302 BELL SYSTEM TECHNICAL JOURNAL 



3.7 Phase-to-Phase Fault at A and Phase-to-Ground Fault at B 

 Consider a fault between phases "fl" and "6" at A and a fault to 

 ground on phase "c" at 5. Then : 



Rac = Rbc = Rbi>= ^ (39) 



and 



Iac = iBa = lBb = (40) 



As explained in a preceding section the three first equations in (3) 

 together with the first in (3a) and the three last equations in (1) may 

 be used for this case. 



Striking out the columns Iac, Ibo and Isb and the corresponding rows 

 Aa — Ac, and Ab — Ac in the three first equations in (3) leaves only 

 the first equation. Similarly by striking out the columns Ibo, Ibi, and 

 the corresponding rows Ba and Bh in the three last equations in (1) 

 leaves only the last equation. Hence : 



CiilAa + CiilAh + CuIbc = 3(1 - a^)E 



(41) 

 A^xlAa + AezlAb + A eel Be = 3a£ 



and finally from {Za) : 



lAa + lAb^O (42) 



from which the three currents can be found. The ^'s and C's are 

 given in Table I and Table II. 



4. Conclusion 



While the probability of all phases being faulted at both locations 

 simultaneously is very remote, the three sets of equations (1), (2) and 

 (3) have been given in such a form that they conveniently will provide 

 a solution for any combination of phases faulted from a single line-to- 

 ground fault at one location to the most involved fault condition. 



In Section (3) of this paper, in which special cases have been treated, 

 only simple types of fault conditions have been shown in order to 

 illustrate the method to be used and to prove that the general equations 

 reduce to well-known formulas. 



The constants given in Table I consist of the nine quantities Sa, 

 Sb, Sc, Ta, Tb, Tc, Ua, Ub and Uc arranged as shown for each set of 

 equations. Table II gives somewhat simpler values for the constants 

 in cases where the positive and negative sequence impedances are 

 assumed equal. 



The voltages to ground at the two fault locations are given by (46) 

 and (47) in the Appendix. 



It is hoped that this development will provide a more unified presen- 

 tation of fault current calculations in power networks. 



