Electric Power Generation, Transmission, and Distribution

GMRs¼geometric mean radius of a neutral strand (ft)

rc ¼resistance of the phase conductor (V=mile)

rs ¼resistance of a solid neutral strand (V=mile)

k ¼number of concentric neutral strands

The geometric mean radii of the phase conductor and a neutral strand are obtained from a standard
table of conductor data. The equivalent geometric mean radius of the concentric neutral is given by

GMRcn¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

kGMRskRk 1

p

ft (21:37)

whereR¼radius of a circle passing through the center of the concentric neutral strands

R¼

dodds

24

ft (21:38)

The equivalent resistance of the concentric neutral is

rcn¼

rs

k

V=mile (21:39)

The various spacings between a concentric neutral and the phase conductors and other concentric
neutrals are as follows:
Concentric neutral to its own phase conductor

Dij¼R[Eq:(21:38) above]

Concentric neutral to an adjacent concentric neutral

Dij¼center-to-center distance of the phase conductors

Concentric neutral to an adjacent phase conductor
Figure 21.7 shows the relationship between the distance between centers of concentric neutral cables
and the radius of a circle passing through the centers of the neutral strands.
The GMD between a concentric neutral and an adjacent phase conductor is given by the following
equation:

Dij¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

kDknmRk

q

ft (21:40)

whereDnm¼center-to-center distance between phase conductors
For cables buried in a trench, the distance between cables will be much greater than the radiusRand
therefore very little error is made ifDijin Eq. (21.40) is set equal toDnm. For cables in conduit, that
assumption is not valid.

Dnm

R R

FIGURE 21.7 Distances between concentric neutral cables.