The types of faults occurring in power systems are symmetrical and unsymmetrical faults. The 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 faults give rise to unsymmetrical currents therefore different fault currents flow in different phases.

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

## Types of Unsymmetrical Faults

Following are the types of unsymmetrical faults in the power system.

### Balanced Three-Phase Unsymmetrical Faults

In balanced three-phase unsymmetrical faults, the fault occurs when all the three phases of the transmission line or the terminals of the machine come in contact with each other.

Here let us consider an unloaded three-phase star-connected alternator. There is balanced three-phase unsymmetrical faults 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 the above matrix form we have,

Finally, we have,

In the case of a balanced three-phase unsymmetrical faults, only the positive sequence network is present in the solution.

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

For single line-to-ground unsymmetrical faults, we consider a synchronous generator where a fault occurs at the ‘a’ phase of the generator with the fault impedance of Z_{f}.

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

Under the single line-to-ground unsymmetrical faults condition, 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 the above equation

Further, we have,

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

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

Also, 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)

For line-to-line unsymmetrical faults, 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 the condition of line-to-line unsymmetrical faults

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 phases 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 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 the double line-to-line fault of the 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.

**ENGINEERING NOTES ONLINE: FAULTS IN POWER SYSTEM**

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