The method of symmetrical components is a mathematical technique that allows the engineer to solve unbalanced systems using balanced techniques. The method of symmetrical components is particularly suited to fault analysis.

This method is formulated by Chalrles Legeyt Fortescue, one of our Engineering Heroes.

Below are high quality links to help further explain, illustrate and give you and idea on the applications of Methods of Symmetrical Components:

Symmetrical Components and Unbalanced Faults
When an unbalanced three-phase fault occurs, we can solve the three-phase circuit using  ordinary circuit theory. This is much more numerically complicated than the single phase circuit normally used in balanced three phase circuits.  The degree of difficulty  increases with the third power of the system size.  For this reason, it is apparent that if we  were to solve three different single-phase circuits, it would be numerically simpler than  solving the one three-phase circuit in one set of equations.

The purpose of this chapter is to break up the large three-phase circuit into three circuits,  each one third the size of the whole system.  Next, we solve the three components  individually, and then combine the results to obtain the total system response.  Read more...

Symmetrical Components Overview
The method of symmetrical components is a mathematical technique that allows the engineer to solve unbalanced systems using balanced techniques. Developed by C. Fortescue and presented in an AIEE paper in 1917, the method allows the development of sets of balanced phasors, which can then be combined to solve the original system of unbalanced phasors.

The Sequence Networks
1. For any three phase system, three sets of independent sequence components can be derived for both voltage and current.
2. Since the three sequence components are independent, we may infer that each sequence current flows in a unique network creating each sequence voltage.  Read more...

Symmetrical Components Presented By Siemens Electric
In a balanced 3 phase system it is possible to treat  each phase as an independant single phase. The other  phases follow with fixed 120°phase displacement.

 Due to Charles LeGeyt Fortescue (1918): "a set of n unbalanced phasors in an n-phase system can be  resolved into n sets of balanced phasors by a linear  transformation” The n sets of balanced phasors are called symmetrical components In the 3 phase system n = 3

Symmetrical Components Tutorials Video 

A Derivation of Symmetrical Component Theory and Symmetrical Component Networks

This paper provides a review of some of the theory behind symmetrical component analysis and  derives some of the basic calculations utilized in power system analysis for short circuit and open phase conditions.

The paper starts with a review of the concepts of system impedances in the phase (ABC) domain and develops the three phase, two port, voltage drop equation, VS - VR = Z·I, in substantial detail. Then, the paper reviews symmetrical component (012) domain theory. The paper shows the conversion of the ABC domain voltage drop equation to the equivalent 012 domain voltage drop equation and, in the process, correlates the terms ZS, ZM, Z0, Z1, Z2, and other impedances and presents the relationship between the ZABC and Z012 impedance matrices. Read more...

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