# Types of Fault

In the following, a single voltage source in series with an impedance is used to represent the power network as seen from the point of the fault. This is an extension of Thevenin's theorem to three-phase systems. It represents the general method used for manual calculation, that is the successive reduction of the network to a single

**Figure 7.10 **Typical transmission link and form of associated sequence networks

impedance and voltage or current source. The network is assumed to be initially on no-load before the occurrence of the fault, and linear, so that superposition applies.

## Single-Line-To-Earth Fault

The three-phase circuit diagram is shown in Figure 7.11, where the three phases are on open-circuit at their ends.

Let I1,1_{2} and I0 be the symmetrical components of I_{R} and let V1, V_{2} and V0 be the components of V_{R}. For this condition, V_{R} = 0, I_{B} = 0, and I_{Y} = 0. Also, Z_{R} includes components Z1, Z_{2}, and Z0.

From equation (7.4)

**Figure 7.11 **Single line-to-earth fault-Thevenin equivalent of system at point of fault

Hence,

Also,

Eliminating Io and I_{2}, we obtain
hence

The fault current,

So

**Figure 7.12 **Pre- and post-fault phasordiagrams-single-line-to-earth fault

The e.m.f. of the Y phase = a^{2}E, and (from equation (7.4))

The pre-fault and post-fault phasor diagrams are shown in Figure 7.12, where it should be noted that only V_{yB} remains at its pre-fault value.

It is usual to form an equivalent circuit to represent equation (7.5) and this can be obtained from an inspection of the equations. The circuit is shown in Figure 7.13 and it will be seen that Ii = I_{2} = I0, and