Inductance: Single-Phase And Three-Phase Line

Understanding the inductance of transmission lines is crucial for efficient design and operation in electrical power systems. This discussion delves into the inductance characteristics of single-phase two-wire and three-phase three-wire transmission lines with equal phase spacing.

Single-Phase Two-Wire Line:

A single-phase line consists of two solid cylindrical conductors, denoted as x and y. Each conductor carries phasor currents i_x and i_y, respectively. Given that the sum of these currents is zero, we can calculate the total flux linking conductor x. This flux linkage is given by:

Where r_x' is the effective radius of conductor x, accounting for the proximity effect.

The inductance per conductor, L_x of conductor x, is then:

Similarly, for conductor y, the flux linkage and inductance are computed. The total inductance of the single-phase circuit, also known as loop inductance, is:

Three-Phase Three-Wire Line:

For a three-phase line, there are three solid cylindrical conductors, a, b, and c, each with equal radius r and equal phase spacing D. Assuming balanced positive-sequence currents, the total flux linking phase a is:

From this, the inductance of phase a is derived:

Due to symmetry, the same inductance applies to phases b and c. For a balanced three-phase operation, only one phase needs consideration since each phase's flux linkages are equal in magnitude and displaced by 120 degrees.

Understanding these inductance calculations helps in the design and analysis of transmission lines, ensuring minimal losses and optimal performance.