### Potential Energy Storage

February 15, 2012

Last year, because of adverse weather, there were quite a few electrical power outages at my house. Several of my neighbors have gasoline-powered generators, generally about 5,000 watt capacity, that seem to work well. Several of them have had transfer switch panels installed alongside their circuit breaker boxes to make powering things in their home more convenient than having many extension cords all over the place. A transfer switch panel is certainly the safer option, although their installation runs about double the cost of the generator.

During one of these blackouts, I started to brainstorm possible energy storage devices that would charge during times when electricity was present, and would give about a 10 kilowatt-hour (kW-hr) reserve. My desire was for a low-cost, low maintenance system, so I immediately rejected storage batteries.

Other storage options, such as flywheel energy storage that I reviewed in a previous article (Flywheel Energy Storage, July 21, 2011), are likewise too expensive for a single home. The best option I could think of using was gravitational potential energy in the form of pumping water up a height, when power was available; and then using the downwards flow to run a generator when power was needed.

At that point, it was time for a back-of-the-envelope calculation.

Gravitational potential energy U is given simply as
U = mgh

where m is the mass in kilograms, g is the gravitational acceleration (9.8 m/sec/sec), and h is the difference in height between the initial and final states in meters. Ten kilowatt hours is 3.6 x 107 joules (1 kWh = 3,600,000 joule).

If we assume a height differential of twenty feet, which is about residential roof height, how many gallons of water does this energy represent? If we crank through the numbers, we get 160,000 gallons, which would occupy a cube about 28 feet on a side.

This is a huge quantity of water, and the structure needed to hold it would be massive. If I were lucky enough to live on the side of a hill, the engineering would be a lot easier, with a pond at the top and bottom of the hill. Of course, this analysis glosses over the inefficiency of the generator and the fact that these water reservoirs would freeze during a New Jersey winter.

Water, which has a density of just 1 g/cc, is not that dense. Most metals, such as iron and zinc, have a density of about seven, although much more expensive tungsten has a density of 19.25, and depleted uranium has a density of 19.1. Common rock has a density of almost three (the density of granite is 2.7). A weight and pulley system, like that used on grandfather clocks, but on a much grander scale, can store potential energy.

Detail from figure one of US Patent No. 383,539, "Pendulum for Clocks," by Albert L. Parcelle, May 29, 1888.

The mass at A' stores the potential energy for driving the clock mechanism.

In a recent arXiv preprint, mathematical physicist, Nadja Kutz, has proposed some methods of weight lifting to store potential energy.[2] She argues that potential energy storage could be a helpful supplement to smart grids, even if the lifted mass is as simple as excavated material. She proposes several example applications in her article. Examples for storing photovoltaically generated energy are explained in somewhat more in detail, but she suggests that similar methods can be used for energy storage from other intermittent sources, such as wind energy.

In one example given in the paper, masses are lifted mechanically in shafts affixed to the outside of high buildings (see figure).[2] The potential energy stored in this fashion may be converted mechanically, by gears and rods, or by a system for air compression. As the weight is lowered, the air in the shaft may be compressed to activate wind turbines or ventilation devices. Thus the shaft may either serve as weather protection or for air compression. It's a simple method that's nearly as easy as the hydraulic pumping of my example.

An imagined potential energy shaft affixed to a building exterior.

In this proposed implementation, photovoltaic energy is used for weight-lifting.

### References:

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