In a power system, the fuel inputs per hour of plants $$1$$ and $$2$$ are given as
$${F_1} = 0.20\,P_1^2 + 30\,{P_1} + 100\,\,$$ Rs per hour
$${F_2} = 0.25\,P_2^2 + 40\,{P_2} + 150\,\,$$

The limits of generators are $$$\eqalign{ & 20 \le {P_1} \le 80\,MW \cr & 40 \le {P_2} \le 200\,MW \cr} $$$
Find the economic operating schedule of generation, If the load demand is $$130$$ $$MW.$$ neglecting transmission losses.

The neutral of $$10$$ $$MVA,$$ $$11$$ $$kV$$ alternator is earthed through a resistance of $$5$$ ohms. The earth fault relay is set to operate at $$0.75$$ $$A.$$ The $$CT's$$ have a ratio of $$1000/5.$$ What percentage of the alternator winding is protected?

Bulk power transmission over long HVDC lines are preferred, on account of

The Laplace transform of $$\left(t^2\;-\;2t\right)u\left(t\;-\;1\right)$$ is