As more and more renewable energy is being used to provide power to the grid, th

Question

As more and more renewable energy is being used to provide power to the grid, the problem of how to store the energy for later use has become important. Solar plants for example only generate power during the day, and wind turbines only generate power when the wind is blowing. To provide a steady source of energy, these plants must be paired with energy storage. Batteries are one option, but they tend to be relatively expensive. Recently a technology called Advanced Rail Energy Storage (ARES) has been developed and tested in Tehachapi, California (http://www.aresnorthamerica.com). The concept is simple: An electric freight train pulls cars loaded with massive concrete blocks up the side of a mountain using the excess power produced by a nearby renewable power plant. At the top the blocks can be unloaded. When more energy is needed by the grid than the power plant can provide, the blocks are loaded on the train at the top and the train is allowed to roll down, with the electric engine acting in reverse as a generator much the way the regenerative braking on a hybrid car works to deliver power to the battery. According to the ARES press kit the baseline system has been designed to provide 333 MW of power for up to 8 hours using tracks at a 7.5% grade that are 8 miles in length. The system has thousands of concrete blocks each with a weight of 240 tons. At the top and bottom of the track are switcher yards that allow multiple trains to park simultaneously

4. How many blocks are necessary to provide the stated energy storage capacity of 333 MW of power for 8 hours for this system? (neglect the weight of the train which carries the blocks for this calculation)

Explanation / Answer

height of the block from the ground is H = l*(7.5/100) = 8*(7.5)/100 = 0.6 miles

each mile = 1609.34 m

then H = 0.6*1609.34 = 965 m

energy produed by each block = gravitational potential energy = m*g*H = (240*1000*9.81*965)= 2.27*10^9 J

energy need to storage is E = P*t = 333*10^6*8*60*60 = 9.59*10^12 J

so no.of blocks required are N = 9.59*10^12/(2.27*10^9) = 4224 blocks needed

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