A little corner of Nevada...

Elon Musk recently said that that "...a corner of Utah and Nevada..." could power the entire United States with solar power.

I wish that were true, but his numbers are way, way off. By multiple orders of magnitude.

Elon Musk's Claims At Face Value

Solar irradiance is a very well understood, and very thoroughly mapped unit of measurement.

Assuming "a corner of Utah and Nevada" sees upwards of 2000 kWh/sq-meter annually, and assuming the solar panels are running at 20% efficiency, this would yield no more than 400 kWh/sq-meter annually.

Annual world energy consumption for 2012 was 524.076 Quadrillion BTU, which converts to 153,596 TWh/year.

To determine required land coverage area, we would divide total world energy consumption (153,596 TWh) by the amount of energy possible per square meter (400 kWh). The US consumes roughly 18% of the world's energy, so only take 18% of the final result.

153,594 TWh / 400 kWh = 383,985,000,000 sq-meters (148,257.44 square miles)

Well, there you go, 26,686 square miles is all that Elon Musk claims we'd need. Except for one little detail, Elon Musk's estimate is not complete yet.

For the remaining discussion, I'm going to upscale the numbers from US-only, to the entire world's energy needs. Don't worry though, for a clear picture, we'll reduce them back to the US's 18% take once we have realistic numbers to work with.

When The Sun Sets

Solar power plants have a best-case capacity factor of around 25%. Meaning they're only good for such peak energy needs during just 6 hours during a 24 hour day. We need power 24 hours a day. Therefore, during this small small 6 hour/day window, we must generate four times as much power to ensure we have sufficient energy during the peak 6 hours, and for the remaining 18 hours in that day.

Assuming the US tried to generate enough power for the entire world, the required 148,257 square miles of solar panels would now become 593,000 square miles.

The state of Alaska is 663,267 square miles.

Elon Musk's estimate is again, still not complete, there's another significant facet to consider.

Comparing The Real World to Marketing Hype

We must take the earlier coverage estimates, and allow for realistic overheads (e.g. mounting space between panels, service/maintenance access, wiring, etc).

Looking at existing PV solar facilities would give us realistic numbers. For instance, the Agua Caliente Solar Project would make an excellent comparison. This 2,400 acre (0.375 square mile, or 9,712,455 sq-meter) facility is expected to produce 626.219 GWh/year (626,219,000 kWh/year). Therefore, this facility produces 626,219,000 / 9,712,455 = 64.48 kWh/sq-meter annually, using panels that are supposedly ~17% efficient.

If we swapped these 17% efficient panels for 20% efficient panels, it would be fair to say that plant efficiency would have been increased by a factor of 1.176.

Now, we have real-world numbers to work with.

Down To The Facts

For consistency, let's assume 2,400kWh/sq-meter solar irradiance. It's higher than Elon Musk's claims, but it matches the value claimed by an existing solar facility:

  • 17% efficient solar PV plant produces 64.48 kWh/sq-meter annually (actual). This yields a real-world panel efficiency of 2.69%.
  • 20% efficient solar PV plant would produce 75.83 kWh/sq-meter annually. This yields a real-world panel efficiency of 3.16%.

Now that we have real world efficiency numbers, we can establish a true land-coverage requirement.

To determine required land coverage area, we would divide total world energy consumption (153,596 TWh) by the amount of energy possible per square meter (75.83 kWh).

153,594 TWh / 75.83 kWh = 2,025,5044,200,000 sq-meters (7,820,516 square miles)

Don't forget to multiply the power requirements by 4, to account for solar's meager best-case capacity factor of 25%.

The Bottom Line

The bottom line is, if we began deploying 20% efficient solar panels into production today, around 320% of North America would need to become a solar power facility, in order to meet today's world's energy requirements.

The 320% figure assumes that solar insolation is constant at ~2400kWh/year, when in reality most of North America sees at best around 1500kWh/year. Acknowledging these facts would require converting upwards of 500% of North America's land mass, to nothing but a solar facility. We'll skip this specifics of this calculation for now though, there's no point in pursuing such a consideration.

Let's take a step back, and assume that solar insolation is constant at 2,400kWh/year, now looking at what the US would need to meet their own energy needs, assuming 100% solar:

  • In 2012 the US consumed 95.058 Quadrillion BTU, or about 18% of the world's total energy.
  • The US would need to cover 1,407,692.88 square miles of land (47% of the country) with solar power plants, before meeting current energy demands.
  • If we adjusted for Real World solar insolation numbers, we're looking at covering upwards of 75% of the United States in nothing but solar panels.
  • Now multiply the land coverage requirements by 4, to account for solar's poor capacity factor of ~25%.
  • After all this is covered (pun intended), don't forget the topic of providing power 24 hours a day. Solar is only good for around 6 hours per day, which means we need upwards of four times the generation capacity; storing the rest for consumption during the remaining 18 hours. How, and where exactly, are we going to store this energy?
  • If you're looking for a good visual comparison, less than 2% of the United States is covered in asphalt.

That's quite a bit more than a small corner of Nevada.

What Now?

Our energy needs are increasing by approximately 20% per decade.

Even with orders of magnitude improvement in efficiency, in cost-reductions, and/or in reduction of raw material needs, solar isn't going to save us. Not now, and most certainly not within the lifetime of any living human.

We need solutions within the next couple of decades.

It's time to stop wasting energy, what are you doing to reduce your energy demands?