Line-to-Line Fault

The faulted segment for an L-L fault is shown in Fig. 8.5 where it is assumed that the fault has occurred at node k of the network. In this the phases b and c got shorted through the impedance Z_f . Since the system is unloaded before the occurrence of the fault we have

(8.8)

Fig. 8.5 Representation of L-L fault.

Also since phases b and c are shorted we have

(8.9)

Therefore from (8.8) and (8.9) we have

(8.10)

We can then summarize from (8.10)

(8.11)

Therefore no zero sequence current is injected into the network at bus k and hence the zero sequence remains a dead network for an L-L fault. The positive and negative sequence currents are negative of each other.

Now from Fig. 8.5 we get the following expression for the voltage at the faulted point

(8.12)

Again

(8.13)

Moreover since I _fa0 = I _fb0 = 0 and I _fa1 = - I _fb2 , we can write

(8.14)

Therefore combining (8.12) - (8.14) we get

(8.15)

Equations (8.12) and (8.15) indicate that the positive and negative sequence networks are in parallel. The sequence network is then as shown in Fig. 8.6. From this network we get

(8.16)

Fig. 8.6 Thevenin equivalent of an LL fault.

Double- Line -to Ground Fault

The faulted segment for a 2LG fault is shown in Fig. 8.7 where it is assumed that the fault has occurred at node k of the network. In this the phases b and c got shorted through the impedance Z_f to the ground. Since the system is unloaded before the occurrence of the fault we have the same condition as (8.8) for the phase-a current. Therefore

(8.17)

Fig. 8.7 Representation of 2LG fault.

Also voltages of phases b and c are given by

(8.18)

Therefore

(8.19)

We thus get the following two equations from (8.19)

(8.20)

(8.21)

Substituting (8.18) and (8.20) in (8.21) and rearranging we get

(8.22)

Also since I _fa = 0 we have

(8.23)

The Thevenin equivalent circuit for 2LG fault is shown in Fig. 8.8. From this figure we get

(8.24)

The zero and negative sequence currents can be obtained using the current divider principle as

(8.25)

(8.26)

Fig. 8.8 Thevenin equivalent of a 2LG fault.