A Pumped-Hydroelectric Store Between Two Reservoirs: Water Volume, Head, Turbine Flow and Evaporation Loss for Fifty Thousand Usable Kilowatt-Hours

This paper sizes a pumped-hydroelectric storage system for a regional grid requiring daily shifting of midday solar surplus into the evening. The duty calls for 5e+04 usable electrical kilowatt-hours delivered at a rated power of 5e+03 kilowatts. Working from a stated specific energy of 1.1 watt-hours per kilogram, an energy density of 1 watt-hours per litre, a usable depth-of-discharge fraction of 0.95, and a round-trip efficiency of 80 percent, the calculation gives a gross stored energy of 5.26e+04 kilowatt-hours, an active-store mass of 4.78e+07 kilograms, a complete system mass of 5.02e+07 kilograms, and a complete system volume of 5.53e+07 litres (5.53e+04 cubic metres). Full discharge at rated power lasts 10 hours, and a full recharge takes 13.1 hours at the stated charge power. Losses amount to 1.18e+04 kilowatt-hours per complete cycle, appearing as heat at average rates of 450 kilowatts during charging and 588 kilowatts during discharge. Standing loss is 0.005 percent of the stored energy per day. Life is limited by the calendar limit, giving 1.5e+04 effective full cycles, about 60 years at the assumed cycling rate, and a lifetime delivered throughput of 7.5e+05 megawatt-hours. All values are computed from the stated assumptions; the system is a design study and has not been built or measured. Status: SIMULATED, NOT MEASURED.