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

24 August 2013

Our Solar Array

[Note: The cost section of the following post was revised on 12/23/13 to correct two important errors and add one useful piece of information. First, our power company pays us for all the energy our array produces, not just the excess energy that we don’t use ourselves. Second, there were errors in calculating the power company’s profit on sales to us. Third, the post now provides our calculated lifetime cost per kilowatt-hour of our little retail array’s electric energy, namely, 4.8¢ per kWh.]

[For reasons why we should not try to “punish” Assad, at least for now, click here. For comment on Assad’s personal and individual responsibility, click here. For an index to other posts on energy and energy policy, click here.]

The look, sound and feel
A little bit of Einstein
The array itself, and how it works
Becoming a paid power producer
Watching the array work online
Why we became generators

[Note: You can magnify any photo or figure on this
page by double-clicking on it.]

The look, sound and feel

Beautiful, isn’t it? Elegant, functional and clean. No noise. No rotary motion. No smoke, fumes, smell, pollution or global warming. Just quiet, clean, unobtrusive power, straight from our Sun.

There are no moving parts because everything is solid state—even the inverters that convert the solar panels’ direct current (DC) into the alternating current (AC) that people’s homes use. The atoms, molecules and crystal structure of the panels and inverters do all the work, at the microscopic level. Forget about rotating generators and oily engines belching smoke; solar arrays don’t use them.

A little bit of Einstein

As our electric meter runs backwards and our power company pays us for our investment, I like to think about Albert Einstein. No, he didn’t discover the “photoelectric effect” that makes solar panels work. But he got the Nobel Prize for his 1905 paper explaining how it works.

Back in 1905, that was no mean feat. Not long before, Lord Rutherford had explained the atom as like a tiny solar system, with the nucleus as the Sun and electrons like little planets revolving around it.

But experiments soon discovered that subatomic reality is more complicated. Electrons aren’t like little planets at all. Sometimes they act like matter, and sometimes they act like waves. The same is true of light. It acts in many ways like a very high-frequency electromagnetic wave. But it also acts like a “photon,” a little packet of massless energy that sometimes works just like a particle.

So Einstein explained that a little photon of light, at just the right energy, can dislodge an electron from its atom. The electron, now homeless, has nowhere to go but into wires arranged to collect it, and ultimately into your TV or computer.

This happens only in semiconductors, because electrons in them are kind of a collective phenomenon—a product of the entire crystal structure. You might say that electrons in semiconductors act like a community, sort of like people who cooperate to generate, use and share clean energy. Although non-sentient (as far as we know), these little particle-waves are good examples for us.

But you didn’t start reading this post to get a lesson in physics or morality. You’re reading, no doubt, to find out what it’s like to own a solar array. Stay with me.

The array itself, and how it works

Figure 1
Figure 2
Figure 3

Figures 1 and 2 show the array from the front and back. The angle of the support racks provides maximum power throughout the year at our latitude. As your array moves closer to the Equator, its angle would approach the horizontal.

The little boxes that you see behind each panel are the solid-state inverters, which convert each panel’s output from DC to AC. You can also see an array circuit-breaker box at the rear, on the right-hand support.

These particular inverters report their performance by WiFi in real time, over the Internet. So I and their manufacturer can see what each one is doing 24/7/365, without leaving our desks. Because the inverters are entirely solid state, they make no noise whatsoever, not even a little buzzing.

Figure 3 shows our metering and junction boxes. The box on the left is our usual mechanical meter, which every home has. The next box to the right is a special (second) circuit breaker box for the array. (Power companies do like their belts with suspenders!) The third box is a cutoff switch, clearly labeled. The fourth and final box, on the right, contains a digital meter showing how much power our power company (PNM, or Public Service Company of New Mexico) is crediting us with producing.

The brown vertical conduit on the left brings power from, and takes our array’s power to, the grid. The second, smaller brown vertical conduit, immediately to its right, connects with our house’s main circuit-breaker panel on the other side of the house. (We put our array on this side of the house to shield it from the gale-force northwesterly winds that sometimes rip through our valley.) The still-smaller vertical gray conduit at the right goes to the array, and the fatter vertical gray tube to its right contains the site map (required by law), which shows electricians where everything is. (We do have to get those boxes and conduits painted the same color!)

Becoming a paid power producer

Video 1 shows what happens when the array is off and you turn it on by throwing the cutoff switch from “off” to “on.” There’s a five-minute delay, required by law, before the inverters start to transfer power. During that delay, the meter ambles along to the right, showing our house’s normal “resting” power drain. That drain most likely comes from all those little transformers (always running!) that charge our mobile devices, all the TV and stereo stuff awaiting commands from our remotes, and maybe a refrigerator or two.

But all of a sudden the meter starts to run backwards, to the left, at several times the speed it was running forward just moments before. That’s when the array kicks in. Now we are generating power to put back into the grid for other folks to use. And PNM is paying us for it. (I had an audio track explaining what was going on in real time, but it disappeared twice on uploading to Google. So I gave up.)

In other words, we don’t pay the power company. It pays us. So we gain on two accounts. First, we get checks monthly for any power that our array generates over what we use. Second, we don’t have any electric bill at all, so we save (at a higher rate) on every kilowatt-hour that we otherwise would have used. And we have the immense satisfaction of knowing that our clean power is cutting someone else’s use of coal—the dirtiest fuel known—which still provides over 80% of the electric energy in Northern New Mexico.

Watching the array work online

Figure 4
Figure 5

Figures 4 and 5 are screen shots of the Web pages that our inverters generate and transmit over the Internet. Figure 4 shows the total power output of our array, in kilowatts, varying as the sun passes across the sky. (The time, in days, appears on the lower x-axis.)

The little dips in output during the day represent clouds passing between the sun and the array. They reduce, but don’t kill, the array’s power.

Figure 5 shows the energy output of each panel, with total output at the side. The right side of both Figures 4 and 5 shows the historical output of the whole array for the past few days.

Not every inverter does this, but the inverters we are using do. They are products of a company called enphase Energy, which provides a special WiFi-like network to transmit system data though our power lines to our WiFi access point and the Web. Using the network, enphase Energy can monitor the performance of each panel and inverter in our array online and alert us by e-mail to any problems. And so can we.


You thought I’d never get to this, didn’t you? Well, I almost didn’t. Our contractor, Amenergy in Santa Fe, initially wanted the terms of our deal to be secret. But once the array was in and we became satisfied customers, they graciously consented to my sharing the cost terms on my blog.

The all-inclusive cost our array, including siting, concrete pads, racks, panels, electrical conduits and equipment, an extra meter and junction box, permitting, and helping with state and federal tax credits, was $37,335. After our 10% state and 30% federal tax credits, which we will take next year, the net expense will be $22,401—about what a good compact car would cost.

In addition to our tax credits, the array gives us three direct financial benefits. First, by generating our own power and using less electricity from the grid, we save all the money we would otherwise pay for electricity, including future charges at presumably higher residential retail rates. Second, for every kilowatt-hour of energy that we generate, including energy we use ourselves, our power company pays us a “renewable energy certificate” (REC) credit of 4 cents. Our current contract continues that rate for eight years. Finally, for every kilowatt-hour that we use to charge an electric car, rather than to buy gasoline for a 30 MPG small car, we save at the much higher rate of about 36 cents.

The 4¢ per kWh REC credit is worth some discussion. For our own solar energy that we use ourselves, we don’t pay the power company at all, by virtue of so-called “net metering.” Instead, we receive the REC credit. So the power company loses money (4¢) on every kilowatt-hour that our array generates and that we use ourselves. It pays us.

But every kilowatt-hour that our array generates that we don’t use ourselves the power company can sell to our neighbors at the going rate of 11¢ to 12¢ per kWh. It still pays us the REC credit of 4¢ per kWh, so its gross profit is, say, 7¢ on a sale of 11¢ or 7/11 = 63.6%.

That's not a bad profit for a regulated public utility! It’s the same as the profit made on energy from natural gas or coal, which costs the company about 4¢ per kWh to generate. (Actually, if the company sells our excess energy to our neighbors, it makes a higher profit because its distribution costs are lower than from a remote power plant.)

There are three good reasons for the company paying us outright for energy we generate and use ourselves. First, by helping us amortize the cost of our array, the power company reduces its generation requirements and therefore its need for future capital investment. Second, we, not the company, bear the cost of maintaining the array. Third, our array helps reduce pollution and global warming from fossil fuel plants.

Anyway, for energy that our array generates and that we don’t use ourselves, the company makes a generous profit. Its gross profit is as high as from conventional means of generating electricity.

The REC credit is good for us, too. It reduces our personal payback period. Without even considering the energy-cost savings of an electric car, Amenergy estimates that we will recover the cost of the array (after tax credits) in 13.25 years. Thereafter, the electricity from our array will be absolutely free for as long as the array lasts.

The makers of the solar panels and inverters warrant their products for 25 years. Even if the panels last only that long, they will provide us with about twelve years of free power. But if they continue to perform as solid state devices, obeying the laws of physics rather than the precautions of lawyers and accountants, they should last for a century, at steadily declining output, until their output drops to about one-third of initial power. We think that almost 87 years of free power is not a bad legacy for our heirs and successors.

There are very good reasons why we can expect our array to continue generating power (at the characteristic slowly declining rate of all solar PV panels) for a century or more. You can read those reasons here.

Because virtually all of the cost of solar photovoltaic power comes from amortized initial capital cost, the key factor for evaluating the economics of solar photovoltaic power is the total installed cost of plant per watt of nominal power production. Since our array generates 6.24 nominal kilowatts, that cost for us is $37,335 / 6,240 = $5.98 per watt, without accounting for the federal and state tax credits. (Note that this cost is not the cost of electric energy, but the cost of plant capacity. In order to get the cost of energy, you have to do some calculation.)

Our total-installed-capacity cost of about $6 per watt is pretty typical for small-scale, high-quality residential arrays like ours. That figure lets us calculate the amortized cost of solar energy for our array over its projected useful life. If we run the array for a century—by which time its output will have dropped to about a third of the initial level, and it will have produced the equivalent of 66 years of full-power output—our amortized cost of power will be 4.8¢ per kWh (extrapolated from this table).

That’s a generating cost, using a small-scale residential-retail array, not much higher than generating cost of our huge (and hugely polluting) coal-fired power plant at Four Corners, which I estimate as 4¢ per kWh. When you consider the 50% costs of distribution and profit, which our solar array doesn’t incur because it’s right next to our home, our little array, for us, beats the fully-loaded cost of convention fossil-fuel power by at least 1.2¢ per kWh. And of course its cost is much lower than the price we would have to pay our power company for conventional power (11¢ to 12¢ per kWh).

For large-scale commercial arrays, the cost advantages of solar PV energy are much bigger. Big arrays benefit from immense economies of scale.

As I’ve explained at length in another post, the total-cost-per-watt parameter is the product of the cost per watt of making the solar panels and something I call the “turnkey factor.” Today the industry state of the art for the solar panels, by themselves, is about 50 cents per watt. So in our case, all the other stuff, including rack, concrete pads, the labor of installation, connecting equipment and permitting, amounts to over twelve times the bare cost of the basic device that Einstein explained. That means the “turnkey factor” is over 12—quite high. Clearly there is a lot of room for further economies in this industry that have nothing to do with the photoelectric effect.

Large commercial arrays do a lot better. There the total installed cost is between $2 and $4 per Watt. As a result, over the projected working lives of the solar panels, commercial arrays can produce power at an amortized cost of between 1.6 and 3.2 cents per kilowatt-hour. That’s cheaper than electric energy produced by any conventional means, except perhaps hydroelectric power.

Why we became generators

So why did we install our array? There are so many reasons that it’s hard to know where to begin. First, there are the cost benefits. We won’t pay much, if at all, for electricity from now on, and the power company will pay us for the excess we produce. When we get our electric car, our savings per kilowatt hour will jump from about 11 cents to about 36 cents for energy used to charge the car. Once we’ve reached payback, we’ll get about twelve years of warranted power, and probably a whole century, for nothing. During that century, out panels will have produced energy equivalent to 66 years of full (initial) power output.

So if nothing strange or unexpected happens to our array, it will produce over half a century’s worth of free power after our payback period. And that’s not counting whatever payment we receive from the power company for contributing to the grid. That free, nonpolluting power is our legacy to our heirs and your grandkids.

Our array is well protected against any foreseeable damage. About the only thing that realistically could damage or destroy it is a tornado (rare in New Mexico) or baseball-sized hail. Our homeowners’ insurance protects the array against those risks (and vandalism), just as it protects our house. The coverage comes under a feature of our State Farm insurance policy called “dwelling extension,” which automatically covers up to 10% of the limit on our house.

But those are just the beginnings of our reasons for going solar. As an ex-physicist and a technophile, I have lusted for an electric car most of my life. But I can’t stomach driving on coal, an horrendous fuel that is ruining the planet on which we evolved with sulfur dioxide, acid rain, mercury pollution, and particulate-induced asthma, not to mention global warming. Now my wife and I can drive on the sun, not coal, and we can save about 36 cents for each kilowatt-hour of charging in doing so. That’s about three three times as much per kilowatt-hour as the money I save by not buying power from the grid.

The more we drive on electricity, the more quickly we will pay off our array. Unfortunately, I can’t provide a good numerical estimate because it depends on how much we drive our electric car. As a retired blogger, I don’t drive a lot, even now. My 2009 Hyundai Elantra has less than 7,000 miles on it, or less than 2,000 miles a year. (My wife, who does most of the shopping, drives a bit more.) The average not-yet-retired Joe or Mary, who drives a lot more than we do, will reduce his or her solar payback period big time.

But I guess the strongest reason for feeling good about our solar array comes from my background as an ex-physicist. I’ve known about the photoelectric effect ever since I first studied quantum mechanics, around 1966. Our species has known about it since well before Einstein’s 1905 paper that won the Nobel Prize. But it’s taken us over a century to put it to practical use.

This is a big, big deal, comparable to primitive Man’s discovery of fire.

Now our family and guests can enjoy free power from the same source that energizes all life on Earth: our Sun. We can enjoy it without noise, fuss, smoke, smog, pollution, global warming, anticipated cost increases, scarcity and panics, or the political struggles that characterize oil and gasoline and even natural gas. And the solar panels we used were made right here in the United States, thereby advancing my Trade Policy for One.

Footnote 1: In a previous post, I analyzed the so-called “linear warranty” of LG solar panels, which is precisely the same. As I noted in another previous post, the slow degradation of power from solar panels depends not on the manufacturer, but on physics. Although makers limit their legal liability to 25 years now, there is no reason why solar panels should not last a century, with power degrading slowing to about one-third of its initial (nominal value). Over that century, the panels would then deliver energy equivalent to 66 years of full-power operation. If our panels do that, we will get over half a century of absolutely free, full-power-equivalent operation, after our 13.25-year payback period. Can we all say “think long term ”?

Syria: Don’t Do it, Mr. President!

Last night on the PBS News Hour, President Obama said he has not yet decided whether to “punish” Syrian Butcher Bashar al-Assad with a “surgical strike” for killing about a thousand of his own people, mostly civilians, with chemical weapons. My advice, for what it’s worth, is “don’t do it.”

That same PBS News Hour later aired a three way debate on the issue. All three participants were distinguished, articulate, highly knowledgeable, and passionate in asserting their points of view. It was one of the best debates I have even seen on TV on any subject. Kudos to PBS for airing it.

Although all three debaters were highly skilled, the “do-nothing” position, at least for now, had the best arguments. Professor John Mearsheimer at the University of Chicago was its exponent.

As readers of this blog know, doing nothing is hardly ever a course of “action” I recommend. Somehow, it seems un-American.

But in this case, it’s the right course, at least for now. A “surgical strike” would be worse than doing nothing because it would accomplish nothing and might well be counterproductive. There are three reasons why.

First, the President has already telegraphed the punch by announcing our internal discussions. Worse yet, since the President wants “legal cover” for his action, he will invariably wait until he has at least a few partners in his “coalition of the willing.” Lining up those partners will take a few days or weeks, by which time Assad could have every important asset of his military hidden or buried under ground. You can’t have an effective “surgical strike” on a body warned in advance and in full armor.

Second, geopolitical conditions make the situation even worse. We have no reasonable prospect for improving conditions in Syria. The civil war there is in part a sectarian battle within Islam, in part a struggle for freedom from a cruel and barbaric tyrant, and in part a war by jihadis intent on establishing an Islamic Caliphate there, or at least reducing Syria to a law-and-civilization-free zone like Waziristan and most of Somalia and Yemen.

The strongest forces among the rebels are the jihadis, who, in the President’s gross understatement, don’t share our values. We have no “partner for democracy” or “partner for peace” there, let alone a partner for victory. We don’t even have a Hamid Karzai, feckless as he is.

Third, the legal justification for a strike, and therefore its legitimacy, is questionable at best. We have not been attacked. Nor is there any reasonable prospect of our being attacked by Syria. So neither self-defense nor the fig-leaf of “pre-emption” that Dubya used to enmire us in Iraq is credible. The whole world—including neutral countries and even some of our allies—would view our strike as just another attempt by a clueless behemoth to intervene clumsily where it has no business.

Our direct interests in Syria are weak and abstract. We abhor the killing. We detest Assad and everything he stands for. We don’t like to see the region awash in Syrian refugees and destabilized. We fear negative long-term consequences for our ally, Israel. And we’d like to see the nonproliferation and nonuse regime for chemical weapons enforced more robustly. But short of full-scale military intervention, we have no reason to believe that anything we can do would improve any of these shameful and dangerous facts. And our recent attempts at full-scale intervention, in Iraq and Afghanistan, have hardly been unqualified successes.

Last night the President asserted that we might “punish” Assad to deter further use of chemical weapons, or his loss of control over them and possible consequent use against us. That’s a rationale worthy of Dubya.

Remember Dubya's puerile plea that “we have to fight them over there so we don’t have to fight them here”? We shot our wad with that sort of speculative pre-emption in Iraq. Saddam’s WMD turned out to be a paranoid fantasy, and our international credibility took its biggest hit since Vietnam.

The simple, stark fact is that Assad has not threatened the United States and is no conceivable threat to us. He can’t even win a civil war against a ragtag bunch of jihadi rebels, with the financial and military backing of Iran and Russia. Whether in allegedly current or “pre-emptive” self-defense, an attack on Assad’s forces would have no international legitimacy. It would only strengthen our reputation as a rogue nation bent on proving its “exceptionalism” with irrational use of force.

But if the worst happened, and some of Assad’s chemical weapons actually got used against us, the entire situation would change. We would have right, law, and the world’s sympathy on our side.

So we should hold our fire for now. But, publicly or privately, we should warn Assad that, should we ever trace to Syria the use of chemical weapons against us, anywhere in the world, we will come after him personally with everything we’ve got. We will use our entire air force, our cruise missiles, our drones, our ninjas, and our conventional and even nuclear bunker-busters to kill him, along with anyone who happens to be near him when the strike comes.

And we will not announce those attacks in advance. Instead, we make them in surprise and silence. We will do so at any time after the moment that we determine, to our own satisfaction and in secret, that any chemical weapons used against us had their origin in Syria.

Carrying our such a threat would be legal, legitimate retaliation. It would be perceived as legitimate, as long as we had good evidence that the weapons had come from Syria. And with the elements of surprise and maximum force, it would be effective.

No one raised a peep when we killed bin Laden. The entire world viewed our assassination as legitimate retaliation for one of human history’s greatest crimes. In contrast, a “limited surgical strike” today, with confessedly no objective of removing Assad, lacks basic human legitimacy, as well as any hope of effectiveness. It might only embolden both Assad and his backers Iran and Russia.

Assad loses assets, forces and people on the ground every day in the two-year-old civil war that he is waging on his own people. A feeble surgical strike, destroying some equipment, buildings and hapless bystanders, wouldn’t even get his attention. But a credible threat to go after him personally, even though contingent, would impose the same sort of personal responsibility on him, in advance, that the Judgment at Nuremburg did in retrospect.

P.S. There is one from of “strike” that might actually do some good. Even if Assad hid or buried most of his armor and aircraft, we could still crater his runways and destroy his control towers and other air-command infrastructure. We could probably do that without significance losses to our own forces.

But craters can be filled, and towers and other infrastructure rebuilt. With resources that the Assad regime probably possesses, these things could be done in days, not weeks.

Therefore, to be effective, this strategy would be nothing like a single “surgical strike.” It would require an extended air campaign of at least weeks, most likely months.

I would support such a campaign, for (mostly humanitarian) reasons that I’ve explained in an earlier post. It is shameful for the world to stand idly by while Assad slaughters his own civilians in large numbers, whatever the kinds of weapons he uses.

But we should be honest with ourselves and our allies what this strategy would mean. First, it would be tantamount to establishing a “no fly zone,” at least temporarily. That’s something the President has said he will not do. Second, with each week of extension, it would increase the risk of significant losses to our forces and greater involvement in the war. Third, it would increase the probability of regime change in Syria. And finally, in so doing, it would increase the risk of eventual jihadi rule or a collapse of the Syrian state into chaos.

There are no riskless options in Syria. If the President wishes to minimize both military and domestic political risk (have you noticed how quickly John Boehner seems to have morphed from warmonger to peacenik?), the best option is that described above. Pass on this alarm, but be ready to make a quick, hard, silent surprise strike, at Assad himself, if the fire ever reaches us.

P.P.S. Some readers may be wondering how the United States could hold Assad personally responsible if some rogue Syrian general or jihadist enemy got ahold of his chemical weapons and used them against us.

Easy. In law there is a practical notion of “but for” cause. In either instance, Assad’s making and keeping chemical weapons would be a “but for” cause of the attacks against us. But for those weapons’ existence and availability, there could be no such chemical attack. Their existence and availability would be the sine qua non.

Futhermore, Assad’s making and keeping those weapons is a clear legal wrong. Syria has signed a treaty to that effect.

The treaty has only weak mechanisms for enforcement, but that’s the fault of the lawyers and diplomats. They need to do a better job next time. Nothing in their lapse excuses Assad from doing something that his nation has solemnly promised not to do, with the most formal kind of promise that nations ever make: a treaty. As absolute dictator of what is left of Syria, he is personally responsible.

But his personal responsibility goes even beyond that. Syria is collapsing as a viable state, due primarily to Assad’s inability to govern it by any means other than slaughtering his own people. A collapsing state makes it far more likely that his weapons will be stolen or diverted and used against third parties like us. Therefore his legal wrongs would be not just a “but for” cause of any such attack, but a substantial contributing cause.

In law, morality and common sense, Assad would have started a chain of events without which such an attack could not occur. And would have done so for the vilest of motives, in such a way as to vastly increase the risk. Keeping chemical weapons for use against his own people in a last-resort act of cowardly desperation is not something even the international community should countenance, let alone a third party (like us or Israel) harmed as a result.

Rather than retaliate collectively against the Syrian people, we or any other such third party could and should hold Assad personally accountable. That is the lesson of Nuremburg. It is also the indirect lesson of Dubya’s ghastly moral and practical blunder: invading and occupying two foreign nations for about a decade in order to stop a few hundred terrorists.



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