Preface

This little book begins a group of two on sources of what is usually called “renewable energy” or, better, “intermittent energy” or “variable energy”. That is, energy or power production that cannot be relied on to be steady as is the case with fossil fuel, nuclear plants, and water power.

The obvious replacement energy sources of this sort are wind energy and solar energy. There is a lot of discussion of this topic now; I cannot supply a review of it and do not even wish to. Mostly this is because my own view is not entirely consistent with much of the discussion by current experts. This is clear from the previous books in this series. The usual-present day--fashion in discussing intermittent energy sources assumes that fossil carbon energy will remain available for a long time--usually in the form of natural gas. This is important because steady fossil carbon energy mitigates the really serious intermittency of wind and solar. Natural gas turbines supply an increasing fraction of our electric power, and this source of power can be rapidly switched on or off. This is often why one reads that wind energy can supply a third or more of our future electricity needs without disrupting our power grid. But this only works if natural gas supplies remain abundant, something I see no good reason for. Present studies also assume that we will use about the same amount of electric power as now. I doubt this as well.

The time scale for common studies is out to about 2050--a time when I think that fossil carbon, probably including natural gas, will be in such low supply as to create serious problems. Looking out to 2100, fossil carbon energy will be so scarce are to be hardly relevant at all. This needs to be kept in mind when reading what follows; the future lack of fossil carbon mitigation of wind and solar variation will be very serious. This is why my concluding view of wind energy viability will turn out quite negative.

These two books (wind and solar) will avoid dealing directly with the often contentious question of “100% renewable energy”--the conjecture that all our energy sources later in this century can be from such intermittent sources. I am a skeptic, and you will in part see why from what follows.

Other books in this series can be found at www.america2100.net

Introduction

The phrase “wind power” today usually means converting energy from the wind to electrical energy. There are many other uses of wind, but that is the one that we now often think of. That energy in wind is really just a consequence of the absorption of solar energy by the surface of the Earth. Winds carry solar heat to the colder poles. So wind is solar energy once removed. [1]

What is remarkable is that this derivative solar energy now generates over 2% of the nation’s “primary energy”. Accounting for the fact that this wind energy does not suffer from the roughly 2/3 waste in fossil carbon primary energy due to reject heat, wind amounts to probably over 5% of our “useful energy”. [2]And this fraction will grow.

The brisk wind speeds we are familiar with are roughly 5 miles per hour--2 meters per second at the ground--apart from infrequent storms. To get higher speeds, we have to go higher up. You can look up the average of speeds at 80 meters (260 feet). On land this average is about 4.6 meters per second or 8 meters per second over oceans. [3] The kinetic energy in wind increases as the square of the wind speed, so to get useful energy from the wind we need pretty tall wind turbines preferably in areas with above average wind speed. (Of course, too much wind speed can be dangerous to wind turbines.)

A striking thing about our everyday experience is just how variable the surface wind speed is. Over the course of a day it will routinely vary from 2 m/s to 5 m/s and over a few days by more than that. Since the kinetic energy in wind varies with the square of the speed, that will vary easily by factors of four or more over a day. [4] Completely still summer days, with no wind at all, are infrequent but not unknown. These periods of wind stillness can last up to a week, but seldom more than that. Wind turbines in an area suffering no wind produce no power at all.

These variations differ from one location to another in the United States. An entertaining thing to do is to find the location of a known wind farm and then go to the National Oceanic and Atmospheric Administration (NOAA) web site, choose that location, and check their three day history link. It is not uncommon to find an hour or even several hours in the last three days when there is no surface wind at all at that location. (The length of time of no wind at a present wind farm is probably less than where you live.) Periods of several hours of no wind do happen and present a serious problem; some other source of energy than that from the local wind is needed then.

It is much more serious if there is a period of days or longer with very little or no wind. This does not happen often, but the consequences are potentially extremely serious.

In addition to short term hourly variability or longer dropouts, wind speed varies with the seasons at most places in the United States. It even varies by year.

With all this going against wind as an energy source, it is not surprising that it has taken a very long time to reach the wind power growth that we see now.

Once, only winds at the surface were used, mostly to grind grain and pump water. The grain only got ground when the wind was blowing and someone was handy to work the job; water pumps could be automated, a big help. The only early big advance was the medieval era wind tower type that we see in tourist brochures. It had a four blade fan with a horizontal axis. It could be moved by hand to orient it to the wind direction. The fan was just a wood latticework that could be covered by canvas to catch the wind. There were thousands of these in Europe. Later, millions of much smaller wind turbines were sold and used on farms to pump water in both Europe and the U.S.

Attempts to use wind turbines to generate electricity in the early 20th century were small scale because near surface winds are too low to overcome much mechanical friction in a turbine and its attached generator. Typical turbines were a few tens of kilowatts on towers seldom more than ten or so meters tall. But by the 1950’s, tens of thousands of these small turbines were sold, and are still available. They were mostly used locally, not connected to the growing power grid of the time. (There were a few exceptions, connecting to a local grid.) Many of the developments from the 1940’s on were in Denmark, largely due to a few early enthusiasts there and their students.

Wind energy in the U.S. really began with the energy crisis of the 1970’s. The Nixon administration  started a number of energy projects, which expanded under the Carter administration and were mostly terminated by the Reagan government, a very unwise decision. One of these projects was to develop the first large U.S. turbines, built by NASA and the predecessor of our present Department of Energy. The first large two bladed turbine was the “Mod-0” turbine, and its successors, around 1975. Here is an early image, from a research facility in Ohio.[5] (NASA image)

These early efforts should have, but did not, lead to a U.S. wind turbine industry due to lack of government support in the 1980’s. The first large scale installations (“wind farms”) were in California, starting in the early 1980’s, using mainly Danish turbines. If you drive into Palm Springs from Arizona on U.S. 10 thru the San Gorgionio pass you could see, at least until recently, the development of wind turbines from the early ones to the more modern types. The wind farm there has (or had) turbines from several generations of development. [6] The following image shows many of the older turbines on their latticework towers (image Jan Tångring)

Modern wind turbines almost all look the same, three blades sitting on top of tube steel towers. This is a typical Danish “Vestas” turbine (image Wikipedia):

The remainder of this book is on the nature of wind power and its possible future.

Chapter 1-Wind Resources in the United States

Wind resources for us here means a number of things:

Where is the wind speed enough to support electrical energy production?

How much does the wind speed vary over minutes and hours?

What are the seasonal, or even yearly, variations in wind speed (hence energy)?

How frequent are “dropouts”, periods of days or a week with little or no wind?

All of these questions will have a big effect on whether and how we can supply needed power to the nation after fossil carbon. Remember, our present national electrical power demand averages about 400 gigawatts or over 3 kilowatts per household. [1](Something to keep in mind is that actual household use is only a third or so of national average power use at present, about one kilowatt. The total U.S. “primary energy” power use, including heat losses, is closer to 10 kilowatts per household.)

It is likely that as fossil carbon decreases, our electric power need will expand to perhaps an average of 800 gigawatts, most of the increase replacing present transportation, commercial and industry needs based on fossil carbon energy now. [2] It is probably a mistake to think that all this extra demand can be much reduced by conservation--eventually that will help, but there will be drastic additional need anyhow. That, in brief, is our national problem in the decades ahead. How much of our need will be met by wind energy we cannot know very well at present.

Our National Renewable Energy Laboratory (NREL) provides a map of wind speed at a height of 80 meters (260 feet), which is about the height of common present generation wind turbine hubs. It looks like this (notice the offshore wind):

Onshore Wind

The highest average wind speeds over land are light to dark purple in the NREL map, and these are thought to be the best locations (average over about 8 meters per second or 29 kilometers per hour. But notice that the historic producing wind farms in California are mostly in very small areas with lower wind speeds, around 6.5-7 meters per second. These California wind farms do work well. By that standard, much of the middle of the U.S. is suitable for wind energy. The coastal areas are also good--recall that wind speeds are higher over the ocean, compared to land. A land rectangle that contains the >7.5 meter per second winds at 80 meters height is about 2000x700 kilometers or 1.4 million square kilometers. That is a huge area, even if not all of it is of the best wind quality. If it could be filled out with turbines generating an average power of 1 megawatt per square kilometer, this would amount to 1400 gigawatts, about four times the present U.S. electric power use. [3] This is surely a gross overestimate of what is possible, but it indicates the scale of potential wind power. I will give some details later.

Incidentally, this map also shows why Texas now has far more wind power generation than California.

The downside of this large wind resource in the center of the nation is that it is far from the areas of largest demand at present. Of course, coastal ocean wind farms might supply at least some of the demand for that part of the country. Many of the Danish wind farms are already offshore, so that is not unrealistic.

An interesting extrapolation is this: if industry converts to electric power from fossil carbon, the center of the nation would be a good place for industrial expansion--that is where most of the potential land wind resource lies. Being close to the generation will reduce the need to transmit power to remote places such as the coasts. [4]

How much kinetic energy is there in these high wind areas? We can calculate this. [5] The kinetic energy flow, expressed as Watts per square meter, is 310 Watts/m^2 for a modest 8 m/s wind speed. It is not unreasonable to assume that the blades of a real world wind turbine cover an area of 6400 square meters (an actual number for the Vestas V90 turbine) so the kinetic energy flow in this area is 2 megawatts at this wind speed. That is quite a lot. (The actual Vestas V90 has a “nameplate” power, including higher speeds, of 1.8 megawatts. This figure includes the fraction of wind kinetic energy that can be actually extracted by the turbine.)

In the Introduction, I already mentioned that most of us often see periods of hours or a couple of days with very low or no land surface wind. (Surface winds are already lower than the wind at an 80 meter turbine height.) Moreover, wind farms can cover a large area, so wind speeds of exactly zero over a whole farm may be infrequent. We do not have data on wind speeds over large areas minute by minute or hour by hour. But there is data on the hourly wind power output for the Texas ERCOT system. [6] If “low wind” means that the power output (not wind speed) is a quarter or less of the average power output, then in 2016 this happened about two to three times per week for ERCOT. [7] The low power periods lasted for hours at at a time. During this time, the power supply to the connected grid has to come from elsewhere--e.g. natural gas turbines or batteries. The graphs in the endnote show that the power output changes rapidly, often varying by a factor two or three in one to two hours, more over longer times. There were several periods of 8-12 hours of low power, one nearly a whole day, but none as long as a week in 2016. There was a period of about a week of abnormally low wind power at the end of May and the beginning of June, 2017; so this is infrequent but not unknown.

These periods of low wind power are a serious concern. These are called “ramp events”--either when power goes very low or very high. There is, again for ERCOT, some information on this. [8] The worst of these downward ramps can lead to power dropping by a factor ten or more over a couple of hours. (The timescale is the same for wind ramps from low to very high power.) Just how to cope with these hours-long wind ramps in the absence of newer natural gas power turbines, which can ramp up quickly, is not at all clear.

Periods of several days to a week of very low wind power present a serious threat--there are at present no ways to deal with these except with fossil carbon backup power. [9] Even the pumped hydro storage discussed in earlier books in this series cannot supply power for such a long time at the very infrequent intervals when many days or week long dropouts might occur.

It is certainly possible, if expensive, to store energy for power dropouts of a few hours a couple of times a week. [10] Realistically storing energy for, say, a year in expectation of an unexpected week long dropout of wind power may be possible, but that must be very expensive. The same applies to seasonal variations. I will return to this in a later chapter. This may well be a fatal problem for wind power towards the end of this century.

Of course, it is possible that combining wind power from widely dispersed wind farms may reduce its variability and perhaps even eliminate week long dropouts (if they are local). This could be checked even now if year long hourly and synchronized wind power data were available, not just from ERCOT but from, say, the large Iowa wind farms as well. I do not know of any data on this. I will introduce a speculative guess at this use of “uncorrelated” wind farms later on.

In thinking about wind variability and longer dropouts, it is important to remember again that later in this century almost all energy use will be via distributed electric power. Major dropouts would be disastrous for the nation.

Another matter is the seasonal variability in wind and thus in wind power generation. Our electricity demand now is biggest in June to September, a consequence of air conditioning. Demand is lowest in October to April, when most heating is by gas or heating oil. How this will change when fossil carbon energy is mostly gone is completely unclear. Industry will likely use power at nearly a constant rate by 2100. Interestingly, homes and commercial power use that now varies a lot by season may become also more constant, due to heat pumps that heat in winter and cool in summer. We just cannot know what the mix will be later in this century. At present, wind power varies with season, highest in April and lowest in August. This is just the opposite of our present demand for electricity.

(I will not discuss yearly variations is average wind power, but that is also a concern.)

Here is a plot by our EIA (Energy Information Administration). In this plot, “capacity” is the fraction of the maximum possible power that is actually delivered for the whole U.S. Note that the ratio of maximum to minimum on this plot is almost a factor 1.7.

There is also a seasonal variation in wind power by region. [11]

Our present experience is that all these variations can be accommodated up to when wind power amounts to around 20% of the total power demand. But some caution would be good here. Given our large Eastern and Western grids, it is easy to export excess power to regions far from places where wind farms are dense. The same is true for imports. Low wind can lead to power imported from nearby states. Also, periods of low wind power can quickly be filled in by power from natural gas power stations. Our ability to absorb wind power fluctuations, seasonal variability, and regional variability may be less than we think if we look forward to 2100.

There is a lot we do not know. Real knowledge will come from building, using and improving very large systems. We do not do that now, with the possible exception of ERCOT. [12]

Offshore Wind

The NREL map of wind speeds also includes offshore wind. The turbines needed at sea are either secured to the ocean floor or floating. There is much more exploitation of offshore wind in Europe, particularly Denmark, than in the U.S. [13] It is worth the obvious stupendous effort for two reasons: wind speeds are generally greater offshore, and turbine siting problems are less offshore.

NREL has published an interesting report on offshore wind, “Assessment of Offshore Wind Energy Resources” [14] Little is known about the difficulties in developing the offshore wind for the U.S. Much depends on the depth of the ocean--that determines whether seabed anchored or floating wind turbines are needed. [15] Also, offshore turbines must survive sometimes violent storms, which are likely to increase in the coming decades, due to climate changes. However, most of the NREL potential lies north of New Jersey--presumably less likely to suffer large storms.

Just how much of this potential wind energy resource can actually be built out is unclear. Right now there is only one commercial project, having five turbines with a total capacity of 30 megawatts. [16] It will take some time to develop larger facilities.

The technical, economic, and social problems of utilizing truly large amounts of power, given the erratic nature of wind, is not addressed very well in reports I have seen. Neither are the connected problems of storing and transmitting the power, offshore as well as onshore, to where it is needed.

Right now all we can say is that there is plenty of possible wind power--several times our present total annual electricity consumption.

The following chapters are a very preliminary and personal view of these issues from the point of view of a physicist.

Chapter 2-Wind Energy Capture

The first chapter presents wind resources--mostly in terms of measured wind power rather than windspeed. This chapter is on how is this conversion of wind speed to power works. I will not discuss the actual internal wind turbine machinery here; there are many good books on the subject. [1]

Smoothly moving air has a certain kinetic energy of motion. (Smoothly moving means not swirly or turbulent.) This kinetic energy is mathematically half the mass of the moving air times the square of its speed. The speed of the moving air is the easy part to understand and can be measured with a device called an anemometer. The mass of the moving air depends on how it is expressed. The mass is its density (in kilograms per cubic meter--about 1.2 kilograms per cubic meter near the surface) times the volume. But what volume? The volume is determined the following way. If I imagine an area perpendicular to the wind then the volume of air passing thru this area, call it “A” in square meters, in a time “t” is the area times the speed of the air times the time t. The volume of air passing thru A depends on the time. So the kinetic energy in this volume--Avt--is, as expressed in an earlier endnote, (1/2)ρ(Avt)v^2; the total kinetic energy in the volume increases because the volume of air flowing thru the area increases. This energy is in Joules or Watt-seconds. We want power in Watts, and this is got by dividing the energy by the time, which gives us power P = (1/2)ρAv^3 and this is what we want. Here is a simplified sketch of a volume Avt of air that will run thru a turbine in t seconds.

This is a long winded way of repeating what was in that earlier endnote.

No wind turbine can extract all this power for a simple reason. To do so would mean that the wind entering the turbine at speed v must exactly come to a complete stop so that the air leaving carries away no kinetic energy at all. This is impossible--the air leaving the turbine must move to get out of the way of the wind entering. So the turbine itself must slow the wind down, but not entirely to a stop. To be efficient, the turbine must produce a stream of air out that has as little kinetic energy as possible. The actually intercepted stream then produces useful (electric) power. This is very difficult to do. As the entering air moves toward the turbine, it slows down and balloons up a bit. As it leaves the turbine area it balloons up a bit more and slows down more. The physics is really more complicated than this because this air leaving is really no longer smooth, it is turbulent. But if the air leaving is smooth (an ideal case), it is possible to use physics to figure out just what fraction of the power in the incoming air can be extracted in principle. This (idealized) fraction is 16/27 = 0.59 (Betz’ law). [2] To account for this, the power that can be extracted from the wind should be written

P = C (1/2)ρAv^3

Real world values of C for well designed wind turbines can reach 0.4, pretty close to the idealized value of 0.59. So a good guess is that about 40% of the incoming kinetic energy or power can be extracted. (The machinery and grid connection of a wind turbine does loose some of this--about 10% as mechanical friction and other losses.)

The dependence on windspeed as v^3 has a limit. If the wind is moving above some particular speed, the turbine has to limit the power it extracts to protect the mechanical components. Above this windspeed, the power extracted is roughly constant up to a very high windspeed, where the turbine has to actually shut down.

The real electrical power output of a turbine increases up to where it is a maximum. This maximum is the “nameplate power”.  Here is a typical plot of nameplate power against windspeed (for a Vestas 3 MW nameplate power turbine). I choose this as an example because in a good location such a turbine can deliver and average power of about a megawatt.

It’s clear that you would like to operate this in windspeeds from about 10 m/s to 25 m/s; the v^3 dependence then pretty much just cuts off power below 7 to 8 m/s.

Watching a wind turbine, it seems odd that it can extract a lot of power using those thin and apparently slowly moving blades. Really, the ends of the blades are moving fast--about 5 or more times the windspeed. For the Vestas, this means a tip speed of 100 m/s at 20 m/s windspeed--360 kilometers per hour or 225 miles per hour. This is why turbines generate noise and why they can be a danger to birds. We don’t realize this just because modern turbines are so big. The blades only seem to be moving slowly.

The key element in modern wind turbines lies in those thin blades. [3] The force that drives the blades around in their circular motion is the same “lift” that moving air produces on aircraft wings. But there are two differences. The lift on turbine blades drives them around in a circle, not just upward as for an aircraft. The other and bigger difference is that the “windspeed” seen by the blades is not the speed of the incoming air mass. Imagine a bug sitting on a blade. At the tip of the blade the bug would see a wind direction mostly opposite to the direction of the blades motion as seen from the ground. It would be the combination of the speed of motion and the speed of the wind as seen from the ground. This total speed would be a bit over the speed of the blade as seen from the ground. As a result, there would be a “lift” force on the blade, causing it to rotate clockwise, again as seen from the ground in front of the turbine. A bug nearer the hub of the turbine would see a wind that is closer to the windspeed. (The blades rotate slower near the hub.) To get the best rotational force on the blades, they will have to “twist” closer to the hub compared to the end of the blade. If you look carefully at a wind turbine blade when it is still in no wind, you will notice this twist of the blade. These blades are a beautiful and practical application of aerodynamics to wind turbines.

Remember that a turbine can extract about 40% of the kinetic energy of the wind. Besides this, downwind of the turbine the air will not only slow down, it will swirl a bit. Both of these things (and more) will make a downwind turbine less efficient. So there has to be some spacing of turbines if you want to build a “wind farm” of many turbines. There is much discussion about just how far apart you can place turbines.

I now want to move on to this and related issues.

Chapter 3-How Much Wind Power?

Just how much wind power the U.S. could produce depends on the location and power and land density of wind turbines. A useful rule of thumb is that a present generation turbine on land in a good area will generate an average electric power of about a third of its rated “nameplate capacity”. (The same applies to a wind farm--it will produce perhaps a third of its “capacity”.)

Because wind turbines disturb the airflow behind them, it is not possible to place them too close together.

Depending on the study, turbines need to be spaced somewhere between seven (an old “rule of thumb”) and fifteen times the rotor diameter. [1] A convenient rough guess then might be ten times the rotor diameter. For example, a field of the Vestas turbines I mentioned earlier would be spaced about 900 meters apart. If I make this an even kilometer, then a field of turbines would have a total nameplate capacity of about 3 MW per square kilometer. Taking into account an average efficiency in real winds of about a third would give roughly 1 MW average delivered power per square kilometer. A field of 1000 square kilometers, about 30+ kilometers on a side, would then produce on average 1 GW. A single large coal fired or nuclear power plant would produce about this much on less than a square kilometer of land. Turbines need lots of space.

The scale of space needed can be got by supposing that very large fields of turbines producing an average of 200 gigawatts--one half the present U.S. demand or, more likely a quarter of future demand. This would amount to 200,000 square kilometers or a strip 200 kilometers wide by 1000 kilometers long. If this were on otherwise empty land, the area under the turbines might be used for crops or grazing animals. This is done now, as is lease payments for the land. The total land area for this example would be about 2% of the total U.S. land area.

Or, another example from earlier, a zone in the middle of the nation 2000 kilometers long by 700 kilometers wide (at this same average per square kilometer) would yield 1400 gigawatts average power. So there is plenty of power available--at least in the middle of the country--given a willingness to use the land at a density of a turbine per square kilometer. (The land area in this example is about 14% of the total U.S. land area.)

The average wind electric power delivered in 2017 was close to 12 gigawatts, 3% of total electric use.[2]

It is hard to relate the large land use here to real practice with so little present delivered wind power. ERCOT in Texas is perhaps a real world example, according to its Wikipedia page. About 40 wind projects have a present capacity of about 26 GW (using my estimate, this would be close to 9 GW average). The average delivered power per turbine in Texas is about a half MW.

These are all rough estimates. Better studies have been done of total U.S. wind capacity, even state by state. The result is that the total land capacity is huge, about 10.6 terawatts (10,600 gigawatts) [3] Remember that capacity is not the same as potential delivered power. But this number, delivered power, can be got from the same study. It presents potential total yearly delivered power, which turns out to be 30,950 terawatt-hours. This is about nine times the present U.S. electrical energy use in a year. [4]

The total potential land capability to deliver actual power from the study is 3540 gigawatts. This includes the fact that delivered power is only a fraction of capacity. This is a huge number that is far beyond any reasonable future need. As I mentioned this is almost nine times present power use.

It is very interesting to think of the total land area for this capacity. It too is huge. [5] It is about 20% of the total land area of the nation. What this means is that productive wind power can be put anywhere on about 20% of the land. How much land is needed depends on how much wind power is actually installed. My earlier estimate of 2% or so of the land area needed for wind energy is probably not far off.

Wind power land use will be a major issue in the future, so it is surprising how little information is available on present land use. One example I found in Texas is the “Roscoe Wind Farm” that seems to take about a square kilometer per turbine with a capacity of around 1.2 MW per turbine. So the above numbers may not be too far off reality. It is still the case that major wind power means major land use.

It is not surprising that NREL studied land use in 2009. [6] This is a pretty complicated issue. Wind turbines are installed in “wind farms” that have quite different turbine layouts depending on the site. Access roads are needed, as are buffer zones around the wind farm. Also, much of the land of a wind farm can be used for other purposes as well as for turbines. The study I mention here does not deal with environmental issues, such as the danger to migrating birds and the like. This all goes beyond my scope, important as it is.

The scale of future wind energy installations is beyond anything we see at present. Just to illustrate this, I use a very simple thought experiment. Imagine that in the near future (perhaps after 2025 or 2030) fossil carbon energy starts decreasing at some percent per year. This might be 2% or 5% or some other number. Let me use 5% decline per year and also assume that this is the rate at which fossil carbon electric power declines. Then 5% per year of, say, 400 gigawatts has to be replaced. Let me assume that this is done using wind turbines. Five percent amounts to 20 gigawatts per year and if this is replacement energy at one megawatt average per turbine, this implies an installation of 20,000 such turbines per year. This is a large number, but not a crazy number.

There are over 50,000 turbines in the nation now, but these are of all sizes. I do not know the U.S. based large wind turbine production rate, but the present installation rate seems to me to be around a thousand turbines per year. So the crude estimate here is that the production rate would have to go up by around a factor 20 to deal with the need to replace fossil carbon electricity with wind energy. This would require new and very large scale industrial development.

Offshore wind energy capacity has been studied by NREL [7] They quote a gross resource of about 1700 gigawatts out to water depths of 60 meters. This will be important for supplying energy to the Northeast grid. I will not go into this further here.

Chapter 4-Intermittency and Storage

The intermittency of wind energy has already come up repeatedly. It is impossible to supply the nation with significant electric power from wind without a clear practical--and real world--understanding of how to deal with erratic wind. Our existing energy infrastructure just does not have this problem. We plainly should not just keep adding wind energy until some part of our power grid brakes down and then figure out what to do. There are lots of studies, and I will mention some of them, but operational experience with real large scale wind farms is going to be essential.

One thing we can do as a nation is to exploit the unique situation of our three mainland grids: Texas, the ERCOT grid, services about a tenth of all national power demand and it is mostly detached from the two main Eastern and Western grids. It is an ideal testing ground. An interesting, if exotic, idea is to pay Texas to be a “guinea pig” for both wind and solar energy. This is already the case with subsidies for wind energy, which has allowed Texas to expand wind power. We should do more: pay them to reduce coal and gas power and expand wind and solar energy. (I favor them keeping the present nuclear power level to produce nearly constant “baseline” power.) Only at first does national support for ERCOT change seem like a crazy idea. But ERCOT is already, in my opinion, well run. So: why not persuade them to continue?

I already showed some plots of wind power versus time from ERCOT. It is fair to say that the fluctuations in wind power are a bit scary. To emphasize the point again, here is a plot from ERCOT data for an entire year, from their Excel file:

The average is about 6000 Megawatts, so this fluctuates from near zero to about twice the average power delivered. Texas power demand also fluctuates, but much less and in a roughly predictable fashion. So the present fifteen or so percent wind power can be accommodated, particularly given the easily ramped up power from natural gas generators. What is not clear is what if the total wind power were to reach or exceed fifty percent. And what would happen if gas generator power were not available to absorb some of the fluctuations?

One partial way around this fluctuation problem would be to use batteries to store energy for some time and release it more gradually to the grid. For example, a battery installation at a wind farm could absorb all power for some time (say four to twelve hours) and then release a quarter or a twelfth of that energy in an hour, replenishing battery storage from the wind power generated in that hour. This can be repeated, smoothing out the delivery to the grid. I already mentioned that this would very roughly double the cost of a wind farm (depending on what large battery installations cost).  This would not really solve the overall problem, because fluctuations would still persist--especially seasonal fluctuations. Battery energy storage at any reasonable cost is short term, hours--perhaps four to twelve hours.

It is useful to carry out a very crude estimate of the total demand on energy storage. One way to do this is to require some imaginary storage to absorb and release energy in such a way as to keep the delivered power constant at the average value. This is easy to do in a spreadsheet and the total maximum stored energy required is huge. In the case of ERCOT, it would amount to many terawatt hours of storage. Here is a plot (it runs for year and the vertical axis is gigawatt hours):

The plot has be adjusted not to go below zero, as appropriate for storage. For comparison, a large hydro plant can store about 20-40 gigawatt hours. The vertical axis then corresponds to almost a hundred such plants.

This is crude for a number of reasons, mainly because there is no real need for such an extreme case where the delivered power is converted from fluctuating to constant. But the issue remains: storage is in the terawatt-hours range, not gigawatt-hours. Batteries cannot do this. Their storage is limited by cost to perhaps 20 or so gigawatt hours for the entire ERCOT grid. [1]

Scaling this crude estimate up to the whole nation, say 200 gigawatts wind energy, would produce fantastic and unrealistic energy storage demands. Worse, much of this would have to be held over to deal with seasonal variations in wind--the energy would have to be stored for fractions of a year.

Fortunately, there is a detailed estimate of the long term storage needs if the Texas ERCOT grid were to be 100% supplied by wind and solar energy. It is important to be aware of this, although it is only one study and may be superseded in time. [2] The study, by Paul Davies, gives a long term storage need of about 14 terawatt-hours for Texas. This includes about 27% over-generation, so that there is more wind and solar capacity than is actually used. This somewhat reduces the need for long term storage. Since ERCOT delivers about a tenth of all electrical power in the nation, scaling this up would give about 140 or so terawatt-hours storage for the United States, not accounting for the likely need for much more electrical power once most fossil carbon is exhausted. It also needs to be kept in mind, though, that wind energy alone varies seasonally for the whole U.S. by almost a factor two! (See an earlier endnote.) This seriously worsens the storage outlook to the borderline crazy level.

Pursuing this line of thought anyhow, where is this amount of storage to come from? One option, discussed by Davies, is to use electric power to convert carbon dioxide gas to burnable hydrocarbons such as methane and then store the methane. Since my view here is that there will be few hydrocarbon resources by the end of this century, there will also be little or no carbon dioxide gas. [3] This leaves hydrogen, produced by using electric power to split water into hydrogen gas and oxygen--electrolysis. This is certainly possible in theory, although the overall efficiency of electricity to gas and back to electricity is about a third. An advantage is that the storage can be local. It is not unrealistic to mine out storage caverns and line them to store some hundred or so gigawatt hours of energy per cavern, as mentioned in an earlier book. So a lot of hydrogen gas storage is not at all hard to imagine. But I cannot see how storage could reach many hundreds of terawatt-hours. My own view--possibly wrong--is that this will never happen. [4] We need to look elsewhere.

I want to remain with studies of ERCOT, because the Texas grid is so useful to me. An interesting study that I found is a paper by Denholm and Hand from NREL. [5] This study simulates the ERCOT grid with conventional power and what they refer to as “VG” or variable generation consisting of wind and solar energy. They ask what needs to be done to reach 80% of demand supplied by variable generation. An interesting thing they do is to consider what happens if the conventional generation can be shut off entirely. This would most simply be to shut off natural gas power generation, which can be done with little advance notice. They call this “100% flexibility” of the conventional generation. What happens in this case is that, to some extent, the VG has to be curtailed--itself shut off. When this flexibility becomes low, not 100%,  then the VG has to be curtailed a lot. This means that there has to be excess wind and solar capacity so that some of it is unused. When the flexibility is high, less variable generation has to be shut off.

There are a number of things that are interesting to me that the study by Denholm and Hand does not answer. This is for a good reason, since they assume that conventional generation will be available and I do not. Here is one question: can you have so much excess wind and solar capacity that conventional generation is not needed at all? This would mean that at any time a lot of their variable generation would be curtailed or shut off. This excess capacity would reduce or eliminate the need for energy storage. I have no idea just how much excess capacity would be needed to do this. From their plots, it must be much more than twice the capacity that could supply on average ERCOTs power demand. How much more I cannot tell. But at least knowledge of this would answer the question of whether and how much one could reduce long term storage. An obvious problem here is that wind farms would also need battery storage to smooth short term fluctuations plus perhaps doubling or tripling the number of wind farms. This could get expensive.

Denholm and Hand answer some related questions. It is interesting that they consider their case of 80% variable generation (or “renewable” generation) when short term battery storage is available. Here is a relevant plot, showing just how much the variable generation has to be curtailed versus the fraction of power from this VG. They assume total 100% flexibility.

My view of this is that it is already unfortunate: even to reach 80% variable generation, both conventional backup are needed and the variable generation has to be curtailed in addition. Plus, this does not address the need for long term storage to cope with seasonal variation. Here ERCOT is not much help, because their seasonal variation is less than that for the whole U.S. Seasonal variation is going to be a big and maybe fatal problem.

Without long term storage, the practical way to cope with wind (and solar) variability is either a conjectural vast increase in capacity over what is needed or significant backup conventional power generation, presumably natural gas.

It might be that combining wind generation from widely dispersed sites will help reduce fluctuations. It is often claimed that the correlation in wind between sites a thousand or so kilometers apart is low. I doubt that this really helps much. [6] ERCOT has wind power data from different years and is a simple exercise to take data for one year (2016 in my case), divide by two and add 2017 data also divided by two. The two sets should at least be uncorrelated on short terms, apart from seasons, and comparing them to one year (2016) should show a significant reduction in fluctuations. But it does not. Here is the plot for this case, mixing 2016 and 2017 and shown by hour for a year:

The fluctuations are still huge, though not quite so bad as those for 2016, shown earlier. I am not confident that combining supposedly “uncorrelated” wind power plots will be effective.

I have not discussed the issue of the effect of large amounts of wind power on the stability of the national grid. This is also another very serious problem, because grid stability now depends essentially on the ability of spinning conventional generators to maintain grid frequency. Large amounts of fluctuating wind power have the capability of destabilizing one or both of the major U.S. grids. It needs to be kept in mind that our present grids are old and the control mechanisms are based on conventional power generation. Small amounts of wind power stress the system, but it appears so far to work acceptably. The last major grid blackout was over fifty years ago. Unconsidered large scale expansion of unbuffered wind power could lead to some new unpleasant surprises.

Chapter 5 Discussion

When there is no proper conclusion to a work, it seems to be conventional to replace that section with a “discussion”. I will do so here.

When I started this book, it seemed that introducing large wind power to replace, say, half of the missing year 2100 fossil carbon power generation, would be a large but manageable engineering challenge. I no longer think that. The variability just seems too extreme. Evening out the wind variability by vastly expanding capacity and introducing huge amounts of energy storage (by factors of a hundred or more) is just to hard to conceptualize as a large scale engineering problem.

My suspicion, and it is no more than that, is that wind power will remain viable just so long as there is natural gas for rapid response to fluctuations. Natural gas generating stations are getting more and more sophisticated and able to start up and shut down quickly. Once our national natural gas supply has declined significantly, wind power will become no longer viable. It will develop to be a short term solution to our fossil carbon crisis. (That is why I suggested that ERCOT, at least, keep baseline nuclear power in the energy mix.)

In the meantime, our national power grids, east and west, will be vulnerable to wind (and solar) energy. It is easy to finance and build a wind farm with no battery backup. But it seems to be quite difficult to form a clear plan for the future of the grid. We do not want to have the entire future of our energy plans disrupted by major wind-induced blackouts, something I now think quite likely.

Introduction

1. There is a big difference between “solar energy” as the power delivered to the Earth by sunlight and the kinetic energy of wind. The first is measured in Watts--1000 Watts of sunlight per square meter for a clear day with the sun directly overhead. The second is energy itself--Joules or “Watt-seconds”--one Joule is one Watt of power times one second. There is continuous delivery of energy from sunlight, but at least the average kinetic energy of the Earth’s winds do not change. So this is measured in Joules, not Watts. The sunlight power (Watts) that goes into producing wind is exactly balanced by the friction losses of the wind (also Watts), so that the average wind speed or kinetic energy does not increase (constant number of Joules). It is common to measure both of these per square meter of the Earth’s surface, to keep the numbers easy to remember. We can guess a “ballpark” number for wind kinetic energy, given a couple of very rough numbers that we will need later. The average windspeed over the ocean at a convenient 80 meters (260 feet) height is about 8 meters per second; over land it is about half that. To get the total kinetic energy per square meter we need the average speed for the whole atmosphere, almost all of which is well above the 80 meters. So we just guess that the average over the whole height of the atmosphere is maybe twice the sea average, or 16 meters per second. Maybe we remember that the mass of the whole atmosphere above us is about that of 10 meters of water, which amounts to 10,000 kilograms. The kinetic energy per square meter is then, roughly, one half times the mass over one square meter times the square of the average wind speed. This is about 1.3 million Joules per square meter or 1.3 megajoules per square meter or 1.3 MJ/m2 . This is close enough to the actual number, 2.5 MJ/m^2 wind kinetic energy. Why is this interesting? Megajoules per square meter is not a small number, compared to other energy sources. But it is small compared to the intensity of solar illumination. The usual maximum is 1000 Watts per square meter (Joules per second). As an aside, you can look up the dissipation rate of global wind and it averages about 2.5 Watts per square meter, much less than the illumination power rate.

2. “Primary energy” includes all sources, including heat energy losses that average about 2/3 of the primary energy. “Useful Energy”  (sometimes called “Energy Services”) is the energy that actually goes to run our economy. This is from the Lawrence Livermore laboratory energy flow “Sankey” diagrams. These diagrams show the energy flow from all sources to their end uses. The most recent diagrams shows “useful energy” at 31% of the primary energy. To the extent that electricity from wind goes directly or almost directly to useful energy, it is more valuable than primary energy from fossil carbon. (In practice, probably about 80% ends up as useful energy, the rest being heat losses of various kinds.)

3. In this book I will stick with the 80 meter height number and the corresponding wind turbines. Very large turbines are just now entering production.

4. We will later see that the actual power from wind varies by the cube of the wind speed, up to the speed at which a turbine has to limit its power output for mechanical reasons. Above this limit, a turbine power output is constant with wind speed. This fact reduces the variability of the turbine power output somewhat.

5. You can find a report on this research on the Web. It is DOE/NASA 1079-23. An early feature of turbines was to use wing aircraft wing airfoils for the blades--this is how NASA got involved. An efficient turbine with airfoil blades needs smooth winds, increasing the importance of putting the turbine high up. An interesting feature of this program was the plan to place later turbines with utilities, connecting them to the grid. Alas, the program was cancelled, and real commercial development only happened later. (Much of the later development used Danish turbines.)

6. An interesting account of the San Gorgiano pass wind farm today can be found in Paul Gipes http://www.wind-works.org/cms/index.php?id=625&tx_ttnews%5Btt_news%5D=2804&cHash=ceac96f5cb7597fd41366e9b4ceeca04

Chapter 1- Wind Resources in the United States

1. We use about 400 gigawatts of average distributed electric power now, very roughly 40% of the “energy services” on the Lawerence Laboratory “Sankey” plot below. Peak use is somewhat less than twice that 400 gigawatts, and U.S. “capacity” is well over 1000 gigawatts (1 terawatt), much of which stands idle when demand is low. To recall some background, here is the LLNL plot I have often referred to as representing our present energy use (I dislike the use of the “Quad” unit, which we can take to be about one “exajoule”--more exactly 1.06 exajoules; one exajoule is 10^18 joules or watt-seconds).

and here is a typical national daily electrical “load” plot for one summer day (the load varies by season, of course). This is from the EIA. The load variation by households is larger than for the nation as a whole.

And here is a seasonal plot, from the EIA website (it has lots of useful data)

2. I got an average future 800 gigawatts, in about 2100, by starting from the Lawrence Lab “useful energy” number of 40 exajoules per year and dividing by the present delivered electric energy of 12 exajoules. This would give, on average, perhaps 1200 gigawatts delivered electric power. I somewhat arbitrarily discounted this to 800 gigawatts, expecting improved use of electric power. This improved use might come from conservation, for example, although I will not discuss energy conservation here. Because of varying power demand, the total “capacity’ might be quite a bit larger than 800 megawatts average.

3. The DOE has published a 2015 “Wind Vision” report DOE/GO-102015-4557, that presents an estimate of the developable wind power on land of 3730 gigawatts. (I got this from their figure for total energy delivered per year, assuming 80 meter turbine towers.) This report has much useful information in it.

4. If power is generated in the middle of the nation and transmitted to the coasts (very roughly 2000 km distance), then very large DC transmission lines would be needed. Similarly long lines would be needed if wind farms in the north and south were connected. There already exists a long 1300 km “pacific intertie” between Washington and Los Angeles at 3.1 gigawatts transmitted power. It is certainly possible to imagine lines with with multiple conductors carrying perhaps 10-20 gigawatts per line. For 200 gigawatts power this would require 10-20 lines, quite a lot and covering a lot of ground area. One such line plus (expensive) AC/DC conversion stations might cost in the ballpark $5 billion. For details on single smaller lines, see a study for the WECC by Black and Veatch. A previous book discussed the nature of power grids.

5. To calculate the kinetic energy in a steady wind with speed v, we need to use the well known formula for kinetic energy, (1/2)mv^2 . The problem is what mass m to use. Recall that kinetic energy is expressed in units of joules. What we want is power in the wind (that is what we need to generate electric power), not energy, so we have to express this in a new form as Watts or Joules per second for some area through which the wind flows. We know that near the surface air has a mass density of about 1.2 kilograms per cubic meter. This is called “ρ”. So the mass that flows through an area A per second is the density of air times the volume of air that flows in one second. This volume is A times v, the air speed in meters in that one second. So the volume is Av cubic meters per second. The mass that flows is then the air density times this volume or ρAv and the kinetic energy that flows per second is (1/2)ρAv^3 (it is v^3 or v times v^2). Substituting in a convenient area of one square meter and v = 8 meters per second (a low value for the best wind areas) gives a kinetic energy flow of 310 Watts per square meter (2 significant figures).

6. Here are two plots of hourly power, one for January 2016 and another for June 2016, from ERCOT data. We will meet the “Capacity Factor” later--it is the fraction of the maximum output power that is actually achieved. For January, this was 29% and for June 34%. (The maximum power, the “Capacity” was 16 megawatts, so the actual amount of power delivered was about a third or a bit less of the “Capacity”. I owe the link to the ERCOT data to an article by Peter Davies that will be discussed later.

7. Plotted by days instead of hours also gives a pretty erratic power. Here is January, 2016, with power as a percent of capacity (i.e. maximum) day by day

8. The following plot of a downward “wind ramp” in 2009 is from NREL technical report NREL/TP-5500-4928 by Yih-huei Wan.

9. There is an ERCOT example of a days long period of very low wind power, late May to June. Here is a plot. The low period lasted a few days.

10. Storing energy to deal with an hours long decrease in wind power was discussed in an earlier book in this series, “The Power Grid and Energy Storage”. A rough estimate there was that including this short term storage would about double the cost of a wind turbine installation. Another alternative, mentioned briefly in the first book, is to build out a large overcapacity of wind generation at, admittedly, also a high cost. See, for example, the article by Budischak et al, Journal of Power Sources 225 (2013) 60-74. One if their options is an approximate tripling of the number of wind turbines over the number needed for average demand. Then either the individual “capacity factor” has to drop or the excess power used somehow (I had suggested, in the first book, diverting it to desalination plants).

11. Wind power varies by both season and location in the United States. Here is an EIA plot of this variation:

The interesting variation is California, where wind power is largest in the middle of the year. Unfortunately, California has low wind resources and probably cannot fill in the low production in the rest of the country during the summer. Thus the bad news is that the variation covers most of the nation.

12. Much of our lack of knowledge is now being filled by sophisticated models. I do not think that models can replace real world experience.

13. There is a Danish government document on offshore wind at

https://ens.dk/sites/ens.dk/files/Globalcooperation/offshore_wind_development.pdf

This is a major effort, as you can see from the image here (cropped from the Danish report).

14. Our own wind energy resources, via NREL, as of 2010, can be found at

https://www.nrel.gov/docs/fy10osti/45889.pdf

Here is a map from the NREL report:

A 2016 NREL report (NREL/TP-5000-66599) goes further, claiming “technical resources” that amount to over an average 820 GW of offshore potential (about twice the average U.S electricity use)

15.  Notice that our East Coast (and the Gulf) has lots of shallow water for turbines, while the West Coast has little shallow water.

16. The only commercial offshore wind farm is the “Block Island” one off Rhode Island. It even has its own Wikipedia page.

Chapter 2-Wind Energy Capture

1. See, for example, “Wind Energy Explained” by J.F. Maxwell et al , Wiley publisher. At present the internal machinery is of two types. One is a gearbox to speed up the turbine rotation to that convenient for a generator. The other is a more ingenious use of a ring of magnets to directly produce electric power at a higher frequency than rotation of the turbine blades. In both cases, high frequency and fluctuating power has to be dispatched to a 60 Hertz grid. The subject is thus very complicated.

2. There is a good discussion of this in Wikipedia.

3. For details on blade design, see the book mentioned in an earlier endnote. A search will also show a number of quite interesting discussions on blade design.

Chapter 3-How Much Wind Power?

1. I got the 15 rotors diameter number from https://www.theengineer.co.uk/wind-turbines-need-to-be-farther-apart-suggests-study/ . This goes back to a John Hopkins study.

2. There is a useful wind fact sheet from the University of Michigan at http://css.umich.edu/factsheets/wind-energy-factsheet.

3. I got this number, 10,640 gigawatts, and the following numbers from a study done for NREL by the firm “AWS Truepower” (now defunct). Its results can still be found on the web. Here is a graph of wind power resources by state. It does exclude places where wind turbines would be unacceptable (urban areas, for example). Unfortunately, it is a bit hard to read.

4. Here is the plot of potential total yearly delivered energy. Dividing by hours per year gives the average power that can be delivered, 3.54 terawatts or 3540 gigawatts, almost nine times the present average electric power use.

5. Here is the NREL, AWS Truepower plot of land area. I have been using a ballpark number of delivered power equalling a third of capacity. This plot shows, for turbines with a hub height of 80 meters, how much land is needed for all turbines having a given “capacity factor”. For a capacity factor of 0.3 and better, about 2 million square kilometers are used--about 20% of the total U.S. land area.

6. For the NREL study of land use for wind power, see “Land Use Requirements of Modern Wind Power Plants in the United States”, NREL/TP-6A2-45834.

7. See “2016 Offshore Wind Energy Resource Assessment for the U.S.”, NREL/TP-5000-66599.

Chapter 4-Intermittency and Storage

1. The cost of large battery installations changes with time. One recent farm in Australia cost about $500 per kilowatt-hour. Although this cost will go down, it is important to understand that large installations are much more expensive than the cost of the battery cells themselves. The cost per kilowatt-hour of the cells can be misleading.

2. The study I refer to in the text is that by Paul Davies and it can be found at his web site beyondthesuperficial.com. Davies has modeled both wind and solar energy in the ERCOT grid, along with the effect of short term battery storage. There is also a response on his web site to criticism by Roger Andrews, whose work can be traced through the website euanmearns.com. Andrews’ work on wind energy is very interesting but, unfortunately, Andrews has died. Since my interest here is in large scale storage, I won’t discuss other aspects of this issue.

3. This is not the place to go into the question of whether or not it is realistic to extract carbon dioxide from the atmosphere at the needed scale. My own personal view is that this is energetically not feasible.

4. I do not wish to go further here into the “100% renewable energy” matter, associated with studies by Mark Jacobson and his collaborators. They appear to think that hundreds of terawatt-hours of storage, in various forms, is realistic.

5. The NREL study of ERCOT by Denholm and Hand is Energy Policy 39 (2011) 1817–1830. It contains many interesting plots from simulations that they ran.

6. On the web, you can find many “correlation plots” of average wind power at various distances.  I will not discuss them in detail. In my view, these plot are not very useful. As mentioned in the text, the problem is fluctuations not simply correlations of average output.

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