Inductance of Single phase lines

r1 r2 D I1 I2

Consider one meter length of a signle phase line consisting of two solid round conductors of radius r and r. The two concoctors are separated by a distance D. Conductor 1 carries the phasor current I and conductor 2 carries return current I = -I

These currents set up magnetic field lines that links between the conductors as shown in above figure.

For D1= r1 and D2= D, the value of inductance external to the conductor Is given by

For a conductor with r1= r2 =r and L1 =L2= L,the inductance per conductor per meter of length of the line is given by L= 2*10 -7 Ln (1/r’) + 2*10 -7 ln D

is known as self-geometric mean distance of a circle GMR is commonly referred to as geometric mean radius The term r ‘ = r e -1/4 with radius r and is abbreviated by GMR and is considered as the radius of a fictitious conductor assumed to have no internal flux but with the same inductance as the actual conductor with radius r.