# Analysis of power systems by symmetrical components

**Analysis (using matrices) of power systems by symmetrical components under**:

(a) **Three phase short circuit**.

The analysis of the three phase electrical power system is done basically by the symmetrical components.Here the three phase voltage is expressed in the form of the phasor notation.

The quantity V with the subscript 0, and 2 denotes the voltage component in the zero,positive and negativephase sequence components respectively.The phase sequence components differ by the phase angle of 120^{0 }

It is to be noted that α ^{3 }=1 so that α^{-1}= α^{2
}

The** Zero sequence** components are equal in the magnitude and are in phase with each other.The **positive sequence** components are equal in the magnitude with the phase difference of 120^{0} and has same phase sequence as the original vector.The **negative sequence** components are e equal in the magnitude with the phase difference of 120^{0 } but opposite in phase with the original vector.

So the voltage component can be written in the matrix form as,

The value of the V_{012} can be written as given below,

The sequence components are generated as,

where

**b)LINE TO line FAULT ANALYSIS**

In the line to line fault analysis the boundary conditions are:

V_{a }= 0

I_{b }= 0

I_{c}= 0

we will write sequence network equation:

**Putting the above boundary condition we get,**

Which further results,

I_{a0} = I_{b0 }= I_{c0 }= I_{a}/3

Sequence network equation in the matrix form can thus be obtained as,

On solving it we get,

V _{a0 }= – I_{a1 }Z_{0}

V _{a1} = E_{a }– I_{a1} Z_{1}

V _{a2 }= – _{ }I_{a1} Z_{2}

**c) LINE TO GROUND FAULT ANALYSIS**

_{ }

The boundary condition in the line to ground fault analysis will be,

1) I_{a }= 0

2) I_{a} + I_{b }=0

3) V_{b} – V_{c} = 0

Using the boundary condition we get,

The above matrix equation becomes as,

From the above equations we can find that in the line to line fault the zero sequence component of current is absent

The sequence network equation can be written as,

next steps are given as below,

I.e E_{1 } – I_{a1 }Z_{1} = – I_{a2}Z_{2}

which gives_{,}

I_{a1} = E_{1}/( Z_{1 }+ Z_{2 })

**D) double line to ground fault analysis**

** **

The boundary conditions in double line to ground fault analysis based upon the circuit dig. Given above

I_{a} =0

V_{a} = V_{b} = 0

The sequence network components are calculated as follows,

The second term of the matrix is taken to left side of the equation for easier calculation,

Hence we obtain the positive seq component as given below…similarly the others can be calculated.

** FAULT SEQUENCE NETWORK INTERCONNECTIONS FOR THE FAULTS..
**

Calculating the three phase fault is a bit easier task than for the unbalanced loads.It requires some imaginations and better concepts.

The sequence network diagram can be illustrated as the diagram which shows the positive,negative,zero sequence components of the network drawn separately then the connection is done according to the fault.

**1)line to ground fault**

**2)line to line fault**

**3) line to line fault**

** **

**RELATED QUESTIONS-ANSWERS**

**1.what are the boundary conditions for L-L and L-L-G fault.
**

** **In the line to line fault analysis the boundary conditions are:

V_{a }= 0

I_{b }= 0

I_{c}= 0

The boundary conditions in double line to ground fault analysis

I_{a} =0

V_{a} = V_{b} = 0

**2.Name the different types of faults which are taken into account**

The different types of the faults are-

- three phase fault
- L-L fault
- L-L-G fault
- L-G fault

**3.what is meant by the sequence network diagram**

The sequence network diagram can be illustrated as the diagram which shows the positive,negative,zero sequence components of the network drawn separately then the connection is done according to the fault.

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This article contains the information about the analysis of power system , how the power is analyed, used everything is explained here. For the ones who have interest in power and its measurement can refer this .

An electric power system is a network of electrical components used to supply, transmit and use electric power.and the analysis of this electric power by the symmetrical component is beautifully explained here.electrical people can get idea about it.