Thursday, August 28, 2008

Dichroics 101

A friend asked for a rundown on dichroics, which are the coatings we put on optical glass (and sunglasses) to optimize the transmission properties of our lenses. So, here is Dichroics 101. You could also check out Wikipedia.

Visible light is made of photons. Each one has a wavelength. Your eyes are receiving a bazillion photons every second in the daytime. At night, your dark-adapted eyes are capable of noticing the flicker of individual photons, but only sometimes. Visible light varies from 420 nm (blue) to 700 nm (red). A nm is a nanometer. 1000 nm is a micron (micrometer, but nobody but Europeans says that), 1000 microns is a mm (millimeter), 1000 mm is a meter.

So, a 420 nm photon is really small. However, atoms are 0.1 to 10 nm across, and we can lay down layers just a few dozen atoms thick, so we can actually build things that are smaller than the wavelength of light. Get back to that in a sec...

Any given transparent material has an index of refraction, which tells you (among other things) the speed of light in the stuff. Air has an index of refraction of about 1, so that the speed of light in air is the same as it is in a vacuum: 186,000 miles per second. Glass has an index of refraction of 1.5 to 1.8 (depending on which kind of glass). Plastics (like polycarbonate, what is most likely used in sunglasses) have an index of refraction around 1.5. So, in plastic, the speed of light is 186,000 miles/second / 1.5 = 124,000 miles/second.

Whenever photons go through a surface, like changing from air to glass or back, some will reflect. The number of photons reflected has to do with the change in index of refraction. The equation is: reflected fraction = (Na - Nb)^2 / (Na + Nb)^2, where Na and Nb are the indices of refraction for the two materials. For example, from air (Na = 1.0) to plastic (Nb = 1.5), the fraction is 0.04, or 4%. When you see yourself in a window (or in someone else's sunglasses), this is what you are looking at. Actually, you see two of these, one off the front surface, and one off the back surface of glass.

Suppose we put a 100 nm thick coating of Magnesium Fluoride (a.k.a. MgF2, index of refraction is 1.38) on a piece of glass (index of refraction 1.5). There will be two reflections: one from the air/MgF2 surface (2.5%), and one from the MgF2/glass surface (1.7%). Because there is a smaller change of index of refraction across each surface, each surface reflects less. If the index of refraction of MgF2 was closer to 1.25, halfway between air and glass, then we'd find that the power of the two reflections, when added, would be less than the power of a single reflection of an air/glass surface. But MgF2 doesn't have that nice property, so why do we bother?

Those photons act like waves: they have peaks and troughs. That 100 nm thickness wasn't just any old number, it is 1/4 of the wavelength of green light in MgF2. Green is ordinarily 550 nm, but going through MgF2 it's about 550/1.38=398.5 nm. The light reflected from the MgF2/glass surface will have travelled two times 100 nm more than the light reflected from the air/MgF2 surface, or one-half a wavelength more. So, the crests of the wave off the MgF2/glass surface will line up with the troughs of the wave off the air/MgF2 surface. When you add those two together, you get... cancellation.

Or... nearly cancellation. The air/MgF2 reflection is a little stronger than the MgF2/glass reflection, so there will be a little wave left over. A 550 nm photon will reflect (2.5-1.7=0.8%). There you have it, the first antireflection coating, as developed for German submarine periscopes in World War II.

Now notice that 420 nm (blue) light will not cancel as well, because the two reflections are 65% of a wavelength offset from one another. The peaks and troughs don't quite line up, so it doesn't cancel as well. The same is true of 650 nm (red) light. So, the reflected light will be purplish: it will have some blue and red, but not so much green.

This is the basis of dichroic filters. You can put several layers of stuff onto a glass or plastic surface, and each additional surface will have a reflection. At each wavelength, you can add up those reflections with their wave offsets to get an overall reflectivity. You end up with a graph which shows how much the thing reflects at each wavelength. By varying the materials deposited and the thicknesses, you can get something which has interesting and useful properties, such as reflecting all the IR (> 670 nm) and UV (< 390 nm).

You can buy such a thing at a good camera store. It's called a B+W 486 filter.

Tuesday, August 19, 2008

Grove's plan

Now I've read Andy Grove's plan (at The American, or via Wired) to fix our energy dependence national security mess. Mr. Grove thinks, as I do, that national security is the most immediate problem we face.

There are flaws in both Grove's and Pickens' plans, but we can take good ideas from both and act on them immediately.

There are two steps to either plan:
  1. Switch our vehicles to a non-petroleum energy form
  2. Make that energy domestically
With Pickens' plan, we switch to natural gas to power cars (step 1), and simultaneously free up domestic methane production by building wind turbines (step 2). If we do step 1 without step 2, we end up switching from imported petroleum to imported natural gas, which suits Pickens quite well because he has lots of gas to sell us.

With Grove's plan, if we do step 1 without step 2, we've got a bunch of electric cars which will plug in at night. The extra demand at night will drive utilities to produce more baseload power -- coal, wind, or nuclear, in that order, all of which is domestic. The advantage of Grove's plan is that step 2 is handled by the market.

The problem with Grove's plan is that converting cars and trucks to electricity instead of natural gas is more costly. The added cost will cripple the plan in two ways:
  1. It is so much more costly that the conversion will happen more slowly. Per year, less petroleum imports will be displaced.
  2. Fewer vehicles, in the end, will be converted.
I think there are good ideas in both these plans that we should isolate and exploit immediately.

There are no forseeable battery technologies that will work on long distance trucks. The obvious substitution here is to move long distance freight by electrified train. We already have most of the rail infrastructure (rights of way are the big issue here), and the nation is already switching some cargoes back to rail. But railroads have been sick for a long time, and we have to fix them before they can help America.

Rail's crushing disadvantage compared to trucking is it's capital structure -- the fact that the same companies own the road and the trucks. Long distance trucking works because multiple companies run trucks over the same routes, which are owned and paid for by the U.S. government via tolls on the trucks and taxes on the diesel they burn. We should change rail to use this structure. The rail infrastructure should be electrified in the process, so that the independent trains can choose to run on cheaper domestically produced electricity where it is available. All the technology necessary is already developed and in production.

The good idea in Pickens' plan is to build lots (many tens of thousands) of wind turbines. Wind turbines displace imported natural gas with domestic labor, and that is the most useful part of his plan. If you then convert cars to run on natural gas rather than petroleum, you in turn displace some imported petroleum with some imported natural gas. This second step is a fine thing too, as petroleum costs more than natural gas per unit energy, but the first step is what is most important.

The United States made a terrible mistake during the 1990s by building nearly a terawatt of natural gas-fired turbines. The choice was driven by utilities who know that fuel costs can always be passed to the consumer, so that cheap gas turbines minimized investment and so maximized return on investment. The problem here is that utilities were allowed to make investments with large externalized costs. Market forces do not work to the advantage of most citizens unless the market is set up to internalize the costs that matter to the citizens. Because utilities have no sons and daughters to send to war, they cannot be allowed to make investment decisions that force us to send our sons and daughters to war.

Electric freight trains and wind turbines will not fix America's imported energy problem. Both, however, can be pursued immediately, are solid steps in the right direction that will not have to be reversed, and will make market-affecting changes in our consumption of imported energy. Both options will buy us some time during which we must develop better options.

In the medium term, we can build more nuclear power plants. These take longer than wind turbines to come on line, but the eventual impact can be much larger. The public discussion of our nuclear options is becoming more sensible, and I am beginning to hope that we may be able to begin building this infrastructure again after a two decade hiatus that has cost us terribly.

Nuclear power generation, if pursued in a sensible way, can drive the cost of electricity in the U.S. down below the cost of coal power in China, in a predictable, long-term way, which I think should be an explicit goal of our national energy policy. This will have the effect of "onshoring" basic industries that we have been moving overseas for decades. The onshoring effect is actually more powerful than displacing imported petroleum, because the imports that are replaced for a given amount of investment have higher added value.

Monday, August 18, 2008

Unreliable Wind Power

The electricity that arrives at your home or business is extremely reliable (if you live in the U.S.). The electricity that comes from a windmill is unreliable -- it only comes 1/3 of the time, and you never know exactly when it's going to come or how much you are going to get. If you want to sell wind energy, you have to convert unreliable wind energy into reliable power. How is it done?

This paper explains how, but it's a tough slog. What follows is my summary.

The utility companies already solve a similar problem. Electricity is not easily stored, and in modern grids it is generally not stored at all. So, when you flick on a light switch, the immediate effect is that the power dissipated by all the lights in your neighborhood drops a little to compensate. Within seconds, some power turbine perhaps hundreds of miles away must twist a little harder on its generator shaft to get everyone's line voltage back up, and the extra thermal or hydroelectric power fed into the turbine to get this extra twist will be just about what your light bulb burns, plus the inefficiencies of getting the power from the turbine input to your bulb.

Turbines can only throttle up to 100% of their rated capacity, and they get inefficient when they throttle down too far, so utilities will shut down or spin up units to make larger changes. Changes like these take a long time, so utilities predict what the expected load at any given time will be, hours or days in advance, and schedule units to be on or off line to match the predicted load. Utilities keep some fraction of their turbines at partial output so that they can immediately crank up to match unexpected increases in the load.

The biggest increase in the load that they plan for is usually an unexpected dropout of one of the generators. If a 1 gigawatt generator suddenly goes off line, the grid controllers might respond by taking four other generators from 700 to 950 MW output. It would be impossible for this to happen instantly, but luckily, when most generators go offline, they do so gradually, and if they coast down over the course of seconds, other generators can crank up to match. If a circuit breaker pops or a line parts, or something else happens very quickly, then there is usually a temporary brownout as the line voltage drops down to the point where the loads match the generation. The backup generators usually ramp up within seconds, and many devices (like your computer or TV) can ride through a partial loss of power for a second or so.

So, the bottom line is that utilities predict the change in demand on their generators, and there is some variation from their prediction, and being ready for this variation costs money because some turbines (the spinning reserve) must be run at partial throttle which is less efficient than flat-out.

Just as an aside: consider how valuable it would be for the utility company to be able to instantly shut down your air conditioner for just a few minutes. This ability would act as part of their spinning reserve. During the summer, air conditioners are a substantial fraction of the total power burned. I'm pretty sure that for most of the U.S., the ability to shut down even a fraction of the air conditioners for 10 minutes would cover the entire spinning reserve requirement. That could save a lot of money, and PG&E (my local utility in California) is experimenting with just that through their Underfrequency Relay Option on the Base Interruptible Program. Anyway, back to the summary.

Wind farms produce electricity whenever the wind blows. Wind speeds can be predicted, and there is always variation from the prediction. When a wind farm is connected to the grid, the total variation in load on the load-following turbines is larger than without the wind farm, and so more turbines must be run in load-following mode, and these incur a cost associated with wind power that is real but not easy to predict before the wind farm is built.

For instance, part of Denmark's grid is connected to Norway's grid. Norway gets most of its power from hydroelectric plants. Hydroelectric plants are very good at load following and so they are usually the first choice of plant to handle variation from plan. Because Norway has lots of hydroelectric plants, and because it has high-throughput connections to Denmark, Denmark can hook up fairly high powered wind farms to its grid and incur relatively low costs for standby power.

Now that utilities are connecting large amounts of wind power to their grids, they are getting more precise numbers on the costs of doing so.
  • Wind works well where you have year-round high winds near hydroelectric dams.
  • The short-term variation from wind farms is usually quite small, since turbines are small (a few megawatts) and don't all shut off at the same time.
  • Big storms give the worst case variation, since when a wind turbine goes too fast it feathers its blades and shuts down, going from full output to nothing, often in synchrony with other wind turbines around it.
  • Wind farms spread over large geographic areas have less total variation (the wind doesn't die everywhere at the same time). Ideally the spinning reserve would thus scale up slower than the total windpower connected, making marginal wind power less expensive. Unfortunately Denmark is too small to see this effect, and it would require very high throughput long distance power distribution.
Wind turbine manufacturers are working on making their turbines play better with the grid. Variable-frequency turbines go offline more slowly by generating power from their blades as they spin down after losing wind. Many manufacturers are shipping wind turbines with extra-large blades, so that the turbine produces a larger fraction of its output more of the time. This reduces the cost of variability in exchange for an increase in the capital cost of the turbine, which is a tradeoff made possible by an understanding of the cost of that variability.

Wind turbines appear to work economically (when the utilities are prodded by a production tax credit, which I support). As more turbines are installed, the best windy areas are used up and the least expensive spinning reserve is committed. On the other hand, wind turbine costs might be coming down some day (maybe -- materials costs are going up), and the need for spinning reserve is decreasing. It's a fairly tense balance.

Personally, I'm happy to see more wind turbines getting installed, since it's domestically produced, mostly-carbon-free, low marginal cost power, and let's have more of that. There is going to be a limit to how much wind power can be installed, but we're nowhere near that limit yet.

At the same time, it's sobering to consider that the United States once built almost 100 nuclear plants in about two decades, bringing new power online at the average rate of 5 gigawatts a year, at a time when our economy was one-third to one-half the size it is now, in real terms. At it's peak, we were building much faster than that. This economic explosion was driven by the business fundamentals as much as it was by overexcited businessmen jumping on the latest bandwagon. And the fundamentals were and are that if we decide on a reactor design (like Palo Verde), we can build and operate them cheaper than coal plants.

To match this performance, and get to 20% of the U.S. grid in 20 years, the wind industry would need to install about 300 gigawatts of nameplate capacity. That would require getting to a peak of 30 gigawatts a year, up from 4 gigawatts in 2007, which is 11 years of sustained 20% growth. The fundamentals for wind are not as good as they were for nuclear in the 1960s. It won't happen without a major breakthrough.

Monday, August 04, 2008

SpaceX launch 3 failure

I watched the YouTube video, which shows launch through 6:16 indicated (T+2:11). Two comments:
  • Can we please get a heater on the on-rocket camera lens cover? It's hard to see much through the condensation.
  • It looks like the rocket has a 5 second roll oscillation that starts as soon as they go supersonic. I don't know if this is fuel slosh, like on the second stage of the last launch, but it doesn't look like other rocket launches to me. Any kind of wobble before seperation could cause the first stage to ding the second stage, as happened on the last launch.
I really hope their next attempt goes better. This launch wasn't obviously progress.

Constraints to wind power

Jesse Ausubel has a pretty good essay which describes what he thinks the future of power production will look like. It's a somewhat rosy picture, and although I'm also optimistic (but not for the next few years), I disagree on a couple of points.

He, like I, thinks that we've got to get away from coal. I don't follow his reasoning for why he thinks we have to get away from coal. It seems he has identified a long term trend towards fuels with less carbon and more hydrogen, and he thinks we should make choices to perpetuate that trend. As near as I can tell, he's skipped the part about why the trend is a good thing. Perhaps he thinks consumers like lower carbon fuels because they tend to burn with fewer combustion byproducts, but he doesn't back this claim up with any market analysis.

I think we as a country need to stop burning coal because
  • we import a lot of oil to burn coal (we spend almost as much on oil to move the coal as on the coal itself), so that the price of coal-fired power is quite sensitive to the cost of oil,
  • it is politically possible to install lots more windpower, but coal is seeing opposition, and it is vital to our economic health to get a lot more electric supply,
  • wind power is inelastic supply, whereas coal power is elastic. That is, a coal plant will shut down if the price of electricity falls below it's operating costs, but a wind turbine costs almost nothing to run and will keep generating through a larger swing in electricity prices, which will make our electricity supply more predictable,
  • and finally and perhaps most importantly, because climate change matters.
My biggest point of disagreement is with Jesse's assertion that windpower is impractical due to land use constraints. Other, perhaps clearer-thinking people have made this same point. Jesse makes a very sobering calculation: he figures a wind farm produces 1.2 watts per square meter, average. To produce all of the U.S. grid's 450 gigawatts (average), you'd need a lot of land. Jesse calculates 780,000 square kilometers. The area of the U.S., for reference, is 9.16 million square kilometers, with 1.75 million square kilometers of cultivated cropland. I don't get quite as large a number as Jesse, but we'll take his 780k km^2 for now.

He figures that's just too much land. But this argument is trite. I'll skip over the point that farmland with wind turbines is still farmed land, and instead focus on a more basic question: How much is too much? I think too much is when the next wind turbine to be installed is projected to make no money. That could be all the farmland plus a lot of offshore turbines, or it could be just a few places in North Dakota. It won't be decided by people getting scared of erecting some more infrastructure on 44% of our existing cropland. Farms in the Netherlands in the 1800s were dotted with windmills, because that's what drove the pumps to keep the water out. Farms in the U.S. in the late 1800s were dotted with windmills, with parts shipped at enormous expense across the continent, because that's what pumped the irrigation water wells. Modern farms aren't currently dotted with wind turbines because they've been using oil instead.

Jesse's argument is also trite because it ignores the huge variation in windiness around the U.S. In North Dakota, the entire state is class 4 or above. That means the power available at 50 meters above the ground is 400-500 watts/meter^2. Even during the summer doldrums, the average power available is 300-400 watts/meter^2.

Jesse's 1.2 watts/meter^2 number comes from a wind farm in Lamar, Colorado. That wind farm has 108 1.5 MW turbines spread over a 11840 acre area. Multiply by a 30% capacity factor, and you get 1.01 watts/meter^2. (I'm not sure how he got the extra 20%.) Why is this number so low?

It's economics. The company that owns the wind turbines pays the company that owns the land on which the turbine is sited approximately $3000 to $6000 per year per turbine. The net present value of that payment stream is $60,000 to $120,000. The turbine costs $1,500,000, which is a lot more. Spacing the turbines farther apart slightly increases the power from each turbine, at small increases in royalty payments and road and cable construction costs. If land scarcity ever becomes an issue for wind farmers, I would expect $ per watt and watts per km^2 to go up. Note that $/watt may go up slightly, while watts per km^2 may go up a lot.

Consider that the first big wind farm, on the Altamont Pass, has a power density of 0.86 watts/m^2, which is lower than Lamar's density. If you follow that link, you'll note that wind farms vary from 0.24 watts/m^2 (Pierce County, N.D.) to 5.3 watts/m^2 (Braes of Doune, Scotland). I think land prices, more than turbine capability, is driving the energy density of these farms.

Note that the wind power map above quotes wind at 10 and 50 meters above the ground. Back when the Department of Energy began collecting data for these maps, those were considered the likely bounds of practically sized wind turbines. However, the Lamar turbine towers are 70 m tall. It turns out that the tower costs are mostly just steel, and the higher up you go, the faster the wind blows. After the industry got experience with the costs of siting, permitting, building, bird strikes, aesthetics, and so forth, it turned out worthwhile to spend more on steel in the tower and concrete in the foundation. As a result, watts per km^2 has gone up.

Is there a limit? Placing turbines closer together can collect more wind energy, but fundamentally most wind power is still being dissipated as turbulence and then heat higher up in the atmosphere. Bigger wind turbines reach farther up to capture more energy. It is hard for me to imagine that ground-based wind turbines are going to get substantially taller than they are now, and so I do not expect the average power yield to increase much beyond, say, 2 or 3 watts/m^2 average. 2 watts/m^2 across all of North and South Dakota would yield 750 gigawatts, which is why you hear wind advocates claiming that the Dakotas can power the rest of the U.S. They could, if you could transport the electricity to market.

Finally, I doubt very much that, even if windpower is wildly successful, it will ever account for anything like 100% of the U.S. grid's production. If many coal plants are forced out of production by lower cost wind plants, I would expect that some very efficient mine-mouth plants will remain. I will be astonished (and pleased) if wind ever produces half the U.S. capacity. If that ever happens, wind turbines will be a familiar sight, but not an overwhelming use of land.

Jesse also complains that wind turbines take significantly more steel and concrete than nuclear powerplants. Obviously the steel and concrete are factored into the current prices of turbines, so it's already part of the price comparisons being made. There are two future risks to large use of concrete and steel, however:
  • Wind turbine prices in the future could be more closely tied to raw material prices (which in turn depend on the cost of energy) than on the price of labor (which depends on the state of the economy). This question resolves to whether future wind turbine prices are more sensitive to the cost of imported energy than electricity from coal is. Coal fired electricity is fairly sensitive to oil prices, so I doubt this is a problem.
  • A large bump in wind turbine construction could use so much concrete and steel that it would distort the markets and cause large price increases.
The second issue got me to pull out the calculator again. Here are Jesse's numbers, actually Per Peterson's numbers, in context of the production necessary to build a 250 GWe average windpower grid (about half U.S. electric consumption):
  • Steel: 460 metric tons per MWe. The U.S. produces about 90 million metric tons of steel every year. Over the 30 years it would take to build a new US grid, wind turbines would require 1.3 years' worth of production.
  • Concrete: 870 cubic meters of concrete. The U.S. ready-mix industry produces about 350 million cubic meters a year, so we'd need 0.6 years' worth of concrete production.
These constitute a nice bump to domestic production, but are significantly less that ordinary year-to-year variation.

The bottom line: if the price is right (or even close), let's have all the wind turbines we can build, because it really could help with our foreign trade deficit, economic sensitivity to energy prices, and global warming.