令：Q?|ZZL| ??argS 并考虑到：ZS?ZR ZSZL2?ZLZSZLZS2?Qe?j?2?Qcos??jQsin? ??1?(1?p)Qe?j?1?(1?p)Qcos??j(1?p)Qsin??? 则：K1?(1?p) 所以；
2?Qco?s?2(1?p)Qco?s?(1?p)Q2 Kr?
1?2(1?p)Qco?s?(1?p)2Q2 Kr?2(1?p)Qsin??Qsin?
1?2(1?p)Qco?s?(1?p)2Q2 取不同的Q值和?值，分别作出Kr和Ki的变化曲线如教材中图2—6所示。 （二）各种短路故障情况下附加阻抗的表达式 1 三相经过渡电阻短路 （d
(3)）
? I? ? I IfCfAfB
ZJAB?ZJB?CZJCA?pZL?Za ZJA?ZJB?ZJC?pZL?Za
?If?R?1R Za?Rf?Kff??ICM1M?I? 式中：C1M?M为正序电流分配系数。
?If(2) 2 两相经过渡电阻短路（dBC）
??0 I? ? IIfAfCfB两相经过渡电阻短路。故障点的边界条件：
??U??1U? ???I?，U??0，I IDBDCDAfAfBfC2???I? U??U??I?(Z?R) IfA1fA2DA1DA2fA12?f 故障点F的各相电压：
??U??I?R?U??2U??2I?(Z?R) UFADAfAfDADA1fA12?f??U??I?R??1U??(I??I?)RUFBDBfBfDAB1B2f2?(Z?R)??2I?R??I?R ??IfA12?ffA1ffA2f2?Z?(?2???1)RI????IfA12?ffA1?(2?Rf?Z2?)IfA1
??U??I?R??1U??(I??I?)RUFCDCfCfDAC1C2f2?(Z?R)??I?R??2I?R??IfA12?ffA1ffA2f?Z?(???2?1)RI????IfA12?ffA1?(2?Rf?Z2?)IfA1故障点F处各相间电压：
2????UFAB?UFA?UFB?[2(Z2??Rf)?(2?Rf?Z2?)]IfA1?[3Z2???2(1??)Rf]IfA12
2????UFBC?UFB?UFC?[(2?Rf?Z2?)?(2?Rf?Z2?)]IfA1??[2(???)Rf]IfA12
????UFCA?UFC?UFA?[(2?Rf?Z2?)?2(Z2??Rf)]IfA1??[2(??1)Rf?3Z2?]IfA1M侧保护安装处的各相电压为：
??(I??3KI?)pZ?U??U? UMAMAM0LFAFA??(I??3KI?)pZ?U??I?pZ?U? UMBMBM0LFBMBLFB??(I??3KI?)pZ?U??I?pZ?U? UMCMCM0LFCMCLFCM侧保护安装处的各相间电压为：
?????? UMAB?UMA?UMB?(IMA?IMB)pZL?UFAB
?????? UMBC?UMB?UMC?(IMB?IMC)pZL?UFBC ?????? UMCA?UMC?UMA?(IMC?IMA)pZL?UFCA
流过M侧保护的各相电流为：
??0 IMA??C?2I??C?I??C(?2??)I? IMB1MfA12MfA21MfA1??C?I??C?2I??C(???2)I? IMC1MfA12MfA21MfA1 M侧的各个相间阻抗继电器测量阻抗分别为：
ZJAB
??U??2(1??)RfUU3Z2?MAMBFAB??pZL??pZL????I???I?IIC1M(???2)C1M(???2)MAMBMAMB1(3Z2???900?2Rf??600C1M
?pZL?ZJBCZJCA2??U??2(???)RfRfUUMBMCFBC ??pZL??pZL??pZL?2??I???I?CII2C(???)1MMBMCMBMC1M??U??2(??1)RfUU3Z2?MCMAFCA??pZL??pZL????I???I?IIC1M(???2)C1M(???2)MCMAMCMA1(3Z2??900?2Rf?600C1M
?pZL? M侧三个接地阻抗继电器的测量阻抗分别为：
ZJAZJB??UUMA??FA?? ??3KI?0IMAM02??2?RfUUZMB2???pZL?FB?pZL????3KI??IIC1M(?2??)C1M(?2??)MBM0MB?pZL?1C1M3
(Z2???900?2Rf??300)ZJc??IMc??2?RfUUZ2?Mc?pZL?Fc?pZL?????3KIIC1M(???2)C1M(???2)M0Mc1(Z2??900?2Rf?300)(1)
?pZL?C1M3 3单相经过渡电阻短路（dA）
? IfA??0 I??0 IfBfC 故障点的边界条件为：
??0，I??I??0， U??0 IDAfAfBfC??I??I??1I? U???(U??U?) IfA1fA2f0fADA1DA2DA03???? UDA2??IfA2(Z2??Rf) UDA0??IfA0(Z0??Rf)
故障点F的各相电压：
??U??I?R?I?R?3I?R UFADAfAffAffA1f??U??I?R?U???2U???U??UFBDBfBfDBDA1DA2?UDA0?(Z?Z?2R)??I?(Z?R)?I?(Z?R) ??2IfA12?0?ffA22?ffA00?f??[(?2??)Z2??(?2?1)Z0??3?2Rf]IfA1??U??I?R?U???U???2U?UFCDCfBfDCDA1DA2??UDA0?(Z?Z?2R)??2I?(Z?R)?I?(Z?R) ??IfA12?0?ffA22?ffA00?f??[(???2)Z2??(??1)Z0??3?Rf]IfA1故障点F处各相间电压：
???? U???2)Z2??(1??2)Z0??3(1??)Rf]IFAB?UFA?UFB?[(fA1???U??[2(?2??)Z)?(?2??)Z?3(?2??)R]I? U?UFBCFBFC2?0?ffA1???? U???2)Z2??(??1)Z0??3(??1)Rf]IFCA?UFC?UFA?[(fA1M侧保护安装处的各相电压为：
??(I??3KI?)pZ?U? UMAMAM0LFA??(I??3KI?)pZ?U? UMBMBM0LFB??(I??3KI?)pZ?U? UMCMCM0LFCM侧保护安装处的各相间电压为：
?????? UMAB?UMA?UMB?(IMA?IMB)pZL?UFAB
?????? UMBC?UMB?UMC?(IMB?IMC)pZL?UFBC ?????? UMCA?UMC?UMA?(IMC?IMA)pZL?UFCA
流过M侧保护的各相电流为：
??I??I??I????IMAMA1MA2MA0?C1MIfA1?C2MIfA2?C0MIfA0?(2C1M??C0M)IfA1
??C?2I??C?I??CI?? IMB1MfA12MfA20MfA0?(C0M?C1M)IfA1 ??C?I??C?2I??CI?? IMC1MfA12MfA20MfA0?(C0M?C1M)IfA1
M侧的各个相间阻抗继电器测量阻抗分别为：
ZJAB??U??UUMAMBFAB??pZL???I???I?IIMAMBMAMB(???2)Z2??(1??)Z0??3(1??2)Rf3C1M1C1M3(Z2??900?Z0??300?3Rf?300
?pZL??pZL?ZJBCZJCA??U??UUMBMCFBC??pZL??pZL??
????IMB?IMCIMB?IMC??U??UUMCMAFCA??pZL???I???I?IIMCMAMCMA(???2)Z2??(??1)Z0??3(??1)Rf?3C1M1C1M3(Z2???900?Z0???300?3Rf??300
?pZL??pZL? M侧三个接地阻抗继电器的测量阻抗分别为：
ZJA??3RfUUMAFA??pZL??pZL???3KI???3KI?[2C1M?(1?3K)C0M]IIMAM0MAM03Rf''C
?pZL?ZJB??UUMBFB??pZL???3KI???3KI?IIMBM0MBM0(?2??)Z2??(?2?1)Z0??3?2Rf[(1?3K)C0M?C1M]3(Z2???900?Z0???1500?3Rf??1200)'C
?pZL??pZL?