1 1(c) 1(b) 1(a) [14] PI 1(c) [15] 3 2 (1) (2) ( ) [2] d (3) 烄 1(b) P EU = UV sin(δ -α)=p umsin(δ -α) X Σ 烅 (1) P ES =I maxusin(δ +β+90 )= 烆 P smsin(δ

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1 DOI /AEPS Vol.41No.12June ( ; ; ) ; ; ; ; 0 [4-5] [1] [6-7] [8-11] [2] [2] [12-13] [3] ( ) ; (2016YFB ); MATLAB/ ( ); Simulink 2 (yndw(2016)000303dd00124) 56

2 1 1(c) 1(b) 1(a) [14] PI 1(c) [15] 3 2 (1) (2) ( ) [2] d (3) 烄 1(b) P EU = UV sin(δ -α)=p umsin(δ -α) X Σ 烅 (1) P ES =I maxusin(δ +β+90 )= 烆 P smsin(δ +β+90 ) I ref d = Iref* d I ref* d I { max (2) I ref q ;P 1 E Fig.1 Controlblockdiagramandequivalent ;ωbase=100π circuitofdroop-controledinverter (4) 1(b) 2 I ref* I max 烄 q I mag I max 槡 I 2 max - (I ref* =烅 2 d ) I ref* d >I max I mag >I max I ref* d I max (3) 烆 0 I ref* d >I max P EU ; P ES ;V ;U ;X Σ ;I max ;δ ;α d V ; β I ;I ref d d I ref q d q ;I ref* d I ref* q d q ;I mag = (I ref* d 槡 ) 2 +(I ref* q ) 2 δ =Δωωbase (4) { Δω =ω -ω0 =m P (P 0 -P E ) ω ( );ω0 ( );m P ;P 0 htp// 57

3 201741(12) O M S =P EO -P E (5) P EO O M S O (4) M M S=P um -P E (P um M ) (1) (4) A C 2 B D 2(a) 2.1 1(b) 1(c) α= 0 β =0 dq q q α β 0 2(b) α β 0 (1) (2) 2(c) O P EO (5) M S α β 2 Fig.2 Virtualpoweranglecharacteristiccurves 2.2 anditstransientdeviationphenomenon α β 2(a) M ; M O 2(a) 1(a) O I ref* d =O d +FI do (6) [2] { I ref* q =O q +FI qo 58

4 F ;I do I qo 3 F =0 X g d q ;O d O q T V qaxis(s) 2.5 Hz; F =0.6 PI T V qaxis(s) 10 Hz 3 I d I q I do I qo 3 烄 s I doest=i d -C est 1+T Vs Vd +ω0cestv q ( ) 烅 (7) s I qoest=i q -C est 1+T V LCL q -ω0c estv d 烆 Vs s ;C est LCL ;I doest I qoest d q ;T V ( T V =0.005s);V d V q LCL 4 d q P 0 A A A1 I do I qo I doest I qoest P 0 ( 4 A A P 0 (4) ) t=4s t=7s P sm =UI max P (7) 0 2(b) V q α V q V ref q T V qaxis(s) V q =T V qaxis(s)v ref q (8) [16-17] V q V ref q T V qaxis(s) 4 Fig.4 Transientinstabilitycausedbyvoltagesag 3 3 TV qaxis(s) Fig.3 BodediagramofTV qaxis(s) (9) 5(a) 烄 ω -ω0 = m ( P P 0 -P E ) I mag <I { max m P (P 0 -P E +S assist ) I mag I max 烅 S assist= ( K SP + KSI s ) ( Q E -Q assist ) 烆 (9) htp// 59

5 201741(12) S assist ;K SP UI max<p 0 Q assist (14) K SI ; Q assist Q E Q assist (14) U> Q assist /I max-x ΣI max (9) Q assist X ΣI 2 max S assist sδ =ω-ω0 Q assist (14) (9) sδ =m Pω0[P 0 -P E + ( ) ( Q E -Q assist ) ] (10) K SP + KSI s (10) s (10) s s 2 δ =m Pω0[sP 0 -sp E + (sk SP +K SI )(Q E -Q assist )] (11) sp 0=0sP E=0s 2 δ =0 sk SP (Q E-Q assist )=0 (11) K SI (Q E -Q assist )=0 (12) Q E Q assist Q E δ Q E =Q assist P E P E = P 0+S assist d Q E =V q I d =(U q +X ΣI d )I d = 5 QE -δ (X ΣI max -Usinδ )I max (13) Fig.5 Transientcontrolstrategyforsynchronismand QE -δ curveduringcurrentsaturation Q E δ 5(b) (9) Q E -δ Q assist 5(b) Q E -δ E 1 E 2 E 1 E 2 ( ) E 1 E 1 Q E -δ Q assist 5(b) ( ) Q assist X ΣI 2 max -UI max Q assist X ΣI 2 max +UI max (14) E 1 2 δe1 (2) 5(b) E 1 P E =P 0 60

6 ; α β A A2(c) PI 4 O d O q 1(a) O d O q ( PI d ±1.1) I max=1.05 S base= ; 10kVAV base= 380 Vωbase =1000rad/sL F = O d O q 0.05( )C F = 0.05( )L g+l l=0.2 ( )m P =0.02m Q =0.1P 0=0.8F=0.6 A A2(d) A2(e) K SP=10K SI=20Q assist=0.2 dq I ref* d I ref* q I ref d I ref q d ( (3)) t=2s ( ) P 0=0.3 P 0 =1.0 6 (7) C est ( α=0 ) 20% 2.1 A A2 4.2 U t=2s t=8s A ; 6 Fig.6 Trajectoryofinvertervirtualpowerangle duringapowerreferencestep A A2(a) V q V q 7 Fig.7 Trajectoryofinvertervirtualpowerangle 0 V q duringvoltagedropandrecovery V q A A3(a) A3(d) A A2(b) α β LCL d ( sin ) q (V d V q ) htp// 61

7 201741(12) A A3(e) 50ms [4] [J] (6) I max= [5] ; (6) (7) (htp// com/aeps/ch/index.aspx) LUZongxiangWANGCaixiaMIN Yongetal.Overviewon microgridresearch[j].automationofelectricpowersystems /AEPS HUANG Linbin ZHANG Leiqi XIN Huanhai et al. Mechanism analysisofvirtualpoweranglestabilityindroop- controledinverters[j].automationofelectricpowersystems (12) DOI /AEPS [3]SIMPSON-PORCO J W D RFLER F BULLO F. Synchronizationandpowersharingfordroop-controledinverters inislanded microgrids[j].automatica201349(9) WU Yunya KAN Jiarong XIE Shaojun.Controlstrategy designforinvertersinlowvoltagemicrogrids[j].automationof ElectricPowerSystems201236(6) [J] (2)39-45.DOI / AEPS XIAOZhaoxiaZHAO QianyuFANG Hongwei.Analysisand establishmentofstate-space equationsforinverter-interfaced microgrid[j].automationofelectricpowersystems (2)39-45.DOI /AEPS [6]VILATHGAMUWA D MLOH P CLI Y.Protection of microgridsduring utility voltage sags[j].ieee Trans on IndustrialElectronics200653(5) [7]PAQUETTE ADIVAN D.Virtualimpedancecurrentlimiting forinvertersin microgrids with synchronousgenerators[j]. IEEETransonIndustryApplications201551(2) [8]POGAKU NPRODANOVIC MGREEN T C.Modeling analysisandtesting ofautonomousoperation ofaninverter- basedmicrogrid[j].ieee TransonPowerElectronics (2) [9]WANG X HRUAN XBLIUS Wetal.Fulfeedforwardof grid voltagefor grid-connectedinverter with LCL filterto suppresscurrentdistortionduetogridvoltageharmonics[j]. IEEETransonPowerElectronics201025(12) [10]LIW WRUAN X BPAN D Detal.Ful-feedforward schemes ofgrid voltagesforathree-phase LCL-type grid- connectedinverter[j].ieee TransonIndustrialElectronics [11]TAO YLIU Q WDENG Yetal.Analysisandmitigation ofinverteroutputimpedanceimpactsfordistributedenergy resourceinterface[j].ieee Trans on Power Electronics [12]ASTROM KJ.Limitationsoncontrolsystemperformance[J]. EuropeanJournalofControl [13]ASTROM K J MURRY R M.Feedback systems an introductionforscientistsand engineers[m].new Jersey USAPrincetonUniversityPress2010. [14]ROCABERTJLUNA ABLAABJERG Fetal.Controlof powerconvertersinac microgrids[j].ieeetransonpower Electronics (11) [15]ZHAO MYUAN X HU Jetal.Voltage dynamics of [1]. [J]. currentcontroltimescaleina VSC-connected weakgrid[j] (19) IEEETransonPowerSystems201631(4) [16]WANGJNICOL S C P CFENG X etal.designofa generalizedcontrolalgorithmforparalelinvertersforsmooth (19) microgridtransitionoperation[j].ieee TransonIndustrial [2]. Electronics201562(8) [J] (12) DOI [17]LIU Q TAO YLIU Xet al.voltage unbalance and 62 harmonicscompensationforislanded microgridinverters[j]. IETPowerElectronics20147(5) ( 99 continuedonpage99)

8 PilotProtectionofPositiveSequenceImpedanceforDistributionNetwork withinverter-baseddistributedgenerator XU Meng 1 ZOU Guibin 1 GAO Lei 2 MA Yuwei 1 (1.KeyLaboratoryofPowerSystemInteligentDispatchandControl(ShandongUniversity)Jinan250061China; 2.JinanPowerSupplyCompanyofStateGridShandongElectricPowerCompanyJinan250001China) AbstractThefaultcharacteristicsoftheinverter-baseddistributedgenerator(IBDG)diferfromthoseoftraditionalresources whichmakesitdificultfortraditionalcurrentrelaytoclearfaultfastandreliably.alsoafectedistheactionperformanceof theexistingtransmissionlineprotectionprincipledirectlyusedindistributionnetwork withibdg.bydrawingoncurrent diferentialprotectionforreferencetheamplitudesofthedefinedpositivesequencediferentialimpedancefortheinternaland externalfaultareanalyzedandanovelpositivesequencediferentialimpedanceprotectionprincipleisproposedtoaccountfor theimpedanceamplitudediference.tofurtherimprovetheperformanceanoperationcriterionwithbrakingcharacteristicis constructedtoovercometheadverseefectsofloadbranch.anauxiliarycriterionbasedontheamplitudeofpositivesequence impedanceandcurrentisformulatedforinternalthree-phaseshortcircuitfaultswithouttransitionresistance.comparedwith thetraditionalcurrentdiferentialprotectiontheproposedprotectionstrategyhasnoneedforsynchronizedmeasurement.the feasibilityofprotectionschemeisverifiedbysimulationresults. This workissupportedby National High Technology Researchand DevelopmentProgram ofchina (863 Program) (No.2012AA050213)andShandongProvinceKeyPlanofResearchandDevelopment (No.2015GGX101011). Keywordspositivesequenceimpedance;diferentialprotection;brakingcharacteristic;inverter-baseddistributedgenerator (IBDG);distributionnetwork 櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧櫧 ( 62 continuedfrompage62) haxwel@sina.com (1989 ) (1981 ) zhangleiqi@zju.edu.cn xinhh@zju. (1992 ) edu.cn huanglb@zju.edu.cn (1980 ) ( ) ControlMethodsforImprovingVirtualPowerAngleTransientStabilityofDroop-controledInverters ZHANG Leiqi 1 HUANG Linbin 1 HUANG Wei 2 XIN Huanhai 1 HU Jiabing 3 (1.ColegeofElectricalEngineeringZhejiangUniversityHangzhou310027China; 2.DispatchingandControlCenterofYunnanPowerGridCorporationKunming650011China; 3.SchoolofElectricalandElectronicEngineeringHuazhongUniversityofScienceandTechnologyWuhan430074China) AbstractLikesynchronousgeneratorstransientinstabilityalsooccurstodroop-controledinverterswhensubjectedtolarge disturbances.owingtothecurrentlimitationthevoltageloopoftheinverterisoutofworkduringthedisturbanceandthe inverterturnstooperatinginthecurrentsourcemode.themechanismofthevirtualpoweranglecurvesdeviatingduringthe transientprocessbecauseofthelimitedvoltagetrackingperformancewhichreducesthestabilitymarginisfurtheranalyzed. Tothisendacurrentfeed-forwardcontrolmethodbasedonestimatingtheoutputcurrentisproposedtoimprovethevoltage trackingperformancesothatthetransientstabilityisimproved.besidestodealwiththelossofequilibriumpointsduringthe transientprocessatransientsynchronouscontrolmethodisproposed.ithelpstheinvertertoreachaproperequilibriumpoint whenthevoltageloopisoutofcommissionandpreventstheinverterfromtransientinstability.finalysimulationsonasingle- machine-infinite-bussystemverifytheefectivenessoftheproposedcontrolmethods. ThisworkissupportedbyNationalKeyResearchandDevelopmentProgramofChina (No.2016YFB )National Natural Science Foundation of China (No ) and Yunnan Electric Power Company (No.yndw (2016)000303DD00124). Keywordsinverter;virtualpowerangle;transientstability;currentlimiting;currentfeed-forwardcontrol;droopcontrol htp// 99

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