The figure shows the single line diagram of a single machine infinite bus system.

The inertia constant of the synchronous generator $$𝐻 = 5$$ $$MW-s/MVA.$$ Frequency is $$50Hz.$$ Mechanical power is $$1$$ pu. The system is operating at the stable equilibrium point with rotor angle $$\delta $$ equal to $${30^ \circ }$$. A three phase short circuit fault occurs at a certain location on one of the circuits of the double circuit transmission line. During fault, electrical power in pu is $$\,{P_{\max }}\,\,\sin \delta .\,\,\,$$. If the values of $$\delta $$ and $$d$$$$\delta $$$$/dt$$ at the instant of fault clearing are $${45^ \circ }$$ and $$3.762$$ radian/s respectively, then $$\,{P_{\max }}$$ (in pu) is _________.

A cylindrical rotor generator delivers $$0.5$$ pu power in the steady-state to an infinite bus through a transmission line of reactance $$0.5$$ pu. The generator no-load voltage is $$1.5$$ pu and the infinite bus voltage is $$1$$ pu. The inertia constant of the generator is $$5$$ $$MW-s/MVA$$ and the generator reactance is $$1$$ pu. The critical clearing angle, in degrees, for a three-phase dead short circuit fault at the generator terminal is

A $$500$$ $$MW,$$ $$21$$ $$kV,$$ $$50$$ $$Hz,$$ $$3$$-phase, $$2$$-pole synchronous generator having a rated $$p.f.=$$$$0.9,$$ has a moment of inertia $$\,\,27.5\,\, \times \,\,{10^3}\,\,kg\,\,{m^2}.\,\,$$ The inertia constant $$(H)$$ will be

A lossless single machine infinite bus power system is shown below:

The synchronous generator transfers $$1.0$$ per unit of power to the infinite bus. The critical clearing time of circuit breaker is $$0.28$$ s. If another identical synchronous generator is connected in parallel to the existing generator and each generator is scheduled to supply $$0.5$$ per unit of power, then the critical clearing time of the circuit breaker will