Question

Hydroelectric power system that its upper reservoir on a 1000 ft hill, and generates 50 MW. The system works during the off-peak hours at night (19 hours) and produces power during peak hours (5 hours). Calculate the amount of water (volume) needed to be pumped uphill and stored off-peak hours to generate 50 MW later at peak hours.

Answer 1

Total energy generated during peak hours is

E = 50x10⁶x 5x3600 J = 9x10¹¹ J

assuming full conversion of the potential energy of water to electric energy (100% efficiency)

Required potential energy uphill = 9x10¹¹ J

The potential energy of water = Volume x density x height x g

assuming density of water = 1000 kg/m³ and g = 9.8 m/s²

height = 1000 ft = 304.8 m

volume of water needed = 9x10¹¹ / (1000x9.8x304.8) = 301301.623 m³

Note: I have answered based on the data provided. For a more detailed solution, detail data should be provided.