Electric Power Generation, Transmission, and Distribution

wherelAAP¼flux linkage from magnetic field of conductor A on conductor A at pointP
lABP¼flux linkage from magnetic field of conductor B on conductor A at pointP
lBBP¼flux linkage from magnetic field of conductor B on conductor B at pointP
lBAP¼flux linkage from magnetic field of conductor A on conductor B at pointP
The expressions of the flux linkages above, per unit length, are

lAAP¼

m 0

2 p

Iln

DAP

GMRA



ðÞWb=m (13:28)

lABP¼

ðDBP

D

BBPdP¼

m 0

2 p

Iln

DBP

D



ðÞWb=m (13:29)

lBAP¼

ðDAP

D

BAPdP¼

m 0

2 p

Iln

DAP

D



ðÞWb=m (13:30)

lBBP¼

m 0

2 p

Iln

DBP

GMRB



ðÞWb=m (13:31)

The total flux linkage of the system at pointPis the algebraic summation oflAPandlBP

lP¼lAPþlBP¼ðÞlAAPþlABP þðÞlBAPþlBBP (13:32)

lP¼

m 0

2 p

Iln

DAP

GMRA



D

DAP



DBP

GMRB



D

DBP



¼

m 0

2 p

Iln

D^2

GMRAGMRB



ðÞWb=m (13:33)

If the conductors have the same radius,

rA¼rB¼r, and the pointPis shifted to

infinity, then the total flux linkage of the

system becomes

l¼

m 0

p

Iln

D

GMR



ðÞWb=m (13:34)

and the total inductance per unit length

becomes

rA

X

rB

D

A B

IA IB

I

IA IB

X

D

FIGURE 13.9 External magnetic flux around conductors in a two-wire single-phase line.

B

(a) P (b)

DAP

A

P

DBP

DAB

lAAP lABP

DAP

A B

FIGURE 13.10 Flux linkage of (a) conductor A at pointPand
(b) conductor B on conductor A at pointP. Single-phase system.