.Power loss in each line section
.Total feeder input kW and kVAr
.Total feeder power losses
.Load kW and kVAr based upon the specified model for the loadBecause the feeder is radial, iterative techniques commonly used in transmission network power-flow
studies are not used because of poor convergence characteristics (Trevino, 1970). Instead, an iterative
technique specifically designed for a radial system is used. The ladder iterative technique (Kersting and
Mendive, 1976) will be presented here.
21.2.1.1 The Ladder Iterative Technique
21.2.1.1.1 Linear Network
A modification of the ladder network theory of linear systems provides a robust iterative technique for
power-flow analysis. A distribution feeder is nonlinear because most loads are assumed to be constant
kW and kVAr. However, the approach taken for the linear system can be modified to take into account
the nonlinear characteristics of the distribution feeder.
For the ladder network in Fig. 21.29, it is assumed that all of the line impedances and load impedances
are known along with the voltage at the source (Vs).
The solution for this network is to assume a voltage at the most remote load (V 5 ). The load currentI 5
is then determined as
I 5 ¼
V 5
ZL 5(21:191)For this ‘‘end-node’’ case, the line currentI 45 is equal to the load currentI 5. The voltage at node 4 (V 4 )
can be determined using Kirchhoff’s voltage law (KVL):
V 4 ¼V 5 þZ 45 I 45 (21:192)The load currentI 4 can be determined and then KCL applied to determine the line currentI 34.
I 34 ¼I 45 þI 4 (21:193)KVL is applied to determine the node voltageV 3. This procedure is continued until a voltage (V 1 ) has
been computed at the source. The computed voltageV 1 is compared to the specified voltageVs. There
will be a difference between these two voltages. The ratio of the specified voltage to the compute voltage
can be determined as
Ratio¼
Vs
V 1(21:194)1
+−Z (^122345)
I 12 I^2 I 23 I^3 I 34 I^4 I 45 I^5
Z 23 Z 34 Z 45
ZL 2 ZL 3 ZL 4 ZL 5
VS
FIGURE 21.29 Linear ladder network.