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 V_{1}, V_{2}and V_{3}by three simultaneous linear equation with constant coefficients. Thus,
V

_{a}= a_{11}V_{1}+ a_{12}V_{2}+ a_{13}V_{3}_{}

V

_{b}= a_{21}V_{1}+ a_{22}V_{2}+ a_{23}V_{3}_{}

V

_{c}= a_{31}V_{1}+ a_{32}V_{2}+ a_{33}V_{3}_{}

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the original vectors has been replaced by three different vectors and can be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.

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