For the system from Problem 2.32, assume that half the time the load is 10MW and 5 Mvar, and for the other half it is 20MW and 10 Mvar. What single value of Qcap  would minimize the average losses? Assume that Qcap  can only be varied in 0.5 Mvar steps.

Problem 2.32

In PowerWorld Simulator case Problem 2_32 (see Figure 2.28) a 8 MW and 4 Mvar load is supplied at \(13.8 \mathrm{kV}\) through a feeder with an impedance of \(1+j 2 \Omega\). The load is compensated with a capacitor whose output, \(\Omega_{\text {cap }}\), can be varied is 0.5 Mvar steps between 0 and 10.0 Mvars. What value of \(\Omega_{\text {cap }}\) minimizes the real power line losses? What value of \(\Omega_{\text {cap }}\) minimizes the MVA power flow into the feeder?

Source Voltage = 14.98 kv Feeder Impedance = 1 + j2 Ohms Power into Feeder at Source 8.42 MW 4.84 Mvar 9.71 MVA Feeder Losses = 0.420 MW 0.840 Mvar 0.0 Mvar 13.80 kV 8.0 MW 4.0 Mvar