298 BELL SYSTEM TECHNICAL JOURNAL 



3. Special Cases 



The application of the three sets of equations (1), (2) and (3), will 

 be illustrated with a few examples. For simple cases, such as a single 

 or double line-to-ground fault at one location, the equations reduce to 

 formulas frequently found in the literature on this subject. 



From set (1) equations for faults to ground at one or two locations 

 can be obtained directly when the zero sequence impedance is finite. 

 Set (2), obtained from (1), is the most convenient set for solutions of 

 faults to ground in isolated systems in which capacitance has been 

 neglected. The phase-to-phase fault currents are best obtained from 

 set (3). 



3.1 Single Line-to-Ground Fault at A 



Consider a fault to ground on phase "6" at ^. The solution can be 

 obtained from (1) by letting: 



RAa = Rac = Rsa = R-Bb = Rbc = =0 (7) 



This results in : 



Iao = I Ac = Isa = Isb = I Be — (8) 



Striking out all columns in (1) containing the currents in (8) and 

 the corresponding rows indexed by Aa, Ac, Ba, Bb and Be only one 

 equation is left : 



^22/^6 = 3a2£ (9) 



The numerical value of A 22 can be calculated directly from Table I, 

 or on substituting the symbolic value of A 22 in equation (9) the 

 result will be : 



^^^ " Zi + Z2 + Zo + SRp- ^^^^ 



where 



Zi = Zai + Zci 



Z2 — Za2 + Zc2 .... 



Zo = Zao ~\~ Zco 



Rf = RAb + RaF 



Equation (10) is the well-known formula for a single line- to-ground 

 fault at one location in a three-phase system. 



3.2 Double Line-to-Ground Fault at A 



Consider a double line-to-ground fault on phases "a" and "6" 

 at -4. Then: 



Rac = RBa = Rsb = Rbc= ^ (12) 



