Z12
P3+jQ3
Figure 1: Single-line diagram of a three-bus power system example from Computational Methods for Electric Power Systems by M. Crow.
(a) The branches in the single-line diagram for the power system have series impedances and shunt admittances described in Table 1. Using this data, compute the admittance matrix Y and report it.
(b) Given the data in Table 2 for the various parameters, set up the 3 equations that can be written as F(x)=0 for x=(0,2,0,3,v).
Real and reactive power injections across the buses are given by
Pi = Pgen - Pdem, Qi = Qgen - Qdem
for i=1,...,n.
Bus i Bus k Rik Xik Bik
1 2 0.02 0.3 0.15
1 3 0.01 0.1 0.1
2 3 0.01 0.1 0.1
Table 1: Branch Data in per units.
Bus i Type Vi
1 Slack 1.05
2 PV 1.00
3 PQ
Pidem 0.0 0.0 0.0
0.0 0.0 1.25 0.55
0.6 0.0
Table 2: Parameters for the 3-bus network in per units.