Is There Enough Room For All Those Solar Panels?

One criticism of solar cells is that they supposedly cannot generate a large enough amount of electricity in a small area--sort of an energy density problem.

Now, I'm a huge fan of solar cells, and I think they are basically going to save the world. But lately I've been thinking--What if we would have to cover a ridiculously large area with solar panels to generate all of the electricity we need?

To get a better handle on the size required, I decided to try and run a few numbers. The question: How much area covered by solar panels does it take to generate the same amount of electricity produced by a typical coal fired power plant?

I would estimate that a typical coal power plant, including the cooling towers, piles of coal, and whatever else, would take up between 2,000 and 3,000 acres. This page from Progress Energy describes a new nuclear plant that will have a 3,000 acre footprint for the entire complex, and a coal plant should take up a comparable amount of space.

I also have made some assumptions about the space required for solar cells, the amount of insolation at a typical site, and the efficiency of the installed solar cells. The basic assumptions are then:

• 300 acres required for typical coal fired power plant
• 1,000 MW of capacity for a typical coal fired power plant
  
• 6 kWh / m^2 / day of insolation
• 16% solar cell efficiency
• 50% of area effectively covered by solar panels (they will need some empty space around them so that they could be directed toward the sun throughout the day, but this number is probably very high)
  

And the calculations:

3000 acres * 4,047 m^2 / acre = 12,141,000 m^2

50% * 12,141,000 m^2 = 6,070,500 m^2 of area effectively covered by solar panels

6 kWh / m^2 / day * 6,070,500 m^2 = 36,423000 kWh / day of insolation on our solar panels

36,423,000 kWh / day * 16% = 5,827,680 kWh = 5,828 MWh of electricity produced each day

Whereas the power plant, operating 90% of the time at peak capacity, would produce:

1,000 MW * 90% * 24 / day = 21,600 MWh of electricity each day

And for comparison:
21,600 MWh / 5,828 MWh = 3.7

Hmm. At first glance that may not seem very encouraging. It would take 3.7 times as much area to produce the same amount of electricity from solar panels as from a coal fired plant. But there are a few more things to consider.

First, we're not taking into account all of the space required for mining the coal, storing the coal off site before transportation, transporting the coal to the plant, and dumping any waste left over from the plant's operation. I realize that silicon must also be mined and processed to produce solar cells, but that process takes place on a much, much smaller scale (perhaps we should look at those numbers in a future posting).

The 3.7 number is just a very rough estimate, and it can be brought closer to or even below 1 by adjusting the area required for the actual entire operation of a coal fired plant. Basically, though, if you wanted to offset the roughly 20,000 billion kWh of electricity that the world produces each year, you would need to cover:

20,000 billion kWh / ( 16% * 6 kWh / m^2 / day * 365 ) = 22,000 square miles

with solar panels. Whew! That's a lot, but consider this:

• The US alone has about 350,000 square miles of paved roads (10% of the 3.5 million square miles of US land)
• As much as 75,000,000 detached homes * 2000 square feet of roof / detached home = 5400 square miles of detached rooftops in the US!

This doesn't even consider warehouses, apartment buildings, schools, factories--only detached homes. Maybe 22,000 square miles isn't so bad after all . . .

I apologize for the length of this post, but I got wrapped up in the calculations. At the end of it all, though, it seems clear that world is not going to run out of room before we are able to convert completely to solar power. The numbers I have used are very conservative, and solar cell efficiencies are constantly improving, shifting the balance more and more in solar's favor.

To see just how much solar cell efficiencies are improving, read my next post.