Concept of Symmetrical Components

Being an Electrical Engineer, it is very important to have clear concept of Symmetrical Components used for the analysis of fault or unbalance in a Power System. Basically Symmetrical Components are mathematical modeling used to simplify the calculation while maintain the physical significance of components.

The concept of Symmetrical Components can be stated as:

A system of n vectors or quantities can be resolved into n different symmetrical group or system, one of which consists of equal vectors and remaining (n-1) systems consists of n equi-spaced vectors.

 Let us consider a three phase system. Any three coplanar vectors V_a, V_b and V_c can be expressed in terms of three new vectors V₁, V₂ and V₃by three simultaneous linear equation with constant coefficients. Thus,

V_a = a₁₁V₁+ a₁₂V₂ + a₁₃V₃

V_b = a₂₁V₁+ a₂₂V₂ + a₂₃V₃

V_c = a₃₁V₁+ a₃₂V₂ + a₃₃V₃

Thus we observe that each of the original vectors has been replaced by three different vectors and can be found by solving the above equations. This is the origination of concept of Symmetrical Components.

According to the concept, three unbalanced vectors V_a, V_b and V_c can be replaced by a set of three balanced system of vectors. Therefore the solution of above simultaneous equation must be unique. The three symmetrical components vectors replacing V_a, V_b and V_c are Positive Sequence, Negative Sequence and Zero Sequence.

Positive Sequence:

Positive Sequence components are those which have three vectors of equal magnitude but displaced in phase from each other by an angle of 120� and have the phase sequence same as the original vectors. Phase sequence means the direction of rotation of vectors.

Negative Sequence:

Negative Sequence components are having equal magnitude and displaced from each other by an angle of 120� but the direction of rotation of the vectors are opposite to the direction of rotation of original vectors. Figure below depicts the sequence voltages for three phase system.

Zero Sequence:

Zero Sequence components have an awesome property.  They are equal in magnitude and phase as shown in figure above.

Notice that Positive Sequence components are designated by subscript 1, Negative Sequence by subscript 2 and Zero Sequence by subscript by 0. Theses subscripts are generally adopted to denote sequence components.