# Unsymmetrical Faults

The types of faults occurring in power systems are symmetrical and unsymmetrical faults. Unsymmetrical fault is the type of fault in which the three phase line of the system becomes unbalanced therefore giving rise to unbalanced currents in the different phases.

In brief the types of unsymmetrical faults we will be discussing are:

- Single line-to ground fault (SLG)
- Line-to-line fault (L-L)
- Double line-to-ground fault (2LG)
- Balanced three-phase fault

Unsymmetrical fault give rise to unsymmetrical currents therefore different fault currents flows in different phases.

Here we will be discussing the types of unsymmetrical faults in relation to a synchronous generator operating at no load.

## Types of Unsymmetrical Faults

Following are the types of unsymmetrical faults in power system.

### Balanced Three Phase Unsymmetrical Faults

This type of fault occurs when the all the three phases of the transmission line or the terminals of the machine comes in contact with each other.

Here let us consider an unloaded three phase star connected alternator. There is three phase fault occurring at the terminals of the generator as a result the phase currents (I_{a}, I_{b} and I_{c}) and voltages to be zero.

Firstly here,

Where, Z_{n} is the impedance through which generator neutral is earthed.

Secondly, representing above relations in matrix form

Further from above matrix form we have,

Finally we have,

In case of three phase fault, only the positive sequence network is present in the solution.

### Single Line-To-Ground Fault (L-G)

Here we consider a synchronous generator where a fault occurs at ‘a’ phase of the generator with the fault impedance of Z_{f}.

The generator is grounded through an impedance of Z_{n}.

Under the condition of fault, firstly we have

Here we use the symmetrical components and represent the fault currents by substituting the above values. As I_{b}=0 and I_{c}=0.

Secondly, from above equation

Further we have,

From sequence network of synchronous generator we have the positive, negative and zero sequence voltages as,

Moreover, substituting the value of equation (i) and (ii) in above equations we have

In addition, we know that

So,

Therefore we have the expression of current as,

Finally, the figure below shows the sequence networks representing the L-G fault.

### Line-To-Line Fault (L-L)

Here we consider a synchronous generator where a line-to-line fault occurs on the phases ‘b’ and ‘c’ with a fault impedance of Z_{f}.

Firstly, under line-to-line fault condition

Here we use the symmetrical components and represent the fault currents by substituting the above values.

Secondly, from this relation we have

Similarly, representing the voltages in terms of symmetrical components.

Further from this equation we have,

Solving the above two equations for V_{a1} and V_{a2}.

As I_{a2 }= – I_{a1} and I_{a} =0 so,

Moreover from equation (iii) and (iv) we have

Finally the figure below shows the sequence network of L-L fault occurring on phase b and c of the generator.

In the terms of Thevenin’s equivalent circuit, the currents are

### Double Line-to-Ground Fault (L-L-G)

Here we consider a synchronous generator where a double line-to-ground fault occurs on between phases ‘b’, ‘c’ and ground with a fault impedance of Z_{f}.

Under the condition of fault

The symmetrical components of voltages are

From the above equation

Now, subtracting V_{a1} from V_{a0}.

The figure below shows the sequence network of double line-to-line fault of generator.

In the terms of Thevenin’s equivalent circuit, the currents are

In the cases of direct short-circuit for all the above fault cases, take Z_{f }=0.

## Leave a Reply