Solar Energy - Do the math

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Thetallestmanonearth's picture
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Solar Energy - Do the math

Can anyone help me out?  I have a debate running on facebook about limits to growth and a relative of mine just landed this gem: "As far as fulfilling our energy needs, our entire energy needs could be met by using a relatively small portion of the globe for solar power infrastructure alone. Add wind, hydro, etc. and we have all the energy we will ever need. Fossil fuels will die out as their use becomes economically disadvantageous, we're already seeing it happen."

At one point I read an article on Do The Math ( that pretty well debunks the renewable as a replacement argument.  I can't find the article, but would love to reference it if anyone can find it since the person I am discussing this with values education and the author, Tom Murphy, is an associate professor of physics at UC San Diego.  I have plenty of other references I could use, but I want to head off the credibility attacks by picking my source carefully to satisfy my audiences concept of qualification.



Tom Murphy is an associate professor of physics at the University of California, San Diego - See more at:
Tom Murphy is an associate professor of physics at the University of California, San Diego - See more at:


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Mike Dill
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Solar panels and EROEI

A few years ago, solar panels were expensive, and all of them were built using rare minerals. While most solar cells are still built using these older and well know processes, there are new cell types out there that are using organics (carbon) and common minerals.

If I recall correctly, the EROEI for PV solar on a residential rooftop now is about 8 to 1, assuming a twenty year lifespan. My panels have a twenty year warranty, and I expect them to last forty years, as there are currently PV systems that are still running at that age.

The new technologies are increasing the EROEI, and this will continue to improve for the foreseeable future, as there are announcements on new breakthroughs almost daily.

So, the current BAU situation probably needs an EROEI of 10 or 12 to 1 in order to continue. This is not happening YET. Battery powered cars have an EROEI of less than that currently, and we do not yet have planes and trains that will work with renewables. The website is probably correct for the CURRENT situation, but fails to foresee the improvements that are coming.

I am waiting for another year or two before buying battery storage to back up my grid tied power system, as the prices there are dropping rapidly, which also implies that the EROEI is improving there.

pyranablade's picture
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You're both right

As far as fulfilling our energy needs, our entire energy needs could be met by using a relatively small portion of the globe for solar power infrastructure alone.


Your relative is correct and you are correct and so is Mike Dill. Your relative's statement, of course, is over-simplistic, because he seems to be saying 'let's harness the sun because of all the power that is there,' without taking into account the EROEI as discussed by Mike Dill above or James H. Kunstler in The Long Emergency. If we'd started on solar 30 years ago and stuck with it, his hopes might be realistic. As it is, we'll have to adjust to a world with less energy.

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Mike Dill
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Solar can power the world - BUT

I did miss a part of the argument here, as I did not mention that solar PV and wind currently only accounts for less than one percent of all energy consumed. If there is a crash right now we are not going to do well as a global community.

If the current growth rates of those two and other renewables continue at the present rate, we should be able to be completely renewable by 2050 or so (exponential growth curves). Reducing our energy footprint is required if the energy system fails to change before that time. Either that, or we have to fall back to the  systems that existed before the 1850's.

cmartenson's picture
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Try this out...

This site has a very good numbers based breakdown of why solar/wind can't make it up:

This analysis just asks and answers the the question "how much energy would be required to install the concrete bases for enough wind turbines to supply 50% of the world's energy needs by 2030?"

The answer is stunning...

RNcarl's picture
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Is the scale wrong?

What I mean is,

It appears that large wind and solar collectors are more energy intensive and hold a greater investment and therefore a greater risk of loss if/when the device fails. Not to mention that the paradigm is still that of a "centralized" production of electricity and then distribution. 

What about smaller, individualized units providing "de-centralized" production using the existing distribution network? 

I don't know, but I think the answer is in smaller, not larger units.

We can build super-tankers and ever larger generating plants. What if that effort was redirected in making small, end user type units? I understand that would change the power (political, investing) and control to different folks.

Either way, to do nothing, yields just that - nothing.


jgritter's picture
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Are the variables wrong?

What happens if, rather then trying to scale energy production up to the current population, we scale the population down to a level that can live with sustainable energy?  The math seems to suggest that the human population must return to a pre fossil carbon level once the fossil carbon runs out.  So if 99% of the human race dies off in the next century and the 70,000,000 survivors self select for intelligence, physical and emotional resilience, and pragmatism, the issue of only being able to generate a fraction of our current energy production solves it's self.  

The question is "How large a population does it take to maintain our current level of technology?"  It seems to me that if you have a couple of dozen population centers with a couple of million people each sprinkled around to globe, some one some were should be able to keep the ball rolling.

Sucks for the rest of us, 

John G

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I haven't read the linked

I haven't read the linked articles except for do the math but here are some issues:

  • The renewable alternatives only provide electricity. This is much less useful than portable chemical fuel. We should have sufficient electricity long after we have widespread collapse from lack of portables fuels. Also, there is no large scale"battery" available to store the intermittent electricity from solar and wind. Good luck running a manufacturing industry on intermittent electricity... But you could get by for your house.
  • The financial collapse will make funding renewables much more difficult as interest rates rise. This will favour capital into the remaining fossil fuels as their net energy return and thus profit will be realized quickly whereas solar panels return the investment over 20 or 40 years... Tom Murphy's energy trap. 
  • our current infrastructure is nowhere near ready to run off electricity. The 40 year oil trade deficit has allocated capital into the worst places in highly distorted markets.  
  • There are a couple hopes. One is that Alberta has a lot of coal which can be turned into oil for a price. Secondly, with the right price incentives maybe someone will figure out industrial processes for artificial photosynthesis and or electricity to hydrocarbon catalysts. 
sunweb's picture
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Scientific studies show it takes years to payback the energy used in solar electric devices. EROI (Energy Returned on Energy Invested) says it takes energy – mining, drilling, refining, transporting, installing, maintenance, and replacement parts – to make the devices necessary to capture solar energy.Spain’s Photovoltaic Revolution: The Energy Return on Investment by Prieto, Pedro A., Hall, Charles  2013.


and  Energy in Australia - Peak Oil, Solar Power, and Asia’s Economic Growth by Graham Palmer

Spain’s Photovoltaic Revolution presents the first complete energy analysis of a large-scale, real-world deployment of photovoltaic (PV) collection systems representing 3.5 GW of installed, grid-connected solar plants in Spain.  Prieto and Hall conclude that the EROI of solar photovoltaic is only 2.45, very low despite Spain’s ideal sunny climate.  Germany’s EROI is probably 20 to 33% less (1.6 to 2), due to less sunlight and efficient rooftop installations.

“Solar advocates can learn from this analysis . . . “  Not looking at the reality of EROI “is not good science and leads to wasted money and energy that could have been better spent preparing more wisely for declining fossil fuels in the future.”

This study does not detail the environmental destructive mining, toxic chemicals or air and water pollution necessary to get the materials for manufacturing and installing solar devices.  It is the sun not the devices that is renewable, green and sustainable.

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This "Math" is totally wrong and misleading

This is the second time peak prosperity has trumpeted this misleading "scientific studies!" Spain analysis of ERoEI as "proof" that solar electric cannot replace significant energy due to poor return on energy investment.

The report starts with lies, and then continues with trumped up math that is totally inappropriate to the future of solar electric.

Let's start with the lies:

1. this is NOT a scientific report and is not "science"  This is simple engineering with assumptions from economists (whom I do not automatically trust), and the analysis, while done by an "environmental" college professor and a telecom engineer with experience in owning and installing big installations, doesn't appear much different from that done by a financial analyst.  This is not rocket science and anyone can understand what these so-called "scientists" are saying.  No need to rely on an "expert" review of the "science" report.  Everyone should read for themselves, dont take anything for face value as we all (including me) are promoting something.

2. this alleged "science" report starts with the lie that the megawatt installations in Spain are the most  efficient in the world and in particular: "these large installations are far less expensive and more efficient that roof-top solar PV"    This is nonsense.  This lie, however, obscures an important and exciting development in solar electric: locally generated and used energy is CHEAPER and does not require bank and megacompany intervention or necessarily government-industry coalition racketeering, which in its benign form increases energy input by charging you with their lobbying energy, their fairs, their lawyers and their taxes and surcharges, and in a more realistic form, increases energy input by forcing an inefficient but centrally controlled big banker owned organization that is engineered to make money for a bank even if less efficient than local installed, controlled and owned.

a.  In fact, as reported by these "experts" who "do the math" themselves in the quoted report, the electric generation and modification equipment beginning with solar panels are only a small portion of the cost, and virtually all or at least most of the other costs are associated with megaplant needs, which VANISH for a DIY homeowner installation. 

2. Furthermore, the wonderful superior efficiencies of the panels themselves and electric delivery at the megawatt plant level are NOT higher and probably lower due to the need for inefficient, energy loss long transmission to get to the end user.  Some electronics engineers say that long distance transmission of AC power consumes 10% although that seems high to me, clearly the ground heats up and the energy is transmitted everywhere, including outerspace.  Such losses are NOT compared with local generated and used DC power from distributed rooftops. These plants are trying to scale up small panels.  There is no inherent advantage of building a company and doing this as a corporation far away in the desert using the same panels we can put on our roofs and then converting to various voltages and AC to feed old grids using old technology from far away, yet these dinosaur energy costs are included in the solar electric energy input costs in this "scientific studies!" report cited.

OK  lets "do" the math:
This "science" report comes up with a total energy cost of 2065 GwH of "energy inputs" to give a horrible ERoEI of 2.45
of this 2065 GwH energy input:
 608 for making modules, inverters, trackers, metallic infrastructure off site
and if only that is counted, the ERoEI would be 8, using old technology in an industry that is making rapid progress.
Tthe main point of the "scientific study" is that the other costs need to be counted, so let's look at these other energy costs:

"doing the math" they add on (to the energy costs of hardware which totals 608) :
 57 for foundations, canals, fences etc (10% as much as the generating/regulating equipment)
4.7 evacuation lines and right of way
139 security and surveillance (1/4 of total cost of generating/regulating equipment)
20 insurance
26 fairs, exhibitions, promotions, conferences
34 admin expenses
14 municipal taxes
9  land cost
16  labor of consultants, lawyers etc
6 market representative
12 equipment theft
178 electrical network/line restructuring 
198 network stabilization costs
This is a small portion of the added costs in this study but I want to make a point:
The total of this subset of MegaWatt Plant Bloatware energy alone (I ignored others) is 715, which is higher than energy costs of all the equipment needed to generate energy (which can be done locally with that same or similar equipment).
If we discard the lie that solar electric must be done by a banker/financier/government big agency at a far away location from a diffuse source, and instead follow the future of locally produced energy in a diffused form that is absorbed locally on individuals rooftops without massive concrete walls and barbed wire and security sentinels, and administraters, and marketers, and network stabilization, and fairs, and insurance, then doing this math, the 2065 GwH energy COSTS drop at least down to 1350 from these factors alone, which improves the ERoEI dramatically. 
MORE MegaPlant Bloatage energy costs that may not apply to locally generated solar electric are included but I want to point out that for a real person in a collapsing future with locally produced energy the energy input to solar electric is MUCH better than what the utiliites and their consultants/advisors/"scientific studies!" portray.  It likely could be 8 or better, because energy use in making and transporting equipment can and wil be reduced when costs rise and the technology is improving rapidly.

The electric solar energy future is much different than what these megaplant-career-industry pundits are telling you.  I dont know what Spain's future is, but the utilities in America are scrambling to get into locally produced solar electric.  They are following the money.

I am biased too.  I am very busy building innovative demonstration circuits that are more efficient than what the megapower industry provides and a self-regulating grid that can easily grow as needed, in my local community. 





davefairtex's picture
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solar: a call option on electric power

I understand all the arguments for EROEI and the rest - people are trying to solve the "society" problem.

I'm just trying to solve the "me" problem, and the way I view solar is, how much does it cost me to make my electricity appear at my home independent of the grid - presumably for 25 years forward.

I dropped about $7500 in 2012, and I got a nameplate 2.6 kw hr system.  (There were various shenanigans with Solar City - leasing, buyouts, tax deductions, etc, but this is the cash cost to me after all was said and done.)

The beast generated 4598 kwhr this year (solar city provides a convenient website to see this), and given SDG&E's 16 cents per kwhr baseline rate, that's $735.  Basic math says that gives me a ROI of 9.8% per year on my investment - paying for itself in (perhaps) 11 years.  Presumably after that, its just gravy.

But I don't care about that quite as much.  What I care about is having the call option on electric power generation for 20 years.  If something bad happens in the next 20 years where electric power suddenly becomes a whole lot more expensive, these panels on my roof insulate me from that. 

Given that we know Something Interesting is likely to happen with debt, fossil fuels, peaking resources, and whatnot during the next 10 years, it seems like a reasonably cheap option to buy.  Plus, no bank regulator can "bail-in" my solar power.  And unlike normal call options that actually *cost* money and decay over time, this call option actually generates power providing me a better-than-market return on investment.  From a financial math point of view, its no-lose.

Were there incentives?  You bet.  But again, I'm solving the "me" problem, not the society problem.

Its an even better option if I get one of those inverters that allow me to disconnect from the grid and operate my appliances on solar power during daylight hours.  In an extended emergency, that would let me live a high-tech lifestyle during daylight hours, and go onto limited (laptop & flashlight) battery power usage at night.  I don't have such an inverter.  They cost about $1600.  I should probably get one.  :-)

Not sure what net metering looks like these days, or what incentives are available.  But having that option sure seems like a good idea.  I don't regret my decision for a moment.


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According to page 3 of the

According to page 3 of the Alberta Energy Regulator (it used to be the Alberta Energy Resources Conservation Board which was a branch of the government, but it recently got handed over to the industry itself to manage...), Alberta has 35 billion tons of established coal reserves. US consumption is 1 billion per year so that is 35 years of consumption. However, that is just established reserves. Estimated ultimately recoverable reserves are over 600 billion tons, which is over 600 years of US consumption. Granted this may be an overestimate but I think it's reasonable to assume that there is at least a century of plentiful coal remaining in Alberta, and that doesn't even include northern BC which has lots, or any other region. So based on this I don't see any major electricity shortages for a long while. Of course price will go up as oil and gas scarcity, and coal exports heat up, but since electricity is now cheaper than it has ever been (electricity rates have stayed virtually the same for a hundred years, UNadjusted for inflation which means it is now 100 times cheaper!), that is what solar power is up against.

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electricity price inflation

So the chart below suggests that electricity is not cheaper than it has been ever.  In 1975 it was 4 cents, and now its 12.4 cents.  Not.  Cheaper.

Also, coal requires liquid fuel to mine, and yet more liquid fuel transport the mined coal to the power station.  And then, power transmission to my home requires the grid to be intact.  An intact grid requires a constant stream of truck rolls, which requires even more liquid fuel.  If liquid fuel rises in price, so will the price of electricity, regardless of the size of the coal reserves in Alberta.

What's more, if the buck ever has a problem, coal prices will jump - causing electricity prices to rise even higher.  Coal has international value, and the price will be set accordingly.

Just from the chart above, it appears that electricity prices have risen 50% over the past 14 years.  So we can add an approximate 3.5% annual inflation hedge on top of the 9.8% power generation returns.  If my math is correct, that's a 13% annual tax free rate of return on my $7500.  That's like a tax free muni bond that will vanish in 25 years, but that pays you 13% per year, every year.  Or a pre-tax return of perhaps 20% annually.

In 25 years, I'll end up having generated the constant-dollar equivalent of $24,375 in power from my $7500 spend.  The arrays will generate even more value if we have problems with liquid fuel and/or the dollar in the future, which I'd rate as "a likely outcome" within the next 25 years.

Does solar make sense for society?  I have no idea.  Did it make sense for me?


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I agree, coal and electricity

I agree, coal and electricity are going to go up in price in the future as I said, but not like 10 X on a real basis. As oil runs out then we'll see coal to liquids plants pop up everywhere and this will increase the price for coal. Also increased international demand will take its toll. This will increase electricity rates but I imagine it won't go much above where we were 50 years ago on a real inflation adjusted basis, and we got by fine 50 years ago with those electricity prices.

As for electricity prices increasing since 1980, yes it seems they have. But go back 100 years and you'll see that overall the price in $ terms has been amazingly constant considering all the other inflation. Sorry I can't provide the reference, a few years ago I went to the library and looked up a book that lists prices of stuff going back a hundred years, I forget the name. It's called "History of Prices" or something obvious like that.

Mark_BC's picture
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OK I googled and it'

OK I googled and it' surprisingly hard to find historical electricity rates. Here is one reference to 8 cents in 1905 and by 1968 it was 2 cents bimonthly so that is 4 cents monthly (I never know if by bimonthly means twice a month or every two months). So it bounces around a little bit but not too much.

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DaveF, best solar argument I've heard

Thanks for the very concise summary of the compelling reasons to invest in a home solar PV system.  When you look on it as: 

1.   a "Call Option" on future electricity price increases,

2.   an investment that has a better-than-market rate of return now

3,   an investment vehicle that is difficult to plunder, and,

4.   an energy source that would endure a catastrophic electrical grid failure,

its pretty hard to doubt that this is a damn good idea.

I forwarded this post with the price of electricity graph over he last 35 years to most of my family and friends.

And thanks, Mots, for methodically deconstructing the solar-doesn't-make-economic-sense article above.

See, this is why I like PP.

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solar: a call option on electric power

Thank you for sharing your installation details.

My summary: Two years ago I spent almost 5000$ on 4500 watts that I installed myself with NO incentives or tax breaks and another 200$ to connect this to my 50 gallon water heater with a circuit sold by a small inventor in Nevada.  I spent 50$ on parts to connect my waffle maker, coffee pot (I reluctantly was forced to design and build the circuit myself because it is not sold by anyone, in fact, much of what I am doing is reluctant and based on extreme dislike of the inefficient and backwards technology we are saddled with from long ago: for example AC is much more dangerous, more expensive than DC even for local power grids).  I spent over 1000$ on fancy Chinese inverters for my 96 volt battery system, which ALL burned out and I am not using my batteries (they are backup).  So I have enjoyed hot water showers and other uses for more than a year now  without buying expensive equipment from big international companies. 

My other solar system is two 200 Watt panels (about 400$, installed, no incentives or tax breaks) which has been running all of my house lights (48 volt 4-lead acid battery system, 75 dollar charge controller, NO inverter since all lights are LED) for almost 2 years, with NO problems.  LEDs use such little power it is easy to run all lights on 2 - 4 batteries and a couple solar panels.  This is so reliable and cheap and is independent of other circuits.  by the way, my house is a rebuilt warehouse so I was able  to install my own DC wiring and LED light fixtures before closing up the walls.

As a separate project my 1800 watt 1500$ garden system (2011) has been powering my 250$ 2000 watt DC to AC inverter and 400$ (4 lead acid batteries) which run my 200$ walmart freezer in the garden shed for almost 2 years with NO problems, and powering my 100$ electric grass trimmer and my 400$ homemade double electric cultivator (shown in my avatar picture) for gardening.  Prices for the panels have only gone done since then.  I dont pay attention to incentives or tax breaks and do not use them, or get any bank or government or utility involved.  I connected  some panels to a grid tie inverter (500 watts, 150$) and have been injecting power into my house wiring (the part that is connected to the grid) for one year now and noticed that it turned off automatically when the power company came by replace their feed-entrance wires with fresh new wires.  Also the power company came by to check for ground leaks periodically and did not find any problem.  This is in Japan by the way, the power companies in the US do not take such care. 

I have had to invent simple circuits that are more efficient than what the international companies sell to connect things and am building a DC grid with upverters and downverters, and which is self regulating, and which is much more efficient that what the big international companies are doing.  However, a bank cannot easily make money on it and there is no need for expensive utility control and administration.  This is totally different both electrically and and management wise and investment wise than what everyone in the old dying paradigm are jabbering about.  The old phone system melted away to make way for cellular, with self-regulating connections.  The old communication system melted away to make way for internet with self-regulating routing.  The old electric system is starting to crack and can be replaced by a self-regulating network organized nodally and with very dispersed energy inputs, based on solar inputs everywhere, and storage nodally everywhere,  The bankers and big utilities are trying to figure out how to make a killing (and control our freedom and money for their benefit) in the new paradigm.  There are articles on this change in the mass media including one in Business Week last Summer.


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Electrickery call options

Dave made some good observations from a consumer perspective, and my comment is for anyone planning to take advantage of rebate-based government schemes for consumers. Be sure to read the smallprint AND to understand longer term implications, particularly where politics are involved in policy decisions.



In my locale in Australia the state government promoted solar schemes which financially benefit business and residential users who feed back more electricity into the grid than they use, based on a predefined rebate tariff... not materially different to similar schemes elsewhere in the world. All good so far. We have an obscene amount of sunshine per annum, which is a solar generator's dream, so naturally there was a mad scramble from consumers to sign up.



Several months ago the state government quietly introduced changes on business electricity bills which impose massive costs on "large users". This effectively switches the basis of charge rates from usage to fixed-rate. Fixed charges were not specifically addressed in solar legislation, while usage tariffs were. Whilst this naked money-grab is only levied on businesses, the same sly move can also applied to consumers if deliberately loose legislation permits it. There've already been some rumblings about similar changes in the private consumer market, none of which surprises me -: I worked on a 2-year project with the state energy provider, and during that time all presentations and strategic costings pointed to off-the-charts infrastructural increases in future.



I trust politicians and governments as much as I'd trust a fox in a chicken coop, so if you're going to join a rebated solar scheme then please do your homework, build some flex into your payback analysis, and if you can hedge then do that too (one rather enterprising tradesman whom I know installed 30+ panels at his property (roof & garden), with an apparent 3-year projected payback. After that, any rebates will accelerate his mortgage debt reduction. Fast. His setup is designed flexibly enough to be quickly scaled back to subsistence usage if legislation / charge rates become too onerous).

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