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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$50$ $Hz$. Mechanical power is $1$ $pu$. The system is operating at the stable equilibrium point with rotor angle 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 _______.

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