Electric Power Generation, Transmission, and Distribution

The following sections will present generalized three-phase models for the ‘‘series’’ components of a
feeder (line segments, voltage regulators, transformer banks). Additionally, models are presented for the
‘‘shunt’’ components (loads, capacitor banks). Finally, the ‘‘ladder iterative technique’’ for power-flow
studies using the models is presented along with a method for computing short-circuit currents for all
types of faults.

21.1.1 Line Impedance

The determination of the impedances for overhead and underground lines is a critical step before
analysis of the distribution feeder can begin. Depending upon the degree of accuracy required,
impedances can be calculated using Carson’s equations where no assumptions are made, or the impe-
dances can be determined from tables where a wide variety of assumptions are made. Between these two
limits are other techniques, each with their own set of assumptions.

21.1.1.1 Carson’s Equations

Since a distribution feeder is inherently unbalanced, the most accurate analysis should not make any
assumptions regarding the spacing between conductors, conductor sizes, or transposition. In a classic
paper, John Carson developed a technique in 1926 whereby the self and mutual impedances for ncond
overhead conductors can be determined. The equations can also be applied to underground cables. In
1926, this technique was not met with a lot of enthusiasm because of the tedious calculations that had to
be done on the slide rule and by hand. With the advent of the digital computer, Carson’s equations have
now become widely used.
In his paper, Carson assumes the earth is an infinite, uniform solid, with a flat uniform upper surface
and a constant resistivity. Any ‘‘end effects’’ introduced at the neutral grounding points are not large at
power frequencies, and therefore are neglected. The original Carson equations are given in Eqs. (21.1)
and (21.2).

Substation

Transformer

Voltage Regulator

Three-phase Lateral

Transformer

“V” Phase

Node

a b c

c b a

a b c

c

a

c

a

a

a

b

c

b

c

Primary Main

Underground Cables

Capacitor Bank

FIGURE 21.1 Distribution feeder.