THREE-PHASE POWER SYSTEMS 293 



The six equations are written in matrix form with the currents and 

 voltages outside the system matrix. For example the first row in (1) 

 is interpreted as : 



AuIau + AniAh + AuIac + AulBa + ^15/b6 + AuIbc = SE 



The values of the ^'s in (1) are given in Table I. It should be noted 

 that of the 36 constants only 13 are distinct. Six of these are in the 

 nature of self-impedances, two are transfer impedances between phases 

 at A and two between phases at B. The remaining three are transfer 

 impedances between the two faults at A and at B. 



Considerable reductions in the constants are obtained when the 

 positive and negative sequence impedances are assumed equal. These 

 values are given in Table II. 



Faults to ground on less than three phases at one or both locations 

 are accounted for by assuming the corresponding fault resistances in- 

 finitely large. The currents to ground in the sound phases are zero. 

 Striking out the columns containing these currents and the correspond- 

 ing rows, indicated by the index at right in equation (1), a reduced 

 set of equations is obtained from which the desired currents can be 

 found. A few examples are given in subsequent sections. 



In power networks with isolated neutral the zero sequence impedance 

 Zco reduces essentially to the capacitance of the system. In this 

 case equations (1) are still appropriate and will give a rigorous solution 

 for the six currents. However, in many cases it is sufficiently accurate 

 to neglect the capacitance of the system. This results in infinitely 

 large values of all of the A's in Table I (Table II), since each depends 

 on Zco which is infinitely large. For this condition it is desirable to 

 transform the set of equations in (1) to a more convenient set with 

 finite constants. 



The transformation required is obtained by observing that, with 

 Zco infinitely large, the sum of the zero sequence currents Iao + Ibo 

 must be equal to zero. Making use of this relation the difference of 

 the zero sequence voltages at A and B (equation (50) of appendix) 

 reduces to : 



Vaq — Vbo — [Zao ~\~ Z bo) I BO 



The last equation shows that subtraction of equations associated 

 with phases at A from those at B removes the infinitely large element 

 Zco- This can be done in nine ways (ignoring reversals of sign), but 

 three of these result in the single equation : 



/.4a + /.-Ift + I Ac + /fia + iBb + Ibc = 



This equation with any five of the remaining six constitutes an inde- 

 pendent set; for convenience in dealing with special cases the redundant 

 set of seven equations is shown in the following array : 



