A power system has two synchronous generators. The Governor-turbine characteristics corresponding to the generators are
P₁ = 50(50 – f), P₂ = 100 (51 – f)
Where f denotes the system frequency in Hz, and P₁ and P₂ are, respectively, the power outputs (in MW) of turbines 1 and 2. assuming the generators and transmission network to be lossless, the system frequency for a total load of 400 MW is

For the $$Y$$-$$bus$$ matrix given in per unit values, where the first, second, third and fourth row refers to bus $$1, 2, 3$$ and $$4$$ respectively, draw the reactance diagram. $$${Y_{bus}} = j\left[ {\matrix{ { - 6} & 2 & {2.5} & 0 \cr 2 & { - 10} & {2.5} & 4 \cr {2.5} & {2.5} & { - 9} & 4 \cr 0 & 4 & {4 - 8} & {} \cr } } \right]$$$

A single line-to-ground fault occurs on an unloaded generator in phase a positive, negative, and zero sequence impedances of the generator are j0.25 p.u., j0.25 p.u., and j0.15 p.u. respectively. The generator neutral is grounded through a reactance of j0.05 p.u. The prefault generator terminal voltage is 1.0 p.u.
(a) Draw the positive, negative, and zero sequence networks for the fault given.
(b) Draw the interconnection of the sequence networks for the fault analysis.
(c) Determine the fault current.

Given the relationship between the input $$u(t)$$ and the output $$y(t)$$ to be
$$y\left( t \right) = \int\limits_0^t {\left( {2 + t - \tau } \right){e^{ - 3\left( {t - \tau } \right)}}} u\left( \tau \right)d\tau $$
the transfer function $$Y\left( s \right)/U\left( s \right)$$ is