THREE-PHASE POWER SYSTEMS 295 



The index to the right indicates which equations of (1) have been 

 used. The values of the C's are given in Table I and Table II. 

 The total ground fault currents at the two fault locations are : 



IaF = lAa + I Ah + I Ac (4) 



IbF = Isa + Isb + I Be (5) 



and the total residual current in the two faults is : 



Ir = Iaf -\- Ibf (6) 



In an isolated system in which capacitance has been neglected this 

 current is zero and equation (6) will be identical with {2a). 



The distribution of these currents in the network can be found as 

 follows. From equations (51) and (52) of the appendix the calculated 

 fault currents are transformed into sequence currents. By working 

 back into the original sequence networks the sequence currents in each 

 branch of the system can be found and later combined from similar 

 expressions as shown in (43) and (44) to obtain the actual branch 

 currents. 



A combination of the equations in (1) and (3) can be used for cases 

 involving faults to ground at one location and faults between phases 

 (not involving ground) at the other location. 



For faults to ground at A and between phases at B, the three first 

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

 constitute the most convenient set of equations for this type of fault. 



It should be noted that if all three phases are involved at B any two 

 of the three last equations in (3) together with the last in (3a) can be 

 used, while for less than three phases involved, the rules for striking 

 out rows and columns automatically will result in the proper equations 

 to be used. 



Vice versa the three first equations in (3) together with the first in 

 (3a) and the three last equations in (1) will give the solutions for 

 phase-to-phase faults at A and ground faults at B. 



This will be illustrated with an example in a later section. 



The voltages to ground at the two locations of faults can be obtained 

 directly from equations (53) and (54) of the Appendix, after the 

 currents have been evaluated. At any other point in the system the 

 voltages to ground are found by adding the voltage drops of the lines 

 in question to these voltages, treating each sequence network sepa- 

 rately, then adding the sequence voltages together according to 

 equations (46) or (47). 



