Suppose you own some land next to a 50 MW wind farm located onColorado’s Front Range. Your land has a fantastic cliff/ridgelinewith an elevation difference of 250 m. Evaluate whether or not youcan make money by building a pumped hydroelectric energy storagesystem on your land that interfaces with the wind farm. Your planis to capture excess energy from the wind farm or buy energy fromthe wind farm when electricity prices are low and sell that energyback to the grid when electricity prices are high (assume that theutility that owns the grid will grant you a fair contract). Youfind that a good power rating for your storage system is 50% of therated wind farm output, or 25 MW. Also your storage system shouldbe able to generate electricity at rated power for 8 h.

a. Determine the flow rate and reservoir size needed toaccomplish the required power output and energy capacity. Pumpedhydroelectric plants generally run at 80%–90% generatingefficiency, depending on the size of the machinery. Suggest areasonable surface area and depth for your two reservoirs.

b. Assume it costs $500 per kW to install your turbomachineryand penstocks, plus $2 per cubic yard to build reservoirs.Calculate the initial capital cost of your pumped hydroelectricsystem.

c. Suppose you can buy energy from the wind farm at $0.035/kWhbetween the hours of 10:00 pm and 8:00 am to charge your storageand sell energy between 1:00 pm and 9:00 pm back to the grid at$0.1/kWh. Select a reasonable simple payback period that wouldmotivate you to invest in energy storage. Calculate the maximumcapital cost expenditure on your energy storage system that wouldallow this payback period.

d. Would you decide to build this energy storage system? Why orwhy not?