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

18 October 2013

Solar PV Energy: Cheapest Now, and Even Cheaper Soon

FLASH! IKEA goes solar! Consumers can now beat
the cost of coal and natural-gas energy!

[For brief comment on how solar PV panels could save Harbin from its horrible coal smog, click here. For a final take on our recently suspended political travesty, click here.]

Cheapest Now
Why Cheapest Now
Why Cheaper Soon
Investing Tip and Disclosure
Uncertainty: Not Much
Saving Harbin from Coal Smog
IKEA goes solar!

Cheapest Now

Right now, as you read this post, solar photovoltaic (PV) energy is the cheapest form of electrical energy known to Man.

Properly accounted for, energy from new large commercial solar PV arrays costs between one and two pennies a kilowatt-hour. According to David Crane, the CEO of Texas utility NRG Energy, as reported in The Economist [subscription required], “new gas-fired generation costs $0.04 per kilowatt-hour, against at least $0.10 for nuclear.” My own estimate of the generating cost of the nation’s biggest coal-fired plant is four cents per kilowatt-hour. And that’s without any accounting for maintenance or the horrendous pollution that burning coal causes, let alone global warming.

Thus solar PV panels beat the cost of all conventional, fuel-based sources of electrical energy by at least a factor of two. In order to understand why—and to account for PV energy properly—you have to know how they work.

Why Cheapest Now

Solar panels make electricity without any fuel, rotary motion, noise, smoke, pollution or global warming whatsoever. They have no moving parts. Instead, they use a subatomic physics process known for over a century as the “photoelectric effect.” The process occurs inside the atomic-molecular structure of semiconductors, in a kind of collective phenomenon not yet completely understood.

Like the working of your computer’s or cell phone’s microprocessor, the entire process is “solid state,” that is, without mechanical action. So is the work of the semiconductor “inverters,” which convert the direct-current output of solar panels into the alternating current that our households and industry use.

So solar panels are not mechanical devices. Not only don’t they have any moving parts. Unlike the rotating turbines used in conventional power plants, they operate at ambient temperature and normal atmospheric pressure. And so they don’t “break down” like engines, turbines or other machines.

Solar panels’ huge economic advantages follow from these points. They need no fuel to make electricity. The have no pollution-remediation cost because they create no pollution. And they have near-zero maintenance expense. Barring their destruction by accidents, sabotage or extreme weather, all they need to keep them running is cleaning off leaves, dust, snow or bird droppings when necessary. They require no “tune-ups,” oiling, maintenance shutdowns, adjusting, or replacing burners or anti-pollution scrubbers, let alone fueling.

So the cost of energy from solar panels depends almost entirely on two variables. These are: (1) the capital cost of building and installing the solar array, and (2) its lifetime, expressed in kilowatt-hours of total energy produced. To a close approximation, within about ten percent, the cost of solar energy is simply variable (1) divided by variable (2).

We don’t yet know precisely what solar PV array lifetimes will be, because we don’t yet have the longevity of experience. But theory, existing experiments and solar-panel-makers’ current “linear” warranties suggest that solar panels can produce useful power for a century or more.

By the end of that century, their power output will have dropped to about one-third of its original value. But by that time, they will have produced energy equivalent to full-power production for about 66 years. All this is simple math, extrapolating the linear warranties that solar-panel makers offer right now, today.

Using the results of this simple math, you can calculate the long-term amortized cost of solar photovoltaic energy. For large-scale commercial arrays, it is already approaching a penny a kilowatt-hour. Soon it will drop below that level.

Why Cheaper Soon

But that’s only the beginning of the good news. Up to now, solar PV industry investors have focused on the most important and sophisticated part of a solar array: the solar cells or panels themselves. We all know the only question most reporters ask. “What’s the cost, per Watt of nominal power generated, of the solar panels themselves?”

In the last several years, that cost has dropped from around $2 per Watt to around 41 cents—a factor-of-five reduction. As this well-visited Internet graph shows, that precipitous drop in panel cost has motivated the present boom in solar-array construction.

As the industry progresses, it will become harder and harder to lower the panel cost without breakthroughs in semiconductor or photovoltaic technology. But that doesn’t really matter any more. Why? Because the cost of the solar panels is just a fraction of the cost of the whole solar array.

From now on, significant cost breakthroughs will come from advances in pedestrian engineering of the infrastructure and its installation. That is, cheaper solar energy will come from reducing the cost of the supporting foundations and racks, inverters, cables, switches and control-and-test elements that turn bare solar panels into a working solar array.

Remember, the cost of solar PV energy depends almost entirely on just two variables: (1) the capital cost of building the whole array and (2) its working lifetime, expressed in kilowatt-hours. The first variable—capital cost—in turn consists of two elements: (1) the dollars-per-Watt (now cents-per-Watt) cost of manufacturing or buying the solar panels; and (2) the cost per Watt of turning the bare solar panels into a working generator.

I express the second element as a dimensionless multiplier [scroll to table], which I call the “Turnkey Factor.” It tells you what you have to multiply the “cents-per-Watt” panel cost by to get the total “turnkey” cost (per nominal Watt capacity) of a working, generating solar array.

Right now, industry experts put the Turnkey cost of large-scale commercial arrays at $2 per Watt. Assuming a 50-cents-per-Watt panel price, that implies a Turnkey Factor of four for large-scale commercial arrays.

Because small, home retail arrays lack economies of scale, the Turnkey Factor for them is much higher. For my family’s own solar array, just installed in August, the Turnkey Factor, based on a putative (not our actual) 41-cents-per-Watt of the panels, was 14.6. (The actual fully-loaded cost of our array, including siting, installation, permits and assistance with federal and state tax credits, was $5.98 per Watt.)

A little arithmetic shows how important these numbers are. With a Turnkey Factor of four, 75% of the cost of the array (and therefore of the cost of energy) comes from the cost of the infrastructure and installation, not the panels. Reduce the infrastructure-and-installation cost by just 15%—or 15% of 75% = 11.25% in absolute percent—and you’ve done as much as cutting the cost of the panels from 25% to 13.75%. That’s the same as cutting the price of cells or panels from 41 cents per Watt to 22.55 cents, almost in half!

For smaller-scale home arrays, the numbers are much more dramatic. With a turnkey factor of 14.6, the solar panels account for only 1/14.6 or 6.8% of the cost of the array. Reduce the infrastructure-and-installation cost by 7.3%, and you’ve done as much as eliminating the cost of the solar panels entirely. Not even a major breakthrough in semiconductor technology could do that!

So from now on, cost reductions in solar PV energy will come primarily from pedestrian (but important!) advances in infrastructure engineering and management that lower the cost of the foundation, racks, inverters, cables and other equipment for solar arrays, and the cost of installing them. From here on out, it’s all about ordinary industrial efficiency.

Let’s take an example from my family’s ground-mounted home solar array, pictured here. It took about six days to prepare the foundation alone: (1) a day (for a six-man crew) to dig the holes for the concrete pads, smooth them, border them, and place and adjust the cables and conduits; (2) a second day to pour the concrete; (3) two days to let the concrete dry thoroughly; (4) a day to drill the holes for and glue in the special bolts for mounting the aluminum racks and to let the glue dry; and (5) another day to mount the racks, panels, inverters and switches and connect everything up.

The ground under our array is not very hard; it’s soft soil. Suppose someone could figure out a way to pound in steel pilings with the necessary attachments in a single day. That improvement alone would probably cut at least twenty percent from the infrastructure and installation cost—almost three times the savings from eliminating the entire cost of the panels themselves.

Not being a soils engineer, I don’t know how practical this idea is. It’s just an off-the-top example. But it’s easy to see how that or similar techniques could make dramatic cost reductions, far beyond incremental reductions in the manufacturing cost of solar panels.

Suppose racks and other infrastructure for small arrays could be prefabricated, pre-assembled, delivered to the site on large trucks, and installed by pounding in key supports with pile drivers. Then a small crew, perhaps with the aid of a specially-designed support equipment, could assemble the rack, attach the panels and inverters, and connect the switches and cables—all in one day. That probably would have cut the total cost of our solar array by at least 50%, more than seven times the savings from reducing the panel cost to zero.

If you’ve ever seen a picture of a fleets of specialized small trucks used for fracking gas and oil, you get the idea. At this point, investment in infrastructure generally, including specialized vehicles and tools to build and install the infrastructure quickly, could produce economies far more quickly than any advance in solar-panel or semiconductor technology.

These sorts of advances don’t require new physics or math or new materials science. They just require good engineering and good business management—something our energy industry is already adept at.

As these advances take hold, you can probably expect concomitant reductions in solar-PV-energy pricing, perhaps down to (or below) half a penny per kilowatt-hour over the life of the solar installation. It shouldn’t take more than two or three years to get there.

Investing Tip and Disclosure

This analysis suggests that the cost “horse race” among solar-panel manufacturers, so avidly covered in our financial press, is largely irrelevant. The biggest reductions in the cost of solar energy are likely to come from greater efficiencies in infrastructure manufacturing and installation, not small reductions in panel cost. That’s why my wife and I own stock in GE (an engineering infrastructure leader) and First Solar (an efficient American solar-panel maker). GE now has a contractual “partnership” with First Solar. I wouldn’t be surprised if, after an extended trial of that “partnership,” it bought First Solar entirely, in order to achieve further efficiencies from vertical integration.

Uncertainty: Not Much

There’s not too much uncertainty in these cost figures. After all, they depend on only two variables: (1) plant cost and (2) plant longevity. The accountants can calculate (1) with a high degree of precision. So the only uncertainty comes from the longevity factor (2), i.e., the plant’s working lifetime expressed in kilowatt-hours of aggregate lifetime energy generated.

Longevity is uncertain only because no one has yet run solar panels for a century or more. So we don’t have the actual experience. That’s not surprising. Albert Einstein explained the photoelectric effect in his famous Nobel-Prize-winning paper in 1905. So it’s only been 108 years since we knew (roughly!) how solar panels work, let alone made practical use of the principle that Einstein explained.

But we do have plenty of shorter-term measurements and theory. Both show that solar panels’ power drops about 2 to 3% in the first two years and then tapers off thereafter in a linear fashion, at about 0.7% per year.

That’s precisely what the so-called “linear warranty” of solar-panel makers says today. It’s now an industry standard, offered by both LG and Solar World. It guarantees that linear tapering of power output for 25 years, with a minimum power output at 25 years at least 80% of the original.

What can we expect after the warranty expires at 25 years? Should we expect the solar panels to just suddenly die, as cars and appliances often seem to do right after their warranties expire?

Not at all. Mechanical-device warranties are relatively short (up to a maximum of five or ten years for some car drive trains) because cars and appliances have moving parts. Engineering projections on which warranties are based use something called a “mean time before failure” or “MTBF” analysis. The MBTF estimate comes from actual tests of moving parts as they fail for all sorts of reasons, including wearing, breaking, cracking, spalling, warping, and other mechanical failure from the heat and mechanical stresses of being a moving part of an engine or transmission.

Engineers use complex statistical techniques to calculate the MTBF for each critical part. Then they use even more complex statistics to put the MTBFs together to deduce a probable time to failure of the engine and drive train as a whole, or at least the point at which it will no longer be economical to offer a warranty.

There is no analogue to MTBFs for solar panels because they have no moving parts. Complete failures simply have not been observed, except when the panel is physically damaged or destroyed.

My solar array installer, for example, reports only one problem of this sort, when a kid drove a baseball through a panel. Insurance covers that sort of damage, as well as destructive weather events.

What has been observed—carefully and over many years and many panels—is the slow, steady, reliable decline of power output, as described in the linear warranty. There is no reason, other than the risk-aversion of lawyers and executives, to expect that power output to drop precipitously, or to continue along a steeper linear path, after the warranty expires.

And even if it did, there would be a limit to the impact on energy pricing. Why? Because, as we’ve discussed, the lion’s share of capital cost—and therefore energy cost—comes from the infrastructure and installation, not the solar photovoltaic panels. If, for example, the Turnkey Factor is four (about the state of the art for commercial arrays now), you would have to replace the panels three or more times before you would double the amortized energy cost.

Since our calculations are based on a century longevity (with the equivalent of 66 years of full-power operation, in accordance with the linear-warranty formula), that is the maximum added-cost exposure that the 25-year warranty would allow. And if even panel failures doubled the amortized cost of solar PV energy from one to two pennies a kilowatt-hour, it would still be half the cost of coal power (4 cents per KWh), without the pollution and global warming.

For home solar arrays, the arithmetic is even more favorable. If the panels cost only 6.8% of the cost of the array as a whole, replacing them three times during the course of the century would raise the amortized cost of energy by less than 21%.

Both these estimates assume that the price of the panels would stay the same, instead of decreasing with advances in manufacturing efficiency and semiconductor technology. Just as it’s bad strategy to bet against Mother Nature, it’s bad strategy to bet against improvements in efficiencies and cost in American industry, especially over time periods as long as a century.

A simple conclusion follows. There is no reasonable projection under which the cost of solar PV energy, from this day forward and properly computed, will ever exceed the cost of electrical energy from coal or natural gas, which produce energy at about the same cost if you ignore coal’s horrendous pollution from sulfur, mercury and particulates, and its double effect in heating our planet. This conclusion also ignores the probable increase in natural-gas prices with increasing use and demand and decreasing supply as even fracked sources become depleted.

Footnote. 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.”]

Saving Harbin from Coal Smog

Today (10/21/13), Harbin, China, suffered record-breaking smog, forty times the international limit. Most of it came from ordinary people burning coal to heat their homes. Today was the first winter day on which authorities permitted that burning, and it was quite an eye closer.

Harbin today is like London in the nineteenth century. Actually, it’s worse because it has more people than nineteenth-century London. And Harbin is colder than London, so people use more coal to heat their home and businesses.

But it’s the exact same phenomenon. The “London fogs” that Charles Dickens and other writers described were not fogs all. They were coal smogs. They miraculously went away when Londoners converted to electric heating, using large power plants away from cities. Those plants still used coal, but they pulled the pollution out of the city. At least they didn’t disperse it uniformly over the inhabited area, as individual coal fires did. Later, with nuclear power and natural gas, the pollution decreased still further.

Could Harbin do much the same thing? Well, the Gobi Desert’s eastern edge is less than 600 km from Harbin. That’s an easy pull for power lines. On average, the Gobi Dessert has 100 mm rain a year. It has lots of sun and wind. China could build huge solar and wind power plants only 600 km away from Harbin and heat Harbin with clean electricity.

What about at night? Well, heat is easier to store than electricity. When I was on fellowship in Cambridge, UK, in the early 1970s, my flat had a big, heavy heater full of bricks. The power came on at night, when electricity rates were cheaper, and heated the bricks all night. The stored heat kept my flat toasty during the day.

Harbin could do the reverse: heat during the day with clean electric power from the Gobi Desert and store the heat in bricks or oil at night to keep people warm in bed. Harbin would have it even easier than London, for two reasons. First, people need less heat at night because they have blankets. Second, cloudy London has no reliable source of sun and wind like the Gobi Desert nearby.

China could do this without any expensive lithium batteries. It would need no high technology beyond existing solar panels and windmills. Just a little sound engineering and a few hundred kilometers of power lines could do it.

Bye, bye smog. With Chinese solar panels and windmills, administrative decisiveness, ingenuity and labor, it wouldn’t take more than two or three years to make this happen.

How much would this solution cost? Let’s do some quick numbers. Harbin has eleven million people. Suppose China gave every man, woman and child there five kilowatts of heating during the day. That’s a total of 55 gigawatts. If China can match the US state-of-the-art Turnkey Price for large arrays of $2 per Watt, the cost for an adequate solar array would be $110 billion.

According to American Electric Power, a Northeastern US utility, a single 765kV high-tension power line can transmit 81.5 gigawatts 550 miles or 880 kilometers. [Search for “Q11”] The actual distance would be less than 600 kilometers, or 360 miles. At a maximum per-mile cost of $ 4 million each [Search for “Q3”], that single line would add 360 x $ 4 million = $1.44 billion to the array cost, or about 1.3%.

How big would the solar array be? A 55 gigawatt solar array would occupy 55,000 times 1.6 acres, or 88,000 acres—137.5 square miles. That’s a square less than twelve miles or twenty kilometers on a side, a drop in the bucket of the Gobi Desert’s half-million square miles.

The Great Wall, with all its tributaries, is over 6,000 kilometers long. China started building it well over two millennia ago, with nothing but muscle power of men and beasts. Think it could build a single 600 km power line and a twenty-by-twenty kilometer solary array? Of course it could. All it needs is political will. Then China could have the first twenty-first-century clean solar city. And think of all the clean, healthy construction jobs.

IKEA goes solar!

IKEA, the Swedish furniture maker, will soon be offering solar arrays at the bargain price of $9,200 for a 3.36 kW system, but only in Britain. Following is the price analysis, without and with federal and state tax credits:

Raw price
before tax credits
Price per
Watt Capacity
Lifetime Price
per kilowatt-hour
$9,200$2.742.2 cents
Price after 30%
federal credit
Price per
Watt Capacity
Lifetime Price
per kilowatt-hour
$6,440$1.921.53 cents
Price after 30%
federal and
10% state credits
Price per
Watt Capacity
Lifetime Price
per kilowatt-hour
$5,520$1.641.31 cents

In comparison, existing coal and natural gas plants produce energy at 4 cents per kilowatt-hour and nuclear plants at 10 cents.

At last rate in our table, you’d be generating energy at less than a third the cost of coal and natural gas, and less than a seventh the cost of nuclear power, with no pollution and no meltdown risk. And you would be saving about 11.5 cents (the national average retail cost of conventional electricity)—for a net savings of 10.2 cents—on every kilowatt-hour your array produces that you use.

If you produce more energy than you use and live in a state that pays you for it, you get a check every month, instead of a bill. My family just got our first $58 check this month. Welcome to practical application of Albert Einstein's "photoelectric effect."

IKEA’s price probably excludes installation. If installation is included, you should run, not walk to your nearest IKEA store and buy an array when (and if) IKEA makes them available here. Even if installation is extra, for a roof it mount probably would not increase the price by more than 30-40%, i.e., less than the federal and state tax credits here.

Sobering Note: Unfortunately, IKEA’s solar arrays will probably not be available in this country anytime soon, and maybe never at this price. IKEA has no present plans to sell them here.

Why? Probably because its Chinese supplier has excess capacity and is selling below cost. Having no domestic solar industry (of which I'm aware), Britain would not object. But we would. Selling below cost is illegal under US and international law, and our strong domestic solar industry and our President would take legal action to stop below-cost imports.

A Conspiracy of Silence?

After two weeks of unremitting political travesty, it was so refreshing to publish a post about something real, like the one above. But before taking what I hope will be (at most) a sixteen-week recess from political insanity, I can’t help but make one comment.

Why will no one in our so-called “mainstream” media call out the Tea Party for what it is: a rump movement born in and driven from the Old Confederacy?

Is there a conspiracy of silence? Is there some sort of misguided geographic delicacy, a desire not to set one region against another? Is it historical amnesia—a counterfactual desire to believe that our Civil War actually ended with the President’s second election? Is it that Southerners have silently taken over our mainstream media, as suggested by the soft Southern accents around the table on this night’s edition of Gwen Ifill’s Washington Week?

I have no idea. But aren’t our media supposed to give us facts, at least some of the time? And isn’t it a fact that just short of two-thirds of the core of 32 self-confessed Tea Party members in the House come from the Old Deep South and the border states? And isn’t it a fact that none of the infamous 32 comes from a city, at least one outside the Deep South?

And isn’t is a fact that the most notorious of all, the Joe McCarthy of our time, sporting the same sort of nasty smirk and personal mannerisms, comes from Texas, our most mentally unbalanced state, whose Republican party at one time wanted to abolish most every agency of the federal government but our armed forces?

Is Ted Cruz really a national movement? Is JimDeMint, former senator from South Carolina, who now heads the arch-conservative Heritage Foundation, and has been heard to say that “he would rather have 30 Republican senators who think exactly as he does than 60 who don’t”?

Does it make any difference that, of all the 38 million people in California, which is by far our largest and most productive state, there is only one Tea Party Member in the House? Does it matter that he comes from a district in the far southeast of Sacramento, which, as far as I can tell from a quick Internet investigation, is a retirement community of old white people who can’t afford to live anywhere in California where people with middle-class incomes prefer to live? And does it matter that the Tea Party has not a single member of Congress from the great industrial states of New York and Illinois?

I’m a reasonable guy, who admit my mistakes. If I’m wrong, show me. Name the Tea Party representatives from our big cities, from our productive industrial areas, from our financial or entertainment centers. Name the ones from our defense centers, where people make the machines and train the men and women that keep us safe.

But if you can't, if there are no such, then tell it like it is. Tell us, again and again, that the Tea Party is a creature of the South, another means to refight the long-lost Civil War, and an attempt by a tiny, atavistic minority to rule this country through procedural machination, self-aggrandizement and media smoke and mirrors. Tell us that it’s all a dark and dangerous form of show business, with the goal of destroying what remains of this nation’s heritage of Reason and greatness.

Please don’t pretend it’s a national movement or anything other than a transient gasp of a dying regional culture. And please don’t let us think so because you’re too lazy to investigate, or you need sensationally dysfunctional personalities like Cruz to sell news. We’ve had quite enough drama and far too little leadership lately, thank you. We don’t need more from our media, let alone PBS.

Footnote: I provide no link because this show was one of the few that simply wasn’t worth watching. Maybe everyone was tired from the nonstop drama.



  • At Fri Mar 07, 12:23:00 AM EST, Anonymous Anonymous said…

    Take heart- you aren't alone and your perspective is logical and reasonable. I call them Confederate Enthusiasts- but I believe that you are right- in that 'Slave State Culture' has actually produced enough ignorance to provide *some* with the Hope that they are in the process of doing anything but 'Lowering Themselves Again'.

    Chris Matthews even elaborates upon it now so it's hit the mainstream and the idea is making rounds.
    Poor PBS.
    Poor 'US'.

  • At Sat Mar 29, 03:13:00 PM EDT, Blogger Jay Dratler, Jr., Ph.D., J.D. said…

    Sorry for posting your encouraging comment three weeks late. I misread Google’s stats on the number of comments.

    Thanks for the good news. If you see this reply, could you post a link to Chris Matthews’ elaboration? It’s not often that a commercial newscaster one-ups PBS, but it’s nice to know it can be done.



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