UNSYMMETRICAL FAULT CALCULATIONS – PART – 01 - INTRODUCTION TO SYMMETRICAL COMPONENTS

When the system is unbalanced the voltages, currents and the phase impedances are in general unequal.

Such a system can be resolved by a symmetrical per phase technique known as the method of symmetrical components or three-component method. 

The analysis of unbalanced cases is greatly simplified by the use of the technique of symmetrical components.

PROFILE OF FORTESCUE

Charles LeGeyt Fortescue (1876–1936) was an electrical engineer born in York Factory (Manitoba, Canada).

Fortescue demonstrated that any set of N unbalanced phasors — that is, any such "polyphase" signal — could be expressed as the sum of N symmetrical sets of balanced phasors known as symmetrical components.

This method was proposed in the year 1918.

The paper was judged to be the most important power engineering paper in the twentieth century.

He was awarded the Franklin Institute's 1932 Elliott Cresson Medal for his contributions to the field of electrical engineering.

A fellowship awarded every year by the IEEE in his name commemorates his contributions to electrical engineering. 

He was born in York Factory (Manitoba, Canada).

FORTESCUE’S THEOREM

An unbalanced set of n phasors may be resolved into (n-1) balanced n-phase systems of different phase sequence on one zero-phase sequence system. A zero-phase sequence system is one in which all phasors are of equal magnitude and angle or they are all identical.

PHASE SEQUENCE

A phase sequence is of the phasors is the order in which they pass through a positive maximum.

R Y B represents positive sequence

R B Y represents negative sequence

The direction of phasor rotation is anticlockwise.

SYMMETRICAL COMPONENT METHOD

According to Fortescue’s theorem, three unsymmetrical and unbalanced phasor voltages or currents of a three-phase system can be resolved into the following components.

1. POSITIVE-SEQUENCE COMPONENTS

Positive phase sequence component – A balanced system of three-phase currents/voltages having positive or normal phase sequence.

Three balanced phasors, equal in magnitude and displaced from each other by 120° same phase sequence as the original phasors (for example R-Y-B)

2. NEGATIVE-SEQUENCE COMPONENTS

Negative phase sequence component – A balanced system of three-phase currents/voltages having negative or opposite phase sequence.

Three balanced phasors, equal in magnitude and displaced from each other by 120° opposite phase sequence to the original phasors (for example R-B-Y)

3. ZERO-SEQUENCE COMPONENTS

Zero phase sequence component – A system of three-phase currents/voltages having equal magnitude and having zero phase displacement.

Three unbalanced phasors of a 3-phase system can be resolved into 3 balanced systems of phasors.

Three equal phasors, equal in magnitude and zero phase displacement from each other. 
The subscripts 1, 2 and 0 are generally used to indicate positive, negative and zero phase sequence.