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

## * ***INDUCTIVE REACTANCE OF BUNDLED** **TRANSMISSION LINE**

**INDUCTIVE REACTANCE OF BUNDLED**

**TRANSMISSION LINE**

Calculate the inductive reactance per phase at 377 rad/s for the bundled transmission line whose conductors are arranged in a plane shown in Fig. 9.6. Assume conductors are ACSR Crow.

Figure 9.6: A bundled transmission line.

### Calculation Procedure

1.Determine GMD

Assume distances are between bundle centers and transposition of phases. Then, GMD=[(9 ^{2})(18)] ^{1/3}=11.07 m. From Table 9.2, GMR _{ c}=0.034 ft (0.01 m). The GMR should include all conductor spacings from each other in the usual product form with, in this case, three values of GMR _{ c}. Because of redundancy, GMR=(0.01 0.45 ^{2}) ^{1/3}=0.127 m.

2.Calculate Inductive Reactance per Phase

*X* _{ L}=377 2 10 ^{ 7} ln(11.07/0.127)=0.337 10 ^{ 3} ?/m (0.544 ?/mi).

** Related Calculations.** For a two-conductor bundle, GMR=(GMR

_{ c}

*D*)

^{1/2}and for a four-conductor bundle, GMR=(GMR

_{ c}

*D*

^{3}2

^{1/2})

^{1/4}. In each case,

^{ }

*D*is the distance between adjacent conductors.

For a two-conductor bundle, GMR=(GMR _{ c} *D*) ^{1/2}, and for a four-conductor bundle, GMR=(GMR _{ c} *D* ^{3}2 ^{1/2}) ^{1/4}. In each case, *D* is the distance between adjacent conductors. For an *n*-conductor bundle as depicted in Fig. 9.7, GMR=( *n* GMR _{ c} *A* ^{ n} ^{ 1}) ^{1/} ^{ n}, where *A* is the radius of the bundle. Similarly, for an *n*-conductor bundle, *r* _{equiv}=( *n* *r* *A* ^{ n} ^{ 1})

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