Electric Power Generation, Transmission, and Distribution

The general equation relating the output (nodem) and input (noden) voltages is given by

½ŠVabcm¼½ŠA½ŠVabcn½ŠB½ŠIabcm (21:199)

In Eqs. (21.197) through (21.199), the voltages are line-to-neutral for a four-wire wye feeder and
equivalent line-to-neutral for a three-wire delta system. For transformers and voltage regulators, the
voltages are line-to-neutral for terminals that are connected to a four-wire wye and line-to-line when
connected to a three-wire delta.

21.2.1.2.2 Shunt Components

The shunt components of a distribution feeder are

.Spot loads

.Distributed loads

.Capacitor banks

Spot loads are located at a node and can be three-phase, two-phase, or single-phase and connected in
either a wye or a delta connection. The loads can be modeled as constant complex power, constant
current, constant impedance, or a combination of the three.
Distributed loads are located at the midsection of a line segment. A distributed load is modeled when
the loads on a line segment are uniformly distributed along the length of the segment. As in the spot
load, the distributed load can be three-phase, two-phase, or single-phase and connected in either a wye
or a delta connection. The loads can be modeled as constant complex power, constant current, constant
impedance, or a combination of the three. To model the distributed load, a ‘‘dummy’’ node is created in
the center of a line segment with the distributed load of the line section modeled at this dummy node.
Capacitor banks are located at a node and can be three-phase, two-phase, or single-phase and can be
connected in a wye or delta. Capacitor banks are modeled as constant admittances.
In Fig. 21.32 the solid line segments represent overhead lines while the dashed lines represent under-
ground lines. Note that the phasing is shown for all of the line segments. In the area of the section entitled
‘‘Line Impedances,’’ the application of Carson’s equations for computing the line impedances for overhead
and underground lines was presented. There it was pointed out that two-phase and single-phase lines are
represented by a 33 matrix with zeros set in the rows and columns of the missing phases.
In the area of the section entitled ‘‘Line Admittances,’’ the method for the computation of the shunt
capacitive susceptance for overhead and underground lines was presented. Most of the time the
shunt capacitance of the line segment can be ignored; however, for long underground segments,
the shunt capacitance should be included.
The ‘‘node’’ currents may be three-phase, two-phase, or single-phase and consist of the sum of the
load current at the node plus the capacitor current (if any) at the node.

21.2.1.3 Applying the Ladder Iterative Technique

The previous section outlined the steps required for the application of the ladder iterative technique. For
the general feeder of Fig. 21.32 the same outline applies. The only difference is that Eq. (21.197) and
(21.198) are used for computing the node voltages on the backward sweep and Eq. (21.199) is used for

Node n Node m

Series Feeder

Component

[Vabc]n [Vabc]m

[Iabc]n [Iabc]m

FIGURE 21.33 Series feeder component.