two percent solution?

Glenn points out a fellow who notes the potential of solar energy:
“If 2 percent of the continental United States were covered with photovoltaic systems with a net efficiency of 10 percent, we would be able to supply all the U.S. energy needs,” said Bulovic, the KDD Associate Professor of Communications and Technology in MIT’s Department of Electrical Engineering and Computer Science.
Um, ok. Glenn notes “Two percent is a LOT of land”, but that’s understating the case a bit I think.
Let’s do some math! (I was told there would be no math. Shhh!)
According to this page, the total land area of the U.S. is 3,537,379 square miles. Take away Alaska and Hawaii to get the continental U.S., and you are left with 2,959,005 square miles. Two percent of that is…
Fifty-nine thousand, one hundred and eighty square miles. That’s 59,180.
For perspective: Over half of the fifty states are smaller in area than 59,180 square miles. The closest in size to that number are Iowa (55,869), Michigan (56,804), and Georgia (57,906).
So: who’s for paving over Georgia?
Because unless I’m missing something, that is what we’re talking about: literally paving over that much area, and I have to assume utterly destroying any flora, fauna, or other living things that are unlucky enough to have been previously occupying it. Unless they happen to, you know, not require sunlight.
Now that would be one hell of an Environmental Impact Study.
Professor Bulovic seems to have thrown out this statistic as a positive for solar energy, but he’s obviously never negotiated with a local zoning board. If that’s the best future we can hope for with solar as our primary energy source, I suspect even the most strident environmentalists will cry out, “Bring on the coal!”


Update: Commenter Eric points out that I shouldn’t be subtracting Alaska, as Bulovic said continental U.S., and he’s right. I’m not updating as the point is still valid (more so!)
Update: Lots of good discussion (and more math!) in the comments. And reader Ric sends in the following, which was a bit too HTML-heavy for the comments section:
Let us begin with data. The U.S. Energy Information Agency estimates total energy usage for the United States for 2004 at 99.74 quadrillion BTU. Converting to watt-hours using Convert.exe gives 29.23 quadrillion watt-hours. A quadrillion is 1015. To make things simple, round up to 3×1016 watt-hours.
The year is 365.242199 days long. If we divide that 3 x 1016 watt-hours by 365.242199, we get about 8.2 x 1013 watt-hours used per day. That energy must be collected while the sun is shining, of course.
The Solar Constant, the amount of energy reaching a flat surface perpendicular to the sun’s rays at Earth orbit, is 1.367 kilowatts per square meter. Atmospheric attenuation of incident solar radiation is from 30% to 90% depending on cloud cover. If we assume that we are in a sunny area with minimum attenuation, the amount of energy reaching the surface is 0.7 x 1.367 = 0.957 kw/m2 or 957 watts per square meter.
It’s fairly obvious that an array big enough to collect 8.2 x 1013 watt-hours is going to be too big to turn so that it always faces the sun. The United States is mostly well above the Tropics, so in order to get one meter of area perpendicular to the Sun’s rays we must have more than one meter of surface area; to be specific, the effective area is n cos alpha, where alpha is the latitude of the site. Most of the nice clear areas are in the desert Southwest, and a good average for the latitude there is 32 degrees. 957 watts per square meter times cosine of 32 degrees gives 811 watts per square meter.
The Sun rises and sets, and the angle of the Solar radiation varies according to a sine wave. Since we can’t move the array, we have to calculate the average energy arriving, which is 0.707 (root mean square of a sine wave) of the peak. 811 times 0.707 gives 574 watts per square meter.
If the solar collector is 10% efficient (we’ll get back to that) we thus recover 57.4 watts per square meter.
Checking the average hours of daylight we discover that the worst case is December, with only about 10 hours of daylight at 32 degrees latitude. Our solar collector has to keep up, so it has to collect the 8.2 x 1013 watt-hours in only 10 hours, at an average rate of 57.4 watts per square meter. That makes the area of the array 1.43 x 1011 square meters. That’s a bit over 55,000 square miles, close to what the Professor came up with.
And there are kickers.
Only 10/24 of that energy will be consumed as it’s generated. We have to store 14/24 of that for use when the Sun isn’t shining. 4.8 x 1013 watt-hours is a lot of energy to store.
Lead-acid batteries store about 41 watt-hours per kilogram. So we need about 1.17 x 1012 kilograms, or 1.17 billion tonnes, of lead-acid batteries to store the energy. Around 3 million tonnes of lead are mined each year, so that’s only a little less than four hundred years of world production. Lead-acid batteries in deep-discharge service last about five years, so the best way to maintain the array would be to round up to 1.4 gigatonnes of batteries; at any given time, 230 megatonnes of batteries would be undergoing reprocessing.
The EPA’s gonna love it, don’t you think?
Note that NiCADs are even worse. NiMH is better at 95 watt-hours per kilogram, but if you think lead is a problem, go look up nickel production. Lithium-ion is even better at 128 wh/kg, but if the production figures don’t give you pause you should look at the safety data pdf.
Oh, by the way, the power’s being produced in the Southwest. Power demand is largely in the Northeast. Add 20% (minimum) for transmission losses. Over that large an area, add another 10% for occasional cloud cover, and a further 20-25% for losses due to dust and dirt on the solar arrays.
And — those solar cells are 10% efficient, remember? Roughly 20% of the loss is in reflection, light reflected back into space from the array. The rest of it, 70% of the incident light or roughly 5.75 x 1014 watts, is heat. How much power will the fans to carry it away use? Will they have blue LEDs inside? Methinks the site will be popular with hang glider enthusiasts, provided they don’t mind being warmed a bit by the reflected light…
Do try to think things through a bit. Wishing isn’t physics.
Regards,
Ric

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67 replies on “two percent solution?”

  1. All of the above assumes that solar cells could simply be made with no expenditure of energy. Whereas actually the creation of solar cells is very energy intensive. In fact, except under “ideal conditions”, a solar cell requires more energy to create it than it will ever generate.

  2. Quote: “No one who is connected to the grid now uses a storage battery with solar. You feed into the grid in the day, and take back at night, with the meter running the same rate both ways. Usually you break even or better.”
    Um, nope. The utility company won’t buy your power unless your state law forces them to. And “usually you break even”? Huh? The system I’m working with will be lucky to defray a third of the bill, I’d be happy with 20%, in summer. You’re right, battery storage is a bad idea. Witness, I have about 40 huge Ni-cads to get rid of. Anyone want them? Someone let them sit for a few years and now they’re just big heavy jugs of poison.
    No, solar is great until you start actually DOING it. Then, it’s a butt pain, plain and simple.
    Speaking of butts though, has anyone factored in the possibility of tiling over Michael Moore’s or Oprah’s butts? Might save a few acres of farmland.

  3. Covering large areas of the Earth in plastics and metal? Has anybody calculated the effect on ground temperature, cloud formation, local microorganisms and so on?
    If all that sunlight never reaches the earth, climate will change. And after being told so for three decades, I´m now against it. Let Gaja breathe!

  4. Why not collect the solar energy on the moon and beam it to micro receptors on the earth? I think a Professor at the University of Houston has published a paper on this energy source.

  5. As and engineer in the power industry, I have to add that 59,180 miles sounds like a lot, but you must remember that it is a small percentage. That 2% calculation was also for an energy conversion efficiency of 10%, which is by the way about the same as a light bulb is able to do making light. There are a lot of commercially available solar cells that are around 20% energy efficiency, and I’ve read about a few that achieve close to 30%. They are three times better at making energy from light then an average light bulb is at producing light from energy.
    Also a lot of people have mentioned that there is a need for energy storage. There are a couple of possible solutions. The best solution would be a world wide very high voltage grid. The sun is always shining on the earth somewhere. However, that solution is probably unlikely. I’ve read that there are some efficient chemical phase change solutions that are being researched (liquid-solid, liquid-gas type of stuff). But the best way is just to produce electricity during the day, when it is used the most, and make up the slack with the existing system. Currently we have to design systems for one day out of the year the peak energy usage. If people begin to produce electricity locally it will reduce the load that we’d have to design for (probably both on the generation and transmission sides), and curb our use of other forms of energy.
    The simple fact is that when solar cells become cheap enough people will just start taking out home equity loans, buying them and installing them.

  6. How about doing the math for a single house.
    A large house is a 200 Amp system. Let’s do a monster house, 600 amps. 600 Amps * 110 Volts = 66000 Watts = 66 Kw. So it would seem that a 66 Kw generator would be sufficient for even a large house.
    Using your calculated value. We can get 57.4 watts/Sq Meter from a solar cell. The size of the solar cell generator then would be 1200 Sq Meter.
    The array would need to be 30M x 40M. A normal house would only be 1/3 of that or 10×40. This is barely on the edge of possibility. I believe that it would be economically feasible if the cost of the entire setup was around $35,000. So each 1 meter cell would have to be around $30.
    Removing only the households from the nation’s energy needs is not a total solution but it is a giant step forward.

  7. If you like solar, try solar. Risk your own money — don’t wait for “the gummint” to do it.
    You may well lose your shirt — but it’s your own.
    I am an engineer. I’ve started up about 15 simple and CC gas-turbine plants. Oh, and I have an MBA and I did my Master’s on the impact of NUG’s on utilities. Does this make me a genius ? Hardly. Does this mean I’ve spent lots of hours looking at energy and electricity from an engineer’s and a businessman’s POV ? And had my conclusions peer-reviewed ? Yes.
    Thanks to Ric who’s done a fabulous job of outlining the majority of the problems. Some of us — myself included — might quibble over one or two of his assumptions, but NOTHING I add or take away changes the conclusions significantly The key points are still valid even if you change a “3.6” to a “3.42.” Unless he’s wildly in error — and I don’t see anywhere he is — the “gummint” can’t do much to save us with solar power on the surface of the earth.
    There are ways we can save ourselves, at least a little. I use solar power right now. It’s not photovoltaic — PV’s are ugly. Generating meaningful, dependable power is a major pain, and a major cost, and they deteriorate and they have about 15 other things that make engineers go “Ick!”
    Instead, I have two collectors on the roof, approximately 4 sq. meters, that in the summer pre-heat and store 50 gallons of water on the inlet side of my NG-fired water heater. In the winter during high sun they supply warm air to my house, inlet into the family room where we spend most of our time. I use this setup specifically because I do not and cannot depend on the sun shining at any particular time. If I have the water warming up, great. If not, the NG heater will do it for me. Likewise the warm-air — the furnace will supply heat if the roof panels can’t.
    The system does not supply all of my energy needs. It doesn’t even supply 50% in the summer. But it’s nearly zero maintenance, has lasted 10+ years without refitting, and was not horribly expensive. With the addition of intelligent thermostats, it’s a welcome addition that reduces my external energy needs somewhat.
    And, and last but not least, someone mentioned solar power from space. This is usually mentioned in the context of orbiting power satellites. This I would be interested in seeing the “gummint” pilot, simply because the entry costs are too steep for most citizens and corporations, and there are a lot of engineering problems to be worked out. Yes, advocates have cited “off the shelf” efficiencies approaching 80%, but (here’s one of those sticky engineering issues) NEVER at the power levels proposed. Simply because you can do it with a 10 Watt beam dows not imply you can do it with a 10 GW beam. Only time and experimentation will tell.
    Is further development of solar useful ? Yeah, probably. I think a diversified energy policy is wise, and blame the Carter administration for not substantially funding one in the late 70’s when it became obvious to all of us that this wasn’t going away.
    But will it substantially alter the energy equations in my lifetime ? Almost certainly not.

  8. You know… it’s obvious that meeting 100% of our energy needs through photovoltaics or other forms of “sun power” is unlikely.
    But wouldn’t it be nice to see what percentage we could get up to anyway?

  9. How long does a solar cell last? How much energy is used in its construction? That’s another factor in the viability of this technology. Refining silicon is very energy intensive (zone refiners use a lot of pwer).
    I personally believe that a cheap 25%-efficient solar cell will lead to widespread adoption of solar as a power generation mechanism, but as always renewables (with the exception of hydro) perform poorly when usec to supply base load.

  10. Query: Why is wind power being overlooked so quickly? Esp vertical turbine windmills?

  11. We don’t need 100% of all energy needs supplied.
    Even if we could only get it up to a sizeable percentage of energy demand in an area during daylight hours, that would e a huge leap foreward.
    If there is excess capacity, then it could be used to charge up your PHEV or EV, and store energy that way.
    The comments about passive heating of water or air are important too. This type of system is much cheaper and has a faster ROI as a consequence, and it puts a dent into the problem.
    Like I noted above, nuclear and clean coal (and wind which will probably max out at around 20% of electrical generation) will all need to be part of the problem.

  12. Round numbers:
    Cost of PV system: $20k
    Tax credits: $10k
    Edison Bill: $90 month
    x12 months
    ==========
    approx $1000 per year
    Ten year return on investment,
    Did you include maintaining the system in your calculations? I don’t have numbers, but I imagine costs associated with maintaining the system could easily double or even triple you projected break-even point. You may be able to do the basic cleaning (though even that would probably require special equipment), but can you do the more intensive scheduled maintenance, and what about repairs? I think your 10-year projection is more than a little optimistic.

  13. We shouldn’t get too caught up in ROI (unless the numbers are really horrible).
    What’s the ROI on owning a house rather than renting? Obviously this depends on several factors and local conditions, but absent ridiculous appreciation, it is probably at least 5 years, sometimes more. And houses require lots of upkeep and maintainence, property taxes, etc.
    Even is the solar systems have a monetary ROI equal to their lifespan (ie they just pay for themselves) it is still worth it in terms of energy saved (as long as they meet their energy ROI), flexibility in the grid, reduced polution and GHG emissions, etc IMO.

  14. Tim asked
    “Query: Why is wind power being overlooked so quickly? Esp vertical turbine windmills?”
    Utilities generally dislike wind power, because they are in the business of maintaining voltage, and letting the current go where it is needed. Wind power usually needs a good deal of other equipment to get the generating stations to maintain the voltage within tolerances.

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