To determine the performance or behavior of the power system under the unbalanced condition it is essential to know the impedances offered by the different power system elements. The impedance is offered by the different power system elements due to the flow of different phase sequence components of the current because of unbalanced loads or unsymmetrical faults. The knowledge of sequence impedance and sequence network is crucial for unsymmetrical fault analysis.

## Sequence Impedance

Sequence impedance of a power system network is positive, negative, and zero sequence impedances.

Positive sequence impedance is the impedance offered by the power system network due to the flow of the positive sequence component of the current.

Similarly, negative sequence impedance is the impedance offered by the power system network due to the flow of the negative sequence component of the current. And, zero sequence impedance is the impedance offered by the power system network due to the flow of zero sequence components of the current.

For a three-phase power system network with phases a, b, c, and n being neutral. Let Z_{a}, Z_{b,} and Z_{c} be the impedance of the load between phases a, b, and c respectively to neutral n.

The sequence impedance then is given by:

Positive sequence impedance is;

Negative sequence impedance is;

Zero sequence impedance is;

### Sequence Impedance Overview

For static devices, the positive and negative sequence impedance is the same. For rotating machines, the impedance offered by the positive sequence components of the current is different from that of the negative sequence components of the current. The zero sequence impedance is different from positive and negative sequence impedance. The zero sequence impedance includes the impedance of the return path through the ground.

For a transmission line, positive and negative sequence impedances are equal while zero sequence impedance is very large compared to positive or negative sequence impedance.

## Sequence Network

Corresponding to the positive, negative, and zero sequence components of the currents there are positive, negative, and zero sequence networks.

A sequence network of a particular sequence is a single-phase equivalent circuit composed of the impedance offered to the current of that particular sequence.

For every power system network, we can form a sequence network carrying the sequence components of current which can be interconnected in different ways to represent the different unbalanced fault conditions. The actual fault currents and voltages can be determined by computing the sequence currents and voltages during the fault.

For symmetrical fault analysis, a positive sequence network is considered. A positive sequence network is similar to a reactance diagram. A negative sequence network is similar to a positive sequence network but differs in the following ways:

- It doesn’t contain any emf source as there are no negative emf sources.
- The negative sequence impedance of rotating machines is different from that of positive sequence impedance. So, for rotating machines positive and negative sequence networks are different.

Zero sequence networks will also be free from internal voltages.

For a 3-phase symmetrical static circuit such as transmission lines and transformers, there is no mutual coupling between the sequence networks. This means the currents and impedance of a particular sequence will cause a voltage drop of that sequence only.

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