Supposing you own some land next to a \(50 \mathrm{MW}\) wind farm located on Colorado's Front Range. Your land has a fantastic cliff/ridgeline with an elevation difference of \(250 \mathrm{~m}\). Evaluate whether or not you can make money by building an energy storage system on your land that interfaces with the wind farm. Your plan is to capture excess energy from the wind farm or buy energy from the wind farm when electricity prices are low and sell that energy back to the grid when electricity prices are high (assume that the utility that owns the grid will grant you a fair contract). You find that a good power rating for your storage system is \(50 \%\) of the rated wind farm output, or \(25 \mathrm{MW}\). Also your storage system should be able to generate electricity at rated power for \(8 \mathrm{~h}\).

The first step in this problem is to evaluate the technical design of candidate energy storage systems.

a. Pumped hydroelectric. Determine the flow rate and reservoir size needed to accomplish the required power output and energy capacity. Pumped hydroelectric plants generally run at \(80 \%-90 \%\) generating efficiency, depending on the size of the machinery. Suggest a reasonable surface area and depth for your two reservoirs.

b. Pulley and weight. You have a feeling that a simpler energy storage system is possible. What if you use a weight and a pulley that stores energy as the weight is lifted (using an electric motor) and energy is released when the weight falls (with an electric generator). You need to dig a shaft. Find the value of weight you would use, and the depth and diameter of the shaft. Is this viable?

c. Propose a new energy storage method. Be creative. Examples may be large springs, thermal storage, steam cycles, batteries, etc. Perform a simple analysis to size the system and say whether or not your creative idea is viable.

The second step is to evaluate the financial aspects of installing and operating your energy storage system to determine whether you could make money.

a. Pumped hydroelectric costs about \(\$ 500\) per \(\mathrm{kW}\) to install your turbomachinery and penstocks, plus \(\$ 2\) per cubic yard to build reservoirs. Calculate the initial capital cost of your pumped hydroelectric system.

b. Suppose you can buy energy from the wind farm at \(\$ 0.035 / \mathrm{kWh}\) between the hours of 10:00 PM and 8:00 AM to charge your storage and sell energy between 1:00 PM and 9:00 PM back to the grid at \(\$ 0.1 / \mathrm{kWh}\). Select a reasonable simple payback period that would motivate you to invest in energy storage. Calculate the maximum capital cost expenditure on your energy storage system that would allow this payback period.

c. Would you decide to build an energy storage system? Why or why not?