Analysis of power systems by symmetrical components

May 18 • Notes • 4847 Views • 2 Comments on 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 phase voltage can be expressed as above

The phase voltage can be expressed as above

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

It is to be noted that α 3 =1 so that α-1= α2

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 1200 and has same phase sequence as the original vector.The negative sequence components are e equal in the magnitude  with the phase difference of 1200  but opposite in phase with the original vector.

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

voltage component in the matrix form

voltage component in the matrix form

The value of the V012 can be written as given below,

value of the voltage component taken into account

value of the voltage component taken into account

The sequence components are generated as,

generated sequence components

generated sequence components

where

The value of the inverse of matrix A

The value of the inverse of matrix A

b)LINE TO line FAULT ANALYSIS

circuit diagram for line to ground fault analysis

circuit diagram for line to ground fault analysis

 

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

Va = 0

Ib = 0

Ic= 0

we will write sequence network equation:

 sequence network equation

sequence network equation

Putting the above boundary condition we get,

using the boundary condition above result is obtained.

using the boundary condition above result is obtained.

Which further results,

Ia0 = Ib0 = Ic0 = Ia/3

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

sequence network equation thus obtained

sequence network equation thus obtained

On solving it we get,

V a0   = – Ia1 Z0

V a1 = Ea – Ia1 Z1

V a2  =  –  Ia1 Z2

c) LINE TO GROUND FAULT ANALYSIS

circuit diagram for line to ground fault analysis

circuit diagram for line to ground fault analysis

 

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

1)      Ia   = 0

2)      Ia + Ib =0

3)      Vb – Vc  = 0

Using the boundary condition we get,

The system components

The system components

The above matrix equation becomes as,

after using the boundary condition

after using the boundary condition

 

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,

 

now the sequence network equation can be written as above

now the sequence network equation can be written as above

next steps are given as below,

further description of the calculation

next steps of the calculation

 I.e E1  – Ia1 Z1 = – Ia2Z2

which gives,

Ia1 = E1/( Z1 + Z2 )

D) double line to ground fault analysis

 

The diagram of double line to ground fault

The diagram of double line to ground fault

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

Ia =0

Va = Vb = 0

The sequence network components are calculated as follows,

sequence network equation can be calculated as it

sequence network equation can be calculated as it

further steps

further steps

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

 

next calculation

next calculation

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

final expression

final expression

 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

 

line to ground fault occurance

line to  ground fault occurrence

2)line to line fault

 

line to line fault occurance

double line to ground fault occurrence

3) line to line fault

double line to ground fault occurance

 

 

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:

Va = 0

Ib = 0

Ic= 0

The boundary conditions in double line to ground fault analysis

Ia =0

Va = Vb = 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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2 Responses to Analysis of power systems by symmetrical components

  1. patlakshi Jha says:

    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 .

  2. Rachita Mishra says:

    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.

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