A $$25$$ $$kVA,$$ $$400$$ $$V,$$ $$\Delta $$ - connected, $$3$$-phase, cylindrical rotor synchronous generator requires a field current of $$5$$ $$A$$ to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is $$360$$ $$V.$$ Neglecting the armature resistance and magnetic saturation, its voltage regulation (in $$\% $$ with respect to terminal voltage), when the generator delivers the rated load at $$0.8$$ $$pf$$ leading, at rated terminal 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 $$100$$ $$MJ.$$ 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.

Two parallel connected, three-phase, $$50Hz,$$ $$11kV,$$ star-connected synchronous machines $$A$$ and $$B,$$ are operating as synchronous condensers. They together supply $$50$$ $$MVAR$$ to a $$11$$ $$kV$$ grid. Current supplied by both the machines are equal. Synchronous reactances of machine $$A$$ and machine $$B$$ are $$1\,\,\Omega $$ and $$3\,\,\Omega ,$$ respectively. Assuming the magnetic circuit to be linear, the ratio of excitation current of machine $$A$$ to that of machine $$B$$ is ____________. (Give the answer up to two decimal places).

A three-phase, $$50$$ $$Hz$$ salient-pole synchronous motor has a per-phase direct-axis reactance $$\left( {{X_d}} \right)$$ of $$0.8$$ $$pu$$ and a per-phase quadrature-axis reactance $$\left( {{X_q}} \right)$$ of $$0.6$$ $$pu.$$ Resistance of the machine is negligible. It is drawing full-load current at $$0.8$$ $$pf$$ (leading). When the terminal voltage is $$1$$ $$pu,$$ per-phase induced voltage, in $$pu,$$ is ______________.