For the analysis of unsymmetrical faults in the power system network, we require sequence impedance and sequence network concept along with the symmetrical components.

The analysis problem will involve positive, negative, and zero sequence components along with its sequence impedance and sequence network.

## Assumptions for Analysis of Unsymmetrical Faults

We make the following assumptions when an unsymmetrical fault occurs in a power system network thereby introducing unbalance conditions.

- All the impedance are constants and also they are independent of the currents.
- The negative and zero sequence impedance which the generator generates during the fault condition is negligible and therefore we can neglect it. Hence, we assume that the machine is only generating positive sequence emf.

So, let us consider a power system network where fault (F) occurs on the transmission side.

With the above assumptions, we can represent the above power system network by three independent single-phase networks as follows.

Each of these networks represents the positive, negative, and zero sequence networks respectively.

Also, we can replace these networks by its Thevenin’s equivalent circuit between the two terminals. These terminals consist of a reference bus and the point of occurrence of the fault. These networks are illustrated more descriptively below.

### Positive Sequence Network

The figure below shows the positive sequence network along with its Thevenin’s equivalent circuit for the power system network that we are discussing above.

Meanwhile, the voltage V_{f} in Thevenin’s circuit is the pre-fault voltage across the fault point and the reference bus.

Z_{1} is the impedance between the fault point F and the reference bus when all the EMFs are short-circuited.

### Negative Sequence and Zero Sequence Network

The figure below shows the negative and zero sequence network along with its Thevenin’s equivalent circuit for the power system network that we are discussing above.

As there are no negative and zero sequence currents flowing before the occurrence of the faults hence, in Thevenin’s equivalent circuit no emf source appears.

The impedance Z_{0} and Z_{2 }are the impedance between the fault point and the reference bus in their respective networks.

### Fault Impedance in Analysis of Unsymmetrical Faults

In some cases the faults occurring may not be a complete short circuit between the lines or the ground. Hence, there may be the presence of some impedance which results in fault impedance Z_{f}.

Under such conditions, we have to add 3 times of Z_{f} i.e. 3Z_{f }in series with the zero-sequence network.

## Sequence Components of Currents and Voltages for Analysis of Unsymmetrical Fault

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

General equivalent equations

Line-To-Line Fault (L-L)

General equivalent equations

Sequence components of currents at the fault point

Sequence components of voltages across the fault

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

General equivalent equations

Sequence components of currents at the fault point

Sequence components of voltages across the fault

## Procedure for Analysis of Unsymmetrical Faults

We have to undergo the following procedure for the analysis of unsymmetrical faults.

- Firstly inspect the single line diagram of the power system network. Then draw the sequence impedance diagram. If there is the presence of earth fault then draw the zero sequence diagram also.
- Secondly set the vault of the sequence impedance in each of the networks.
- Thirdly, reduce the network in their equivalent impedances as Z
_{1}, Z_{2,}and Z_{0}. - Furthermore, connect the equivalent networks as discussed above. Doing so carefully observe the type of faults occurring (it may be L-L, L-L, L-L-G).
- Further, we have to obtain the sequence components of the currents and the voltage. We can obtain this by using the equations discussed above.
- Finally, obtain the currents in different phases from the sequence components of currents. For this also we have to use the equations discussed above.
- Further, if we have to calculate the voltage then we can do so by the knowledge of impedances and sequence networks.

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