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Re: [Phys-l] Efficiency problem



At 16:49 -0400 05/28/2010, Peter Schoch wrote:

I've had a former student return with a question that I could use some help with...

In his community, a developer wants to convert an old quarry that is now a man-made lake into a power generation scheme. The developer would excavate under the quarry. Then, during the day, they'd let the water run from the "lake" down into the holding tanks underneath, in the process turning a generator and creating electricity. Then, at night they'd pump the water back up to the "lake" when the electricity was cheaper. In this way they'd generate electricity and the claim is that this is "green" electricity.

The student came to me because he remembered (yes, I did jump for joy that someone remembered something I had presented them as part of the class!) that no process could have an efficiency of 1, so his thought was that this process is not "green" as advertised. He thought that due to this loss, this process would ultimately consume more electricity than it would generate and that it was just a "shell game" for making money.

Well, my first inclination is to agree with him. However, I did tell him that he was trying to apply an efficiency concept from Thermodynamics to electricity generation. I assured him I'd do a bit of digging and get back to him. Well, I can't seem to find how I might calculate the efficiency for this process and how to determine if it is truly "green" or not -- thus being a way to make money but not be green.

Any suggestions and/or help would be appreciated,
Peter

Actually, not a bad scheme--provided the difference in what he can sell the electricity for during the day is sufficiently more than what he will pay for the electricity he will buy at night. The process is called "pumped storage" and is being used in several locations around the country, but typically, it works by pumping the water with renewable energy (solar or wind) generated "off-grid" which it then sells to the grid when the renewable energy is not available (like at night or when the wind is not blowing).

To put numbers on the process, assume he can sell the electricity during a high-demand period for $0.15 per kWh, and that during this high-demand time he generates 10,000 kWh, thus earning $1500. Now assume that during a low-demand time, he is able to buy the electricity he needs to restore the lake to its prior state for $0.08 per kWh, but that, due to inevitable losses in the pumping process it takes 12,000 kWh to pump the water back up the hill, so he pays $960 to restore the lake to its prior state, for a net profit of $540 for the night. If the purchase price he must pay for the restoring electricity is greater than $0.125 per kWh, he will lose money. This is where the efficiency losses come into play. Although energy is conserved, money is not, so this process can be a money-maker if it is done right.

My simplistic analysis doesn't include any capital costs for excavating a lower reservoir, or installing the generators and pumps, or for the daily operating costs for the process--personnel, maintenance, taxes, etc., to the selling price probably has to be significantly higher than the buying price to cover those costs and yield a reasonable profit.

The advantage of this process is two-fold. First the pumping can be considerably more energy efficient than a thermal process (nuclear, coal, or natural gas turbine) which is limited to usually bout 30-40% thermal efficiency, and second, the process can be turned on or off quickly, thus responding to short-term changes in demand more easily than a coal or nuclear plant, which typically take hours or days to bring on line, can be.

But the economic analysis has to be carefully done or it can quickly turn into a large money sink for the producer.

Hugh

--
Hugh Haskell
mailto:hugh@ieer.org
mailto:haskellh@verizon.net

So-called "global warming" is just a secret ploy by wacko tree-huggers to make America energy independent, clean our air and water, improve the fuel efficiency of our vehicles, kick-start 21st-century industries, and make our cities safer. Don't let them get away with it!!

Chip Giller, Founder, Grist.org