Consider a single line- to- ground fault from phase a to ground at the general three- phase bus shown in Fig. 9.7(a). For generality, we include a fault impedance ZF. In the case of a bolted fault, ZF=0, whereas for an arcing fault ZF is the arc impedance. In the case of a transmission line insulator flashover, ZFincludes the total fault impedance between the line and ground including the impedances of the arc and the transmission tower, as well as the tower footing if there are no neutral wires.

The relations to be derived her e apply only to a single line-to-ground fault on phase a. However since any of the three phases can be arbitrarily labeled phase a, we do not consider single line-to-ground faults on other phases.

From Fig. 1:

Fault conditions in phase domain     Ib=Ic=0               (1)
Single line-to-ground fault          Vag=ZFIa              (2)

Fig. 1 Single Line-to-Ground Fault in General three phase bus

- Line-to-Line Fault

Consider a line-to-line fault from phase b to c, shown in Fig. 2. Again we include a fault impedance ZFfor generality. From Fig. 2:

       Fault conditions in phase domain        Ia=0                  (3)
       Line-to-Line fault                      Ic=-Ib                 (4)
                                             Vbg-Vcg=ZFIb         (5)

Fig. 2 Line-to-Line Fault in General three phase bus

- Double Line-to-Ground Fault

A double line-to-ground fault from phase b to c through fault impedance ZF to ground is shown in Fig. 3. From this Fig.:

   Fault conditions in the phase domain               Ia=0              (6)
   Double line-to-ground fault                       Vcg=Vbg           (7)
                                                  Vbg=ZF(Ib+Ic)       (8)
   Transforming (6) to the sequence domain          I0+I1+I2=0          (9)

Fig. 3Double Line-to-Ground Fault in General three phase bus