Solar must abide to TNSTAAFL

Using solar radiation for energy / electricity generation is certainly a great idea.  In terms of solving current CO2 production (if current concerns prove true), eliminating environmentally devastating coal mining operations and a dependence upon a depleting supply of raw crude oil,  it’s almost one of those stupid simple solutions that somehow we’ve neglected for hundreds of years, even though it was there, shining on us each day.   A strong case to support using direct solar energy (versus, say, fossil fuels) can be made quickly and easily, and might go something like this:

Efficiency of solar panels or solar trough / Rankin cycle technology for electrical generation (electrical generation): ~15%

Efficiency of fossil fuel electrical generation: (E = E_ecosys * E_organic matter to fossil fuel * E_mining and processing * E_burning and electrical generation)

Since this number is hard to calculate, lets simplify it to the favor of fossil fuel: E = E_ecosys * E_burning and electrical generation, taking E_ecosys as 2% and E_burn and electrical generation = 60% we find:

E_fossil fuel electrical generation : <<1.2%

So, use the sun’s energy with 15% eff, or 1.2% eff?  The choice seems obvious.  Best of all, using the direct method is FREE!  You don’t have to pay to mine, process, transport and burn the fossil fuel, you just have to collect solar radiation!  But wait, everyone knows you are not supposed to used the “F” word, because the “F” word violates one of the few time tested truths of humanity “there is no such thing as a free lunch”.  But what does using the sun cost, and why do some (Ken Zweibel, James Mason and Vasilis Fthenakis) suppose that the US could solely rely on solar electrical generation by as early (or late) as year 2100?

The cost of solar is land, because the issue at hand is energy density.   Though expectantly much less environmentally damaging than say, coal mining, solar harvesting requires an unheard of amount of land for el. gen.  Coal and oil mining undoubtedly occupy many thousands of square miles in the U.S. and the world over, but likely less than an equivalent area capable of producing the same energy content via direct solar el. gen.  This is a bold statement, solar would use more land than coal and oil mining?  But there is so MUCH solar energy, how could this be?!  4500 quadrillion BTU’s (4500,000,000,000,000,000) of solar radiation is dumped down on just the southwestern United States every year (Zweibel et. al.)!  Or almost 45x MORE energy than the U.S. uses each year!  So the answer is simple, just cover 1/45th of the southwest United States with solar technology like PV cells and trough / Rankin systems! And voilà, the world’s (or at least the U.S.’s) problems are solved- besides constructing a nation wide grid and the pesky and relentless enormous necessity of land!  Complaints aside, how much land will be required for the U.S. to be direct solar dependent?  Using a current U.S. energy consumption of 100 quads per year, and a 15% solar to electricity conversion efficiency, and a 6.5 kWh/m^2 / day solar intensity in the southwest we need:

Energy use: 100E15 BTU / yr           =       2.93E13 kWh / yr         =        8.027E10 kWh / day


Southwestern solar energy available: 6.5 kWh/m^2 / day


Land required is:

Energy Use / Energy Available per m^2          =        1.23E10 m^2                =               ~5000 sq. miles.

However, this number assumes 100% efficiency, so accounting for eff.:  5000sq. mi. / .15 eff      =  33,300 sq. mi.

Therefore, at a minimum, we would need something on the order of 33,000 square miles, which is on the order of magnitude of the size of a large state, every square inch of an entire state!  Surprisingly, the proponents of the “Solar Grand Plan”, by Zweibel et. al., determine through presumably more realistic calculations that an overwhelming 165,000 square miles is actually required to support the U.S.’s energy needs.  Now like I said at the beginning, solar is very attractive for many reasons, but can we expect it to be feasible to cover 165,000 square miles? That is this big, by the way (orange):

and would be even larger if you wanted the ground to receive sunlight so that plants could grow, or you wanted a city every so often within this massive area for civilization (which the power is for, remember), or you wanted any open space (like a park or forest) to get away from the dense arrays of solar collectors or panels.  At any rate, it just intuitively feels infeasible to cover such a vast expanse of land with equipment for solar power electricity generation. Don’t get my wrong, I support the use of solar, but I am unsure if it is feasible for the United States to rely 100% on solar energy power production due to the shear square miles required.

Lastly, the cost of building something of this magnitude is said to be in the $400B range, and would require national policy, not unlike the American Recovery and Reinvestment Act, but maybe more direct in assisting construction.  Alternatively,  a $.05/kWh  tax could pay for the construction says Zweibel et. al., which seems reasonable- and also leading to my conclusion that it’s not the cost of building solar facilities, but the cost of land usage that will prevent the “free” fuel from succeeding at supplying 100% of the U.S.’s energy needs.



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4 responses to “Solar must abide to TNSTAAFL

  1. tsoenen

    I agree with you. The idea that the U.S. will have a 100% solar energy electricity supply is fairly unrealistic, even with significant efficiency improvements.

    As you mentioned, according to “Solar Grand Plan”, by Zweibel et. al., by 2100, assuming no efficiency improvements since 2020, we would still need to cover 165,000 sq. mi. of land with solar systems to provide for 100% of the U.S.’s electricity needs. Assuming that there will be no technological improvements in 80 years is probably not a great idea. So, let’s look at some numbers to see what the land requirements would be with some substantial efficiency improvements.

    Since Zweibel et. al., didn’t mention what the efficiencies of solar systems would be in 2020, let’s assume that realistic commercial panel efficiencies reach the performance level of panels being produced in labs today, 16.5% (Zweibel, 2008).

    165,000 sq. mi.*0.165= 27,225 sq. mi.

    That means with 100% efficiency in 2020 the realistic land requirements would be 27,225 sq. mi.

    Now lets assume that there are some major breakthroughs in solar technology and the efficiencies go up.

    27,225 sq. mi./.2=136,125 sq. mi.
    27,225 sq. mi./.3=90,750 sq. mi.
    27,225 sq. mi./.4=68,062.5 sq. mi.

    Even with the best case scenario with an efficiency of 40%, we would still need to cover an area about the size of Florida with solar systems. Although that is a big area, if we get desperate I guess it is possible. I just don’t see it happening. The cost of research and installation would be extremely high.

  2. What happens if you factor in transmission losses? In other words, how much extra land do you need to get the electricity to a faraway place? Assuming that the US is 100% dependent on solar energy (though in reality, wind would be an important factor) that is located in the American southwest there will be significant losses that increase the required area even more.

    For instance, let’s take New York City as a case study.

    New York City residents use about 40,000 million kWh/yr or 108 million kWh/day (this is electricity for residential purposes). Using your value of 6.5 kWh/m2 irradiation, the city requires about 6.4 square miles. Factoring in 15% efficiency, 42.75 square miles are needed of pure solar panels. Using your ratio of 5:1 for actual to ideal land required, this number jumps to 213.7 square miles or 709 ft2/person. This is about a quarter the size of Rhode Island or half the size of NYC. For a distance of about 2,600 miles, the transmission losses in a High Voltage Direct Current (HVDC) would be about 20% and even more for High Voltage Alternating Current (HVAC)! Factoring in transmission losses at 20%, the required area jumps to 256.4 square miles or 850 ft2/person. Or each NYC resident requires 1.5% of a football field for residential electricity. Houston residents use 3 times as much per capita on residential electricity and with lesser transmission losses (~2%) require 2127 ft2 or 3.7% of a football field.

    Interestingly, one of the longest HVDC lines in the US is called the Pacific DC Intertie and runs from Northern Oregon to Southern California (846 miles). This takes advantage of the energy demand depending on season. Our theoretical HVDC line of 2,600 miles vastly overshadows the Pacific DC Intertie and an entirely new infrastructure would need to be developed for it.

    HVDC and HVAC are well known technologies, but transmission losses will always occur. It’s important to keep in mind these losses when designing systems very away from cities. The lack of wind or solar resources in the northeast will make it even more difficult to rely 100% on sustainable sources. Power plants will have to be over designed to account for the very significant losses.

    Also, if the average transmission losses are 10%, this increases your required land area to 181,500 square miles.

    [Assuming 8.4 million people in NYC and 468.9 miles2, residential 4696 kWh/year-person]

  3. dmcp123

    Rather than looking at using solar to offset ALL energy consumption (which I agree requires a ridiculously huge amount of area), how much solar land area would be required to offset only current electricity consumption? It turns out that this land area is much smaller and more reasonable:

    According to the EIA’s most recent electricity sales data [1], the US has 1100GW of nameplate capacity and used 2,999.8 TWh (2.9998E12 kWh) of electricity in 2009.

    If you assume that 100% efficient solar PV is put in the desert southwest with 6.5kWh/m2/day (=2373 kWh/m2/yr), this works out to needing 1.264B m2 of area. This equals 488 sq. miles, or a square only 22 miles on a side. Of course this is using a non-existent 100% conversion efficiency system. Using a more realistic 5% overall efficiency (there are 20% DC efficiency panels commercially available, but in addition to typical DC-AC conversion losses of ~25%, there is always unused area due to spacing and roads) this works out to needing 9760 sq. miles, or a square 99 miles on a side. Even small efficiency improvements in panels,inverters, or ground coverages will make a significant impact to this total land area required. Also, some areas, such as Dagget, CA can get up to 9.1 kWh/m2/day if single-axis tracking systems are used [2].

    Further, coal and natural gas fired electricity power plants produce roughly 70% of our electricity, but are responsible for ~40% of all US CO2 emmisions [3]. If all we wanted to do was eliminate these plants (and a huge chunk of our CO2 emissions), we would only need to offset their portion of electricity generation. So now, that land area becomes a square 83 miles on a side. Although this is still a large number, it is not that large when you consider that there is estimated to be over 19 billion sq meters (>7500 sq miles!) of commercial and residential rooftop space available for PV systems in the US – an average of 65 m2 per person [4]. After adjusting for roof tilt, shading, and solar resource, it turns out that rooftop systems, if fully utilized, could account for 500GW to 710GW of production capacity, or as much as half of what the US currently requires. Here’s another nice plot from NREL that shows projections of rooftop PV capacity under various scenarios [5]. Their middle-of-the-road base case analysis shows that rooftop PV could easily account for ~20% of the overall US electricity supply.

    NREL Rooftop PV Supply

    So if distributed, rooftop solar develops to this point, then the amount of remaining land area needed for a PV solar farm to offset fossil-fuel burning power plants is only (70%-20%)*9760 sq miles = 4880 sq miles or a square 70 miles on a side. This is roughly the size of the black dot in CA seen in this plot of the US. While still large, this is easier to imagine (70 miles is less than the distance from Austin to San Antonio) and definitely seems more doable.

    Dot represent the PV area needed to displace coal and gas-fired power plants


  4. Patrick Pace

    Offsetting only current electrical generation would be more feasible and would make a large impact as you suggest. I think it would be neat to also power transportation with clean energy which would increase the electricity demand quite a lot, getting back to concerns over large land requirements.

    I forgot to factor in the capacity factor of ~30% at a high, and that explains the gap between my 30k sq. mi. number and Zweibals 165k sq. mi. number.

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