# A Solar Thought Experiment

Note: This is a work in progress. I am modifying the calculations as I get constructive feedback. Credit goes to several people for that. I think I have figured out the best approach to solving this problem in my latest effort.

A comment over at The Oil Drum got me to thinking about what it might take to replace all of our current electricity consumption with solar power. There was an error in that calculation, and some of the information was dated, so I decided to do the calculation myself.

Here is the question. Considering only our electrical usage, how many square miles of solar panels would it take to supply that much demand? And how much would it cost? I actually have no idea how it’s going to turn out, but I want to document the results.

According to the EIA, electricity capacity in 2005 was 882,125 megawatts. That is the capacity required to meet peak demand. Actual demand was somewhat less at 746,470 megawatts.

I have been browsing through some performance numbers for solar cells, and I am finding pretty consistently that one square foot of solar cell can generate about 12.5 watts at peak power. Here is an actual cell from GE (PDF download) that produces 200 watts in 15.68 square feet (12.75 watts per square foot). So, let’s conservatively say 12.5 watts per square foot. To match U.S. electricity capacity would then require square footage equal to 882,125 million watts/12.5 watts/sq ft, or 70.57 billion square feet. This is equivalent to 2,531 square miles, or an area of 50 by 50 miles of nothing but solar panels.

That’s a lot of area to be sure, but it’s not an immediate deal-breaker. Next, I want to know how many square feet are available on houses in the U.S. This is going to be tougher, because only south-facing surfaces are going to relevant.

According to U.N. statistics, in 1997 there were around 100 million houses in the US (another PDF download). Given a population of 300 million, that sounds reasonable. In order to supply our electrical needs on rooftops, that requires the average house to have 70.57 billion square feet/100 million houses, or 70.57 square feet. That’s a square of 8.4 feet on a side. That seems feasible, but a lot of roofs won’t have any south-facing area. Still, it isn’t completely out of the question that we might supply our (current) electrical demands with just rooftop solar power. Of course we would still require conservation and higher efficiencies (both in solar cells and in our electrical items).

And as some readers point out, we have a lot more than rooftops. Of course we do. That wasn’t the point. I just wanted to see if there was enough rooftop space on houses. But we have lots of space on commercial buildings as well.

How Much Will It Cost?

I will take a stab at this as well. This is a bit more difficult, because it isn’t just the cost of 10 billion solar panels. We need to include all of the associated equipment plus the costs of installation. According to this site, you can probably assume conservatively \$7 a watt. In large quantities, it might be less. But let’s go with \$7. Taking our 882,125 million watt capacity number times \$7 then gives \$6.2 trillion. If the solar panels last 20 years (probably more, but then I am ignoring maintenance costs), that’s \$309 billion a year (ignoring the time value of money, which is very simplistic).

To frame that problem, right now the U.S. uses 21 million barrels of oil a day, which is costing us \$65 * 365 * 21 million = \$500 billion per year (and climbing).

Anyway, it’s just a thought experiment, but I found it helpful to go through it so I have an idea of the challenge in front of us. There are many caveats. We can produce electricity from lots of other sources (hydro, wind, nuclear, biomass, even coal for now), so solar doesn’t have to assume the entire load any time soon. However, I haven’t even considered the increase in electrical demand that would be required from a mass move to electrical transport.

Definitely a Manhattan Project, but not one that is clearly out of reach. Just difficult, and in need of the right kind of leadership.

I will probably expand this calculation in the future to consider contributions from solar thermal, wind, hydropower, etc. In other words, determine how much solar would realistically have to contribute to offset just our fossil-fuel derived electricity.

## 102 thoughts on “A Solar Thought Experiment”

1. How do these numbers change if you include non-PV solar generation, e.g. solar thermal?

2. Sorry, one more quibble: Are you sure that the demand number from EIA is average, not peak demand? Your calculations assume that it is average demand.

3. Actually that was total yearly demand, so your point is well-taken. You have to have enough to meet peak demand.

But, there are many, many things that would make these numbers a lot better. Solar thermal, for instance, as you mention in your first comment. But I am too tired to tackle that one right now.

4. Doug says:

I think you’ve overestimated the productivity of the panels. They don’t produce their rated capacity for anything like 10 hours per day. There is a chart (sorry, I can’t find the link) that gives you a number (in hours) for insolation, depending on where you live. For example here in sunny northern cal, the number is around 4.5 hours. Another factor that must be considered is DC/AC conversion. According to solar contractors I’ve consulted re. a possible system for my home, you have to lop off an additional 10% from the production. (In principle, we could switch houses and appliances to DC and get a double savings – avoid the losses in the inverter and avoid losses in appliance power supplies.)

5. I think limiting it to houses is short-sighted, although maybe you’re just being conservative.

At least in the West we have square miles upon square miles of tilt-up flat-roofed office, retail, and industrial buildings. And cos(90 – latitude) of those roofs are “facing south”, so to speak. There may also be better economies of scale with a 20,000-square-foot installation than with a 1,500-square-foot project.

6. Doug M says:

Your last few posts have been very thought-provoking. Keep up the good work!

Have you considered what the energy storage costs will need to be? We need to be able to keep the lights on at night, you know! That would probably necessitate some sort of battery for each house. I have no idea what that would cost.

One quibble that I have with these kinds of thought experiments (even though they are fun to do!): They force us into a “one solution” mindset, when diversification of energy sources should be a goal as well. If you have a good mix of sources, then you cover all of the bases, and each source can also be “tuned” to what it does best (i.e. nuclear/wind/wave for baseload, solar for distributed load (and some peaking) and natural gas for peaking.)

7. Doug says:
8. Doug says:

Sorry, one more time:

nrel

You can get a nice chart showing hours and/or kwh available across the US, averaged, or by month, or whatever. I like the averaged 2-axis plot.

9. Robert – check your math. You are confusing Watts and Watt-hrs again. According to my link in the EIA , the US generated 3,953 billion kWh. Divided by 8,760 hours per year gives us 451 gigawatts of average production.

Except that power consumption in the US peaks in the day and during the summer months. So the installed capacity has to be about twice the the average. Peak summer capacity is 948 gigawatts. So the US uses just under 50% its total installed capacity to generate. So which do you want to use average production or peak capacity?

Your figure of 10-12 watts/sq. ft is about right. So to generate the average power of 451 gigawatts, would need 41 billion square feet of solar cells. Or 1,470 square miles. That is a square 38 miles on each side. I’m getting 410 square feet per house (20′ x 20′).

That assumes though that homes consume all the electrical power. There are lots of FLAT roofs where solar panels would work. Think supermarkets, warehouses, factories, office buildings, etc. Solar panels could be mounted in south facing racks.

10. You are confusing Watts and Watt-hrs again.

OK, let’s run through this. From a link:

A one hundred Watt light bulb, for example, is rated to consume one hundred Watts of power when turned on. If such a light bulb were on for four hours it would consume a total of 400 Watt-hours (Wh) of energy. Watts, therefore, measure instantaneous power while Watt-hours measure the total amount of energy consumed over a period of time.

But my EIA link showed the annual consumption in megawatts, not megawatt hours. So how am I to interpret this?

I want this analysis to be correct, so I really want to understand the discrepancy.

11. Benjamin Cole says:

The PHEV crowd claims that since PHEVs will plug in at night, the current grid can more or less handle it.

A quibble with your calculations: You left off commercial buildings. Jeez, in Los Angeles, we have something like 1 billion square feet of warehouses. (We have huge ports). There may be more square feet in commercial than residential nationwide.

Also, checl out recent The Energy Blog news items. They are talking about painting your house and the whole house becomes a solar panel.

Your calculations show we can move to a post-fossil economy rather easily. Remember, solar does not have to do it alone. Germany is doing tons with wind.
And recently in the USA, two plants have opened, one to convert wood to ethanol, and another orange peels.

I define the post-fossil economy as one which uses less fossil oil every year. We are almost there now, almost at Peak Demand. This year’s summer oil spike may push us through.

The weak link is that once we start down the road to a post-fossil economy, we may see an oil glut. Permanent declines in demand set up a “corrective” action in prices, and then we are back on the bandwagon for another generation…..

12. I think you’ve overestimated the productivity of the panels.

You may be right about that. Working through the math here:

I get about 50 watt hours per day, or a little under half what I used.

13. A quibble with your calculations: You left off commercial buildings.

Must I define thought experiment each time I conduct one? They are not meant to encompass everything. I can find things that would sway the calculation in both directions. The purpose is merely to frame the problem; to get an order of magnitude estimate. Before I do thought experiments, I generally have no idea of the magnitude of the answer.

14. Optimist says:

To frame that problem, right now the U.S. uses 21 million barrels of oil a day, which is costing us \$65 * 365 * 21 million = \$500 billion per year.
On a minor quible: oil prices are more like \$75/bbl (and climbing). So it’s more like \$575 billion per year.

All in all, a very interesting calculation!

15. Optimist says:

At 8,760 hours in a year, that works out to be 746,470 megawatts * 8,760 hours/365 days = 17,915 gigawatt hours (GWh) per day.
It’s not that complicated: to convert MW to MWh/d, just multiply by 24h/d. In this case you did it right, just more complicated than what was needed. And from a quick review it seems you did just fine on the MW estimate: You are getting there, Robert!

Is it too early to call for a BTU funeral, like the DOS funeral Bill Gates had a few years ago? I can assure you, going metric greatly simplify things…

16. It’s not that complicated: to convert MW to MWh/d, just multiply by 24h/d. In this case you did it right, just more complicated than what was needed. And from a quick review it seems you did just fine on the MW estimate: You are getting there, Robert!

I had just about redone the entire calculation, figured that it couldn’t possibly be correct, and was headed back to the original calculation. Glad to see your comment here. I am going to have to resolve the apparent discrepancy now in my mind of King’s KWh demand number, and the megawatt number reported by the EIA. Can you resolve the two?

17. Optimist says:

Earth calling King. Did you see
this?

Ping. Ping. (Getting flashbacks to The Hunt for Red October ;)) Then again, as Mad Magazine commented: I just paid 7 bucks to watch nothing happen!

18. I did some research into a similar question a few weeks ago (I was actually trying to figure out what it would take to move one residence to zero net grid power using PV), and the rule of thumb I found was that one watt of PV will produce about one kWh over the course of a year.

This rule applies for Minnesota and areas with similar potential (which, surprisingly, includes Florida and Texas). It’s probably a good ballpark number for most parts of the U.S.

My calculations are here.

19. Robert – I’ve always heard US demand is around 4,000 billion kWh. I think the demand tables you quoted are an attempt to calculate available net capacity, not the amount of power actually generated.

I’ve looked at solar a couple of times. I can get a grid-tied 6,300 W system installed for about \$45,000 (\$7.14/W) At 5 hours per day average, this would generate 1,000 kWh per month, or about 30% of my total bill. Assuming my after-tax rate of return is 5%. A \$45,000 investment in solar power is equivalent to \$0.20 /kWh. In Texas you can sign up for a 100% renewable contract for \$0.15/kWh. So it doesn’t make a lot of sense for me to do this.

Here is an intersting concept though:

Interesting concept. They must be banking on economies of scale driving their costs down. Also they get to deduct the depreciation on the solar panels from any profits. They claim they would be willing to lease me a solar system for \$0.106/kWh.

20. Anonymous says:

There is already a thriving industry installing solar panels on stores and warehouses, e.g.,

There are enough of these installations that we should be able to come up with a good real-world estimate for how much power they generate per square foot. The rated capacity for solar panels is pretty much a PEAK output under ideal conditions (blazing sunshine, noon). Real world production is going to be a LOT lower, especially in winter outside the tropics.

The design life of a solar panel is generally 20 years or so (although there is no reason why they can’t continue at slightly lower capacity indefinitely). So you can take the total cost of the panels and installation, estimate maintenance (mainly cleaning), calculate using real world examples how much power they will actually generate in the chosen lifetime, and come up with cost of the power. I would guess that it will still be pretty high, but there are less hidden costs than coal or nuclear. Like wind though, it is not at all continuous power, so there needs to be backup capacity in the form of stored energy (underground pressurized air, pumped water) and/or gas generating plants that can be turned on and off to meet peak demands.

21. Well it appears that I’m not the only one skeptical of CitizenRe:

It would seem to me that if the going rate for a PV system is \$0.20/kWh it would be hard for them to make money selling me one for \$0.10/kWh. This company has caused some controversy in the solar world.

22. Optimist says:

I had just about redone the entire calculation, figured that it couldn’t possibly be correct, and was headed back to the original calculation. Glad to see your comment here. I am going to have to resolve the apparent discrepancy now in my mind of King’s KWh demand number, and the megawatt number reported by the EIA. Can you resolve the two?
Saw King’s comment (3,953 billion kWh), and could not make sense of it – neither could I get to his link, but that’s beside the point.

3,953/4,000 billion kWh (per year)corresponds to about 450,000 MW of power, or 60% of the number quoted by the EIA as “Net Internal Demand for the Contiguous U.S.A. in 2005”. It is interesting to note that the EIA number shows a steady increase form 1994 to 2000 (~10 to 20,000 MW a year), is steady from 2000 to 2004 (680 – 690,000 MW), and then increases by 50,000 MW from 2004 to 2005.

I see one of two possibilities:
1. Perhaps King’s number is just a bit dated (early 90s?). Maybe the number held steady at 450,0000 MW in the early 90s the way it held steady in the early 00s.

2. Perhaps the document you reference is based on “planned capacity” in other words peak capacity as opposed to actual demand. Maybe King’s number is closer to actual average/total demand.

23. John Smith says:

The EIA number of 746,470 is defined in the footnotes as:

Net Internal Demand represents the system demand that is planned for.

So that is capacity, not usage. It’s similar to a 2 gallon per minute showerhead. I don’t use 2 gpm around the clock. Nor do the power plants run at full capacity around the clock. You are engineering the solar KWH production for an unrealistic worst case and overestimating the cost.

Second, you are inviting a misleading comparison when you compare the cost of solar electricity with the cost of oil. A more useful comparison would be amount we currently spend to produce the electricity we use. Some electricity is generated by burning oil but much of it is not. On the other hand, most oil is used for purposes other than generating electricity.

Third, that \$7/watt is very misleading as it does not include any storage mechanisms. Our existing electricity infrastructure works even at night and you’d have to spend a lot more money to get the same capability with solar. By underestimating the cost, you make an error in the opposite direction of the first error but I wouldn’t just say “it all cancels out”.

24. Anonymous says:

Robert

It’s hard to believe your having trouble with this. Why don’t you just stick to liquid fuels. I would like to see you discuss the H2Car in more detail. Why is it overated? Is it wrong?

25. It’s hard to believe your having trouble with this.

Trouble with what? My original calculation turned out to be correct. I have made a couple of modifications (lowered the hours of available sunlight and captured peak demand) but the first answer I got was pretty close to the answer I have now (and the answer I posted in the last section). So, no troubles.

26. Second, you are inviting a misleading comparison when you compare the cost of solar electricity with the cost of oil.

I was not suggesting that we produce electricity from oil. In fact, we only produce about 3% of our electricity from oil. I was just trying to show that the numbers, while big, are comparable to our current spending on oil. I don’t say nor imply that using solar for electricity will displace oil (unless we begin to electrify transport).

By underestimating the cost, you make an error in the opposite direction of the first error but I wouldn’t just say “it all cancels out”.

Some of you absolutely do not understand the concept of a thought experiment. I didn’t include storage mechanisms, but it also wasn’t necessary for me to displace electricity that is currently being produced by hydropower, renewables, or nuclear. That’s the thing about a thought experiment. You can always think of things to swing the numbers one way or another. It is a very rough approximation – say within half an order of magnitude.

27. Oh, I forgot to address this:

You are engineering the solar KWH production for an unrealistic worst case and overestimating the cost.

As others have rightly pointed out, the system has to be engineered for peak demand. So you have to have enough cells in place to meet peak demand – even if your average is a lot less than that.

28. Benjamin Cole says:

Okaym kudos on your thought experiment.
I think the cost, say \$1.5 trillion a year, is a bit high. We soend \$100 billion a year on the Iraq mess, and \$750 billion for imported oil.
On the other hand, once the system is installed, it will probably last another few decades. And, if the doomsters are right, we go to \$100 a barrel. And we get clean air and less global warming.
It appears that Rapier’s though experiment shows that even with current technologies, relying only on solar, we could go to a post-fossil economy w/o too much sweat.
In fact it would be a boon for working Americans. Imagine all the construction and design work it would mean for average Joes, instead of paying for imported oil. Who knows, G-d forbid, we might even skew the income curve back towards the middle a little bit.
The transition to a post-fossil economy is ver doable, as even back of the envelope calculations by Rapier indicate.

29. Anonymous says:

You still don’t have it right. You assume peak demand happens 24/7/365 and the use that number to calculate the area. Try dividing the peak demand you quoted 746,470 MW by the 12.5w/sqft and see how that turns out.

30. Anonymous says:

Orders of magnitude are pretty big by the way, thats why people like to say it. So half an order of magnitude would be what? A factor of five? Lets see, the area of all the roof tops in the country or five times that amount. Yeah, that is a pretty rough calculation.

31. You assume peak demand happens 24/7/365 and the use that number to calculate the area. Try dividing the peak demand you quoted 746,470 MW by the 12.5w/sqft and see how that turns out.

I was about to say you are wrong, but in fact I think you are correct. The demand number I got per day was by assuming peak demand for 24 hours. You are correct, that isn’t accurate. Doing it your way significantly cuts down the area – to a 46 mile by 46 mile square. (I have bumped up the total demand number though – to the EIAs Capacity Resources – which includes capacity under construction. That bumps up demand to 882,125 megawatts.

I am starting to understand why I have seen 6 different versions of this calculation with 6 different answers, but my intention is to get it right. The order of magnitude has remained the same (which is the whole purpose of the thought experiment), but I think I can nail a down a bit closer to reality. But it’s late in Scotland, so I will have to tackle it again tomorrow.

32. Anonymous says:

I still want to hear what is overated/overstated about the H2Car process.

33. So half an order of magnitude would be what? A factor of five? Lets see, the area of all the roof tops in the country or five times that amount. Yeah, that is a pretty rough calculation.

But that frames the problem. If you came up with 100 times the roof tops, you immediately know that it’s a no go. If you come up with 1/100th of the rooftops, it’s easily doable. But all the rooftops or 5 times puts the problem in the ballpark of “this is worth additional checking.” It’s done in engineering all the time to immediately disqualify an idea, or to decide whether to pursue it further.

But, I would point out that the actual variance in these calculations has only been 1/5th of an order of magnitude. The answer I have now is the answer I had after the first round: Difficult, but not clearly impossible.

34. That bumps up demand to 882,125 megawatts.

35. I think we are confused because of the units involved. Watts, kW, MW, GW. Then add reporting capacity as actual or peak in, kW or kWh and the fact that we can’t use scientific notation in blog postings – very confusing.

Here is my original source at EIA. This is a 2004 number: EIA, US Electricity “In 2004, the United States generated 3,953 billion kilowatthours ( kWh ) of electricity”

I chose to run my numbers on actual power produced. Robert did his on PEAK capacity available. The US on average only uses about 50-60% of the available capacity in the system. The grid is designed to deliver peak power plus a capacity margin (typically 10-15%).

The table that Robert quoted looks to me like it is some kind of regional comparison of capacity, demand, and capacity margin. State utility commissions require generators to maintain a capacity margin. The table wasn’t intended to tell you how much power was actually generated. It tells you how much is available on the peak day. If you go up one level from the table Robert quoted you find the electricity summary page: 2005 Electricity Summary Which says:
Net generation of electricity increased 2.1 percent from 2004 to 2005, reaching 4,055 billion kilowatthours

So, the bottom line is Robert ran his numbers off the peak net capacity (probably some day in August): 746,470 MW, which is 85% of the peak capacity 882,125 MW. If we ran at PEAK all year the system would produce 6,539 billion kWh.

The point for the thought experiment, I think, is to show whether generating all our power from solar is even achieveable. (It is.) Similar to showing we can’t replace all our gasoline with ethanol because there isn’t enough arable land.

36. Anonymous says:

The 12.5w/sqft equates to an efficiency of about 13.7% by my calculation, assuming a solar flux of 1000W/m^2. What kind of efficiency can we expect in the next few years and at what cost?

37. Well, I couldn’t go to bed knowing that the calculation was still not quite right. So, I have rerun the numbers. They look a lot better.

Check them out, and comment if you see a problem. I am going to bed now.

38. The point for the thought experiment, I think, is to show whether generating all our power from solar is even achieveable. (It is.)

Give that man a cookie. You must be some kind of engineer. ðŸ™‚

39. As a thought experiment, OK. As a practical matter it won’t work.

The electrical distribution system is designed to push power from large centralized generating stations out to individual consumers. It wasn’t designed for distributed power to be shared among millions of generators/consumers.

Then you have the whole AC vs. DC. thing, the need for capacitance and reactive power to start motors. That is even before we get to what happens when the sun goes down.

Putting in solar to supplement peak afternoon power makes some sense. But we still need to get it down to \$3/W or so.

40. Anonymous says:

kingofkaty said

“Then you have the whole AC vs. DC. thing”

Have you ever heard of inverters, and transformers and grid tie?

Have you been to http://www.greenwatts.com/pages/solaroutput.asp?

“As a practical matter it won’t work.”

What won’t work? Having the entire grid powered by solar? Why would we want to or even need to?

41. You’re within half an order of magnitude, that’s good enough for me. (Yes, I’m some sort of engineer.) For those who say he overestimated the area needed, well then that’s room to grow into, or extra capacity to account for transmission, inverter and battery/storage losses.

I agree with Doug M’s quibble that these thought experiments derail some people into the “one mindset” thinking. On the other hand I think it’s great when you can point out that any one of solar, wind or whatever, currently has the technology to be able meet current demands, which means it’ll be all that more easy to meet demand when we mix solar and wind with hydro, geothermal, biomass, etc as suits the local resources and demand.

I got curious about available rooftop area. According to
http://www.ef.org/documents/EF-Final-Final2.pdf page 31 of 94, in 2003 there was 62,436 million sq ft of residential and commercial rooftop space available for PV assuming you only use 22% of total residential roof area and 65% of total commercial roof area. Some people like to claim that solar doesn’t scale up because it takes up so much land. But this thought experiment shows it doesn’t have to take up much land at all, since existing rooftops have enough space for over half a TW of capacity.

42. Anonymous says:

So what if the grid wasn’t designed for it? That just means that the engineers weren’t thinking about it at the time. Will it handle customers connecting to the grid? It already is, it is called net metering.

You don’t need capactive or inductive power to start motors. Motors cause reactive power. Actually they cause IDUCTIVE power. Reactive is both capacitve and inductive.

43. Robert, interesting post as usual. But I think I found an error (or an unstated assumption) in your calculations. Your numbers assume a 12.5 Watt/Sq Ft generating capacity during the entire day. While in real life the panels will only hit those numbers for about 5 hours per day (this number varies depending on where you are but I am using northern California as the example). So your surface area numbers would only apply during the 5 hours of peak sunlight.

I thought I would try and see how much space we’d need to generate 100% of the electricity using solar. Using the 4,005 billion KW-Hr generated in 2005 as the benchmark, I get ~175 billion sq ft instead of your 70 billion sq ft assuming we only have 5 hours per day to generate all this power.

44. I meant to say “inductive”.

Yes, you can use inverters to convert DC to AC. But you lose about 5% of the power in the process. A lot things in your house use rectifiers to convert the AC back to DC, losing another 5-10%. If you had solar, you might want to think about installing a low voltage DC system to run some things.

Assuming that we have a total solar grid, how do we ship the power around? If my solar panels produce more than I need, I can sell power to my neighbor. But what happens when everyone on my circuit produces too much power? The grid was designed to send power down to users, not the other way around. IT COULD be designed that way but it isn’t.

My 4-ton AC unit pulls 98 amps at 220 V of inrush power. That is more current than a grid-tie solar inverter able to output. Now I am able to pull that power directly off the grid.

What happens in the case of a large industrial motor starting up? Say 4,000 HP. How much inrush current will that bad boy need?

Today, some central authority dispatches out power. It instructs generators to turn on or off and how much power to produce. It manages the loads on the power lines. Within a given system there could be hundreds of producers. In a solar world with millions of rooftops, who controls? How does it tell which solar panels to turn on and off?

As long as solar power is just a small percentage of the total generated load, these questions are manageable. But at 50% or more then you would really need to rethink the entire system.

45. Jim Coombes says:

-My understanding is the US averages (both geographically and over the year) 200 W/sq m. Production of 12.5 W/sq ft. implies a pretty high efficiency. (25%+ if I’m thinking correctly). So, you would need to focus PV cells in the sunny areas (which seem obvious, but Germany and California haven’t quite figured out how to use their capital efficiently, thereby wasting a lot of \$).

-What does this amount of silicon (assuming its silicon) work out to as a % of total silicon production? Can we get this much, or are we again making a leap based on faith in technological improvements? (And we know how you feel about that!)

-If these PV cells aren’t put on roof tops, then there are additional costs to connect them all to the grid. Part of the argument for solar power is the possibility to put it close to the power-user.

So, just wanted to highlight this tradeoff:

If we do focus on roofs, we then have to put cells in un-sunny areas. If we focus on sunny areas, we have to pay to connect them all to the grid.

46. Anonymous says:

Terry,

Actually Robert assumed 4 hours/day, but he assumed 12.5w/sqft across the whole country and all year. Using NREL solar map data, the US average annual solar radiation for a south tilted flat plate is about 5kwh/M^2/day. That accounts for night time, clouds etc. Using 13.7% efficiency this works out to about an 80 mile square or 175 billion sqft, as you said.

Of course we would need extra for peak power, but a lot of it could be handled with storage.

47. Jim Coombes says:

I can’t vouch for the accuracy of these numbers, but they come from p 241 of Solar Fraud, by Howard C Hayden.

MUCH smaller than the 1,000W/m^2 figure someone else threw out.

And of course, these are averages, so to address the peak issue, note that the noon solar energy on the equator is listed at 950 W/m^2!!!

Watts / m^2 of land area:

-At earth’s outer atmosphere 1,367

-Surface, noon, tropics, clear sky 950

-Max conceivable 24-hr avg, equator, no clouds 300

-Albuquerque, NM, yearly avg 240

-US, 48 state, year round 24 hr avg 200

-Connecticut yearly avg 160

48. Jim Coombes says:

If you want an outer-boundary argument to refute, Hayden argues:

*To generate 100% of US electricity, would require 15,000 km2 of PV at 10% efficiency.

*He then points out the the TOTAL silicon ever produced for all purposes is “a few square kilometers”.

I can’t vouch for the accuracy, but there’s the bookend from a seasoned solar skeptic.

Do you have to wash these things? I understand that they have people washing the mirrors in the California desert every couple weeks. At least its a way to give a real job to the guy washing my windows at the traffic light downtown.

49. Anonymous says:

kingofkaty

If we decided to do it, yes we would have to have local storage and standby generators, but there would be plenty of time to do this as it would take decades to add all that solar capacity.

50. Anonymous says:

Jim

You have to multiply the 1000w/m^2 by the solar panel efficiency and by the effective hours/day. For the average annual solar radiation, you can look at the NREL data here:

http://rredc.nrel.gov

Even using Hayden’s numbers, 15,000km^2, that is only a square 122km on a side, or about 80 miles on a side.

51. J C says:

Can we really think about installing solar panels as truly “creating” jobs? The history of human society has been about destroying jobs that create energy, so only a few really smart people (such as all of you) have to do it, while the rest (like me) no longer have to spend the day gathering firewood, or picking for coal (like we did back in the day when everyone’s job was making the energy they consumed).

Sure, we have to transition from the coal mining jobs to making silicon, uranium, or algae. But we should recognize that putting MORE people to work creating our energy is a step backwards economically. Possibly a necessary step backward, but not an end in itself.

52. Anonymous says:

Also, it looks like Hayden made those average, around the clock wattages, e.g. CT

160w X 24hr = 3840whr (3.84kwr/day)

That pretty much checks with the NREL maps.

53. Anonymous says:

Well, then we won’t have any unemployment.

54. Geekaholics anonymous. We should compare peak power to peak power or total energy to total energy.

1) Peak power consumed was 750,000 MW. Given that solar power is a peaker producing more power on hot summer afternoons when the peak load occurs, about a million megawatts of solar panels should do it. The additional wattage accounts for panels not tilted at their latitude, clouds etc. If it’s really cloudy, the air conditioners won’t be working hard. Say 200 watts/ square meter. 5 billion square meters. 5,000 square kilometers. 70 kilometers by 70 kilometers.

2) total energy consumed 4 billion megawatt hours. Go with 1 kWh
produced per year per watt of rated solar panel capacity. 4 million megawatts of solar panels. 4 times as large as before so 140 kilometers by 140 kilometers.

Divide 4 million megawatts of rated solar panels by 100 million roofs and we get 40 kilowatts per roof. That’s quite a bit. at 200 W/m^2 thats 200 square meters or 14 meters by 14 meters. We are in the ballpark where we can’t rule it in or out. Commercial buildings will probably need to participate.

55. Geewiz says:

/And as some readers point out, we have a lot more than rooftops./

Generally most rooftops for houses in citys with a large population are concentrated in masterplanned communities. where restrictions are highly enforced. gotta love those homeowner associations!

I have not taken the time (and likely never will) to run the numbers on the percentage of USA homes located in a masterplan community, but i guessing its very high, over 70%.
don’t think I am against Solar, on the contrary, i would love to see solar and wind provide all my energy. even if it’s half the day!

56. Actually Robert assumed 4 hours/day, but he assumed 12.5w/sqft across the whole country and all year.

I had that in the first version, and then allowed myself to be talked out of it. What makes this calculation so tricky is that a few assumptions can change the numbers by quite a bit.

For instance, yes, I have installed enough panels in the calculation to meet peak demand. And peak demand is going to correspond to peak sunshine, as air conditioners crank up. But, as the sun is on one horizon or another, how does demand vary? That’s the key. Maybe peak demand isn’t the real issue. The real issue is meeting demand when the sun is not straight overhead, and then we are back to the 100 mile by 100 mile array.

As far as meeting demand at night, there is no reason that you couldn’t electrolyze water in local substations, and then use the hydrogen to produce electricity at night. I know a couple of people who have suggested this, and I can’t think of a reason it wouldn’t work. Of course you don’t want individuals making their own hydrogen, but if they are all tied into a local grid, a local utility could do that.

57. robert, how could you confuse energy (kilowatt hours) and power (watts)?

I have had solar panels on my roof since January 2004. I have 18 Kyocera 167 watt panels, rated to produce around 130 W/square meter (12.1 watt/sq foot, but PLEASE can we stick to SI units)

So far my 3006 watt DC peak system has made around 4500 kWh AC per year, which works out to about 200 kWh per square meter per year and 1.5 kWh per year per peak watt. I live in northern California. I have cleaned the panels a couple times, otherwise no maintenance.

Since 2004 the technology has improved, the same size panel from Kyocera is now 175 watts.

The SunPower 315 panel is rated at 193 watts/sq meter (17.9 W/sq ft) which is almost 50% higher than my Kyocera panels

Here’s a US DOE report that has useful stats:
Report on the Basic Energy Sciences Workshop on Solar Energy Utilization

Some excerpts:

“Covering 0.16% of the land on Earth with 10% efficient solar conversion systems would provide 20 TW of power, nearly twice the worldâ€™s consumption rate of fossil energy and the equivalent 20,000 1-GWe nuclear fission plants.”

[for US energy]
“For calibration purposes, the required U.S. land area is about 10 times the area of all single-family residential rooftops and is comparable with the land area covered by the nationâ€™s federally numbered highways.”
—-

Note that 10% efficiency is quite conservative, Kyocera panels are over 16% and SunPower panels are 19.3%

Current retail prices for solar panels are about \$4.50 per peak watt. It’s hard to find prices for the SunPower panels on the internet, I assume they are higher, so it depends if you are trying to optimize the cost per kWh or the area per kWh.

6 kW inverters cost around \$0.60/watt, I expect the price would be less for utility scale. Balance of plant + installation runs about \$2-\$3/watt, again that would be less for large installations.

SunPower is about to open a 330 MW plant. “The inauguration of our second solar cell fab is an important step for SunPower,” said CEO Tom Werner. “When fully built out, Fab 2 will quadruple our total manufacturing capacity and create economies of scale that are an important element in our plan to reduce installed solar system costs by 50 percent by 2012.”

58. robert, how could you confuse energy (kilowatt hours) and power (watts)?

Actually, I didn’t. I had it correct the first time, and then let others cast doubts that the numbers I used were wrong. But they number I got from the EIA was the power number – which I then used to calculate the kilowatt hours by multiplying by 8760 hours per year. And that is accurate. See Optimist’s post above confirming my calculation.

I don’t work much with electricity, as I have stated previously. So, this isn’t second nature to me. But I did get the power/energy notations right from the first post.

59. there’s a great reason to not electrolyze water when it’s sunny, and run the hydrogen through a fuel cell when it’s not: energy losses are too high.

there are utility scale (ie. megawatt) sized pumped hydro storage systems already in use, check out http://electricitystorage.org

60. The SunPower 315 panel is rated at 193 watts/sq meter (17.9 W/sq ft) which is almost 50% higher than my Kyocera panels

Mike, do you know prices? Which one has the lowest cost per watt?

61. there are utility scale (ie. megawatt) sized pumped hydro storage systems already in use, check out http://electricitystorage.org

That’s pretty good. I want to spend some time understanding how that system works. I am going to revisit this whole idea soon, because I have a better handle around some of the key parameters. And storage was definitely missing from the calculation.

62. The sunpower 215 series is five bucks a peak watt. I know because I bought some. They haven’t announced pricing on the 315 as far as I know.

Some states prevent HOA from vetoing solar homes and some states do not.

63. According to the Edison Electric Institute

* The U.S. electric power industry’s total installed generating capacity was 1,067,019 megawatts (MW) as of December 31, 2005

* Total U.S. electricity generation in 2005 was 4,054,688 gigawatt-hours (GWh)

an equivalent peak capacity in SunPower 315 panels would occupy 2134 square miles, about 46 miles on a side. This assumes no space between the panels, which is silly, so I’d say 50×50 miles is a lower bound.

scaling up the 200 kWh per year per square meter I’m getting with my system to the 2005 yearly total above would require 90×90 miles with no space between.

64. The sunpower 215 series is five bucks a peak watt. I know because I bought some.

Do you know what tends to give you the most economical solution? Do you improve your cost per watt by going high efficiency, or does higher the cost eliminate any advantage? The reason I ask is because if I am going to scale a system up, I want the most cost effective solution. That might be a 3% efficient, super cheap cell (just hypothetically). But I don’t know.

65. Using froogle.google.com I found the Kyocera KC200GT for \$875, or \$4.375 per watt.

The leading panel makers are Sharp and Kyocera.

http://solarbuzz.com has lots of useful info, and their “price survey” says the current lowest price is \$3.95/Wp

66. scaling up the 200 kWh per year per square meter I’m getting with my system to the 2005 yearly total above would require 90×90 miles with no space between.

While those Edison numbers are 20% higher than the EIA numbers, we are still in the range of the numbers we have been talking about since the first post. Basically, I am trying to get my mind around the scale of the problem. I wanted to know if it would take an area the size of Texas to produce the electricity we need. No. So, while I conclude that we aren’t going to displace our liquid fuel needs with biofuels, it still looks to me like solar – even though still relatively expensive – has no such limitations.

67. Do you know what tends to give you the most economical solution? Do you improve your cost per watt by going high efficiency, or does higher the cost eliminate any advantage?

if space isn’t an issue (i.e. middle of the Mojave desert), then choose the cheapest per watt, which tend not to be the highest efficiency.

the higher efficiency modules are more expensive per watt, they can make sense where space is at a premium, e.g. residential roofs

68. 1. NREL says that the annual average solar radiation available (insolation) to a flat plate collector, such as a photovoltaic panel, oriented due south at an angle equal to the latitude of the location, in the US ranges from 3.5 to 5.5 kWh/m^2/day. The highest number in the US is 6.5 — 7 in the desert around the CA, AZ, NV borders. 5 would probably be a better average based on land area weighting, but a lot more people live in the cold dark Northeast so I will use 4 kWh.

2. “The total impervious surface area [highways, streets, buildings, parking lots and other solid structures] of the 48 states and District of Columbia is approximately 112,610 square kilometers [43,480 square miles], and, for comparison, the total area of the state of Ohio is 116,534 square kilometers [44,994 square miles].” Link h/t Randall Parker.

3. A Joule is one Watt Second, so 1 kWh is 3,600,000 Joules. A solar collector in the US would collect 14,400,000 J/m^2/day or 5,256,000,000 J/m^2/yr or 5.3*10^9 J/m^2. An area of 120,000 km^2, therefor receives 5.3*10^9 J/m^2 * 1.2*10^11 m^2 or 6.4*10^20 J of solar radiation annually.

4. EIA says that the US consumed about 99,740 trillion BTUs in 2004 [PDF]. One BTU is approximately 1055 J. So the US consumed about 99,740 10^12 * 1055 J or 1.1 * 10^20 J. 4. If you captured 20% of the incoming solar radiation on 120,000 kM, you would be able to cover the US’ annual consumption of energy — more or less.

5. Electricity was 40% of the total, so it would require 48,000 kM^2.

6. 1 Terawatt/yr= 365*24*60*60 = 31,536,600 Terawatt seconds= 3*10^7 * 10^12 J = 3*10^19 J, so the annual consumption of 1.1 * 10^20 J is about 3.7 TW/yr, or the continuous operation of about 3700 GW of capacity. This would imply a “nameplate capacity” of about 15,000 GW of solar.

6. All of this ignores the issue of matching production to consumption. A recent article on Sodium-Sulfur batteries suitable for use a power stations said they cost \$2,500/kW. the price would come down with mass
production, but they may not be all that cheap. Note that the \$2,500/kW figure is ballpark for the cost of a nuclear power plant. 3700 GW of batteries would be very expensive (3700*10^6*\$2500) would be about 9 Trillion dollars (about 70% of GDP). That much spent on nuclear wouldn’t need the batteries.

5. Disclaimer: I am neither an engineer nor a physicist, nor I did stay at a Holiday Inn Express last night.

69. it still looks to me like solar – even though still relatively expensive – has no such limitations

I agree 100%.

The DOE report I linked in an earlier comment says the total solar energy falling on the earth is 120,000 terawatts, about 9000 times our energy use (all sources, not just electricity)

So even allowing for storage and conversion losses there should be plenty.

http://nanosolar.com/ used to claim they will hit \$1/watt but I can’t find it on their site, so for the moment take it with a grain of salt. But if they get anywhere close there will be a revolution.

70. Robert, your current calculations are right for power, and the calculations you were talked out of with the 4 hours/ day were right for energy. But if you want your array to meet both criteria of meeting instantaneous peak power output and total energy used over a year, you have to pick the larger of the two areas. That was the one you were talked out of, which was, if I recall correctly, about 79 miles x 79 miles. You can’t simply convert from peak power to total energy with the 8760 hours per year because solar doesn’t run at full capacity 24 hours per day. It runs at an equivalent of 4 to 5 hours/day in the US. That’s why you correctly previously used that 4 hours/day.

But as you say, either way, the conclusion is the same. You can’t do it with just existing rooftops, but there is no fundamental problem with it (as you found with ethanol) if you are willing to use deserts and parking lots and brownfields as we are already doing. It would be very expensive but not impossibly so if we were silly enough to put all our eggs in one energy technology basket.

71. That was the one you were talked out of, which was, if I recall correctly, about 79 miles x 79 miles.

Actually, I think it’s even more complicated. The real answer lies in between. I am working on a compromise solution. We need to meet peak demand, which corresponds to peak sunshine. But then the real answer depends on how demand falls off and peak sunshine falls off. This is the key. If, for instance, they fell off at the same rate, then the peak demand number would be OK (with some storage kicking in at night).

I have been looking at Google solar project, and studying how ouput climbs, peaks, and falls each day. I need to compare that to the behavior of demand. The limiting factor is going to be determined by a combination of the 2.

72. According to my driller, the US will drill 40,000,000 m of temperature characterization wells in the next 8 years. This is sufficient for 12,000 projects. If these average 20Mwe, the total will ~ 24Gwe.

Regarding Nuclear, look at this blog.

http://lpsc.in2p3.fr/gpr/english/MSR/MSR.html

or this one….

http://thoriumenergy.blogspot.com/

As you do your research into MSR(s), you find it cheaper, safer, and produces much less waste.

73. RR,

\$5.00 a watt is clearly more expensive than \$4.50 a watt. My house faces east and west with a small amount of south facing roof over the garage. I paid a premium for the most efficient panels on the market.

Kyocera guarantees their panels power output for 20 years. Sunpower 25 years. If you want to get into the nitty-gritty, 100 years from now, I bet the cost per watt is the same. What is the bid price on the CBOE for July 2107 electricity?

I don’t have any data on manufacturing costs. Maybe Sunpower charges five bucks a watt because they can. Pure refined silicon is expensive and material costs dominate. Photons will penetrate silicon for some depth, so 100 micron thick silicon is more efficient than thin film silicon but more expensive.

I don’t believe utilities will get any economies of scale buying inverters in quantity or in the megawatt sizes. Unless there is data to the contrary. 4000 amps at 240 volts? When the sizes get too big, they are better off having a DC motor drive an AC alternater.

Walmart for example is putting solar panels on their roofs and there are a lot of Walmarts and they have big roofs. Commercial customers might well be the early adopters of rooftop solar.

Robert

74. Anonymous says:

Robert

Its not so much your number, but how you arrive at the number. I doubt you would have gotten so many comments if your original calculations made sense. Thats why you were “talked out” of your number. Just be consistent.

75. Anonymous says:

Robert said

“But my EIA link showed the annual consumption in megawatts, not megawatt hours. So how am I to interpret this?”

Where is the link that shows consumption in megawatts?

76. Michael Cain says:

Census Bureau figures from 2005
http://www.census.gov/hhes/www/housing/ahs/05dtchrt/05dtchrt/tab2-1.html

suggest 108M households, but also provide important information on the type of dwelling. The figures suggest to me that it might be more appropriate to assume 70M available roofs. One reason for the smaller figure would be excluding the buildings in inner cities, which may be shaded by other buildings. Another reason is to exclude, eg, households in buildings of 20 or more households, which probably have very little available roof space per household.

This won’t change your conclusion, but it does address one possible concern over the accuracy of the back-of-the-envelope scale calculation.

77. Robert – your revised calculations are correct, but the question you asked originally was on consumption. Getting a handle on the electric system is a lot more difficult, since most of the time generating capacity is running at only a fraction of its peak. But for your thought experiment, the area required is a square somewhere between 40 miles on a side and 80 miles on a side. There are counties in Texas bigger than that!

Generating all your power on solar raises some interesting control and storage questions. Some posters have suggested exotic battery systems or electrolysis. I believe they are overworking the problem.

Once the solar panels are installed, the power is “free”. Efficiency then isn’t really much of an issue. Go with what is cheap and works best. That is likely potential energy storage (lifting weights, pumping water, pressurizing vapors in salt caverns, whatever), or thermal storage (hot water reservoirs, reversible chemical reactions).

Any solar system would need some sort of load following generator capable of dispatching power quickly as voltage in the system dipped or peaked from large consumers turning on and off.

78. Its not so much your number, but how you arrive at the number. I doubt you would have gotten so many comments if your original calculations made sense. Thats why you were “talked out” of your number. Just be consistent.

The problem is – and this is why I have seen so many different answers from this calculation – is that it isn’t as simple as it first appears. My first calculation provides one boundary: Enough solar panels to produce all of the electricity needs – but in just a few hours a day. But that’s not the way to do it. The other boundary – just enough panels to meet peak demand – is also a boundary. The real answer is in between.

I am doing a graph right now that tracks solar cell output and California’s electric demands versus time. It shows just why this is not a trivial calculation. Peak demand does not coincide with peak output from the sun, which I have always heard.

79. Where is the link that shows consumption in megawatts?

I wrote consumption, but I meant capacity. From the orginal post, prior to modification, I wrote this:

According to the EIA, electricity capacity in 2005 was 746,470 megawatts. That is the capacity required to meet peak demand. At 8,760 hours in a year, that works out to be 746,470 megawatts * 8,760 hours/365 days = 17,915 gigawatt hours (GWh) per day.

That is in fact accurate, but I don’t believe that’s the way to approach the problem. I am working on some graphs that I will post as soon as I get a chance.

80. Jim C says:

80 miles x 80 miles is still a large area. The downside is that doesn’t factor in growth in electricity usage, or conversion to an all electric economy. But the good news is that hitting even 10% of peak power would be helpful.

Cost doesn’t seem out of the ballpark, but timing and scalability are key questions. Particularly if climate change is truly at a “crisis” point.

If we’re producing 100s of times more PV than has ever been made – and banking on new technologies to reduce silicon content – when might all this happen?

Is there even an argument that production / installation / subsidization should be slowed down while we allow technology to develop, so we get the most bang for our buck? Or does increasing production yield scale economies that drive down prices even without technological improvements? (Solar Revolution argues that scale is more important than efficiency improvements).

Also – query what the true maintenance cost of all this PV would be? If they are on rooftoops, are we just assuming that people will be responsible for cleaning the leaves and gunk themselves? Judging from the yard maintenance here in Pacific Heights, it shouldn’t be much of a problem to keep 100 million rooftops well-cleaned. Or out in Barstow and Bakersfield…does PV require less cleaning than the mirrors do? I just don’t know, but it does get dusty out there.

If meeting even 10% of our electricity usage is 10 or 20 years off, should we really be viewing solar as the long term solution for 2057?

Does this dictate a strategy of either relying on coal for a while and not feeling guilty about it? Or building nuclear plants as fast as we can to get us through 50 years, and then decommission them when PV plantations come online?

81. California ISO has a live graph of electricity supply and demand. Demand usually peaks at 4 pm.

The Live Solar Network page has a bunch of graphs of residential systems. The peak is usually between 12-1 pm, which you would expect with daylight savings time.

It will be a long time before we have enough solar capacity installed that we need to worry about energy storage, given the worldwide PV manufacturing capacity. It makes sense to offset peak demand with solar now.

The nice thing about solar is even though it has pretty high upfront costs, those costs are well understood. Compare that with nuclear, where the costs of securing the facility and solving the waste problem are crude estimates. Not to mention “peak uranium”, i.e. most of the high EROI uranium has already been mined.

I think it is nuts to build more nuclear until we have clearly addressed the concerns mentioned by this UCS Position on Nuclear Power and Global Warming and the nuclear safety section of their web site.

82. California ISO has a live graph of electricity supply and demand. Demand usually peaks at 4 pm.

New post up top. I think the problem is now framed correctly.

83. I presume the good folks of Barstow and Bakersfield own garden hoses. When you got a square mile of mirrors deep in the Mojave desert and you are paying someone to hose them down and where do you get water in Mojave, it becomes an issue.

84. Anonymous says:

Mike Wiese said

“I think it is nuts to build more nuclear until we have clearly addressed the concerns mentioned by this UCS Position on Nuclear Power and Global Warming and the nuclear safety section of their web site.”

Do you think the UCS would ever be satisfied? What would it take to satisfy them?

What should we do about other contries who are developing nuclear power? Should we stop them?

So lets say we abandon nuclear power. The waste and uranium mines would still be there and the terrorists would still be able to make a bomb. So we would still have to pay to guard it, without the benefit of the electricity.

85. Anonymous says:

Robert

I have not read all your articles on solar so you may have already considered the infrastructure costs. I cannot vouch for its accuracy but I found the following comments at this site interesting [http://dpodbori.livejournal.com/3590.html]. It suggests that we may have real problems in refining the aluminum needed to build large-scale solar arrays:

“Nonetheless, let us say that we decide to go ahead and implement a US economy-scale solar solution on systems such as SES’ — in anticipation of completely replacing our energy base from rapidly depleting petroleum to renewable solar. As Sandia and others are fond of repeating, a 100 x 100 miles swath of desert anywhere in the South West could provide enough capacity to satisfy (today’s) energy demand of the entire US economy. As the solar encampment on the WSJ article mentions, 20,000 units occupy 4 square miles, so on 100 x 100 = 10,000 square miles we will need to allocate
20,000 x 10,000 / 4 = 50,000,000 (fifty million) units. Let’s say (purely hypothetically) that starting next year we will be manufacturing and bringing online 1.5 million units per year, on average, thus smoothly completing the transition from petroleum to solar in a little over 30 years.

“Before appreciating the implications of the above proposal (and I am not saying that this cannot be done), we need to consider the following numbers. 1.5 million units per year, with 1.8 tons of aluminum per unit will constitute 2.7 million tons of aluminum. Well, you may be interested to know that 2.7 million tons, per this statistics by USGS, was the entire US aluminum production in a recent year (2003). Of course, a lot of aluminum in the current economy is recycled, however we are discussing here an enormous scale development of gigantic solar dishes — you don’t expect the aluminum for them to come from recycled empty Coca Cola cans, do you? And you would still need to produce aircraft, packaging, electrical equipment, buildings, and consumer durable items to which the currently produced aluminum goes, as one would expect under “normal” economic conditions. “

The author points out that, ironically, we need to be an energy-rich nation in order to be able to afford to build replacements for our current energy systems.

best wishes

Wayne Hooper

86. Anonymous says:

Oh No! We are going to run out of Aluminum! It is only the third most common element in the Earth’s crust!

87. According to that WSJ article, each dish will take 24MWh to produce the aluminum and produce 60MWh per year giving us a EROEI of around 5 months. The Aluminum industry has been leaving the United States for places with cheap electricity like Iceland and Oman for quite some time. No question that the scale to replace all of our energy needs with solar power is enormous. The USA is importing 40% of our aluminum now, and I don’t quite see why we can’t import more. This 100 square miles of aluminum dishes will certainly take a generation to construct. We just don’t have another choice. And we aren’t going to run out of Aluminum or Silicon. Only oxygen is more abundant in the Earth’s crust.

88. Robert,

Have you considered extending your solar thought experiment to include the energy requirements for electrifying transportation you considered in your The Future is Solar post?

Now that will be a challenge!

89. Have you considered extending your solar thought experiment to include the energy requirements for electrifying transportation you considered in your The Future is Solar post?

I was already framing that problem in my mind last night. I want to do that, and I want to calculate how much electricity just to displace coal and natural gas-fired power plants.

90. Electrifying transportation. http://thefraserdomain.typepad.com/energy/2007/07/epri-nrdc-repor.html says that the Electric Power Research Institute (EPRI) concluded that a 60 percent U.S. market share for PHEVs would use 7 percent to 8 percent of grid-supplied electricity in 2050. That involves a whole lot of assumptions and projections.

Page 48 of 70 of the report at http://www.epri-reports.org/Volume1R2.pdf has some interesting 2006 conversions from mpg to Wh/mile for various weight classes of vehicles from passenger cars to heavy duty diesel vehicles that weigh over 9 tons. That could be useful in doing one’s own thought experiment.

91. I commend you for going down this path…most people don’t attempt the work of developing/understanding the real world implications of specific policies. To more fully understand the effort and constraints related to switching to solar, I suggest you add to your consideration a few more elements, such as:

1. Worldwide electrical energy consumption and installed electrical generation capacity…not just USA
2. Estimate of presently unmet electric requirements or likely switch from other point generation, e.g. stand alone generators in areas with highly erratic power..consider Iraq, China, Lebanon, etc. as examples; lighting/heating/etc. presently supplied by inefficient sources such as kerosene lamps (yup, still quite a bit of that too). While you probably don’t need to consider this for a first order estimate, you may be surprised at the results when you do factor these in.
3. Other key & little considered elements…present pv cell/array production capacity & production capacity ramp-up rate. As an example, assume for ease of calcs present worldwide PV production capacity of 1 GW/annum doubling every 3 years for the next 24 years = 128GW production capacity/per year by ~ 2032. Then assume “best, base, worst” case electric consumption growth rates, say -1%, 1%, 3% (conservation/recession, staus quo/plugin hybrids & economic growth)= ? worldwide consumption by 2032 (you pick the actual scenarios) Yes, I know this is quite simplistic economically, but it provides an example of further developing a context for understanding the effort in switching to solar. Depending on assumptions, you may find that 30 years from now we will have come a long way and could still be more than 100 years from “100% solar” worldwide.
3. PV cost by cost element, e.g. cost of cell; cost of array; cost of install; profit; etc. What you will find here is that a substantial portion of the final installed cost, particularly in advanced countries, is in marketing, installation and profit. This has serious implications for type of installs and payback.
4. Impact of energy cost inflation of solar; e.g. does cost of solar go up in tandem with overall energy cost increases?

Answers to these questions provide further context for understanding market acceptance of solar.

best regards

92. As best I can tell, one third the cost, \$1.50 of a \$4.50 one watt solar panel is the silicon. I’ll assume sand is free and that is all energy. There is capital costs for the equipment to refine silicon but I’ll ignore it.

Most states require you to use a licensed contractor to get their rebate. Let’s say \$9.00 installed. My contractor didn’t itemize by materials, sales commision, profit etc. so all I know is the bottom line.

The interesting thing, is the PV manufacturer can decide how thick to make their cells. If it is 100um thick, they capture all the photons and pay \$1.50 in silicon. If it is 50um thick, they pay \$0.75 for the silicon but capture say 75% of the photons. So they can only charge 3/4th of \$4.50 or \$3.38. So they lose 50 cents.

My guess is, when the current silicon shortage eases, nobody will be interested in thin films for stationary applications.

Has anybody thought to put a mirror under the silicon? Is that more expensive than just doubling the amount of silicon? Sunpower, for example, puts their contacts on the bottom of the cell to avoid shading the silicon.

What happens when the cost of generic energy goes up? The price of silicon goes up but isn’t there energy use in almost all the other costs too? Even the salesperson wants a bigger paycheck if it costs more to gas up his truck. I don’t think that will prompt them to make thinner silicon. Perhaps it means they can charge more for the higher electricity output cell.

I have no knowledge of thin film CIGS, cascaded semiconductors, quantum dots etc. I do not know how and if they change the game.

93. KingOfKaty writes:
The grid was designed to send power down to users, not the other way around. IT COULD be designed that way but it isn’t.

The wires don’t care.  The transformers don’t care.  The control systems might need some new software, but we’re going to need that anyway to manage the PHEV’s, ice-storage air conditioners, and other DSM elements.

Note that we are going to get these DSM elements, solar economy or not.  The electrical grid in California (and many other places) is strained to the limit during peaks and under-used much of the rest of the time, so there is a huge amount of value to be captured by matching these things more closely.  The ice-storage stuff is already on the market, and PHEVs are not far behind.

What happens in the case of a large industrial motor starting up? Say 4,000 HP. How much inrush current will that bad boy need?

It’s probably a wound-rotor machine and connected through resistors or a controller to manage that.  Suppose it takes 5 MVA to start, with the limiters.  If the PHEVs in the local parking lots are all plugged in with 220 V 32 A connections, each one can pump out 7 kVA.  It would take about 700 of them to feed the beast if they were float-charging, just 350-odd if they all switched from max charge to max discharge.

Jim Coombs writes:
What does this amount of silicon (assuming its silicon) work out to as a % of total silicon production? Can we get this much, or are we again making a leap based on faith in technological improvements?

70.57 billion square feet is 6.56 billion square meters.  Evergreen Solar’s string ribbon process can continuous-cast silicon in 100-micron thickness.  They are only getting 12% efficiency now, so multiply the area by 1.25:  8.20 billion m^2.  At 0.0001 m thickness, the total volume of silicon required would be 820,000 cubic meters.  This is a volume which would fit in most football arenas if you didn’t mind stacking it up on the bleachers.

We don’t produce this volume of semiconductor silicon now (not even close), but we can produce lower-grade silicon from many other sources.  The volume of silicon for that quantity of panels would be a small fraction of the volume of glass, and they can both be made from quartz.

We wouldn’t need to meet “peak demand”.  The peak is determined largely by A/C loads, which can be pre-paid using ice storage; it occurs later in the afternoon anyway.  The name of the game is meeting energy needs.

94. In your calculation of roofing area, you divided a billion by 100 million and got 1 . This is why you estimate 70sq feet per household instead of the more correct 700sq feet.

You might want to compare the cost of the panels with the amount spent on electricity each year. At 4,000 G kwh of electricity sold for around \$0.10/kwh, that’s \$400G per year the U.S. spends on electricity. (Ok, ok, commercial and industrial rates are much lower, and I rounded residential rates up quite a bit.)

95. http://minerals.usgs.gov/minerals/pubs/commodity/silicon/silicmcs07.pdf

The world produces about 4700 thousand metric tons of silicon metal per year. The solar and electronics industry currently refine about 1% of that into high purity silicon. Silicon (think beach sand) is an easily available naturally occuring mineral.

The world currently produces about 3GW of solar per year. The initial thought experiment was for 800GW of solar in just the U.S., presumably built out (sustainably) over 30 years — call it 30GW/year. With current technology, that would consume about 10% of all silicon metal produced.

One thing you may want to consider… If we produced 30GW/year of panels just for the U.S. that sort of volume would drive down manufacturing costs, increase cell efficiency, reduce silicon per watt, lower installation costs, …

96. Anonymous says:

What about when you need power at night? You would either need to create and store additional power in batteries or have backup power. Both not very practical. Solar effectively stops every evening at sun down.

97. BilBb says:

He probably lives next door to your there in the netherlands.

98. WOV says:

Navigant did much of the roof area potential calculation for you in a study they prepared for the Energy Foundation – http://www.ef.org/documents/PV_pressrelease.pdf

announces the availability, but I forget where the actual document can be found.

99. At one point I tried this same type of calculation on energy usage of the entire world as opposed to just the US (since I easily found numbers for world energy usage first) and thought it was a fun experiment to do. I’m glad that others are thinking about this too!

BTW: When researching around the companies I found who do solar PV installations estimated in their FAQs that an owner should expect \$9-12/watt installed, batteries and all. This would increase prices surely, but if this is just a thought experiment we might as well assume also that the price *could* drop to \$7/watt due to volume purchased.

100. Please how do I know the size of Solar panel required to generate 20KVA output supply. I am very new to this. Could anyone direct me on how to go about this or some materials that cover these calculations?
Thanks.
Clem