Electric Power Generation, Transmission, and Distribution

33. Continue the backward and forward sweeps until the calculated voltage at the source is within a
    specified tolerance of the source voltage.


34. At this point, the voltages are known at all nodes and the currents flowing in all line segments are
    known. An output report can be produced giving all desired results.

21.2.1.2 The Unbalanced Three-Phase Distribution Feeder

The previous section outlined the general procedure for performing the ladder iterative technique. This
section will address how that procedure can be used for an unbalanced three-phase feeder.
Figure 21.32 is the one-line diagram of an unbalanced three-phase feeder. The topology of the
feeder in Fig. 21.32 is the same as the feeder inFig. 21.31. Figure 21.32 shows more detail of the
feeder however. The feeder in Fig. 21.32 can be broken into the series components and the shunt
components.

21.2.1.2.1 Series Components

The series components of a distribution feeder are

.Line segments

.Transformers

.Voltage regulators

Models for each of the series components have been developed in prior areas of this section. In all cases,
models (three-phase, two-phase, and single-phase) were developed in such a manner that they can be
generalized. Figure 21.33 shows the ‘‘general model’’ for each of the series components.
The general equations defining the ‘‘input’’ (noden) and ‘‘output’’ (nodem) voltages and currents are
given by

½ŠVabcn¼½Ša½ŠVabcmþ½Šb½ŠIabcm (21:197)

½ŠIabcn¼½Šc½ŠVabcmþ½Šd½ŠIabcm (21:198)

Source Node

10

12

13

5

6

7

8

2

a b c

a b c c b a

a

4 

3 

a

b

c

b

c

c

a

a

c

1

3

4

9

11

FIGURE 21.32 Unbalanced three-phase distribution feeder.