Electric Power Generation, Transmission, and Distribution

A transmission line is defined as a short-length line if its length is less than 80 km (50 miles). In this
case, the shut capacitance effect is negligible and only the resistance and inductive reactance are
considered. Assuming balanced conditions, the line can be represented by the equivalent circuit of a
single phase with resistanceR, and inductive reactanceXLin series (series impedance), as shown in
Fig. 13.1. If the transmission line has a length between 80 km (50 miles) and 240 km (150 miles), the line
is considered a medium-length line and its single-phase equivalent circuit can be represented in a
nominalpcircuit configuration [1]. The shunt capacitance of the line is divided into two equal parts,
each placed at the sending and receiving ends of the line. Figure 13.2 shows the equivalent circuit for a
medium-length line.
Both short- and medium-length transmission lines use approximated lumped-parameter models.
However, if the line is larger than 240 km, the model must consider parameters uniformly distributed
along the line. The appropriate series impedance and shunt capacitance are found by solving the
corresponding differential equations, where voltages and currents are described as a function of distance
and time. Figure 13.3 shows the equivalent circuit for a long line.
The calculation of the three basic transmission line parameters is presented in the following sections
[1–7].

13.2 Resistance

The AC resistance of a conductor in a transmission line is based on the calculation of its DC resistance.
If DC current is flowing along a round cylindrical conductor, the current is uniformly distributed over
its cross-section area and its DC resistance is evaluated by

RDC¼

rl

A

ðÞV (13:1)

wherer¼conductor resistivity at a given temperature (V-m)
l¼conductor length (m)
A¼conductor cross-section area (m^2 )

Is XL

Load

R

Vs

IL

FIGURE 13.1 Equivalent circuit of a short-length
transmission line.

Is XL

Load

R

Vs

IL

Iline

YC

2

YC

2

FIGURE 13.2 Equivalent circuit of a medium-

length transmission line.

V Load

s

IL

Iline

Is

sin h g l

Z

tan h (g l/2)

2

Y

g l

g l/2

FIGURE 13.3 Equivalent circuit of a long-length transmission line.Z¼zl¼equivalent total series impedance (V),
Y¼yl¼equivalent total shunt admittance (S),z¼series impedance per unit length (V=m),y¼shunt admittance
per unit length (S=m),g¼

ffiffiffiffiffiffiffiffi

ZY

p

¼propagation constant.