Curve fitting the wind: A calculation involving the "exponential growth" [View All]

[NNadir]

of wind power.

Frequently in response to my advocacy of nuclear power as a tool in the struggle against global climate change, I am met with remarks about the "exponential growth" of various renewable energy schemes.

Those who are familiar with my thinking - and who understand it correctly - will recognize that I welcome renewable energy, and with the exception of hydroelectric plants, I am generally in favor it it. The big caveat that often leaves me assuming an unpleasant mocking tone is that I do not regard renewables as having much capability to provide base load power, especially economically acceptable base load power. In all cases, I see renewable power as a viable strategy for displacing natural gas peak type capacity and not coal capacity. To replace coal capacity - and I strongly believe that we must replace coal capacity - we must in my view have nuclear power.

In these debates, I frequently note that the scale of renewable energy, in spite of the hype, remains small: The promised potentials have never been realized. To demonstrate these unpleasant facts, I often refer to data on this issue, using links like this one:

http://www.eia.doe.gov/cneaf/solar.renewables/page/trends/table5b.html

When we look at the table in this link, we see that over the last four years recorded, the growth of renewable technologies has been, measured in units of energy, been rather flat with one exception: The growth of wind power. Everyone should know that I support wind power with enthusiasm, and I hope that this capacity will grow quickly - I have high, but realistic, hopes for it.

If you graph this growth it looks (nosily) linear in growth, but suppose we assume that the growth is exponential. What would the exponential function look like?

It happens that curve fitting techniques for exponential functions are well known and readily available. I happen to have built a spreadsheet around this technique which is clearly spelled out here: http://mathworld.wolfram.com/LeastSquaresFittingExponential.html

When I apply the equations contained in the links I find that the "exponential growth" curve for the growth of wind power has the following form, measured in quads (1 quad approximately equals one exajoule) E = 0.0487 e^0.213t where E is the energy, and t is the time, measured in years.

Using this equation, for what it's worth, one can estimate the time required for wind power energy production to grow to be comparable to modern hydroelectric energy production, which is 2.725 quads (about 3% of total US energy demand). If one does this by the appropriate technique, one sees that the answer is 18.9 years.