Introduction
The sequence circuits and the sequence networks developed in the previous chapter will now be used for finding out fault current during unsymmetrical faults.
Three Types of Faults
Calculation of fault currents
Let us make the following assumptions:
- The power system is balanced before the fault occurs such that of the three sequence networks only the positive sequence network is active. Also as the fault occurs, the sequence networks are connected only through the fault location.
- The fault current is negligible such that the pre-fault positive sequence voltages are same at all nodes and at the fault location.
- All the network resistances and line charging capacitances are negligible.
- All loads are passive except the rotating loads which are represented by synchronous machines.
Based on the assumptions stated above, the faulted network will be as shown in Fig. 8.1 where the voltage at the faulted point will be denoted by Vf and current in the three faulted phases are Ifa , I fb and I fc .
We shall now discuss how the three sequence networks are connected when the three types of faults discussed above occur.
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Fig. 8.1 Representation of a faulted segment.
Single-Line-to-Ground Fault
Let a 1LG fault has occurred at node k of a network. The faulted segment is then as shown in Fig. 8.2 where it is assumed that phase-a has touched the ground through an impedance Zf . Since the system is unloaded before the occurrence of the fault we have
 | (8.1) |
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Fig. 8.2 Representation of 1LG fault.
Also the phase-a voltage at the fault point is given by
 | (8.2) |
From (8.1) we can write
 | (8.3) |
Solving (8.3) we get
 | (8.4) |
This implies that the three sequence currents are in series for the 1LG fault. Let us denote the zero, positive and negative sequence Thevenin impedance at the faulted point as Z kk0 , Z kk1 and Z kk2 respectively. Also since the Thevenin voltage at the faulted phase is Vf we get three sequence circuits that are similar to the ones shown in Fig. 7.7. We can then write
 | (8.5) |
Then from (8.4) and (8.5) we can write
 | (8.6) |
Again since
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We get from (8.6)
 | (8.7) |
The Thevenin equivalent of the sequence network is shown in Fig. 8.3.
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Fig. 8.3 Thevenin equivalent of a 1LG fault.
