DSTATCOM建模总.docx

DSTATCOM建模总DSTATCOM建模总结 真实反映DSTATCOM 装置的模型是为了了解该装置的性能、特性、及研究其运行、控制规律的主要基础，因此DSTATCOM装置的建模从一出现就备受研究者的重视，目前的建模方法主要有“拓扑”建模法和“输出”建模法。 “拓扑”建模是根据装置在不同的运行状态下不同的拓扑结构分析写出其微分方程组，然后根据要解拓扑的前一个拓扑结构对应的微分方程组定出本拓扑对应微分方程组的初值，从而解出微分方程组；在本拓扑结构结束时，微分方程组的解给出下一拓扑对应微分方程的初值，按整个装置具有多种拓扑结构及拓扑结构转移顺序依次解出拓扑结构对应的微分方程组，从而求出了装置的解。如图11所示。其缺点是建模过于复杂，对于周期性的变拓扑模式，显得过于繁琐，计算量较大，且不便于实现控制。 拓扑1 拓扑N 拓扑2 拓扑3 拓扑K 11拓扑建模法示意图 “输出”建模的基本做法是将整个装置的输出电压用一个阶梯波电压源u(t)代表，将整个装置等效为一个电压源u(t)外接电阻、电感、再与系统相接，即得到一组微分方程，而直流侧电容电压又取决于DSTATCOM的能量交换，从而可建立一联立方程组，即为DSTATCOM模型。它的缺点是对DSTATCOM装置内部一概忽略，如要详细得了解装置的内部的性质就很困难。 本文直接从DSTATCOM的稳态分析出发，利用dq变换建立DSTATCOM的数学模型。 12DSTATCOM装置原理图 由上图可得到DSTATCOM装置变流器总的输出电压为 ìïUia(t)=KUdcsin(wt-d)ï2ïU(t)=KUsin(wt-p-d) íibdc3ïïU(t)=KUsin(wt+2p-d)icdcï3îK为比例系数，d为DSTATCOM输出电压与系统电压的夹角，系统三相电压为 ìïUsa(t)=2Ussinwtï2ïíUsb(t)=2Ussin(wt-p) 3ïïU(t)=2Usin(wt+2p)scsï3î根据图可列出DSTATCOM的a、b、c三相数学方程 ìdia(t)ïLdt=Uia(t)-Usa(t)-Ria(t)ïd(t)ïib=Uib(t)-Usb(t)-Rib(t) íLdtïïLdic(t)=U(t)-U(t)-R(t)icscicïdtî将代入可以得到 dia(t)ìL=KUdc(t)sin(wt-d)-2Ussinwt-Ria(t)ïdtïd(t)22ïibL=KU(t)sin(wt-p-d)-2Usin(wt-p)-Rib(t) ídcsdt33ïïLdic(t)=KU(t)sin(wt+2p-d)-2U(wt+2p)-Ri(t)dcscïdt33î而直流侧电容电压的方程由能量关系得到 U2dc(t)R2+ddt(12CU2dc(t)=-Uia(t)ia(t)+Uib(t)ib(t)+Uic(t)ic(t) 将代入得到 Udc(t)C×R2+dUdc(t)dt=-Ké22ùi(t)sin(wt-d)+i(t)sin(wt-p-d)+i(t)sin(wt+p-d)abcúCê33ëû可得到 dia(t)ìL=KUdc(t)sin(wt-d)-2Ussinwt-Ria(t)ïdtïdi(t)22ïLb=KUdc(t)sin(wt-p-d)-2Ussin(wt-p)-Rib(t)ïdt33ídi(t)22Lc=KUdc(t)sin(wt+p-d)-2Ussinsin(wt+p)-Ric(t)ïdt33ïKé22ùïUdc(t)dUdc(t)+=-i(t)sin(wt-d)+i(t)sin(wt-p-d)+i(t)sin(wt+p-d)abcúïC×RdtCê33ëû2î 利用经典派克变换将式中a、b、c三相电流进行dq变换 派克变换矩阵为 éêcoswt2êC=ê-sinwt3êêêëcos(wt-sin(wt-23232ùp)p)cos(wt+ú-sin(wt+p)ú 3úúúû2p)ú3éid(t)ùéiaùêúêú令iq(t)=Cib êúêúêúêëûëicúûéidêdêiqdtêêëUdcééidùùéùêdêúúêdúêdtêiqúúêdtú=êêêëúûúúêúêdúUdcúêûêëdtûêëìéiaùüùìéiaùéiaùüdêúïïêúïúïìdüêúCi+CiCiýíêbúýúïíêbúïïîdtþêbúïdtïêiúïú=í êúêúëicûëicûýîëcûþúïïdUdcdïUdcúïïïúdtþdtûî=ì22éùisinwt+isin(wt-p)+isin(wt+p)abcïêú33ïú2ê22ï-wêiacoswt+ibcos(wt-p)+iccos(wt+p)úï3ê33úíêúïêúëûïïdUdc(t)ïdtî+éé222222ùé222KUcosdsinwtcoswt+sin(wt-p)cos(wt-p)+sin(wt+p)cos(wt+p)-KUsindcoswt+cos(wt-p)+cos(wt+p)úêdcdcêê333333ëûëê2ê22ù2222ùé2é22-KUcosdsinwt+sin(wt-p)+sin(wt+p)+KUsindsinwtcoswt+sin(wt-p)cos(wt-p)+sin(wt+p)cos(wt+p)údcdcêúê3Lê333333ëûëûêêêë-2222ù22ùéé2Usêsinwtcoswt+sin(wt-p)cos(wt-p)+sin(wt+p)cos(wt+p)ú-Rêiacoswt+ibcos(wt-p)+iccos(wt+p)ú3333û33ûëë22ù22ùé2é22+2Usêsinwt+sin(wt-p)+sin(wt+p)ú+Rêiasinwt+ib(wt-p)+icsin(wt+p)ú33û33ûëëüïïïïýïïïïþ=éêé222222éùêKUdccosdsinwtcoswt+sin(wt-p)cos(wt-p)+sin(wt+p)cos(wt+p)-KUdcsindcos2wt+cos2(wt-p)+cos2(wt+p)êêú 333333êëûëê2222222éùéù222ê-KUdccosdêsinwt+sin(wt-p)+sin(wt+p)ú+KUdcsindêsinwtcoswt+sin(wt-p)cos(wt-p)+sin(wt+p)cos(wt+p)ú3Lê333333ëûëûêêUdcê-êC×R2ë-2222éù2Usêsinwtcoswt+sin(wt-p)cos(wt-p)+sin(wt+p)cos(wt+p)ú3333ëû22éù2222Usêsinwt+sin(wt-p)+sin(wt+p)ú33ëûùúúúúúúúúû+ ìü22R222R2222R2-wsinwt-coswt -wsin(wt-p)-(wt- p) -wsin(wt+p)-cos(wt+p) ïï33L333L3333L3ïïéiùa22R222R2222ïïïï-wcoswt+sinwt -wcos(wt-p)+sin(wt-p) -wcos(wt+p)+cos(wt+p)êúíýêibú33L333L3333ïïêiúïKïëcûKK2K2K2K2ï-sinwtcosd+coswtsind-sin(wt-p)cosd+cos(wt-p)sind-sin(wt+p)cosd+cos(wt+p)sindïïCC3C3C3C3ïþîC=éêé222222ùéêKUdccosdsinwtcoswt+sin(wt-p)cos(wt-p)+sin(wt+p)cos(wt+p)-KUdcsindcos2wt+cos2(wt-p)+cos2(wt+p)êê333333úêëûë2ê22ù2222ùé2é22ê-KUdccosdêsinwt+sin(wt-p)+sin(wt+p)ú+KUdcsindêsinwtcoswt+sin(wt-p)cos(wt-p)+sin(wt+p)cos(wt+p)ú3Lê33û3333ûëëêêUdcê-êC×R2ë-ù2222éùú2Usêsinwtcoswt+sin(wt-p)cos(wt-p)+sin(wt+p)cos(wt+p)úú3333ëûú22úéù222+2Usêsinwt+sin(wt-p)+sin(wt+p)úú-33ëûúúúúû-ìïï2ïí3ïïï-îwsinwtwcoswtKCKCwsin(wt-wcos(wt-232323p)p)sinwtcosd-sin(wt-p)cosdüwsin(wt+p)ï3ïéiùa2ïïêúwcos(wt+p)ýêibú+3ïêiúïëcûK2-sin(wt+p)cosdïïC3þ2-RLRLcos(wt+2323ìR-coswtïLïR2ïïsinwt+íL3ïïKïcoswtsindïîC-RLRLcos(wt-sin(wt-232323p)p)p)sin(wt+KCp)23KCcos(wt-p)sindcos(wt+p)sindüïïéiùaïïêúýêibú ïêiúïëcûïïþ223ì222cosx+cos(x-p)+cos(x+p)=ï332ï223222ïsinx+sin(x-p)+sin(x+p)=332ï2222ï由下列三角公式ísinxcosx+sin(x-p)cos(x-p)+sin(x+p)cos(x+p)=0 3333ï22ïcosx+cos(x-p）cos(x+p)=0ï33ï22sinx+sin(x-p)+sin(x+p)=0ï33î3ìü-KUsinddcéidùüìé0-wïïì2ï3ïïRêúïïê3iw02UsïïLêqúïïê2ï-KUdcsind+2í2ý-íý-íêêúëûë3Lïïïïï3K3KïïïUdcsindidïïcosd-þî2Cïïî2CRC2îþùéidùüúêúïiúêqúïý úûêëúûïïiqþRé-êLêê-w=êêê3Ksindêë2Cw-3K2CRLcosdùsindúéidLúêK-cosdúêiqLúêúê1úëUdc-úR2Cû-Kùé0ùúêú2Us1ú+êú úLêúúêú0ëûûéR-êLùêúê=-wúêúûê3Kê2Csindëéidd可得到DSTATCOM数学模型为êiqdtêêëUdcw-3K2CRLcosdùsindúLúéidKê-cosdúiqLúê1úêëUdc-R2Cúû-Rùé0ùú1êú+2Us úLêúúêûë0úûéR-êLéid(s)ùêêúiq(s)×s=ê-wêúêêúU(s)ê3Këdcûê2Csindëw-3K2CRLcosdùsindúLé0ùúéid(s)ùK1êúêú-cosdúiq(s)+2Us úLêúLúêê1úêëUdc(s) úûë0úû-R2Cúû-RùsindúLé0ùúéid(s)ùK1êêúú-cosdúiq(s)=2Us úLêúLúêê1úêëUdc(s)úûë0úû-R2úû-K-1é1ê0êêë0010éR-êL0ùéid(s)ùêúêú0iq(s)×s-ê-wúêúêêú1úU(s)ê3Kûëdcûê2Csindëw-3K2CRLcosdéRS+êLéid(s)ùê1êúêiq(s)=wêúLêêê3KëUdc(s)úûê-2Csindë-wS+-3K2CRLcosdùsindúLúKcosdúLú1úS+R2CúûKé0ùêú2Us êúêë0úûéid(s)ùêúiq(s)=êú3RRK2cosd-2R2êëUdc(s)úûL2-2Lw22+6KwR2Lcosdsind22éS×2R2CLw+2Lw-3R2Ksindcosdê222S×2RCL+S(2L+2RRC)+2R+3KRsind222êêS×3KLcosdR+3KRcosdR+3KLwsindR222ëùúú2Us úû利用拓扑法建立的模型 单相桥(a) (b) (c) (d)四种状态结构 ìUUïiL=coswt-+iL0(a)í wLwLïudc(t)=udc0îtUwCìi(t)=C(-Ccost+Csin)-coswt212ïLL1-LCwLCLC (b)í ttUïudc(t)=C1cos+C2sin+sinwt2î1-LCwLCLCUUìïiL(t)=coswt+cos(d-b)+iL(d-b+p)(c)í wLwLïudc(t)=udc(d-b+p)îìCttUwCi(t)=(-Csin+Ccos)-coswtïL342ïL1-LCwLCLC(d)í ttUïudc(t)=C3cos+C4sin-sinwt2ï1-LCwLCLCî单相桥经由(a) (b) (c) (d)四种状态结构后再回到状态,不断周期的循环下去，只要将状态的终值作为状态(a)的初值 即可将电路的状态解出，将前一状态的终值作为后一状态的处置不断地解微分方程组，即可将整个电路在无穷长时间内运行的状态解出，这就是“拓扑”建模法。 利用“开关函数”法，建立DSTATCOM 的模型 ìïïïï íïïïdu(t)dc=-ïCdtîLLLdia(t)dtdib(t)dtdic(t)=63Ksinsinsinq2p63Kudc(t)sin(wt-d)-2Ussinwt-Ria(t)°q2p63Kudc(t)sin(wt-d-120)-usb(t)-Rib(t)q2udc(t)sin(wt-d+120)-usc(t)-Ric(t)°°°dt63Kppsinq2(ia(t)sin(wt-d)+ib(t)sin(wt-d-120)+ic(t)sin(wt-d+120)该模型在dq坐标下的模型方程组： ìdid(t)2UsR63Kq=-i(t)+wi(t)-sinu(t)sin(a+d)+sinaïdqdcLLp2Lïdt2UsR63Kïdiq(t)=-wi(t)-i(t)-u(t)cos(a+d)+cosadqdc í dtLLpLïdudc(t)93Kqï=sinid(t)sin(a+d)+iq(t)cos(a+d)ïdtCp2î