The Role of Fault Quotient in Determination of the Distance to a Transmission Line Fault

The notion of fault quotient refers to single-phase-earth and phase-to-phase faults in one-terminal and two-terminal (double fed), single or parallel power lines at determination of the distance to a fault place using the apparent impedance method. The fault quotient is determined as the ratio of the current through a fault place (fault current) to the current in a faulty phase at single-phase-earth faults and to the difference of currents in faulty phases at phase-to-phase faults. For one-terminal lines at single-phase-earth faults, neglecting capacitive and load currents, this ratio is 1, and for phase-to-phase faults it equals 1/2. For other cases it is a complex quantity, with the absolute value > 1 for single-phase-earth faults. Its significance grows with the fault resistance R_f. At R_f = 0 this ratio loses its significance for determination of the distance to a fault place. The tangent of the fault quotient angle with a real axis enters into the ultimate expressions for the reactance to fault place and for the fault resistance. The use of such a quotient facilitates reiterative calculations of the distance to a fault place.