For bundle conductors, the GMRbundlevalue is determined, as in the single-phase transmission line case,
by the number of conductors, and by the number of conductors per bundle and the separation among
them. The expression for the total inductive reactance per phase yields
XLphase¼m 0 fln
GMD
GMRbundle
ðÞV=m (13:58)where GMRbundle¼(dn^1 GMRstranded)^1 =nup to three conductors per bundle (m)
GMRbundle¼1.09(d^4 GMRstranded)^1 =^4 for four conductors per bundle (m)
GMRphase¼geometric mean radius of phase conductor, either solid or stranded (m)
GMD¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(^3) DABDBCDCA
p
¼geometrical mean distance for a three-phase line (m)
d¼distance between bundle conductors (m)
n¼number of conductor per bundle
f¼frequency (Hz)
13.5 Capacitance and Capacitive Reactance
Capacitance exists among transmission line conductors due to their potential difference. To evaluate
the capacitance between conductors in a surrounding medium with permittivity«, it is necessary to
determine the voltage between the conductors, and the electric field strength of the surrounding.
13.5.1 Capacitance of a Single-Solid Conductor
Consider a solid, cylindrical, long conductor with radiusr, in a free space with permittivity« 0 , and
with a charge ofqþcoulombs per meter, uniformly distributed on the surface. There is a constant
electric field strength on the surface of cylinder (Fig. 13.14). The resistivity of the conductor is
assumed to be zero (perfect conductor), which results in zero internal electric field due to the charge
on the conductor.
The chargeqþproduces an electric field radial to the conductor with equipotential surfaces concentric
to the conductor. According to Gauss’s law, the total electric flux leaving a closed surface is equal to the
total charge inside the volume enclosed by the surface. Therefore, at an outside pointPseparatedx
meters from the center of the conductor, the electric field flux density and the electric field intensity are
DensityP¼
q
A
¼
q
2 px
ðÞC (13:59)
r
P 1
P 2
- dx
l
r
x 1
x 2
Electric Field Lines
Path of Integration
Conductor with Charge q+
q
FIGURE 13.14 Electric field produced from a single conductor.
- dx