Analysis of power systems by symmetrical components

May 18 • Notes • 7948 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 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 120⁰ 

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

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

value of the voltage component taken into account

The sequence components are generated as,

generated sequence components

where

The value of the inverse of matrix A

b)LINE TO line FAULT ANALYSIS

circuit diagram for line to ground 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:

sequence network equation

Putting the above boundary condition we get,

using the boundary condition above result is obtained.

Which further results,

I_a0 = I_b0 = I_c0 = I_a/3

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

sequence network equation thus obtained

On solving it we get,

V _a0   = – I_a1 Z₀

V _a1 = E_a – I_a1 Z₁

V _a2  =  –  I_a1 Z₂

c) 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)      I_a   = 0

2)      I_a + I_b =0

3)      V_b – V_c  = 0

Using the boundary condition we get,

The system components

The above matrix equation becomes as,

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

next steps are given as below,

next steps of the calculation

 I.e E₁  – I_a1 Z₁ = – I_a2Z₂

which gives_,

I_a1 = E₁/( Z₁ + Z₂ )

D) double line to ground fault analysis

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

I_a =0

V_a = V_b = 0

The sequence network components are calculated as follows,

sequence network equation can be calculated as it

further steps

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

next calculation

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

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 occurrence

2)line to line fault

double line to ground fault occurrence

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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