Single Line-to-Ground Fault

Generally, a single line-to-ground fault on a transmission line occurs when one conductor drops to the ground or comes in contact with the neutral conductor. Such types of failures may occur in power system due to many reasons like high-speed wind, falling off a tree, lightning, etc.

Circuit diagram of single line-to-ground fault

Suppose the phase a is connected to ground at the fault point F as shown in a figure below. I_a, I_b and I_c are the current and V_a, V_b and V_c are the voltage across the three phase line a, b and c respectively. The fault impedance of the line is Z_f.

Since only phase a is connected to ground at the fault, phase b and c are open circuited and carries no current; i.e fault current is I_a and I_b = 0, I_c = 0. The voltage at the fault point F is V_a = Z_f I_a.

The symmetrical component of the fault current in phase “a” at the fault point can be written as

This relation can also be found by matrix method as follows:-

In the case of a single line-to-ground fault, the sequence currents are equal. The sequence voltage at the fault point is determined by the equations:-

Where, E_a0, E_a1, and E_a2 are the sequence voltages of phase a, and Z_a0, Z_a1 and Z_a2 are the sequence impedances to the flow of currents I_a0, I_a1, and I_a2 respectively. For a balanced system

We know that

On substituting the I_a0 = I_a1 = I_a2 = I_a in above equation we get,

The sequence current is given by equation,