A three-phase voltage source inverter with ideal devices operating in $${180^ \circ }$$ conduction mode is feeding a balanced star-connected resistive load. The $$DC$$ voltage input is $${V_{dc}}.$$ The peak of the fundamental component of the phase voltage is

A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating of 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 cycles, the value of the power angle after 5 cycles is ________ electrical degrees.

A 3-phase 50 Hz generator supplies power of 3 MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25 $$\Omega $$ and 3.925 $$\Omega $$ respectively. If the voltage at the generator terminal is 17.87 kV, the power factor of the load is ________.

In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is $$\,100\,\, \times \,\,100.$$ If there are $$20$$ PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is ________.