In the figure, the voltages are

$${v_1}\left( t \right) = 100\cos \left( {\omega t} \right)$$

$${v_2}\left( t \right) = 100\cos \left( {\omega t + {\pi \over {18}}} \right)$$

and $${v_3}\left( t \right) = 100\cos \left( {\omega t + {\pi \over {36}}} \right)$$.

The circuit is in sinusoidal steady state, and R << $${\omega L}$$. P₁, P₂ and P₃ are the average power outputs. Which one of the following statements is true?

The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are 𝑗0.1 pu, j0.05 pu and j0.01 pu respectively on the machine rating base. The machine is unloaded and working at the rated terminal voltage. If the grounding impedance of the generator is j0.01 pu, then the magnitude of fault current for a b-phase to ground fault (in kA) is __________ (up to 2 decimal places).

The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, P = 1.4 sin $$\delta $$ + 0.15 sin 2$$\delta $$, where $$\delta $$ is the load angle. Newton-Raphson method is used to calculate the value of $$\delta $$ for P = 0.8 pu. If the initial guess is $$30^\circ $$, then its value (in degree) at the end of the first iteration is

A 1000 $$ \times $$ 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are _____ (up to 2 decimal places).