There are two stages to the operating cycle of a pumped storage system (PSS):the lower ro00 • a generating stage when water falls from the upper to the lower reservoir• a pumping stage when water is returned to the upper reservoir.

Show that the theoretical maximum power Pmax available from the water during the generating stage is given by P_{\max }=\rho g h \frac{\Delta V}{\Delta t} \text { - } \rho \text { is the density of the water }

In one PSS, h is 320 m and Pmax is 440 MW. \text { Calculate } \frac{\Delta V}{\Delta t} \text {. } p=1.0 × 10³ kg m-³X The PSS has an efficiency of 90% during the generating stage. Suggest two sources of inefficiency in the PSS during the generating stage.

Determine, in J, the net electrical energy output of the PSS for the 24-hour period shown in Figure 5. Explain why the overall efficiency of the PSS, for the 24-hour period, is significantly less than the generating efficiency of 90%. Explain two reasons why pumped storage systems are useful.