300 BELL SYSTEM TECHNICAL JOURNAL 



currents becomes quite involved and it is advisable to substitute 

 numerical values of the constants before solving for the four currents. 

 The total fault currents at A and B, respectively, are (from (4) and 

 (5) in connection with (19)) : 



IaF = I.ia + I.ib (21) 



Ibf = Isa + Ibc (22) 



In a similar manner faults to ground for any other combination of 

 faulted phases can be found. 



3.4 Single Line-to -Ground Faults at A and B in an Isolated System 

 Consider a fault-to-ground on phases "a" at A and "6" at B in 

 an isolated system in which capacity can be neglected. Then : 



i?.46 = Rac — Rsa — Rbc = '^ (23) 



and 



lAb = I Ac - iBa = Ibc^ (24) 



Striking out the columns of (2) containing the currents in (24) and 

 the corresponding rows Aa — Be, Ah — Ba, Ah — Be, Ac — Ba and 

 Ae — Bh (all rows containing Ah, Ac, Ba and Be), leaves only one 

 equation in (2), which together with (2a) gives: 



B.jAa + B.Jsb = 3(1 - a')E 



lAa + iBb = 



Solving for these currents the result is : 



_ _. 3(1 - a^)E 



J-Aa — — iBb — -^ B~ K^^J 



Inserting the values of the B's from Table I this reduces to: 



7^, = - Ij,, = 3(1 - a')E ^27) 



Zu 4- Zzi + Zoi + 3(i?A + Rb) 



Zii = Za\ + Zbi + 3Zci 



^2i — Za2. + Zb2 + 3Zc2 



Zoi = Zao + Zbq (28) 



Ra = RAa + RaF 



Rb = Rsb + Rbf 



The subscript i (isolated) is used to distinguish these impedances for 

 the isolated system from those used in (11), (17) and (38). 



