An Alternative Approach for Finding the Expression for Inductive Reactance

An Alternative Approach for Finding the Expression for Inductive Reactance

For standard conductors generally the values for GMR are available. These tables are also useful for calculating inductive reactance as well as shunt capacitive reactance and resistance. The units used in these tables are inches, feet and miles as used by the industries in the United States.

Normally value of inductive reactance is required rather than the inductance. The inductive reactance of one conductor of a single phase two conductor is given by,

The GMR found from the tables is an equivalent D_s which takes into account skin effect which affects the value of inductance appreciably.

Expanding the above equation we have,

Considering both D_m and D_s to be expressed in feets, the first term in the equation is the inductive reactance of one conductor of a two conductor line having a distance of 1 ft between them. Hence the first term is called inductive reactance at 1 ft spacing xa. It depends upon the GMR of the conductor and frequency. The second term is called inductive reactance spacing factor X_d. This term is independent of type of conductor and depends only on frequency and spacing.

When D_m = 1, the spacing factor is equal to zero. When it is less than 1, the spacing factor value is negative. The inductive reactance at 1 ft spacing value is available from the table. To that value, the value of inductive reactance spacing factor is added which is also available at desired line frequency.