The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude E are constant. If one line is tripped at time t₁ by opening the circuit breakers at the two ends (although there is no fault), then it is seen that the generator undergoes a stable transient. Which one of the following waveforms of the rotor angle $$\delta $$ shows the transient correctly?

The incremental costs (in rupees/$$MWh$$) of operating two generating units are functions of their respective powers $${P_1}$$ and $${P_2}$$ in $$MW,$$ and are given by $$${{d{C_1}} \over {d{P_1}}} = 0.2{P_1} + 50$$$ $$${{d{C_2}} \over {d{P_2}}} = 0.24{P_2} + 40$$$
Where, $$$\eqalign{ & 20\,MW \le {P_1} \le 150\,MW \cr & 20\,MW \le {P_2} \le 150MW. \cr} $$$
For a certain load demand, $${P_1}$$ and $${P_2}$$ have been chosen such that $$\,\,d{C_1}/d{P_1} = 76\,Rs/MWh\,\,$$ and $$\,d{C_2}/d{P_2} = 68.8\,Rs/MWh.\,\,$$ If the generations are rescheduled to minimize the total cost, then $${P_2}$$ is ____________.

A $$3$$-phase transformer rated for $$33 kV/11kV$$ is connected in delta/star as shown in figure. The current transformers $$\left( {C{T_s}} \right)$$ on low and high voltage sides have a ratio of $$500/5.$$ Find the currents $${i_1}$$ and $${i_2}$$, if the fault current is $$300$$ $$A$$ as shown in figure.

A $$3$$-bus power system network consists of $$3$$ transmission lines. The bus admittance matrix of the uncompensated system is
$$\left[ {\matrix{ { - j6} & {j3} & {j4} \cr {j3} & { - j7} & {j5} \cr {j4} & {j5} & { - j8} \cr } } \right]\,pu$$
If the shunt capacitance of all transmission lines is $$50$$% compensated, the imaginary part of the $$3$$^rd row $$3$$^rd column element (in $$pu$$) of the bus admittance matrix after compensation is