PYQs Based test 11: Power Systems

A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating 250 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running steadily at synchronous speed and delivering 60 MW power at a power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 10 cycle, the value of the power angle after 5 cycles is ________ electrical degrees.

The inductance and capacitance of a $400kV$, three-phase, $50Hz$ lossless transmission line are $1.6mH/km/phase$ and $10nF/km/phase$ respectively. The sending end voltage is maintained at $400kV$. To maintain a voltage of $400kV$ at the receiving end, when the line is delivering $300MW$ load, the shunt compensation required is

The Y${}_{bus}$ matrix of a two-bus power system having two identical parallel lines connected

between them in pu is given as Y_bus = ≤ft[ {*20c - j8&j20\\ j20& - j8 } ].

The magnitude of the series reactance of each line in pu (round off up to one decimal place) is ____________.

Two single-core power cables have total conductor resistance of 0.7 Ω and 0.5 Ω, respectively, and their insulation resistances (between core and sheath) are 600 MΩ and 900 MΩ, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is ______ × 10⁶.

The series impedance matrix of a short three-phase transmission line in phase coordinates is ≤ft[ {*20c z_s&z_m&z_m\\ z_m&z_s&z_m\\ z_m&z_m&z_s } ]. If the positive sequence impedance is (1 + j 10) Ω, and the zero sequence is (4 + j 31) Ω, then the imaginary part of Z${}_m$${}^{\text{­}}$ (in Ω) is _______ (up to 2 decimal places).