An area of an interconnected power system has two fossil-fuel units operating on economic dispatch. P ₁ and P ₂ are in megawatts (MW). The total load demand PD = 900 MW The variable operating costs of these units are given by

The transmission losses are given by

When the system incremental operating cost ?= 16 $/MWh, Determine the economic dispatch of the generation units total transmission losses, the penalization factor of bus 2.

x C = 10P + 8 10-P ($/h) C = 8P + 9 10-p ($/h) P = 1.5 10-4P? + 2 10-5PP + 3 10-5P (MW)