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 Zf . 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 Zf 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.
