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By Robert Rapier on Jul 27, 2007 with no responses

A Solar Thought Experiment

Note: This is a work in progress. I am modifying the calculations as I get constructive feedback. Credit goes to several people for that. I think I have figured out the best approach to solving this problem in my latest effort.

A comment over at The Oil Drum got me to thinking about what it might take to replace all of our current electricity consumption with solar power. There was an error in that calculation, and some of the information was dated, so I decided to do the calculation myself.

Here is the question. Considering only our electrical usage, how many square miles of solar panels would it take to supply that much demand? And how much would it cost? I actually have no idea how it’s going to turn out, but I want to document the results.

According to the EIA, electricity capacity in 2005 was 882,125 megawatts. That is the capacity required to meet peak demand. Actual demand was somewhat less at 746,470 megawatts.

I have been browsing through some performance numbers for solar cells, and I am finding pretty consistently that one square foot of solar cell can generate about 12.5 watts at peak power. Here is an actual cell from GE (PDF download) that produces 200 watts in 15.68 square feet (12.75 watts per square foot). So, let’s conservatively say 12.5 watts per square foot. To match U.S. electricity capacity would then require square footage equal to 882,125 million watts/12.5 watts/sq ft, or 70.57 billion square feet. This is equivalent to 2,531 square miles, or an area of 50 by 50 miles of nothing but solar panels.

That’s a lot of area to be sure, but it’s not an immediate deal-breaker. Next, I want to know how many square feet are available on houses in the U.S. This is going to be tougher, because only south-facing surfaces are going to relevant.

According to U.N. statistics, in 1997 there were around 100 million houses in the US (another PDF download). Given a population of 300 million, that sounds reasonable. In order to supply our electrical needs on rooftops, that requires the average house to have 70.57 billion square feet/100 million houses, or 70.57 square feet. That’s a square of 8.4 feet on a side. That seems feasible, but a lot of roofs won’t have any south-facing area. Still, it isn’t completely out of the question that we might supply our (current) electrical demands with just rooftop solar power. Of course we would still require conservation and higher efficiencies (both in solar cells and in our electrical items).

And as some readers point out, we have a lot more than rooftops. Of course we do. That wasn’t the point. I just wanted to see if there was enough rooftop space on houses. But we have lots of space on commercial buildings as well.

How Much Will It Cost?

I will take a stab at this as well. This is a bit more difficult, because it isn’t just the cost of 10 billion solar panels. We need to include all of the associated equipment plus the costs of installation. According to this site, you can probably assume conservatively $7 a watt. In large quantities, it might be less. But let’s go with $7. Taking our 882,125 million watt capacity number times $7 then gives $6.2 trillion. If the solar panels last 20 years (probably more, but then I am ignoring maintenance costs), that’s $309 billion a year (ignoring the time value of money, which is very simplistic).

To frame that problem, right now the U.S. uses 21 million barrels of oil a day, which is costing us $65 * 365 * 21 million = $500 billion per year (and climbing).

Anyway, it’s just a thought experiment, but I found it helpful to go through it so I have an idea of the challenge in front of us. There are many caveats. We can produce electricity from lots of other sources (hydro, wind, nuclear, biomass, even coal for now), so solar doesn’t have to assume the entire load any time soon. However, I haven’t even considered the increase in electrical demand that would be required from a mass move to electrical transport.

Definitely a Manhattan Project, but not one that is clearly out of reach. Just difficult, and in need of the right kind of leadership.

I will probably expand this calculation in the future to consider contributions from solar thermal, wind, hydropower, etc. In other words, determine how much solar would realistically have to contribute to offset just our fossil-fuel derived electricity.