Inductance: Single-Phase And Three-Phase Line

Consider single-phase two-wire and three-phase three-wire transmission lines with equal phase spacing.

The single-phase line consists of two solid cylindrical conductors, x and y, each carrying a phasor current.

Given that the sum of currents is zero, the total flux linking conductor x is computed, followed by its inductance.

Similarly, the total flux linking conductor y is computed and its inductance is determined.

The loop inductance, also known as the total inductance of the single-phase circuit, is then calculated.

If the radii of both conductors are equal, the total circuit inductance can be simplified.

Now, the three-phase line consists of three solid cylindrical conductors, a, b, and c, of equal radii and phase spacing.

Assuming balanced positive-sequence currents such that the sum of currents equals zero, the total flux linking phase a conductor is calculated.

From this, its inductance is determined. Due to symmetry, the same result applies to phases b and c.

However, for the balanced operation of this line, only one phase needs consideration since each phase's flux linkages have equal magnitudes and 120-degree displacement.