Sunday, March 8, 2009

More Mathematical Mumbo Jumbo.

The other day I pointed out the diminishing retrurns of increasing a Module's Conversion Efficiency. The folks on Daily Kos nicely pointed out how trivial the results really were. Well, I can live with that. I think the post still serves to make very clear that the percentage change in output Energy is, in fact, proportional to the percentage change in Conversion Efficiency (I don't know, I guess I just had to see it for myself).

As usual, if there are errors, please let me have it; though please point out a specific or two rather than just saying "check your math."

So, turned into a simple equation, increasing a module's Conversion Efficiency increases the total energy panel output per unit time and per unit area by (Conversion_Efficiencyfinal / Conversion_Efficiencyinitial - 1) * 100%.

For example, the percentage difference between the Annual Energy Output of a 16% Efficient Panel and a 20% Efficient Panel would be (20/16 - 1) * 100% = 25% (assuming constant Area).

Following from this, I'd like to get a few more bits of information from these variables.

Effects on Surface Area of Improving Conversion Efficiency:

It could be said that PowerPeak (W) = InsolationPeak (W/m2) * Area (m2) * Conversion_Efficiency (%).

Setting PowerPeak and InsolationPeak as Constants, then we can say that C = Area * Conversion_Efficiency.

Take two scenarios, say, Case 1 and Case 2.

C1 = Area1 * Conversion_Efficiency1.

C2 = Area2 * Conversion_Efficiency2.

C1 = C2

Area2 / Area1 = Conversion_Efficiency1/Conversion_Efficiency2

Let's imagine a Solar Manufacturer and set today's average Conversion Efficiency at 16%, and let's say that by 2012 the average Conversion Efficiency will be 22% for some company.

Area2 / Area1 = .16/.22 = .72 = 72%

So, in order to generate the same amount of Peak Power at 22% Conversion Efficiency vs. 16% Conversion Efficiency, the manufacturer need produce only 72% as much area of PV material. Nice.

I'm not sure how "deep" this thought is, but I'm putting it out here, at the very least as a future resource for myself.

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