A simple, effective electric load leveling technique is to use excess produced electricity to pump water into a hill top reservoirs during off peak hours and then discharging it during peak electrical demand periods. This simple, old style energy storage concept is increasingly being used to have a more effective power generation system by addressing the peak power demand load. The drawback to this technique is that one has to operate it in a hilly or mountainous region. Someone has suggested an alternative that can be applied at any location. In this alternative, a reclaimed concrete mass is to be raised using excess generated electrical power. The density of the reclaimed concrete is the same as concrete. This mass will be raised using a pulley-motor combination when there is excess electrical power production. During the peak power demands the mass will be lowered using a pulley-electric generator to produce power. The effect of the friction in the pulley is a tangential force that operates at the outer pulley circumference that interfaces with the cable. This force, F _fric , is proportional to the mass being lifted by the following relationship: F _fric = 0.08(lifted weight) [note: the force is proportional to the weight, a force, not the mass]. There is a similar loss in the cable-winding pulley, but the relationship is F _pulley = 0.05(lifted weight). Frictional losses are ultimately converted to heat losses to the environment. The mass will be raised or lowered into a pit dug into the earth’s surface. The depth of this pit is 60 m and the mass cannot extend above the earth’s surface. The device can be considered to be isothermal during these processes.

1. Determine the footprint (the land area needed) of the pit required to store an excess uniform power production of 250 kW over a 12 hour period assuming that the electric motor has an efficiency of 0.91. The stored energy is used to meet a peak power demand over a three hour period. The power generated is uniform over the three hour period. The generator efficiency is 0.89. NOTE: I am leaving it up to you to determine the geometric shape of the concrete mass. The choice of this variable will affect the lift height and the footprint; you have to decide this shape.

2. Determine the energy storage efficiency of this concept. The energy storage efficiency is defined as the ratio of the energy output of the system to the energy input to the system. Discuss the feasibility of this concept. Your discussion should include technically and qualitative economic points. For example, how does it compare to the efficiency of a battery storage system or the hydro power storage systems.

3. If the geometric shape is a rectangular shaped solid in which the height is L and the sides are multiples of the height, such N*L. Determine the value of N which would maximize the energy storage efficiency. Discuss your result.