Electric Power Generation, Transmission, and Distribution

SubstitutingEqs. (13.7)and(13.8)in Eq. (13.6)we can obtain the conductor ampacity at given
temperatures

I¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

SwðÞcþwr

R

r

ðÞA (13:9)

I¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

S

R

Dt 0 : 0128

ffiffiffiffiffi

pv

p

Tair^0 :^123

ffiffiffiffiffiffiffiffiffiffi

dcond

p þ 36 : 8 E

Tc^4 Tair^4

10004

!

vu

ut

ðÞA (13:10)

Some approximated current-carrying capacity for overhead ACSR and AACs are presented in the section
‘‘Characteristics of Overhead Conductors’’ [3,9].

13.4 Inductance and Inductive Reactance

A current-carrying conductor produces concentric magnetic flux lines around the conductor. If the
current varies with the time, the magnetic flux changes and a voltage is induced. Therefore, an
inductance is present, defined as the ratio of the magnetic flux linkage and the current. The magnetic
flux produced by the current in transmission line conductors produces a total inductance whose
magnitude depends on the line configuration. To determine the inductance of the line, it is necessary
to calculate, as in any magnetic circuit with permeabilitym, the following factors:

1. Magnetic field intensityH


2. Magnetic field densityB


3. Flux linkagel

13.4.1 Inductance of a Solid, Round, Infinitely Long Conductor

Consider an infinitely long, solid cylindrical conductor with radiusr, carrying currentIas shown in
Fig. 13.6. If the conductor is made of a nonmagnetic material, and the current is assumed uniformly
distributed (no skin effect), then the generated internal and external magnetic field lines are concentric
circles around the conductor with direction defined by the right-hand rule.

13.4.2 Internal Inductance Due to Internal Magnetic Flux

To obtain the internal inductance, a magnetic field with radiusxinside the conductor of lengthlis
chosen, as shown in Fig. 13.7.
The fraction of the currentIxenclosed in the area of the circle chosen is determined by

Ix¼I

px^2

pr^2

ðÞA (13:11)

I

I

Internal Field

External Field

r

FIGURE 13.6 External and internal concentric magnetic flux lines around the conductor.