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ExtendingthereactivecompensationrangeofadirectAC-ACFACTSdeviceforoffshoregrids
ABSTRACT
 TheauthorssuggesttousehybridmodulationschemestoimprovethereactivepowercompensationcapabilitiesofthedirectAC–,,thedirectAC–-Vector-.
Introduction
LargescaleintegrationofwindenergywillcallforthanincreaseduseofFlexibleACTransmissionSystems(FACTS).ForoffshoreACgrids,appropriateFACTSdeviceshouldpossessthetwofollowingfeatures:-ACFACTSdevicecomposedofamatrixconverterandapermanentmagnet(PM)synchronousmachine,,isbothcompactandreliablemainlybecausetheDClinkcapacitoris
Eliminated.
In[1,-ACFACTSdevicewaspresentedin[3,4],[1],
hybridmodulationschemespresentedin[5-8][8]theFACTSdevicesuggestedhereandin[4]isidentifiedasapossibleapplicationforthe
hybridmodulation.
ThereactivepowercompensationrangeoftheAC-(ISVM).InSection3thelimitationsthattheISVMcausesonthereactivepowercompensationrangeoftheFACTSdeviceareanalyzed
Thehybridmodulationcanbeusedtoextendthereactivepowercompensationatanylowoutputpowerfactorvalue,howeverforthesakeofbrevity,-Vector-Scheme(3VS)[9,10].Howeverthe3VSisinterestingasitisbased
,theresultsofthesimulationstudycarriedoutusingMatlabSimulinktocomparewiththeanalyticalfindings,.
-ACFACTSdevice
Asimpleper-phaseequivalentcircuitoftheFACTSdevice,,,thematrix
Phasor
Magnitude(peakvalue)
Magnitude(RMSvalue)
Input/outputvariableofthematrixconverter
Phaseangleofvariabley
Powerfactorangle
Voltagetransferratio
Currenttransferratio
Normalizedmodulationindex
Active/reactivepower
Switchingperiod
Dutyratio
Activeorzerovoltage/currentvectors
Voltage/currentspacevector
Angleofspacevector
Armatureresistance
Synchronousreactance
Excitationvoltage
;=V;LO,intotheoutputvoltage,Vi=
frompollutingthegrid,:
IntheparticularcaseofnoloadontherotorshaftofthePMmachine,noactivepoweristransferredthroughthematrixconverter,theoutputpowerfactorzero,correspondingtotheFACTS
deviceprovidingpurereactivepowercompensation.


TheconventionalISVMconsidersthematrixconvertertobeoftheindirectfarm,see
(VSI)spacevectormodulationandCurrentSourceRectifier(CSR)spacevectormodulation,,,.(3)and(4)areusedforcalculatingthedutyratiosdrsanddrtcorrespondingtothecaseoftheinputcurrentspacevectori;.}plyinginthesectorformedbytheactivevectorsi,,},representedrespectivelybythefirstandsecondletterinthesubscript.
Similarlywhentheoutputvoltagespacevectorvo..spislyinginthesectorformedbytheactivevectorsu},anduputhedutyratiosare
calculatedasinEqs.(5)and(6).(p)orlower(n)switchisON.
.(8),thefollowingexpressionoftheDClinkcurrentcanbefound:
ItisclearfromEq.(11).(9)inEq.(11)themaximumcurrenttransferratioisobtainedas'

Thereactivepowerattheinputofthematrixconverterdepends
ontheactivepoweraccordingtoEq.(13):
Toobtainamoreinsightfulexpressionfortheinputreactivepower,:
Aftersimplifications,equationsfortheactiveandreactivepowersarefoundthatdependonlyoncircuitparameters:Theinput