Electric Power Generation, Transmission, and Distribution

21

Distribution System

Modeling and Analysis

William H. Kersting
New Mexico State University

21.1 Modeling .......................................................................... 21 -1

Line Impedance.Shunt Admittance.Line Segment

Models.Step-Voltage Regulators.Transformer Bank

Connections.Load Models.Shunt Capacitor Models

21.2 Analysis........................................................................... 21 -44

Power-Flow Analysis

21.1 Modeling

Radial distribution feeders are characterized by having only one path for power to flow from the source
(distribution substation) to each customer. A typical distribution system will consist of one or more
distribution substations consisting of one or more ‘‘feeders.’’ Components of the feeder may consist of
the following:

.Three-phase primary ‘‘main’’ feeder

.Three-phase, two-phase (‘‘V’’ phase), and single-phase laterals

.Step-type voltage regulators or load tap changing transformer (LTC)

.In-line transformers

.Shunt capacitor banks

.Three-phase, two-phase, and single-phase loads

.Distribution transformers (step-down to customer’s voltage)

The loading of a distribution feeder is inherently unbalanced because of the large number of unequal
single-phase loads that must be served. An additional unbalance is introduced by the nonequilateral
conductor spacings of the three-phase overhead and underground line segments.
Because of the nature of the distribution system, conventional power-flow and short-circuit programs
used for transmission system studies are not adequate. Such programs display poor convergence
characteristics for radial systems. The programs also assume a perfectly balanced system so that a
single-phase equivalent system is used.
If a distribution engineer is to be able to perform accurate power-flow and short-circuit studies, it is
imperative that the distribution feeder be modeled as accurately as possible. This means that three-phase
models of the major components must be utilized. Three-phase models for the major components will
be developed in the following sections. The models will be developed in the ‘‘phase frame’’ rather than
applying the method of symmetrical components.
Figure 21.1 shows a simple one-line diagram of a three-phase feeder; it illustrates the major
components of a distribution system. The connecting points of the components will be referred to as
‘‘nodes.’’ Note in the figure that the phasing of the line segments is shown. This is important if the most
accurate models are to be developed.