## SYMMETRICAL COMPONENTS IN POWER SYSTEM ANALYSIS BASIC AND TUTORIALS

Symmetrical Components, first developed by C.L.Fortescue in 1918, is a powerful technique for analyzing unbalanced 3f systems. Fortescue defined a linear transformation from 3f components to a new set of components called symmetrical components.

The advantage of this transformation is that for balance three phase networks the equivalent circuit obtained for the symmetrical components, called sequence networks, are separated into three uncoupled networks.

Further more, for unbalanced three phase systems, the three sequence networks are connected only at the points of unbalance. As a result, sequence networks for many cases of unbalanced three phase systems are relatively easy to analyze.

The symmetrical component method is basically a modeling technique that permits systematic analysis and design of three phase systems. Decoupling a detailed three phase network into three simpler sequence networks reveals complicated phenomena in more simplistic terms.

Sequence network results can then be superimposed to obtain three phase results. The application of symmetrical components to unsymmetrical fault studies is indispensable.

DEFINITION OF SYMMETRICAL COMPONENTS:
In accordance with Fortescue, the three phase voltages, VR , VY , and V B are resolved into three sets of sequence components:

1. Zero sequence, consisting of three phasors with equal magnitudes and with zero phase displacement.

2. Positives equence, consisting of three phasors with equal magnitudes, ±120 o phase displacement and positive sequence.

3. Negative sequence, consisting of three phasors with equal magnitudes, ±120 o phase displacement and negative sequence.

NOTES:
1. The sequence components do not exist as physical quantities in the network.

2. A balanced system has no negative or zero sequence components therefore: actual balanced system = positive sequence system

3. The generated emf is balanced, and therefore positive phase sequence only.

4. In a 3phase 3wire system, there are no zero sequence components, because there is no neutral connection.