Three phase to ground fault takes place at locations $${F_1}$$ and $${F_2}$$ in the system shown in the figure.

If the fault takes place at location $${F_1}$$, then the voltage and the current at bus A are $${V_F1}$$ and $${{\rm I}_{F1}}$$ respectively. If the fault takes place at location $${F_2}$$, then the voltage and the current at bus A are $${V_{F2}}$$ and $${{\rm I}_{F2}}$$ respectively.

The correct statement about voltages and currents during faults at $${F_1}$$ and $${F_2}$$ is

A 2-bus system and corresponding zero sequence network are shown in the figure.

The transformers T₁ and T₂ are connected as

In an unbalanced three phase system phase current $${{\rm I}_a} = 1\angle \left( { - {{90}^0}} \right)\,\,pu,\,\,$$ negative sequence current $$\,{{\rm I}_{b2}} = 4\angle \left( { - {{150}^0}} \right)\,\,pu,\,\,$$ zero sequence current $$\,\,{{\rm I}_{c0}} = 3\angle {90^0}\,\,pu.\,\,\,$$ The magnitude of phase current $${{\rm I}_b}$$ in $$pu$ is

The fuel cost functions of two power plants are
Plant $${P_1}:\,{C_1} = 0.05\,Pg_1^2 + AP{g_1} + B$$
Plant $${P_2}:\,{C_2} = 0.10\,Pg_2^2 + 3AP{g_2} + 2B$$
Where, $$P{g_1}$$ and $$P{g_2}$$ are the generator powers of two plants and $$A$$ and $$B$$ are the constants. If the two plants optimally share $$1000$$ $$MW$$ load at incremental fuel cost of $$100$$ $$Rs/MWh,$$ the ratio of load shared by plants $${P_1}$$ and $${P_2}$$ is