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BELL SYSTEM TECHNICAL JOURNAL 

 Isolated System — Capacitance Neglected 



(2) 



lAa + lAb + Iac + Ibg + Isb + Ibc = (2a) 



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

 been used. The values of the 5's are given in Table I and Table II. 



In case of faults to ground on less than three phases, as in equations 

 (1), columns and rows associated with sound phase currents are to be 

 deleted; with respect to the rows, however, the index is double and 

 all rows having the index of the sound phase or phases are deleted. 

 If, for example, the sound phase is Aa, rows 1 and 2, each of which 

 contains Aa in its index, as well as column 1, are deleted. This leaves 

 only four equations, which together with (2a) give the necessary five 

 equations for the five currents. For this reason all six equations are 

 given in (2), since any phase might be involved in special cases. 



Phase-to-phase faults are obtained from the general case (1) by 

 allowing the resistances Raf and Rbf to become infinite. In this case 

 phase-to-phase quantities at the same location remain finite and the 

 appropriate set of equations is obtained by subtracting equations 

 having the corresponding phase indexes; thus Aa — Ab, Aa — Ac and 

 Ab — Ac indicate subtractions at A. There are six possible ways of 

 doing this, ignoring reversals of sign. The resulting set is given in (3). 

 The four equations obtained by taking any two of the first three and 

 any two of the last three equations in this set together with the two 

 equations (3a) relating to the sum of the currents at each fault location, 

 which from physical considerations equal zero, constitute an inde- 

 pendent set. For convenience in dealing with special cases all eight 

 equations are given below: 



Phase-to-Phase Faults 



lAa + lAb + I Ac — 

 iBa + iBb -\- I Be = 



(3) 



iU) 



