The potential of rooftop solar

I think a lot about residential solar installations, and so I thought it’d be interesting to think about how much of a difference solar rooftop installations could make in the U.S. So I’m going to go through some back-of-the-envelope calculations to see how much electricity we could generate if all of the roofs in the U.S. had solar PV (photovoltaic) modules on them.

Before I start, please keep in mind that these are pretty rough calculations. There will be a lot of assumptions made. I’m just trying to get a ballpark number.

Here is the main result I came up with...to see how I got this number, read through the paragraphs following!

Installing solar PV on all of the single-family detached homes in the U.S., using current technology, could potentially offset about 2/3 of the country's residential electricity use. That number is an estimate, and probably a bit high. The discussion following talks about the assumptions I made.

On to the calculations. First let’s calculate roughly how big the average roof is in the U.S. From this link, I learned that the average size of a home in the U.S. is 2330 square feet (http://www.infoplease.com/askeds/us-home-size.html). Now we have to figure out how much that average home area is in terms of roof space. If I assume that the average home is two stories, that would mean that two floors of 1,165 square feet (since 2,330/2 = 1,165) are covered by one roof of 1,165 square feet. But, that’s assuming that roofs are flat, and we can be pretty confident that for single-family detached homes, that’s generally not true. They’re pitched, and that actually gives us a bit more roof area. Let’s assume that the average roof has a typical roof pitch such as 6:12, meaning for every 12” of horizontal extent, the roof drops 6”. So, I can use some simple trigonometry that I won’t bore you with (having already bored myself with it), to calculate that the roof area we started with of 1,165 should be multiplied by 1.12 to get a better estimate of the roof area. Multiplying gives our new roof area of 1302 square feet.

Let’s find out how many single-family detached homes there are in the U.S. From the 2000 census, I see that there are about 70 million of them (see Table 1 on page 2 of this link: http://www.census.gov/prod/2003pubs/c2kbr-32.pdf).

If I multiply those two numbers, number of homes and roof area per home, I come up with 91,175,671,783 square feet of roof space, or, put into scientific notation, and rounding off so as not to be silly, 9.12E+10 square feet. Now, because my teachers in school told me the metric system was the wave of the future, I’ll convert that number of square feet into square meters, which gives me 8.47E+09 square meters. About 8.5 billion square meters.

But now we need to consider how much of those rooftops are exposed to the sun. Since all of the U.S. is north of the equator, to get the maximum sun exposure solar modules should ideally be pointing south. Any modules mounted on a north roof will get little or no sun. East or west facings will get some sun. For the sake of simplicity, let’s say that half of all the roofs in the U.S. have a ridge running east-west (giving you a north and a south roof face), and the other half have a ridge running north-south (giving you an east and a west roof face). So one quarter of all roof area is facing south, and gets the full benefit of sun—we’ll take that roof area at full value. One quarter of all roof area is facing north, and gets no sun/very little sun—we’ll take that roof area as being of zero value for solar, and we certainly wouldn’t go to the trouble and expense of putting solar modules on north-facing roofs. One half of all roof area is facing east or west, and gets moderate sun—we’ll take that roof area as being half-value for solar purposes. Our effective “fully useful” roof area then becomes: 8.47E+09 square meters x [(1/4 x 1) + (1/4 x 0) + (1/2 x 1/2) = 4.24E+09 square meters. A bit over 4 billion square meters.

A big assumption I made in the previous paragraph is that all of the roofs that have sun exposure are not shaded. This is clearly not true; plenty of homes have roofs that are partially or even fully shaded. In the solar business they would be described as not having a full "solar window;" a full solar window would have unshaded access between 9 AM and 3 PM, year-round. So my assumption means that the final number I come up with for potential electricity generation is going to be high. There ARE ways for some of those homes to get better solar access--pole-mounting the solar array immediately comes to mind--but not in every case, I'm sure.

Well, how much electricity could we generate if all of those roofs were covered with solar PV modules? To calculate this, we need to know how much sunlight hits a south facing, and how often it hits it. That can get complicated, because the amount of sunlight coming in at a particular location depends on the time of day, the time of year, the weather, and any shading of the modules. Fortunately, metrics have been developed that help deal with these complexities. The concept of “peak sun” tells us how much solar energy we are going to get under optimum conditions at the Earth’s surface—sun directly overhead, no cloud cover, and so on. The value of peak sun is 1000 watts/square meter. This leads to the idea of “peak sun hours,” which means how many hours of maximum sunlight you get in a day at a given location. This doesn’t mean how many hours between sunrise and sunset at a location, but rather, if we summed up all of the solar energy on a given square meter at a given location over the course of a day, how many equivalent hours of “peak sun” (1000 watts/sq. meter) would we get. So using peak sun-hours for a location, we can determine how good or how bad a site is for solar energy capture.

Peak sun hour data is tabulated at many internet sites; you can look at maps by region, or look up data for specific cities. Listings are for daily averages over the course of a month, or over the course of a year. Unfortunately, I haven’t been able to find a U.S. average number over a year…the best I have found is average number over a year for a given region, as shown in this map here: http://www.wholesalesolar.com/Information-SolarFolder/SunHoursUSMap.html. So I’m unfortunately just going to have to guess at a national average. The worst zone, Zone 6, gets about 3.5 peak sun hours/day, year round. The best zone, Zone 1, gets about 6 peak sun hours/day, year round. A lot of the country falls into Zones 3, 4, and 5, so let’s just call Zone 4’s value of 4.5 peak sun hours/day the U.S. average value.

Whew! From all this, we can estimate how much energy is falling on our roofs on an average day—it’ll be more in the sumer months, less in the winter months, but on an annual basis it’ll average out.

4.24E+09 square meters x 1000 watts/square meter x 4.5 hours/day = 1.91E+10 killowatt-hours per day. (I quietly converted watts into kilowatts). But how much of this could our solar modules capture? For this calculation, let's plan on using the "traditional" silicon PV modules, with efficiencies around 13%, rather than thin-film modules which have substantially lower efficiency (but which have the benefit of lower cost). So if we multiply the amount of incoming energy by our efficiency that should give us the amount we could hope to capture in a day.

1.91E+10 kWh/day incoming energy x 13% efficiency = 2.48E+09 kWh/day potentially captured

Over the course of a year, that could provide 2.48E+09 kWh/day x 365 days = 9.04E+11 kWh total. That’s 907,000,000,000 kWh, or 907 billion kWh annually.

How does that compare to the total amount of electricity generated in the U.S.? From the EIA (Energy Information Administration: see http://www.eia.doe.gov/cneaf/electricity/epa/epat1p1.html), I see that the total amount of electricity generated in the U.S. in 2006 (the latest year for which they list the data) was 4.06E+12 kWh, or 4 trillion kWh.

Diving the two numbers, we find out that we could replace about 22% of our total electricity generation needs using just rooftops of single-family detached homes! If we look at it just on the basis of powering residences, I calculate you could offset about 67% of total residential electricity use with just single-family detached rooftop solar! (See http://www.eia.doe.gov/cneaf/electricity/epa/epat7p2.html for a breakdown of electricity use by sector).

I realize there are other issues involved than just kWh generated per year. Rooftop PV isn't just a drop-in replacement for power plants. The electricity generated from rooftop PV is variable, and not controllable, in the sense that 1) you can't just bring it on-line or take it off-line to match electrical demand, like you can with gas-fired generation, or 2) you can't use it 24 hours a day for baseload generation, like you can with coal/nuclear. I'm just trying to be as up-front as I can with the limitations of this estimate.

But as an estimate of the order of magnitude of what could be accomplished, even with today’s technology, I find the potential of solar photovoltaics to be quite impressive!

Hope you enjoyed this!