Software Phase Locked Loop Design Using C2000 ...

1 ApplicationReportSPRABT4A November2013 SoftwarePhaseLockedLoopDesignUsingC2000 Microcontrollersfor ThreePhaseGridConnectedApplicationsManis hBhardwajABSTRACTG ridconnectedapplicationsrequirean accurateestimateof the grid angleto feedpowersynchronoustothe is achievedusinga softwarephaselockedloop(PLL).Thisapplica tionreportdiscussesthedifferentchallenge sin the designof softwarephaselockedloopsfor threephasegrid connectedinvertersand presentsa methodologyto illustrate,two well knownPLL structures[1], [2] are discussedand ControlSuite.

2 Of Figures1 Transformationof VoltageFromThreePhaseto Stationaryand TransformsFromThreePhaseto 3ph-Basedon Responseto VaryingGrid NegativeSequenceof Responseto VaryingGrid phaseangleof the utilityis a criticalpieceof informationfor the operationof powerdeviceslike PVInvertersthat feedpowerinto the PLL is a closedloop systemin whichan internaloscillatoriscontrolledto keepthe time and phaseof an externalperiodicalsignalusinga qualityof the lock directlyaffectsthe performanceof the controlloop in grid tied line notching,voltageunbalance,line dips,phaseloss and frequencyvariationsare commonconditionsfacedbyequipmentinterfac ingwith the PLL needsto be able to rejectthesesourcesof errorandmaintaina cleanphaselock to the grid ,ControlSuiteare trademarksof othertrademarksare the propertyof November2013 SoftwarePhaseLockedLoopDesignUsingC2000 MicrocontrollersforThreePhaseGrid ConnectedApplicationsSubmitDocumentation FeedbackCopyright 2013,TexasInstrumentsIncorporated000 0cos( )

3 Sin( ) 0sin( ) cos( ) 000 1 VTVdqdqvvdvX vqvvooababqqaqqb= = - 001 cos(2 3) cos(4 3)cos( )220 sin(2 3) sin(4 3)sin( )331110222 VTVabcabcVVtaVX Vt VbVcVoababppwappwb= == aVbVcVAlphaBetadqVnetqw32p-34p-cos( )cos(- 2 / 3)cos(- 4 / 3)VtaVVtbwtVcwwpp = threephasesystems,it is commonto transformthreephasetime varyingquantitiesto a dc system(in arotatingreferenceframe).Equation1 showsthat the sequenceof the voltagesis Va Vc Vband the frequencyis.

4 (1)Figure1. Transformationof VoltageFromThreePhaseto Stationaryand RotatingReferenceFrameFor transformingthe threephasequantitiesto rotatingreferenceframe,the first step is to transformthethreephasequantitiesinto an orthogonalcomponentsystem(alpha,betaalso calledstationaryreferenceframe)by takingthe projectionsof the threephasequantitieson an is calledtheClarketransform(seeEquation2).( 2)In the stationaryreferenceframe,the net voltagevectormakesan angle with the orthogonalreferenceframeand rotatesat a frequencyof.

5 The systemcan thenbe reducedto DC by takingthe projectionofthe stationaryreferenceframecomponentson the is calledthe Parktransform(seeEquation3).(3)2 SoftwarePhaseLockedLoopDesignUsingC2000 MicrocontrollersforSPRABT4A November2013 ThreePhaseGrid ConnectedApplicationsSubmitDocumentation FeedbackCopyright 2013,TexasInstrumentsIncorporatedcos()2s in()30vtdvtqvowqwq - =- cos( ) sin( ) 0 cos( )cos( ) * cos( ) sin( )sin( )22sin( ) cos( ) 0sin( )sin( ) * cos( ) cos( )sin( )3300 100vtttdvXt Vtt Vqvoqqwqwqwqqwqwqw + =-=-+ Phase Reference Frame Projection (Clarke Transform)

6 Reference Frame Projection (Park Transform) Simulationof TransformsFromThreePhaseto RotatingReferenceFrame2 SynchronousReferenceFramePLLThe role of the PLL in threephasecontextis to accuratelyestimatethe anglethe net voltagevectorismakingby measuringthe anglethe PLL estimatesis and the actualangleis *t, ABC->DQ0transformcan be writtenusingEquation2 and Equation3:(4)Usingtrigonometricidentitie s,Equation5 can be reducedto:(5)WhenPLL angleis closeto the actualvoltagevectorangle,( *t- ) is smallor closeto zerothensin( *t- ) ~ = ( *t- ).

7 Therefore,it can be said for a balancedthreephasesystemwhenPLL is Locked ,the q-axiscomponentin the rotatingreferenceframereducesto zeroand whenit is not lockedor has smallerrortheq-axiscomponentis linearlyproportionalto the error:Vq (wt )(6)This propertyis usedin the SynchronousReferenceFramePLL for threephasegrid threephasequantitiesare transformedinto the rotatingreferenceframeand the qcomponentis usedas the low passfilter/PIis thenusedto eliminatesteadystateerrorand the outputfed to a VCO,whichgeneratesthe angleand sine November2013 SoftwarePhaseLockedLoopDesignUsingC2000 MicrocontrollersforThreePhaseGrid ConnectedApplicationsSubmitDocumentation FeedbackCopyright 2013,TexasInstrumentsIncorporated1( )0 1*1( )

8 1ylf zBBzynotch zz-+=--[ ] [ 1] * 1[ ] * 0[ 1] * 1ylf nylf nAynotch nBynotch nB=-++-4vKgrid pnTivT Kgrid i pwz==22( )222snnH sssnnzwwzww+=++: ()( )( )( )( )( )22( )( )1( )(:) ( )2kpvk sgridpsTLF soutiHsokClosed loop Phase TFClosed loop error transferssLF spinsvk svgrid pgridTiVsssdEsHsookssLF spinfunctiok sTinspqqq+===+++= -==+++Measure Vgridnf)sin(_inagridavv6 ipkkLPF+of1/sout6cosSinVCOABC->DQ0 TransformDvQv)32sin(_56 inbgridbvv)34sin(_56 SPLLfor 3ph-Basedon StationaryReferenceFrameIt is knownfromEquation6 that any errorin the anglelock will showup on the q termand that the relationbetweenthe errorfor smallvaluesis linear,see Equation7.

9 Err Vgrid( grid - PLL)(7)Smallsignalanalysisis doneusingthe networktheory,wherethe feedbackloop is brokento get the openloop transferequationand thenthe closedloop transferfunctionis givenby:ClosedLoopTF = OpenLoopTF / (1+ OpenLoopTF)(8)The PLL transferfunctioncan be writtenas follows:(9)Comparingthe closedloop phasetransferfunctionto the genericsecondordersystemtransferfunction :(10)Now,comparingthis with the closedloop phasetransferfunction,the naturalfrequencyand the dampingrationof the lineralizedPLL is givenas:(11) PI ControllerThe loop filter or PI is implementedas a digitalcontrolleras shownin Equation12:(12)Usingz transform,Equation13 can be re-writtenas.

10 (13)4 SoftwarePhaseLockedLoopDesignUsingC2000 MicrocontrollersforSPRABT4A November2013 ThreePhaseGrid ConnectedApplicationsSubmitDocumentation FeedbackCopyright 2013,TexasInstrumentsIncorporated2 **2 **0and 122 KKTKKT pipiBB-+ == - 111* ln( )2 Whereandand1sscttcecetsncndndsssswsVwwV ww--- = - = ====-( ) 1sin()ty tcetdswj-= -+2( )222nH sssnnwzww=++2 **2 **122( )1( )1 KKTKKT pipizylf zynotch zz+- -- =--21( )1zsT z-=+( )( )Kylf siKpynotch ss=+ is knownthat the LaplaceTransformof the loop filter (PI controller)is givenby:(14)Now,usingBi-lineartransforma tion,replace, whereT = SamplingTime.