Find the peak load of a power plant for the given load equation
Preamble

One of the benefits of the hydro power plant is that it can be throttled all the way down to zero.  Hydro power plants are good at supplying peaky loads.  If a standalone hydro power plant has spare capacity, it just throttles down and conserves the water, rather than pumping it back up into the reservoir.  These considerations make your problem (in its original form) look less intuitive and realistic.

However, your problem will look more intuitive and realistic if you imagine that the nominal power Pnom = 10 GW is coming from an external supply other than the hydroelectric plant.  This external supply can not throttle up or down.  Also, there is a local hydroelectric facility, which can pump the reservoir when Pload &lt; Pnom and use it to augment the power supply when Pload > Pnom.  This scheme can support Pload,max > Pnom.

Approach



At τsw the hydroelectric system switches from pumping storage to using it.
$$P_{nom}=P_{load,max} \cdot cos(\pi \tau_{sw}/24)$$

Energy is in [GW⋅h] units. Energy balance of the pumped storage.
$$E_{storage,out}=0.7 E_{storage,in}$$

Substitute the appropriate integrals for the energies, and you get a system of two equations with two variables τsw and Pload,max.