##### From Handbook of Electric Power Calculations, Third Edition

## * ***INDUCTANCE OF STRANDED-CONDUCTOR** **TRANSMISSION LINE**

**INDUCTANCE OF STRANDED-CONDUCTOR**

**TRANSMISSION LINE**

Determine the inductance of a transmission line having six identical round conductors (Fig. 9.2) arranged so that the currents on each side occupy the conductors equally with uniform current density.

Figure 9.2: Stranded-conductor transmission line.

### Calculation Procedure

* 1. Calculate Flux of One Conductor*

The flux linkages of conductor 1, which carries one-third of the current, can be deduced from the method established for the two-conductor line by: * ?* _{1}=( /2 ?) ( *i*/3) [1/4+ln( *D* _{11'}/ *a*)+ln( *D* _{12} _{ '}/ *a*)+ln( *D* _{13} _{ '}/ *a*) ln( *D* _{12}/ *a*) ln( *D* _{13}/ *a*)], where *D* _{11?} is the distance between conductors 1 and 1 ? and so on. When terms are collected, the equation becomes: * ?* _{1}=( *i*/2 ?) {ln[( *D* _{11'} *D* _{12'} *D* _{13'}) ^{1/3}/( *r ?D* _{12} *D* _{13}) ^{1/3}]} Wb turns/m. The flux linkages of the other two conductors carrying current in the same direction are found in a similar manner.

2.Calculate the Inductances

The inductances of conductors one, two, and three then become: *L* _{1}= * ?* _{1}/( *i*/3)=(3 2 10 ^{ 7})[ln( *D* _{11} _{ '} *D* _{l2} _{ '} *D* _{13} _{ '}) ^{1/3}/( *r ?D* _{l2} *D* _{13}) ^{1/3}] H/m, *L* _{2}= * ?* _{2}/( *i*/3)=(3 2 10 ^{ 7}) [ln ( *D* _{2l} _{ '} *D* _{22'} *D* _{23'}) ^{l/3}/(

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