From Handbook of Electric Power Calculations, Third Edition
INDUCTANCE OF TWO-WIRE TRANSMISSION LINE
Consider a transmission line consisting of two straight, round conductors (radius a meters), uniformly spaced D meters apart, where (Fig. 9.1). Calculate the inductance of the line.
Figure 9.1: A two-wire transmission line.
1. Consider Flux Linkages
It is realistic to assume uniform and equal but opposite current density in each conductor. The oppositely directed currents, there- fore, produce a net total flux linkage of zero because the net current in any cross section of both conductors is zero. This is true for any multiconductor system whose cross-sectional currents add to zero (for example, in a balanced three-phase system).
2. Calculate Inductance of One Conductor
Use ?=( i/2 ?)[1/4+ln( D/ a)] Wb turns/m. Because L= ?/ i, L=(2 10 7) [1/4+ln( D/ a)] H/m. Inductance L may be expressed in more compact form by L=(2 10 7) ln( D/ r ?), where r'= a exp( 1/4) is the geometric mean radius, GMR. The value of r ? is 0.788 a.
3. Calculate Total Inductance, L T
L T =2 L=(4 10 7) ln( D/ r ?) H/m. In more conventional units, L T=1.482 log( D/ r ?) mH/mi.
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