The figure shows a two-generator system supplying a load of $${P_D} = 40\,MW,$$ connected at bus $$2.$$

The fuel cost of generators $${G_1}$$ and $${G_2}$$ are: $${C_1}\left( {{P_{G1}}} \right) = 10,000\,\,Rs/MWhr$$ and $${C_2}\left( {{P_{G2}}} \right) = 12,500\,\,Rs/MWhr$$ and the loss in the line is $$\,{P_{loss(pu)}} = 0.5\,\,P_{G1\left( {pu} \right),}^2\,\,\,\,$$ where the loss coefficient is specified in pu on a $$100$$ $$MVA$$ base. The most economic power generation schedule in $$MW$$ is

A cylindrical rotor generator delivers $$0.5$$ pu power in the steady-state to an infinite bus through a transmission line of reactance $$0.5$$ pu. The generator no-load voltage is $$1.5$$ pu and the infinite bus voltage is $$1$$ pu. The inertia constant of the generator is $$5$$ $$MW-s/MVA$$ and the generator reactance is $$1$$ pu. The critical clearing angle, in degrees, for a three-phase dead short circuit fault at the generator terminal is

The unilateral Laplace transform of f(t) is $$\frac1{s^2\;+\;s\;+\;1}$$. The unilateral Laplace transform of tf(t) is

The input x(t) and output y(t) of a system are related as $$\int_{-\infty}^tx\left(\tau\right)\cos\left(3\tau\right)d\tau$$.The system is