Say there are 3 buses of:
Bus 1: Slack bus with a voltage source of E=1.0 and phase of 0°
Bus 2: a generator and a load.
Bus 3: a load.
The line impedance are given below:
z12 = 0.05 + j0.1
z13 = 0.02 + j0.05
z23 = j0.05
z11 = -j100
z22 = infinity
z33 = -j40
The generators and loads are given...