An alternator is connected to an infinite bus as shown in figure. It delivers 1.0 p.u. current at 0.8 p.f lagging at V = 1.0 p.u.. The reactance X_d of the alternator is 1.2 p.u. Determine the active power output and the steady state power limit. Keeping the active power fixed, if the excitation is reduced, find the critical excitation corresponding to operation at stability limit.

For the network shown in figure the zero sequence reactances in p.u. are indicated. The zero sequence driving point reactance of the node 3 is

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?