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 $$75$$ MVA, $$10$$ kV synchronous generator has X_d $$= 0.4$$ p.u. The X_d value (in p.u.) is a base of $$100$$ MVA, $$11$$ kV is

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