Diatribes of Jay

This is a blog of essays on public policy. It shuns ideology and applies facts, logic and math to economic, social and political problems. It has a subject-matter index, a list of recent posts, and permalinks at the ends of posts. Comments are moderated and may take time to appear. Note: Profile updated 4/7/12

22 January 2015

Solar Photovoltaic Energy: Real Cost Accounting FAQs

[Erratum: for less than a day, a brief unfinished essay about Paris’ lawsuit against Fox appeared in this current slot. That was error: that essay is only “on deck”; this one is much more important. For brief comment on the President’s State-of-the-Union Speech, click here.]


1. Why use the big word “photovoltaic”?

2. Why is solar photovoltaic energy the cheapest source of electricity known, even without subsidies?

3. I often read of a solar-industry price parameter expressed in dollars (or cents) per Watt? Right now, it’s hovering around fifty cents per Watt. Doesn’t that mean solar energy is expensive?

4. If the cents-per-Watt figure is the cost of buying the solar panel, and not the cost of the energy it produces, how can we compute the energy cost?

5. If the capital cost of a solar photovoltaic array is the only significant cost of producing solar photovoltaic energy, how do you compute the cost of the energy itself?

6. Formulas are fine, but how can I calculate real numbers, in dollars and cents?

7. So now we have pinned down the “capital cost of array” in whole. What about the lifetime energy produced? How long can the array be expected to produce useful energy, and how much?

8. Now how do we estimate the total energy output of the solar panels over their entire guaranteed working period of 25 years? In other words, how do we estimate the part of the “lifetime energy produced” that solar panel makers guarantee?

9. So far, we have only capacity figures. Don’t they assume that the sun is always shining, day and night? How do we make them more realistic?

10. To account for solar “intermittency,” we must account for three real phenomena: (1) variation of the Sun’s irradiance with latitude, (2) day and night, and (3) weather. How do we do that?

11. So what are the calculated and projected unsubsidized costs of energy from a small-scale, ground-mounted residential solar array?

12. What’s the similarly calculated unsubsidized cost of energy from a utility-scale commercial or industrial array?

13. What happens if—contrary to all experience, experiment, physics theory and expectations—the solar panels die shortly after their guarantees, aka “linear warranties,” expire in 25 years?

14. Now can we finally get to the bottom line?

Comparison Table


Several posts on this blog have concluded that solar photovoltaic energy provides the cheapest source of electricity now known to our species. (See, in inverse chronological order, 1, 2, 3 and 4.) Not only that: it is likely to get even cheaper, while fuel-based sources of electricity are likely to get more expensive—let alone more price-volatile—as fuels supplies dwindle.

Unfortunately, the calculations proving these points are scattered over several posts. That’s not surprising: good data to prove them has emerged slowly, over several years, as the solar industry progressed and my wife and I installed our own personal solar array and learned from doing so. Now, with over a year’s worth of actual energy-production data from our own small-scale, ground-mounted residential solar array, it’s possible to project long-term energy production with some confidence.

Up to now, this blog has made it tedious to review precisely the calculations proving the solid economic value of solar photovoltaic energy. This post brings all the calculations together in the simplest way I know, so that anyone with the patience to read a few pages can review and verify my logic and calculations.

1. Why use the big word “photovoltaic”?

There are two kinds of solar energy, and both are in use today. Solar thermal energy systems use the Sun’s heat (infrared rays) to boil a fluid and turn a mechanical generator. Except for the source of heat, these systems work just like electrical generators that use the heat from burning coal or natural gas. In contrast, solar photovoltaic energy comes from a “solid-state” process that exploits the intrinsic properties of special materials known as “semiconductors.” It uses no heat and requires no moving parts.

2. Why is solar photovoltaic energy the cheapest source of electricity known?

Solar photovoltaic energy is absolutely unique in the electrical industry. Our species has never used anything like it before. It requires no fuel. It requires very little maintenance: just brushing snow, dust, leaves or debris off the solar panels as needed. In operation it produces no effluent or pollution whatsoever, so it doesn’t impair human health, harm other species or cause global warming. It requires no moving parts or rotating machinery. It makes no noise.

No other means of generating electricity has these characteristics. Our species has known about this unique source of electricity now for over a century. While he didn’t invent it, Albert Einstein described and explained the underlying physics, called the “photoelectric effect,” way back in 1905. In 1921, he won the Nobel Prize in physics for his paper explaining it.

3. I often read of a solar-industry price parameter expressed in dollars (or cents) per Watt? Right now, it’s hovering around fifty cents per Watt. Doesn’t that mean solar energy is expensive?

No. This is a common misconception, encouraged by the morons on Fox.

The industry parameter of which you speak is now indeed around 50 cents per Watt. But it has nothing directly to do with the cost or price of electric energy. It’s the manufactured price of a solar cell or solar panel per Watt of capacity, i.e, per Watt of power that the panel can produce in direct, full sunlight. In short, it’s the price of the equipment that produces the energy, not the energy itself.

If you’ve taken (and passed!), high-school physics, you know another reason why this number cannot possibly be the cost of energy. A “Watt” is a unit of power, not energy. It represents energy delivered per unit time, i.e., per second.

Physics—and your electricity bill—measure energy in entirely different units, namely kilowatt-hours. A kilowatt-hour is one thousand times the amount of energy delivered by a one-Watt power source running for a whole hour, or 3,600 seconds. If power from a solar array actually cost fifty cents per Watt, a kilowatt-hour would cost 1,000 x 3,600 x $.50 = $1.8 million! No one would even think of using solar power in that case!

4. If the cents-per-Watt figure is the cost of buying the solar panel, and not the cost of the energy it produces, how can we compute the energy cost?

This is the most important question, and the secret to the cost advantages of solar energy. Remember, solar photovoltaic energy requires no fuel and produces no pollution or global warming, which impose costs on all of us. Economists call these costs “externalities” because they are “external” to the normal production and use of electricity. But they are real costs nevertheless.

The average maintenance cost for all sources of electricity in 2011, when solar photovoltaic energy provided around 1% of the total, amounted to less than 13% of the cost of the energy itself. So we can safely assume that solar arrays, which have no moving parts and require minuscule maintenance, have maintenance costs of 10% or less, probably a lot less.

So, to an approximation of less than ten percent, there is only a single, solitary cost associated with energy from a solar photovoltaic array. It’s the capital cost of building and installing the array itself.

In accounting terms, the cost of energy from a solar photovoltaic array is (within 10%) the amortized capital cost of the array. In economic terms, it’s a “fixed” or “sunk” cost. Why? Because, to an accuracy of ten percent or less (for low maintenance expense), solar photovoltaic energy has no variable costs at all.

5. If the capital cost of a solar photovoltaic array is the only significant cost of producing solar photovoltaic energy, how do you compute the cost of the energy itself?

In principle, the calculation is simple. It’s what accountants call “amortized capital cost” and ordinary people call an “average.” You just divide the cost of building and installing the solar photovoltaic array, in dollars, by the total number of kilowatt-hours (kWh) of energy that the array is expected to produce over its useful lifetime. Thus:

Energy cost ($/kWh) = Capital cost of array ($) / Lifetime energy produced (kWh)

6. Formulas are fine, but how can I calculate real numbers, in dollars and cents?

This is where it gets a bit complicated, but only a bit. We need no more math than simple arithmetic.

The first step is to calculate the full capital cost of the array. The industry-standard parameter, in dollars or cents per Watt of generating capacity, is the cost of buying the solar panels only.

But there’s a lot more to a working solar array than just the solar panels. There’s the supporting structure, which has to support the weight of the panels and keep them fixed in wind and weather. There are the solid-state “inverters,” which convert the direct-current (DC) output of the panels to the alternating current (AC) that homes and industries use. There are wires, connectors, circuit-breakers, and control and monitoring devices. These include power meters and often (as in the case of our own solar array) devices that report the array’s operating data over the Internet in real time. Finally, there is the cost of installing, i.e., erecting, connecting and testing, the array, which can be substantial.

To make all these costs simple to handle and useful for comparison, it’s customary to express the total capital cost of the working array—with its supporting structure, all necessary auxiliary equipment and installation—as the price of the solar panels alone, multiplied by a “Turnkey Factor” that inflates the bare solar-panel price to the total cost of the working array, thus:

Capital cost of array (per Watt capacity) = (Panel price per Watt) x (Turnkey Factor)

The “Turnkey Factor” is a dimensionless number. It’s always greater than 1 because the working array’s total capital cost is always greater than the cost of the panels alone. Often the Turnkey Factor is much greater than 1. This point has important consequences for the cost of energy, which we explore below.

For example, our own personal 6.24 kW-capacity ground-mounted solar array cost $37,335, including solar panels, concrete support pads, aluminum support structure, all auxiliary equipment, and installation. This cost included help in claiming federal and state tax credits. But it does not include any deduction for those credits. In other words, this cost to us was without any subsidy whatsoever.

So the unsubsidized cost of our array, per Watt capacity, was $37,335, divided 6,240 Watts, or $5.98, i.e., just under six dollars. That number was typical of the retail cost of small-scale ground-mounted residential solar arrays in 2013, when we installed ours. Roof-mounted systems are cheaper and therefore produce cheaper energy.

If you assume that our solar panels met the then industry “state of the art” for panel price per Watt, namely, about 60 cents/Watt, our own personal Turnkey Factor was six dollars divided by 60 cents, or about ten. (We don’t know precisely how much our panels actually cost because our supplier didn’t give us a detailed cost/price breakdown.)

7. So now we have pinned down the “capital cost of array” in whole. What about the “lifetime energy produced”? How long can the array be expected to produce useful energy, and how much?

Here again, the answer is a bit complicated, but only a bit. The solar-panel industry appears to have settled on a standard warranty of 25 years for solar panels. At least two major solar-panel producers, Solar World and LG, offer that warranty.

Should we expect the panels to break down and stop producing energy shortly after their warranties expire, the way cars and household appliances often seem to do? That’s a vital question, which implicates the uniqueness of solar photovoltaic energy and fixes the economics of its use.

Remember, solar photovoltaic panels have no moving parts. So there’s nothing in them to “break down” like the moving parts of a machine, including the moving parts of solar thermal generators. Solar photovoltaic panels produce electrical energy at a microscopic level, within their microscopic solid-state crystal or amorphous structures, and they “break down” only at that level.

So far, all experiments and experience with solar panels point to no complete breakdown at all. Solar panels just suffer a slow and steady decrease in power output, over very long periods of time.

That’s precisely what the Solar World and LG warranties offer. These so-called “linear warranties” guarantee a minimum power output, as a percentage of initial output, that drops about 3% the first year and 0.7% per year thereafter, for a minimum power output at 25 years of 80%. (The actual linear calculation yields 79.5%, but apparently there’s enough leeway or “safety factor” in the linear formula for the two firms to guarantee an 80% minimum level after 25 years).

8. Now how do we estimate the total energy output of the solar panels over their entire guaranteed working period of 25 years? In other words, how do we estimate the part of the “lifetime energy produced” that solar panel makers guarantee?

This bit is easy. It’s just the average annual energy output over the twenty five years. That output begins at 100% of initial capacity and falls to 80%, for an average of 90%. Therefore the total legally guaranteed energy output over the 25-year warranty period, taking into account the slow and steady power reduction due to microscopic physical processes, is just 90% of 25 = 22.5 times the initial annual output.

9. So far, we have only capacity figures. Don’t they assume that the sun is always shining, day and night? How do we make them more realistic?

Yes, of course. We have to correct the calculation so far for the nature of solar power, including its “intermittency.” The sun doesn’t shine the same way everywhere on Earth. Nor does it shine at night. And it shines with less power through clouds and rain.

To correct for these effects exactly requires some science and a lot of calculation. You must account for the Sun’s varying “irradiance” at different points on the Earth’s surface and at different times of the year. You must also have good projections for the weather at its precise location.

But we don’t need rigorously precise figures to compare solar photovoltaic energy with other sources of electricity. All we need is rough approximations, to within twenty or thirty percent. As we will see, those approximations amply show the cost advantages of solar photovoltaic energy.

More important, with over a year’s worth of actual measured data from my own small-scale residential solar array, I’m now in a position to compare actual measured energy output with calculated projections. As we will see, the two match fairly well. So far, the calculated projections of energy output have been nearly 20% low.

10. To account for solar “intermittency,” we must account for three real phenomena: (1) variation of the Sun’s irradiance with latitude, (2) day and night, and (3) weather. How do we do that?

It’s not hard to make some useful and pretty accurate estimates.

For factor (1), we can now use actual figures, not theory, from our own ground-mounted residential solar array, pictured and described here. At our array’s actual latitude (south of Santa Fe, New Mexico), the most power it has ever delivered is 5.4 kW, while the array’s rated capacity or “full” rated output is 6.24 kW. (NOTE: roof-mounted solar arrays have lower installation and capital costs and therefore lower energy costs.)

So at our latitude, the solar irradiance factor is roughly 5.4 / 6.24 = 86%, rounded down to the nearest whole percent. This factor will be higher at lower latitudes, including large parts of the American Southwest and the American South, all of Mexico and most of Central America, and large parts of South America, Africa and Australia. It will be lower in higher latitudes. But, again, within 30% it’s a good approximation of the solar irradiance factor for any place were people are likely to make the long-term investment in one or more photovoltaic solar arrays.

To account for night (and twilight), we make a simple assumption that the Sun shines only 8 hours per day, or one-third of the 24-hour day. At our latitude, night varies from about 8 hours in summer to 12 hours in winter, so this is probably an underestimate. The resulting reduction factor is one-third (8/24 = 1/3 = 0.33).

Finally, for average weather, we assume that the sun shines on two days out of three, and not at all on the rest. That again is a very conservative assumption, at least for Northern New Mexico, because the array actually produces substantial energy output on cloudy and overcast days, especially on days with scattered clouds.

So how much energy does a one-Watt panel (or part of a panel) produce at our latitude and location over an entire year? Measured in kilowatt-hours, the answer is 8.76 kilo-hours (the number of kilo-hours in a year), multiplied in turn by each of the factors discussed under this FAQ, thus:

Rated 1-Watt Panel Produces annually: 8.76 x 0.86 x 1/3 x 2/3 = 1.67 kWh

Before moving on to the rest of the calculations, let’s do a reality check. According to actual measurements of energy output from our solar array, which our equipment transmits weekly over the Internet, in 2014 our array actually produced 12.9 megawatt-hours of energy, or 12,900 kWh. The array’s rated capacity is 6.24 kW, or 6,240 Watts. So the amount of measured first-year annal energy output, in kWh per each one-Watt rated panel, is just:

12,900 kWh / 6,240 = 2.07 kWh.

Note two things. First, our rough theoretical calculation produced a number (1.67 kWh) within 19.3% of the actual first-year output of our solar array (2.07 kWh). That’s well within our goal of 20 - 30% accuracy. Second, our theoretical number was lower than the actual annual output of our array, showing that our rough theoretical estimates are conservative.

11. So what are the calculated and projected unsubsidized costs of energy from a small-scale, ground-mounted residential solar array?

Good question. It took us this much thinking and arithmetic to get to this point, but now we are nearly done.

We can estimate—as accurately as we estimated the annual (not just rated) energy output of our own array—the probable annual output, per Watt of rated capacity, of any array working at our rough latitude and in roughly the same weather conditions, i.e., pretty much throughout the American Southwest. Weather conditions in the tropics are probably similar or better, where the latitudes are lower, and weather conditions in Australia’s Outback are probably much better.

For our own solar array in Northern New Mexico, we’ve already made this estimate in FAQ 10. The answer is 1.67 kWh annually. Using that estimate, we can calculate the lifetime energy produced for use in the formula in FAQ 5.

If we’re looking only for legally guaranteed energy output, we multiply the annual number by 25—the number of years warranted—and by 90%, the factor calculated in FAQ 7 that reflects the solar panels’ decaying energy output over the 25-year warranty period, thus:

Guaranteed lifetime energy (per Watt capacity) = 25 x 1.67 x 0.9 kWh = 37.6 kWh.

So the calculated Lifetime energy produced by our 6.24 kW = 6,240 Watt capacity array over the guaranteed lifetime is 6,240 x 37.6 kW = 234.6 megawatt-hours, or 234,600 kWh. In comparison, the projected energy output over the 25-year guaranteed life, based on the actual measured first-full-year (2104) output, or 12,900 kWh, multiplied by 25 years and the “declining factor” 0.9, is 12,900 kWh x 25 x 0.9 = 290.2 megawatt hours, or 290,200 kWh. The discrepancy between calculated and projected output based upon first-year measured output is less then 20%—well within our desired 30% error bars.

If we take the lower number to continue our conservative estimation, the guaranteed and unsubsidized cost of energy from our solar array is then just its unsubsidized capital cost, namely $37,335, divided by the guaranteed energy output of 234,600 kWh, thus:

Unsubsidized guaranteed energy cost = $37,335 / 234,600 = 16 cents per kWh.

This unsubsidized and guaranteed energy price is higher than the US average residential retail price of conventional electricity. But do we really think solar panels will stop working or “break down” just after the makers’ warranties expire? That’s highly unlikely. Solar panels have no moving parts and so “break down” only at the level of their molecules or crystal or amorphous structure. The only evidence we have of that breakdown is the slow and steady decline in power output reflected by the linear warranties.

So the most likely—albeit not legally guaranteed—result of using solar panels beyond their 25-year warranty period is that their power output will continue to decline, slowly and regularly, according to the very same linear formula.

Initially, the array will produce annually the adjusted amount of energy calculated in FAQ 9, namely 1.67 kWh per Watt of rated capacity. By the time the first century of operation ends, that annual level of energy production will have fallen to 100% - 3% (first year) - 99 years x (0.7%/year) = 27.5% of its original magnitude. So the total century’s energy output will be roughly the average of the beginning and ending values (100% and 27.5%), multiplied by 100 years, thus:

Century lifetime energy (per Watt capacity) = 1.67 kWh x 100 x (127.5/200) = 106.5 kWh per Watt of rated capacity.

Accordingly, the unsubsidized century energy cost from our solar array will be just the unsubsidized capital cost, divided by this number times the capacity figure 6,240, thus:

Unsubsidized century energy cost = $37,335 / (106.5 kWh x 6,240) = $37,335 / (664,560 kWh) = 5.6 cents/kWh.

This is less than half the US average residential retail price of electricity for 2013, which is above 12 cents per kWh.

This result assumes that the array operator will replace the solar panels, or abandon the array, after a century, when their power level has dropped to 27.5% of the initial output. Yet nothing requires the operator to do so, for the array will still produce useful power for roughly another 27.5 / 0.7 = 39 years.

After a century, advances in technology and energy conservation might allow the operator to achieve the initial results of electrical use with only 27.5% of the initial energy. Or the operator might replace, or might have replaced, the solar panels, keeping the array’s supporting structure and equipment without additional cost. We will explore these possibilities below.

12. What’s the similarly calculated unsubsidized cost of energy from a utility-scale commercial or industrial array?

For utility-scale commercial or industrial arrays, the economics are much improved, as compared to a small residential retail array like ours. While our small array had an unsubsidized capital cost per Watt of rated capacity of nearly $6, utility-scale arrays can reduce unsubsidized capital costs to $2 per Watt capacity, i.e., three times lower.

Thus, for a utility-scale array operating at the same latitude and under the same weather conditions as our small-scale residential array, the relevant energy costs would be reduced by a factor of three, thus:

Unsubsidized and guaranteed energy cost = 16/3 = 5.3 cents per kWh
Calculated, unsubsidized century energy cost = 5.63 /3 = 1.9 cents per kWh

The latter cost is lower than the cost of any conventional source of electricity—whether burring coal or natural gas or nuclear power—and without accounting for any externalities of conventional sources.

13. What happens if—contrary to all experience, experiment, physics theory and expectations—the solar panels die shortly after their guarantees, aka “linear warranties,” expire in 25 years?

Good question. This is not likely to happen, as the “linear warranty” is not a product of experience, experiment or physics theory. Instead, it’s a product of the risk-aversion of lawyers and business executives, namely, those in the solar industry.

But it’s always useful for engineers to plan for worst-case scenarios. So let’s suppose that the solar panels all poop out after 25 years. What then?

Here’s where things get interesting indeed, and in solar power’s favor.

Remember the Turnkey Factor from FAQ 6? And remember how it’s always greater than 1, often much greater? For our own actual ground-mounted solar array, for example, it was around 10.

That point is vitally important for costing, because the Turnkey Factor is the ratio of the total installed cost of the solar array, before any subsidies, to the cost/price of the solar panels alone (in both cases, per Watt of rated capacity). The Turnkey Factor is greater than 1—often much greater—because the cost/price of the panels is only a fraction of cost/price of the whole array, including installation.

What this means is that replacing the panels if they die is much less expensive than rebuilding and re-installing the array. All you have to do is unplug the old panels, remove their bolts, install the new panels, bolt and plug them in, test them, and power up. That’s much less difficult and costly than buying and installing a whole new array.

Because installing the new panels is so simple, the lion’s share of the cost of replacing them is just the cost of the new/replacement panels themselves. Relative to the initial cost of the whole array, that’s just the reciprocal of the Turnkey Factor (i.e., 1 divided by the Turnkey Factor).

For example, actual figures from our own solar array put the Turnkey Factor at around 10, assuming the “state of the art” panel price per Watt was then 60 cents/Watt. That means that the whole array (price plus installation, before subsidies) cost about ten times what the panels cost. In other words, the panels represent only 10% of the cost/price of the whole array, including installation and before subsidies.

So even if all the panels die promptly after their linear warranty expires—a highly unlikely occurrence!—replacing them three times during the century lifetime of the array (at the 25th, 50th and 75th anniversaries of the initial array installation) will increase the lifetime capital cost of the array by only about 30%, plus installation. But it will also increase the lifetime energy produced, to four times the Guaranteed lifetime energy produced, thus:

Lifetime energy (for three panel replacements) = 4 x Guaranteed lifetime energy = 4 x 37.6 kWh = 150.4 kWh (per Watt of rated capacity).

This is 41% more than the lifetime energy capacity of the array (106.5 kWh per Watt of rated capacity) running for a century with steadily decreasing power output and no panel replacement. As a result, while three panel replacements increase the total capital cost of the array by around 30% of the capital cost of the array and its installation, plus the panels’ installation cost, the denominator of the energy-cost equation (FAQ 5) increases by 41%.

If we assume that panel-replacement installation will cost 20%% of the price of the panels, each time, the three panel replacements will increase total capital costs by 36%, while the denominator of the energy-cost equation will increase by 150.4/106.5. So the three panel replacements will increase the lifetime cost of energy by roughly a factor of 1.36 x 106.5/150.4 = 0.96. That is, the energy-cost with three panel replacements will be about 4% less than for no replacements.

For large-scale commercial arrays, the calculation is different because the Turnkey Factor for them is much lower than for small-scale retail residential arrays like ours. For example, the state-of-the-art in 2013 was a total array cost of about $2 per Watt. Assuming a state-of-the-art panel cost/price figures of 50 cents per Watt, the Turnkey Factor is around 4.

With that small a Turnkey Factor, the panel price/cost would be 25% of the total capital cost, plus installation, so three panel replacements would increase the total capital cost by upwards of 75%. If we make the same assumption that the installation of each set of panels costs 20% of their price, the resulting increase in total capital cost will be 90%. Therefore the three panel replacements will increase the lifetime cost of energy by 1.90 x 106.5/150.4 = 0.35, or 35%.

14. Now can we finally get to the bottom line?

Yes, we can. The basic equation is the one derived in FAQ 5 above, thus:

Energy cost ($/kWh) = Capital cost of array ($) / Lifetime energy produced (kWh).

As we discussed in FAQ 6, the capital cost consists of two parts, the per-Watt-capacity panel price and the Turnkey Factor—a dimensionless multiplier reflecting how much the rest of the array (besides the panels) and its installation cost. Thus:

Capital cost of array (per Watt capacity) = (Panel price per Watt) x (Turnkey Factor).

Putting these two equations together lets us calculate the cost of energy from solar arrays under various assumptions, thus:

Energy cost ($/kWh) = (Panel price per Watt) x (Turnkey Factor) / Lifetime energy produced.

The following table shows the cost of solar photovoltaic energy, in cents per kilowatt-hour, depending on the size and scale of the array, whether the panels’ lifetime is assumed to end when the 25 year linear warranty does, whether the operator replaces the panels when their warranties expire (i.e., three times in a century), or whether the panels produce power at a declining rate for a century, after which the operator discards them and the array (although it still produces some useful power). For comparison, the table also presents, the national-average retail prices of various kinds of conventional electricity, and the costs of generating electricity from the most common fuels, namely, natural gas, coal and nuclear fuels. The various sources of electricity are presented in the order of decreasing energy cost. Here’s the table:

Comparative Costs of Electrical Energy from Conventional Sources
and Solar Photovoltaic Energy

Energy SourceCost of Energy
(cents per kilowatt-hour)
Our residential solar array, unsubsidized, over guaranteed 25-year panel life16
Conventional electricity, US average residential retail price (2013)12.16
Conventional electricity, US average commercial-use price (2013)10.34
Nuclear electricity, generated cost for new nuclear plants10
Conventional electricity, US average industrial-use price (2013)6.86
Our residential solar array, unsubsidized, projected over century of use, no panel replacement5.6
Our residential solar array, unsubsidized, projected over century of use, with 3 panel replacements5.6-minus
Utility-scale solar array, over 25-year guaranteed panel life5.3
Coal electricity, generated cost4
Natural-gas electricity, generated cost4
Utility-scale solar array, unsubsidized, projected over century of use, 3 panel replacements2.6
Utility-scale solar array, unsubsidized, projected over century of use, no panel replacement1.9

NOTE: These figures do not include the cost of “externalities” such as air, ground and water pollution and climate change. Nor do they include the costs of the risks of nuclear energy. Solar photovoltaic energy has virtually no such costs, although cadmium telluride solar panels may have some risk of pollution, depending upon how exhausted panels are recycled or otherwise disposed of.

Footnote 1. Precise links to warranty information may vary, as manufacturers tweak their websites. As of this post’s publication, you could find the linear warranty on LG’s website at this link by clicking on the “Technical Specifications” tab and “Certifications and Warranty” subtab. For Solar World, you could find the same linear warranty here, complete with a helpful graph. [Scroll down to “Performance guarantee.”]

Footnote 2. “David Crane, the boss of NRG Energy, which scrapped plans to build two [nuclear] reactors in Texas in 2011 after sinking $331m into the project, estimates that new gas-fired generation costs $0.04 per kilowatt-hour, against at least $0.10 for nuclear.” The Economist, June 1, 2013.

Footnote 3. This is my own estimate of the generating cost of the Four Corners coal-fired power plant, the largest in the nation. My calculations can be found here, below the table.

The President’s State-of-the-Union Speech, 2015

Readers may want to know why I’ve made no comment on the President’s State-of-the-Union Speech. There are two reasons.

The first is a practical one. I was in the air on a trip half way around the world when he gave the speech. I was able to see and hear it only 36 hours afterward, over the Internet in a hotel room.

In retrospect, I’m glad I waited. The complete, official YouTube version shows facts, figures and news on the right-hand side of the screen, brilliantly synchronized with the audio/video of the President speaking on the left. It’s a multimedia presentation worthy of the twenty-first century—an advance in presidential communication as striking as FDR’s “fireside chats” on radio. Apparently the President’s team continues to experiment successfully with new technologies of communication, the lifeblood of politics.

The second reason why I’ve waited to comment is more somber. The subjects of today’s principal post—energy and, indirectly, climate change—are even more important than the state of our Union. According to my calculations, we have between 18 and 43 years to find effective substitutes for oil, and maybe a decade or two longer for natural gas.

If we don’t find substitutes and transition to them by then, our civilization will falter. Or burning coal will drive climate change to a tipping point, and it will run away. By “our” I mean not just us Yanks, but our entire species.

This doesn’t mean that Obama’s speech wasn’t a masterpiece. It was. He, too, emphasized the urgency of climate change, pointing out the present historical temperature anomalies and weather disasters that require immediate action. He was right to do so.

In his succinct review of foreign affairs, he reminded our ever-present warmongers of the importance of his own thoughtful and careful approach to diplomacy and international relations, in winding down the War in Afghanistan, in pressuring Russia to behave in Ukraine, in avoiding yet a new and so-far unnecessary war with Iran, and in relying on allies and coalitions to wage successful war against IS. He was right to do so.

Obama was also right to emphasize “middle class economics” at the outset and at length. His general proposals for more easily accessible child care and post-secondary education, higher minimum wages, and equal pay were right not only as a matter of substance, but also as a matter of politics. The Dems and effective government need women’s votes, women’s support and women’s leadership, with Hillary and Elizabeth waiting in the wings.

The President has long been a team player and a long-term thinker, as he showed so brilliantly by appointing Hillary his first Secretary of State. His hitting the so-called “women’s issues” in his speech was just more evidence of the same, if any were needed. It made you wonder whether, had the tables been reversed, Hillary would have done as much for him.

But the rightest thing the President did was to throw away any list of specific proposals (and its customary advance distribution) and speak from the heart about values. At times, he seemed close to tears. But at times he had even the cynical and disputatious Congress in the palm of his hand.

Among them were times when he spoke of his own unlikely rise to the White House. Later, he reminded members of Congress how depressed they, too, often feel when contemplating the gridlock they have helped create and how far it falls from what inspired them to seek elective office. At those times, the House was utterly still and the attention of all in it rapt.

The multimedia production on the right-hand side of the YouTube screen vastly enhanced the impact of these moments. While the President spoke of his own personal history, for example, there were photographs of him as a child, as a youth hugging his grandmother, and as a short-Afro-wearing young law student, with a copy of the Harvard Law Review that he ran in his hand.

But for that copy, it was easy to imagine him as of one of the many unarmed young “black” men shot down by our over-militarized and overly racist police. The graphic juxtaposition was brilliant and deeply affecting subliminal imaging.

When the President attacked the crushing and embarrassing burden of ceaseless money-chasing in Congress, he didn’t mention the latest development: the Koch Brothers’ personal vetting sessions for GOP presidential candidates. But he didn’t have to. Undoubtedly every member of Congress present knows about them.

In these sessions, GOP candidates for president are supposed to genuflect to the Brothers and their “Oil-is-still-King” agenda. They must do so in order to receive the campaign largesse that Citizens United makes possible and that, if not a guarantee of winning, is at least perceived as indispensable.

It was there that the theme of today’s principal post and the State of our Union and species coalesced. The Kochs represent the dismal past, in energy, in politics and in so-called “soft” corruption. If their short-sighted personal agenda wins, and if we cannot make the transition to clean and sustainable sources of energy, time may run out on our species, and we may suffer broadly and terribly. Despite all the majesty, brilliance and emotional power of the President’s speech, nothing save the threat of general nuclear war is more important than that.

But the video did have its memorable moments. My favorite was the President’s brief reference to his unilateral change in Cuba policy, away from the stiff-necked abysmal failure of fifty years. As evidence of the change, he pointed to the gallery and to Alan Gross, the American political prisoner held in Cuba for fifteen years and released as part of Obama’s rapprochement with the Cuban government.

The now-old white man had a bald head and a white beard and sideburns. Clad in an ill-fitting suit, he was missing most of his front teeth. Yet he was by far the most enthusiastic visitor in the gallery whom the President recognized. He stood up, clapped vehemently, smiled, visibly mouthed the words “thank you” over and over, and pointed toward the President as if he were a football star who had just made a touchdown.

Maybe it was just my mood. But Gross seemed to me to stand for all the tens of millions of old white men, including me, who support the President wholeheartedly. We want to thank him for every grey hair on his head that sprang from his relentless effort to make our nation better, stronger and fairer, despite the mindless opposition of nasty little self-righteous shopkeepers like Boehner.

Like any masterpiece, Obama’s 2015 State-of-the-Union Speech has no review that can compare with the original. Every American citizen who hasn’t done so already should watch the multimedia version. Then they can see what America once was and can be again, if members of Congress can extricate themselves from the crushing machine of money and influence in which they’ve trapped themselves and follow the President’s leadership. Unfortunately, it will probably take several of the vetoes that he promised to wake enough of them from their zombie-like servitude to the bosses and their cash.


08 January 2015

What Will Oil Prices Do Now?

[For comment on the puzzling paucity of natural-gas-burning cars and light trucks, click here.]

In an essay published just three weeks ago, I argued that the Saudis have no economic motive for letting oil prices plunge as they have. At just under $49 a barrel for WTI crude yesterday, oil prices have dropped by more than 50% in less than one year. That has been a huge plummet, with enormous global economic consequences, not the least for Saudi Arabia and every other petro state.

The question on everyone’s mind now is how long the low prices will last.

My reasons for calling the Saudis’ decision to let prices fall non-economic were simple and sound enough. Oil and its end-product (gasoline or petrol) are what economists call “price inelastic” commodities. In fact, they are about the most price-inelastic commodities in widespread industrial use today. I explained the reasons in an earlier essay; more about this later.

What this inelasticity means in practice is that small changes in global supply of or demand for oil can produce huge price shifts. In my recent essay, I calculated (roughly, using the behavior of gasoline prices during the Crash of 2008 as a proxy) how much the Saudis would have had to decrease their own production, unilaterally, to have kept global oil prices stable. The answer was 7.5%.

The total revenue received by any vendor selling oil equals the quantity sold times the price. By dropping their production (and hence sales) by 7.5%, the Saudis could have kept prices stable, incurring a total loss of only 7.5%, even if no other oil producer also cut production. As it happened, neither the Saudis nor anyone else cut production, so the price of oil has dropped over 50%. The result is that the total oil revenue of every petro state, including Saudi Arabia, Iran, Iraq, Russia and Venezuela, has dropped by over half. Needless to say, that’s much more than 7.5%.

That outcome, I concluded, was economically irrational for the Saudis to have caused deliberately. So I looked for political motives for the Saudis’ action. I quickly focused on a vital political goal: pressuring Iran and its patron, Russia, to make a deal to avoid Iran becoming a nuclear state.

This strategy would offer a blandishment as well as a threat: the implicit promise of a return to “normal” oil prices after success in the nuclear talks with Iran. So if that analysis is right, oil prices should bounce right back up if and when the Iran talks yield a credible and verifiable positive result. We could be back to gasoline at close to $4 a gallon in just a few months.

But in that analysis, I focused only on short-term economic motives. What if the Saudis and the other petro states have been thinking long-term?

As it turns out, there are indeed long-term business and economic motives for keeping oil prices low, which have nothing to do with politics. In failing to see and discuss them last time, I was ignoring the lessons of my own earlier posts on this blog.

To put it simply, oil now has stiff competition for its primary market, ground transportation. The best way to see why is to reproduce here my table of energy costs per mile for driving a car, for various sources of automotive energy. Following is the latest (2013) version of that table, with the current (2015) low price (highlighted) of oil’s end product, gasoline, now about $2 a gallon in many parts of the United States:

Energy Cost of Driving, in Cents per Mile,
for Various Automotive Energy Sources

Energy SourceUnderlying Price ParameterCents per Mile Driven
 March 2012Late 2013March 2012Late 2013
Gasoline$3.78 per gallon$2.00 per gallon
(early 2015)
(early 2015)
Natural Gas (Residential)$1.28 per gal. equiv.$1.89 per gal. equiv.4.36.3
Nuclear Electricity4.4 ¢ per kWh15 ¢ per kWh1.55.1*
Conventional Electricity
11.6 ¢ per kWh12.5 ¢ per kWh44.3
Conventional Electricity
6.8 ¢ per kWh7.23 ¢ per kWh2.32.4
Natural Gas (Industrial)$0.55 per gal. equiv.$0.53 per gal. equiv.2.2**2.0**
Solar Photovoltaic
Electricity (Residential)
N/A4.6 ¢ per kWhN/A1.5
Solar Photovoltaic
Electricity (Commercial)
5.1 ¢ per kWh2.4 ¢ per kWh1.80.8

* For new plants
** Assuming that service station’s retail sale of industrial gas would add only 20% for operating expenses and profit.

So right now, today, oil has serious price competition from both natural gas and electricity as a source of energy for powering cars and light trucks. Not only that. For that purpose it’s now the highest-cost alternative, whether the natural gas or electricity is priced at residential retail, commercial or industrial rates.

To add to that inconvenience, oil is likely to run out before either natural gas or electricity, whether the electricity comes from natural gas, coal, or nuclear power. According to OPEC’s own global reserve figures, and present consumption rates (including their present rate of increase), global oil will run out somewhere between 18 and 43 years from now, depending upon how accurate OPEC’s figures for global reserves are.

In comparison, our Yankee natural gas reserves will last for 39 years even if we substitute natural gas for coal in making electricity and convert our entire light-transportation fleet to run on natural gas. If we use the sun, wind and nuclear power to replace coal instead, our own natural gas will last for 53 years, even if we run all our cars and light trucks on it and continue present uses.

So if you take our Yankee figures as estimates of the global longevity of natural-gas reserves, those reserves are likely to outlast global reserves of oil. In other words, the last fossil-fuel-powered car or truck will likely run on natural gas, not gasoline or petrol.

What does all this mean practically? Three things. First, the Saudis and other petro states are offering the high-priced commodity, still today, even after the recent price plunge.

Second, the commodity they offer is likely to run out before any substitute. As it runs out, all the enormous industrial infrastructure for extracting, refining, transporting, distributing and selling oil, plus burning its end product in internal combustion engines, will become useless and mostly worthless. The same sad fate will not befall solar arrays, windmills, or nuclear power plants, or (at least in the same short time frame) natural-gas vehicles or power plants. Primarily for this reason, an earlier post urged universities and pension funds to divest their investments in oil producers.

Third, as these facts dawn on producers of energy and vehicles, the economic structure of the global transportation industry will begin to shift. Because substitutes for oil offer both cheaper and longer-lived energy for driving, even now, industry will begin to make cars and trucks that use those substitutes, namely, natural gas and electricity.

As that happens, the extreme price inelasticity of oil and gasoline will begin to moderate, and with it the power of the Saudis and petro states to control the price of oil by manipulating global production. If they try to raise prices too high, more people will shift more quickly to cars and light trucks that run on natural gas and electricity.

None of this is the least bit odd. It’s all economics 1A.

When you have a unique commodity with no real substitutes—as oil has been for about a century for most ground transportation (and still is for air transportation)—you can pretty much charge what you please. When there are reasonable substitutes, your power over price decreases. It decreases even faster when your commodity is not only the highest-priced alternative, but is also not far from running out.

What’s not economics 1A, and in fact is unpredictable, is the response of global industry. Elon Musk’s new “Gigafactory” for electric cars is just one of many possible responses. Major car makers converting part or most of their fleets to run on natural gas and/or flex-fuels might be another. The economic motivation is there, but the strength and speed of the response is unknown and probably unknowable.

The price-inelasticity of oil and gasoline depends directly on how quickly car and light-truck makers offer vehicles that run on natural gas (or flex-fuels) and electricity. And that, in turn, depends somewhat on the price of oil, which the Saudis at present control. So in addition to involving imponderables, the calculation involves an unknowable feedback loop.

Saudi Arabia and other petro states could, of course, still boost the price of oil by cutting production. But that would only hasten the transition to cheaper and longer-lived alternatives. If other petro states refused to go along, but instead strove to increase their market shares, oil would run out faster. In the end, some petro states might even be left with oil to sell and no customers after fleet conversion reached completion.

Of course the Saudis’ motives, like anyone else’s, can be mixed. Pressuring Iran and Russia at this critical geopolitical moment is probably among them. After all, the Saudis were Iran’s arch-enemy before Israel existed.

But there are also other, longer-term economic motives. For the first time since oil became King (and electric cars with primitive lead-based batteries failed) a century ago, oil now has real competition.

The writing is on the wall, underlined by Elon Musk. It will be interesting to see how the petro states will read it. If Iran makes a nuclear deal, will they raise prices back up and try to make as much money as they can in the near term, thereby strengthening others’ motivation to switch to natural-gas and electric vehicles? Do they even have the collective discipline to do so? Or will they continue to try to beat the competition in the most direct and businesslike way possible, by increasing production and lowering prices?

As the great baseball catcher Yogi Berra once said, the future is one thing that’s hard to predict. But it’s now distinctly possible that oil prices will stay down, and perhaps even go lower, until the last human culture poor or stupid enough to bet its long-term future on oil pays the supreme price for a commodity still in demand but about to run out. Current global oil-reserve estimates suggest that that sad day is only a few decades away.

Footnote: Another away to estimate the Saudis’ economic power over oil prices is to consider what increases in global supply might have caused (belatedly) the recent price plunge. The two most probable sources of increased production are Iran’s increased production due to interim lessening of sanctions (less than 1.5 million barrels per day) and our Yankee increase in shale-oil production (less than one million barrels per day). The total of these two increases is less (probably a lot less) than 2.5 million barrels per day, or less than 21% of Saudi Arabia’s estimated 12 million barrels per day production. So even if these high numbers for new production are right, the Saudis could have kept their short-term revenue losses down to 21% (and could have avoided any losses at all to other petro states), rather than forcing all petro states, including their own, to endure losses over 50%.

Coda: The Natural-Gas Enigma

One of the biggest head-scratchers in modern industrial history is the failure of global auto makers to make and sell more cars and light trucks that can run on natural gas.

For several years, natural gas has enjoyed a substantial price advantage over gasoline, on an energy-equivalent basis. The recent plummet in oil prices has nearly erased that advantage, but only for residential retail prices.

Even today—and for the foreseeable future—cars and light trucks that can run on natural gas offer both drivers and vehicle makers a number of substantial advantages, including price advantages. Here they are:
    1. “Gassing up” at home. Even at residential retail prices for natural gas, which are now at rough energy-equivalent parity with gasoline, consumers have the advantage of “gassing up” at home, using the same natural-gas sources they use for heating their homes or for cooking. All they need is a compressor, which costs far, far less than any car. Businesses can enjoy similar advantages: avoiding the cost, delay and loss of employee time to find a gas station, fill up, and go there and back.

    2. Still lower prices. Due in part to the odd economics of natural-gas distribution, commercial and industrial prices for natural gas are substantially lower than residential retail prices. So consumers and businesses willing to “gas up” at a natural-gas station can still enjoy nearly a factor-of-three reduction in the per-mile energy cost of driving with vehicles that run on natural gas, as compared to gasoline.

    3. Lower energy-price volatility. A few liquified natural gas (LNG) shipping terminals and tankers exist, and more are planned. But it will be a long time, if ever, before there’s a global market in natural gas like that for oil. In many parts of the world, natural gas is priced locally. No petro state has much influence over price or supply in these markets. Europe and Japan are about the only parts of the developed world that depend heavily on foreign suppliers for natural gas. This means that other parts of the developed world, including us Yanks, could escape forever from extreme energy-price volatility—and the influence of petro states over the price of ground transportion—simply by converting our car and light-truck fleets to natural gas.

    4. Lower distribution costs. Although much crude oil and some refined products travel by pipeline, the vast majority of retail gasoline gets distributed in tanker trucks. Therefore distribution costs for gasoline are subject the same price disadvantages of oil products as gasoline and diesel fuel themselves. In contrast, virtually all natural gas travels to its final point of consumption by pipeline—a much cheaper, safer and less cost-volatile means of distribution.

    5. Lower pollution. Natural gas burns much more cleanly than even the best gasoline, let alone diesel fuel. Switching to natural gas for light vehicles would avoid the cost of afterburners and pollution-control systems, reduce car and truck pollution, and make big cities more liveable.

    6. No refining. Natural gas doesn’t require refining to power vehicles. Crude oil does. In fact, the whole purpose of the controversial proposed Keystone XL pipeline is to transport crude oil from Canadian tar sands to our Yankee refineries on the Gulf Coast (which have excess capacity) for export of the refined products. Insofar as concerns the part of our vehicle fleet that runs on natural gas, refineries are obsolete, as is all the unhealthy pollution they produce.

    7. Ease of using and converting infrastructure. Although you might get a bit better mileage, power or range by tweaking them for natural gas, the internal-combustion engines now used for gasoline work fine with natural gas. All they require is new or modified fuel-storage and fuel-injection systems. So the vast majority of the industries and supply infracture that build gasoline cars today is easily and cheaply modifiable to produce natural-gas vehicles. It likely costs less and takes less effort to convert an existing gasoline-vehicle design to natural gas than it does to make a new design for a new model year.

    8. Less environmental damage. Natural gas is a gas. In the event of a spill outdoors, it dissipates naturally. The risk of permanent damage to people, property and other species from a spill is therefor much lower than with oil or gasoline.
As against these enormous advantages of cars and light trucks that run on natural gas, I’m aware of only three disadvantages: (1) slightly higher capital cost for the vehicle, (2) possibly lower range, and (3) fewer places to fuel up.

All these “problems” have self-evident solutions. At commercial or industrial natural-gas prices—or the slightly greater prices that commercial natural-gas stations could offer—the fuel-cost savings could recoup the added capital cost of a natural-gas vehicle in a decade or less, depending on the comparison car and the yearly mileage driven. The recoupment time would drop with greater volume of and experience in manufacturing, not to mention the saving on afterburners and exhaust systems for natural-gas-only vehicles (as distinguished from flex-fuel ones that can burn gasoline, too).

The other two “problems” are trivial. Greater range requires only bigger natural-gas storage tanks. And most consumers and small businesses can “fuel up” at their homes or offices, which already have natural-gas supplies for heating and/or cooking. Small businesses in particular already enjoy lower commercial rates for natural gas.

* * *

So as a one-time engineer, I just don’t get it. Toyota and Hyundai are now offering fuel-cell cars that run on hydrogen. Their technology is exotic, untested at scale, and hideously expensive, at least for the time being. And gaseous hydrogen, to put it mildly, is hardly available in every home or small business. It’s also much more flammable and dangerous than natural gas.

Don’t get me wrong. Hydrogen-fueled cars and light trucks, powered by hydrogen taken from water electrolyzed with solar, wind or nuclear power, are a possible future solution to our species’ twin energy and climate-change crises. They could cure the intermittency of solar and wind power and create a global market for cheap stored renewable energy, in the form of compressed or even liquified hydrogen.

But any such solution is at least a decade or two away. In the meantime, car makers could convert a substantial share of their products to run on natural gas in a mere year or two.

So why aren’t Toyota and Hyundai, as well as our Yankee car makers, offering and pushing cars that run on natural gas? It beats me. Japanese and South Korean car makers at least have the plausible excuse of having headquarters in fossil-fuel-poor countries at the mercy of foreign suppliers. Maybe they just don’t understand that we Yanks produce all of our own natural gas and have enough of it to outlast today’s projections of oil reserves by a decade or two.

As for our own Yankee car makers, what can you say? Maybe—except for Tesla and Chevy with its Volt—they’re just as dumb, happy, lazy and un-innovative as they’ve been for half a century. Maybe they’e so caught up in the rush to offer vehicles at the lowest possible initial capital cost that they can’t see anything beyond their initial-price blinders. Maybe they don’t believe in the power of their own marketing to sell the substantial advantages of natural-gas vehicles listed above.

More likely, finance guys (they are virtually all guys) and the most un-imaginative engineers at work today continue to dominate American car makers, as they do our electric-power industry. To say there’s a business opportunity here for an entrepreneur with a little guts and imagination would be an understatement of Obamanian proportions. But our plodding Yankee auto “engineers” (if you can dignify them with that title) will probably just keep doin’ what they’re doin’ until the oil runs out.