## 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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