A power system has two generators with the following cost curves
Generator $$1:$$ $${C_1}\left( {{P_{G1}}} \right) = 0.006\,P_{G1}^2 + 8{P_{G1}} + 350$$ (Thousand Rupees/Hour)
Generator $$2:$$ $${C_2}\left( {{P_{G2}}} \right) = 0.006\,P_{G2}^2 + 7{P_{G2}} + 400$$ (Thousand Rupees/Hour)
The generator limits are
$$\eqalign{ & 100\,MW \le {P_{G1}} \le 650\,MW \cr & 50\,MW \le {P_{G2}} \le 500\,MW \cr} $$

A load demand of $$600$$ $$MW$$ is supplied by the generators in an optimal manner. Neglecting losses in the transmission network, determine the optimal generation of each generator.

A power system has two synchronous generators. The Governor-turbine characteristics corresponding to the generators are
P₁ = 50(50 – f), P₂ = 100 (51 – f)
Where f denotes the system frequency in Hz, and P₁ and P₂ are, respectively, the power outputs (in MW) of turbines 1 and 2. assuming the generators and transmission network to be lossless, the system frequency for a total load of 400 MW is

For the $$Y$$-$$bus$$ matrix given in per unit values, where the first, second, third and fourth row refers to bus $$1, 2, 3$$ and $$4$$ respectively, draw the reactance diagram. $$${Y_{bus}} = j\left[ {\matrix{ { - 6} & 2 & {2.5} & 0 \cr 2 & { - 10} & {2.5} & 4 \cr {2.5} & {2.5} & { - 9} & 4 \cr 0 & 4 & {4 - 8} & {} \cr } } \right]$$$

A $$75$$ MVA, $$10$$ kV synchronous generator has X_d $$= 0.4$$ p.u. The X_d value (in p.u.) is a base of $$100$$ MVA, $$11$$ kV is