Here's Elon Musk's Plan To Power the US on Solar Energy (inverse.com)

An anonymous reader shares an excerpt from Musk's keynote speech: Tesla CEO Elon Musk -- whose company makes electric cars and has a new solar roof panel division -- reminded more than 30 state governors at the National Governors Association meeting this weekend exactly how much real-estate is needed to make sure America can run totally on solar energy. "If you wanted to power the entire United States with solar panels, it would take a fairly small corner of Nevada or Texas or Utah; you only need about 100 miles by 100 miles of solar panels to power the entire United States," Musk said during his keynote conversation on Saturday at the event in Rhode Island. "The batteries you need to store the energy, so you have 24/7 power, is 1 mile by 1 mile. One square-mile." It's "a little square on the U.S. map, and then there's a little pixel inside there, and that's the size of the battery park that you need to support that. Real tiny."

Comments

Re:ONE SQUARE MILE?!

[Daetrin]

Okay, let's do some Fermi math.

The US uses about 4 trillion kWh/year. https://en.wikipedia.org/wiki/...

But given a sufficient number of solar panels we only need to store enough for about 12 hours. 4 trillion / (365 * 2) = about 5.5 billion kWh, or 5.5 trillion Wh.

Watt hours to mAh is (Wh)*1000/(V) =(mAh): https://milliamps-watts.appspo...

The US generally uses 120 volts for power so that would be 45.6 trillion mAh.

I have on the desk in front of me a phone with a battery that holds about 3000 mAh and when stood on end takes up a surface area of about 618 mm^2.

45.6 trillion mAh / 3000 mAh/phone = 15.2 billion phones * 618 mm^2 = 9.4 trillion mm^2.

There are 1,000,000 mm^2 / m^2 so that would be 9.4 million m^2, and there are about 2.59 million meters per square mile, so 9.4 million / 2.59 million = 3.6 square miles.

So in order to get in down to one square mile you'd need a stack of phones four deep. This phone happens to be 129 mm high, so a stack of 4 would be 516 mm, or about 1 foot, 8 inches.

On the one hand you'd also need a lot of infrastucture to support those batteries which would also take up some area. However i'm also pretty sure that connecting over 15 billion phones in series would be far from the most efficient way to get the required battery storage.

I believe all that math works out?

Re:The problem includes many incorrect claims...

[stomv]

... including yours. I'm referring specifically to:

Most of those [pumped-hydro] locations are already tapped.

For context, there's about 21 GW of pumped hydro capacity in the United States, which is about 1/5th of the capacity of all operating nuclear power plants in the US. But are most of those locations tapped?

No. I'll give you two general counterexamples.

1. One counterexample is the "west coast" of the lower peninsula of Michigan. There is one pumped hydro facility there, called Ludington. It's roughly 2 GW in capacity (with roughly 18 GWh in storage), and about 1000 acres in surface coverage. The lower reservoir is Lake Michigan; the upper reservoir is a man-made pond. But the geological features aren't unique to Ludington, MI -- it's prevalent on much of the lower peninsula's Lake Michigan coast, the result of dunes formed over millennia as debris blew west to east across Lake Michigan. Bottom line: there's no physical reason why one couldn't build a dozen facilities the scale of Luddington, also using Lake Michigan as a lower reservoir.

2. A second counterexample can be found at Taum Sauk mountain. The Taum Sauk Hydroelectric Power Station is a pumped hydro facility with 450 MW of capacity and 3,600 MWh of storage. The lower reservoir wasn't a pool of water at all until the facility was built; it was merely a fork of the Black River. The upper reservoir is an above ground swimming pool, built on top of the mountain. It's entirely man made. The geographic feature needed -- an elevation delta of a few hundred feet (860 in this case), with a slope common for forested mountainside, near a river -- isn't unique by a long shot.

That's two counterexamples off of the top of my head -- the Michigan coast of Lake Michigan and anywhere you've got a mountainous region with a river nearby. Plenty of technical potential.

The reason we don't have more pumped hydro is because the energy market price differential (LMP or system lambda, depending on region) between 3 am and 3 pm simply isn't large enough. It doesn't make economic sense to build more pumped hydro so long as we continue to burn coal and gas unabated, because the gap between the daily highs and lows aren't adequate. However, if we continue to retire coal and gas (and nuclear as it ages) and we continue to build solar PV, we'll see a flip where the peak price of energy drifts from early afternoon to 9 pm -- and storage will be economic, buying energy at 11am and selling it after sundown. Michigan could be the evening power center for the entire Midwest, and scattered new pumped hydro facilities on select Appalachian and Rocky terrain could easily store significant amounts of solar and wind output nearer the coasts.