Unbalanced Fault Analysis: Line to Line Fault

Line to Line Fault

Line to line fault happens when two phases of the three phase line accidentally connected each other. In this case, the fault current will flow for both phases involved. From the given diagram, the fault occurs in phases B and C while phase A remain unfaulted.

From this scenario, the system parameters can be considered as follows:

• Fault current at phase A = 0 (since no fault current is flowing in phase A)
• Fault current at phase B = If-A
• Fault current at phase C = If-C. 
• Here we can also see that voltages at phase B and phase C will be equal during fault, thus VB = VC.

See article: How to Develop Sequence Network in an Unbalanced System?

Using sequence network matrix formula, we can plot the given values as follows. 

Symmetrical Components Matrix Formula in Line to Line Fault

From this matrix equation, we can get a value of,

• Ia0 = 0
• Ia1 = - Ia2

Which means, the zero sequence current in a Line to Line fault is not involved while the positive sequence current and negative sequence current is opposing each other. 

In the sames sense, the matrix formula can also gives us the value of the voltages, 

Symmetrical Components Matrix Formula of Line to Line Fault

Note that in this case, VB = VC. By manipulating equations we can get Va1 = Va2. 

From the result of two matrix equations involving current and voltage, we can develop a sequence network which describes as that the positive and negative sequence is in parallel with each other. 

Equivalent Sequence Network for Line to Line Fault

This figure satisfies the equation Va1 = Va2 and Ia1 = (-Ia2).

For sample calculation, see the following article Example: Line to Line Fault Calculation