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

The figure below shows a half-bridge voltage source inverter supplying an $$RL$$-load with $$R = 40\,\,\Omega $$ and $$L = \left( {{{0.3} \over \pi }} \right)H.$$ The desired fundamental frequency of the load voltage is $$50$$ $$Hz.$$ The switch control signals of the converter are generated using sinusoidal pulse width modulation with modulation index. $$M = 0.6.$$ at $$50$$ $$Hz$$, the$$RL$$-load draws an active power of $$1.44$$ $$kW.$$ The value of $$DC$$ source volts is

Consider an overhead transmission line with $$3$$-phase, $$50$$ $$Hz$$ balanced system with conductors located at the vertices of an equilateral triangle of length $$\,{D_{ab}} = {D_{bc}} = {D_{ca}} = 1\,\,\,$$ m as shown in figure below. The resistance of the conductors are neglected. The geometric mean radius (GMR) of each conductor is $$0.01$$ $$m$$. Neglect the effect of ground, the magnitude of positive sequence reactance in $$\,\Omega $$/$$km$$ (rounded off to three decimal places) 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.