Line-to-Line Fault

A line to line fault or unsymmetrical fault occurs when two conductors are short circuited. In the figure shown below shows a three phase system with a line-to-line fault phases b and c. The fault impedance is assumed to be Zf. The LL fault is placed between lines b and c so that the fault be symmetrical with respect to the reference phase a which is un-faulted.

line-to-line-faultThe symmetrical components of a fault current in phase ‘a’ at the fault point can be divided into three component. The zero sequence component of current at phase a is

line-to-line-fault-eqaution-1In the equation(1) Ib = -Ic. Positive sequence component of phase a is expressed as

line-to-line-fault-equation-2and the negative sequence component of phase a is given by the equation,

line-to-line-fault-equation-3The sequence current can also be found by matrix method

line-to-line-fault-equation-4Therefore, we get

line-to-line-fault-equation-5Expressing Va, Vb and Vc regarding voltages at the fault point are found by the relations given by

lint-to-line-equation-fault-equation-6Combination of equation (1), (4) and (5) gives

ine-to-line-fault-eqaution-7The sequence current of voltage at the fault point are determined by the relations shown below

line-to-line-fault-equation-7From equation (8) and (9) we get

line-to-line-fault-10Combination of equation (4), (10) and (9) gives

Line-to-line-fault-equation-8The fault current is given by the equation

line-to-line-fault-equation-10From equation (1) it is clear that the line-to-line fault the zero sequence component of current Ia0 is equal to zero. Equation (4) shows that the positive-sequence component of current is opposite in phase to the negative-sequence component of current

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