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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.