A three-phase, $$11$$ $$kV,$$ $$50$$ $$Hz,$$ $$2$$ pole, star connected, cylindrical rotor synchronous motor is connected to an $$11$$ $$kV,$$ $$50$$ $$Hz$$ source. Its synchronous reactance is $$50\Omega $$ per phase, and its stator resistance is negligible. The motor has a constant field excitation. At a particular load torque, its stator current is $$100$$ $$A$$ at unity power factor. If the load torque is increased so that the stator current is $$120$$ $$A,$$ then the load angle (in degrees) at this load is ____________.

A non-salient pole synchronous generator having synchronous reactance of $$0.8$$ $$pu$$ is supplying $$1$$ $$pu$$ power to a unity power factor load at a terminal voltage of $$1.1$$ $$pu$$. Neglecting the armature resistance, the angle of the voltage behind the synchronous reactance with respect to the angle of the terminal voltage in degrees is ____________.

A $$20$$-pole alternator is having $$180$$ identical stator slots with $$6$$ conductors in each slot. All the coils of a phase are in series. If the coils are connected to realize single-phase winding, the generated voltage is $${V_1}.$$ If the coils are reconnected to realize three-phase star-connected winding, the generated phase voltage is $${V_ 2}.$$ Assuming full pitch, single-layer winding, the ratio $${V_1}/{V_2}$$ is

There are two generators in a power system. No-load frequencies of the generators are $$51.5$$ $$Hz$$ and $$51$$ $$Hz,$$ respectively, and both are having droop constant of $$1$$ $$Hz/MW.$$ Total load in the system is $$2.5$$ $$MW.$$ Assuming that the generators are operating under their respective droop characteristics, the frequency of the power system in $$Hz$$ in the steady state is ____________.