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 = -I1 2

1 2

1

• 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 conductorIs given by

L = 2*10-7 ln D2/D1 H/m

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.