A 132 kV transmission line AB is connected to a cable BC. The characteristic impedances of the overhead line and the cable are 400$$\Omega $$ and 80$$\Omega $$ respectively. Assume that these are purely resistive. A 250 kV switching surge travels from A to B.

(a) Calculate the value of this voltage surge when it first reaches C.

(b) Calculate the value of the reflected component of this surge when the first reflection reaches A.

(c) Calculate the surge current in the cable BC.

A synchronous generator is connected to an infinite bus through a lossless double circuit transmission line. The generator is delivering 1.0 per unit power at a load angle of $${30^0}$$ when a sudden fault reduces the peak power that can be transmitted to 0.5 per unit. After clearance of fault, the peak power that can be transmitted becomes 1.5 per unit. Find the critical clearing angle.

A single line-to-ground fault occurs on an unloaded generator in phase a positive, negative, and zero sequence impedances of the generator are j0.25 p.u., j0.25 p.u., and j0.15 p.u. respectively. The generator neutral is grounded through a reactance of j0.05 p.u. The prefault generator terminal voltage is 1.0 p.u.
(a) Draw the positive, negative, and zero sequence networks for the fault given.
(b) Draw the interconnection of the sequence networks for the fault analysis.
(c) Determine the fault current.

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.