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

## * ***INDUCTANCE OF TWO-WIRE** **TRANSMISSION LINE**

**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.

### Calculation Procedure

* 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.

##### Products & Services

##### Topics of Interest

INDUCTIVE REACTANCE OF TWO-WIRE TRANSMISSION LINE Calculate the inductive reactance of 10 mi (16.1 km) of a two-conductor transmission line (Fig. 9.1), where D=8 ft (2.44 m) and a=0.1 in. (2.54 mm)...

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...

INDUCTANCE OF THREE-PHASE TRANSMISSION LINES Determine the inductance per phase for a three-phase transmission line consisting of single conductors arranged unsymmetrically (Fig. 9.3). Figure 9.3: A...

INDUCTANCE OF SIX-CONDUCTOR LINE Calculate the per-phase inductance of the transmission line of Fig. 9.5 where the conductors are arranged in a double-circuit configuration. Figure 9.5: 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.