THREE-PHASE POWER SYSTEMS 303 



Acknowledgment 



The author wishes to express his appreciation to P. A. Jeanne and 

 J. Riordan for valuable suggestions and checking of the mathematical 

 relations in preparation of the paper. 



APPENDIX 



The standard notation for phase and sequence quantities is usually- 

 indicated by a subscript. Thus /„, h, etc., means the current at the 

 point of fault of phase "o" and "&," respectively, /i, a^Ii and ali 

 are the positive sequence currents in phase "a," "&" and "c," re- 

 spectively. In this treatment, however, complication arises from the 

 fact that two points of faults are involved and it will be necessary to 

 distinguish between the quantities at these two locations. This is 

 most conveniently done by a double subscript, the first referring to the 

 point of fault and the second to the phase or sequence in question. 

 Thus lAa, iBa, etc, are the currents in the fault at A and B of phase 

 "a" and Iai, Ibi the positive sequence current at the two points of 

 fault, respectively. Making use of this notation the fundamental 

 equations for the sequence currents at fault A are : 



Iao + ^Al + Ia2 = lAa 



Iaq + o^Iai + alA2 = I Ah (43) 



7^0 + ClIax + CL^lAi = I Ac 



And at fault B : 



Ibo + Ibi + Ib2 = iBa 

 Ibo + a^/si + alB2 = /b6 (44) 



Ibo + alsi + a^lB2 = Ibc 



where the coefficient "a" is the sequence operator, having the value: 



1 , .V3 

 2 1 . V3 



(45) 



The voltages to ground at the two fault locations are given by : 



VAa = Vao + VaI + Va2 



= {RAa + RAF)lAa + RafIaI + RafI Ac 



VAb = Vao + a^VAi + aVA2 



= RafTao + (RAb + RAF)lAb + RafIac 



Vac = Vao + aVAi + a^VA2 



= RafIao + RAF^Ab + {Rac + Raf)Iac 



(46) 



