GATE 2023 Electrical Engineering PYQ

Question

A 50 Hz, 275 kV line of length 400 km has the following parameters:

Resistance, R = 0.035 $$\Omega$$/km;

Inductance, L = 1 mH/km;

Capacitance, C = 0.01 $$\mu$$F/km;

The line is represented by the nominal-$$\pi$$ model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by $$V_S$$ and $$V_R$$, respectively) maintained at 275 kV, the phase angle difference ($$ heta$$) between $$V_S$$ and $$V_R$$ required for maximum possible active power to be delivered to the receiving end, in degree is ___________ (Round off to 2 decimal places).