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# Fact checking Elon Musk’s Blue Square: How much solar to power the US?

By Andrew ZP Smith, on 21 May 2015

How much power do solar photovoltaic systems produce per unit of land area? And does it matter: is it a constraint in the real world?

At Elon Musk’s glitzy launch of the Tesla PowerWall and PowerPack batteries, the Tesla CEO showed a map of the US, with a small square in the North-West corner of Texas marked in blue, and said that solar panels over that surface area would be enough to enable US electricity to go carbon-free.

Here’s a quick fact-check on that claim.

How the calculation works
We are comparing current US electricity consumption, to see how it compares to the amount of electricity that would be generated from solar PV panels covering the area shown.
I’ll calculate the PV generation by multiplying the surface area by the efficiency of PV in capturing sunlight and by the amount of PV that could be installed per unit area.

Assumptions
We’re talking specifically about current US electricity consumption. Not all energy, just electricity.
The graphic isn’t about building a solar farm there, to supply the whole US: that would be preposterous. Instead, the graphic is designed to describe the physical area of panels required. i.e. it’s a data visualisation; not a project proposal.

Inputs to the calculation
US electricity consumption is about 425 GW on average
The EIA give a figure of 3,725,101 thousand Megawatt Hours of total electricity sales in 2013, i.e. 3725 TWh in a year. That’s equivalent to 425 GW.

The area shown is 10,000 km2 in NW Texas
Looking at the map presented by Elon Musk, and comparing it with a scale map of the US, leads me to an estimate that the square, in North-West Texas, is about 100km along the side, and thus has a total surface area of 100km x 100km, i.e. 10,000 km2

Average PV yield in NW Texas is about 21%
The USA National Renewable Energy Lab (NREL) provides an online calculator for PV yields, called PVWatts. I looked at the data for location TMY2 Amarillo, TX, which seems close to the area in question. A 1 kW system would generate 1,838 kWh per year (on a 10o slope facing south), which is equivalent to 210W; that gives a ratio of generated power to capacity of 21%.

The highest efficiency we currently get from solar modules is about 24%
Table 2 of Green et al’s Solar cell efficiency tables (Version 45) gives the best PV module as being 24% efficient. And that translates to installed capacity of 0.24 GW/km2, given the standard measure of 1 full sun being equal to 1 kW/m2.

Calculation
10,000 km2 x 0.24 GW/km2 x 21% = 500 GW
Which is more than current US electricity consumption of 425 GW.

Summary
Yes, the area shown is reasonable, as a visualisation of the surface area of panels required to generate electricity equal to total US electricity consumption, on a multi-year average: that area of panels would generate about 500 GW, which is above the current US annual average electricity consumption of 425 GW, with enough spare to account for resistance losses. And do bear in mind that the claim wasn’t about whether demand could meet demand second-by-second, but whether the total amount over time could be met. The whole point of the presentation that the claim occurs in was to sell storage, which is there to bridge gaps between generation and demand.

Photo credit: Activ Solar some rights reserved under creative commons license

### 10 Responses to “Fact checking Elon Musk’s Blue Square: How much solar to power the US?”

• 1
Tomer D. Tamarkin wrote on 18 June 2015:

For a detailed analysis of the surface area required to generate all the electricity currently comprising American baseload power generation by solar please see my article “The Green Mirage.” It is on-line at: http://fuelrfuture.com/review-of-forbes-on-line-magazine-article-solar-energy-revolution-a-massive-opportunity/

• 2
Footprint2Wings wrote on 2 July 2015:

Also, the @EIA gives total US electricity consumption in 2014 as 4093 TWh http://www.eia.gov/tools/faqs/faq.cfm?id=427&t=3 or 467 GW Elon said the blue square was just the amount currently being supplied by fossils which is 67% per the EIA, or 313 GW This is 2.7 times the 114 GW supplied by the blue square

• 3
Footprint2Wings wrote on 2 July 2015:

Thanks for this factcheck. @DavidJCMackay says real solar parks in USA produce much less – about 100 kWh/year per m2 of land area. Because not all slopes are ideal, and you need area around panels for service, etc. http://www.inference.eng.cam.ac.uk/sustainable/book/tex/RSsolar.pdf so a 10,000 km2 area would be 114 GW – so you need four blue squares.

And that’s just electricity. Earlier in the video, Elon said, “People aren’t clear on how much surface area is needed to generate enough power to COMPLETELY GET THE US OFF OF FOSSIL FUELS” and then he switched to “electric generation”. That is misleading. He’s lulling people into thinking this is enough, and first of all, it’s just electricity, which is 1/3 of energy use, and second, it’s only 1/4 of electricity, so the true amount of area required by the US is 12x the blue square or the area of the state of Ohio.

Is that right? That seems huge. Check that math. Also, electric motor efficiencies when you switch from combustion engines to electric – so we’re probably looking at a state the size of Indiana.

• 4
Footprint2Wings wrote on 2 July 2015:

@UCL_Energy Hi I just did a check of your @elonmusk blue square check and it’s off: http://t.co/rSqxeOOZAZ my comment awaits moderation.

• 5
Footprint2Wings wrote on 3 July 2015:

Also, the @EIA gives total US electricity consumption in 2014 as 4093 TWh http://www…. http://t.co/QPMeNqs13P

• 6
Footprint2Wings wrote on 3 July 2015:

Thanks for this factcheck. @DavidJCMackay says real solar parks in USA produce much l… http://t.co/EV0vnj2FvH

• 7
Andrew Smith wrote on 3 July 2015:

A single number for power per unit area for the whole of the USA isn’t really meaningful: there’s very big variation across the 50 states, and Arizona and Alaska have different climates. Elon Musk was very specific about the geography, and so I’ve used the insolation for that area.

And as I write above, panels of that area would generate average electricity of 500GW. Footprint2Wings is correct that if the panels were spaced out further, the same area would generate less power. But we see from the presentation and the data that what Elon Musk was referring to was solar panels of the area shown in the blue square. And he is explicit that he’s talking specifically about electricity. Yes, of course if one were to start from a different reading of what he said, one comes to a different answer; but to do so is to choose to misunderstand what he said.

By the way, it’s worth bearing in mind that electric vehicles are about four times the efficiency of internal combustion engines, so electrifying land transport would give a significant net reduction in energy demand. If you are interested in how the US can meet its energy demand from 100% renewables affordably, securely and sustainably, there is some very valuable work by Mark Z. Jacobson (http://thesolutionsproject.org) & colleagues and by Sandy Macdonald & Chris Clack (http://www.esrl.noaa.gov/events/seminars/seas/2014/052714.html).

Existing solar farms are not designed to maximise generation per unit land area. There’s no reason why they should have been designed to do that, because that would not be the most economic solution; and that’s true of the future too: there’s an absolutely huge surplus of land & sea available for energy in North America, as in every other continent – many times more than needed to meet energy demand. Availability of space was always a red herring, and Elon Musk’s blue square is a beautiful illustration of why this is the case.

• 8
Dwight Black wrote on 2 July 2017:

Andrew I find your study on Solar Energy very illuminating but on a smaller scale such as a 3 square mile city would solar energy work for a northern city of that size.

• 9
Jeff Gaston wrote on 31 January 2017:

Please consider the feasibility of building US National Solar Farms along the path of (and in lieu of) President Trump’s proposed Border Wall. The inherent security around the solar farms could serve the dual purpose of providing clean energy and border security. This idea could unite the entire country. The only possible objection is expense.

• 10
Alberto Enriquez wrote on 2 September 2017:

Some commenters indeed seem deliberately to misunderstand that this is a presentation NOT a construction proposal. Musk specifically states that most of the space needed is already available as rooftops––adequate space has never been the issue––but given that rooftops are dispersed all over the continent there is an energy savings that isn’t mentioned here by either Musk or these shoot-from-the-hip critics. Overall energy losses from power companies to consumers is estimated at 8 to 15 percent. That’s enormous and would be worth pursuing even if it were the only benefit.