Dd ( t ) (29) (30)  Vd ( t )   Vd ( t ) Sd ( t ) Sd ( t )=0  Sd ( t )   Sd ( t )=0 (31)  ed ( t ) (32) Fig.2Controlstructureofthethree-phasegrid-tiedinverterofFig.1.  vg  ωg = ωe Gridfilterresistance, 0.2 Ω Gridfilterinductance, 2mH Invertercapacitance, 1500μF(±20%) Invertermodulationfrequency, 20 kHz PVopencircuitvoltage, VOC (25°C,1000W/m2)670 V PVsortcircuitcurrent, ISC (25°C,1000W/m2)4.9A PVmaximumpowerpointvoltage, VMP (25°C,1000W/m2)595 V PVmaximumpowerpointcurrent, IMP (25°C,1000W/m2)4.4A PVmaximumpower, PMP (25°C,1000W/m2)2618 W Loadinductance, 1mH Loadresistance, 98 Ω Loadcapacitance, 2000μF(±20%) Asynchronousreferenceframephase-lockedloop(SRF-PLL)isusedforextractionofgridvoltagephase,frequency,andamplitudeasshowninFig.1.ThePLLPIcontrollergainsareadjustedasindicatedin[32]withanatural frequencyof628 rad/sandadampingfactorof1[33]. Theimplementedmaximumpowerpointtrackingalgorithmistheperturbation-observation(P&O).ThepowerfortheP&OiscalculatedusingEq.(4)withthemeasuredgridvoltageandtheinvertercurrent,avoidingtheuseof aDCcurrentsensorintheoutputofthePVarray.Thegridsuppliestheloadaveragepowerandtheinstantaneousharmonicpowershouldbesuppliedbytheactivepowerfilter.Therefore,theaveragepowershouldbefilteredusinga lowpassfilter.Takingintoaccountthatthegridfrequencyis50 Hz(andthepowerharmonicswillbeevenhigher),agoodcutoffrequencyforthelowpassfiltercouldbe1/5ofthegridfrequency.Alsotheexperimentalresultsshown thattheusedcutofffrequencyisadequate.Thevoltageperturbationisastepof2 Vandisrealizedevery300 ms.TheparametersoftheSMCinverterDCvoltagecontrollerareadjustedtakingintoaccountSection2.1anditsoutput, ,isthenecessarycurrentcomponenttomakethePVworkatthemaximumpowerpoint.However,theMPPTalgorithmsetstheminimumvoltagelevel,thusoperatingoutsidetheMPPpoint,ensuringavoltagelevelonthe DCbuswithoutlosingregulationandthuskeepingtheactivefiltercharacteristicworkingproperly. TheactivepowerfilterreferenceisobtainedasexplainedinSection2.2andwiththecalculated and currentreferences,theinvertertotalreferenceisdeterminedasshowninthefigureandindicatedinEqs.(16) and(17). ThetotaldandqcurrentcomponentsareregulatedusingtwoSMC,generatingtheinverterdandqvoltagereferences.BothSMCshavebeenadjustedwiththecriteriaexplainedinSection2.3. TheemployedPVisanemulatedarraywiththecharacteristicsshowninTable1.ThevoltagepowercharacteristiccurvesofthearrayfortwotemperaturesandthreelevelsofirradianceareshowninFig.3.Theshadedarea showsthepossibleoperatingzonefortheinverter.Thatis,thezonewheretheinverterinputvoltageishigherthanthegridpeakvoltageplusthevoltagedropintheinductance.  Rg  Lg  C  fPWM  LL  RL  CL      Thereisaslightdegradationofthegridcurrent,THDis9%,buttheregulationisgoodenoughdespitethenoiselevel,whichshowstherobustbehavioroftheslidemodecontroller.TheinjectedpowertothegridwhentheDC voltageis600 Vis2200 W. ThecontrolstructurewiththePIcontrollersisshowninFig.16wheretheSMCcontrollershavebeenreplacedforPIcontrollers.ThePIvoltagecontrollerhasbeentunedexperimentallyobtainingKp = 0.2andKi = 10. The currentPIcontrollershavebeenadjustedusingZiegler-Nicholstechnique,thustheKp = 0.5andtheKi = 140.However,duetothenoisethePIgainshavetobereducedinordertoensurethestability.Theresultobtainedcanbeseen inFig.17,whereincreasesthesettlingtimeandthecurrentdistortiongetsworse,THDisnow11%.IncreasingthebandwidthonthePIregulatorsbringsthesystemclosertoinstability. Fig.15APFDCvoltageandcurrentwithnoisyintheDCvoltageof±20 Vto150 Hz.VoltageSMCcontroller. Fig.16ControlstructurewiththePIcontrollersinsteadoftheSMCcontrollers. Table2showsthesummaryoftheperformancecharacteristicsofcurrentandvoltagecontrollersbetweenSMCandPIcontrollersquantitatively.BasedonthedatatabulatedinTable2,SMChasthefastestsettlingtimeandthe lowestovershootinboothcontrollers.Accordingtothesteadystateerror,bothofthecontrollershadshownveryexcellenceperformancebygivingzeroerror.Intermoftherisetime,theSMCandthePIcontrollershaveasimilar behaviour. Table2CurrentandvoltageSMCandPIcomparison. Parameter SMC(current) PI(current) SMC(voltage) PI(voltage) Risetime 1.1 ms 1.2 ms 46 ms 48 ms Steadystateerror 0 0 0 0 Settlingtime 2.1 ms 2.4 ms 152 ms 162 ms Maximumovershoot 3% 6% 1% 3% InordertoanalyzetherobustnessagainstLgandRg,somesimulationsarecarriedout.Fig.18showsthebehaviorfortwononlinearloadvalueswhentherealvalueofLgisused,2mH.Upto0.4 stheresistiveloadRLis196 OhmandfromthatmomenttheloadbecomesRL = 98Ω.Thenonlinearloadcurrent,theactivefiltercurrent,thegridcurrentandthedcomponentreferenceandrealcurrentarepresented.Asexpected,thegridcurrentissinusoidal andtheregulationofthedcurrentcomponentwiththeSMCisverygood.However,nomentionablechangesinthesignalsareproducedinthesimulationswhenvariationsonRgof±50%aretested. WhentherearevariationsinthevalueofLg,therearealsovariationsintheperformanceofthesystem.Therefore,variationsinLgby±40%and±25%havebeensimulated.Thus,Fig.19showsthecurrentobtainedinthegrid fordifferentvaluesofLg.Thefurtherawayfromthenominalvaluethemoredegradationthecurrentsuffers,howeverthesystemremainsstableinspiteofthesevariationsshowingtherobustnessleveloftheSMCused. Fig.17APFDCvoltageandcurrentwithnoiseintheDCvoltageof±20 Vto150 Hz.VoltagePIcontroller. Fig.18Dynamicandstaticbehaviourforaloadstepint = 0.4 swhenthereisnotmismatchinLgandRg. ThespikesobservedinthegridcurrentareduetotheincreasedvalueofLgandthelowvalueoftheDCvoltageasindicatedinEq.(33). 5.4Overallefficiency TwoSVPWMtechniquesaretestedtomeasurethesystemefficiencyandcurrentTHD.BothhavethePVpanelworkingtothesamepower,2600 W.Whenthe7segmentsSVPWMistheselectedmodulation,theobtainedTHDis 4.7%andthemeasuredefficiencyis86%asitisshowninFig.20.However,the5segmentsSVPWMimprovesslightlytheefficiencyduetolowerswitchinglosses,87.2%butTHDgetsworse8.2%.Withthe7segmentsSVPWMthe obtainedcurrentTHDislowerthanthevaluelimitedbytheIEEE-519(currentTHD < 5%)(IEEEStd519–2014). Theefficiencyofthepowerinvertercanbeimprovedbyreducingtheswitchingfrequency.However,thiswouldresultinanincreaseinthecurrentripple,worseningthecurrentTHD. 6Conclusions Inthispaper,theactivepowerfilterfeatureisaddedtotheinverterusedinthePVMPPcontrol.Thedesignedcontrolloops,fortheDCbusvoltageaswellasforthecurrentaremadewithslidingmodecontrollers.These controllerswerefirstadjustedbymeansofseveralsimulationsandfinallyretouchedintherealsystem.ThestabilityoftheSMCsisdemonstratedusingthewell-knownLyapunovtheory.TheusedMPPTmethodistheperturband observemethodwiththemodificationofthepowermeasurementattheACsideoftheinverterinordertoavoidtheuseoftheDCsidecurrentsensor.TheactivepowerfiltercharacteristichasbeenimplementedusingthePQtheory. Thegoodstaticanddynamicbehaviorofthemaximumpowerpointaswellasthecharacteristicoftheactivefilterhavebeendemonstratedexperimentally.Therobustnessofthesystemagainstdisturbancessuchasnoisein themeasurementsandgridinductanceisalsosatisfactorilytested.Inaddition,thesystemefficiencyandcurrentqualityareshownfortwotypesofmodulation,theseven-segmentandfive-segmentvectormodulation.Forallthese reasonsitcanbeconcludedthatthepresentedsystemprovidesanefficientmaximumpowertrackingandagoodpowerfiltercharacteristicwiththepresentedslidingmodecontrollers. Acknowledgment Fig.19Behaviourforaloadstepint = 0.4 swhenthereismismatchinLg.Lgchangesfrom+40%to−40%. Fig.20SVPWMdutycycle,gridcurrent,PVvoltageandcurrentandgridcurrentFFTforSVPWMof7and5segments. 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