Prof. Howard Hayden
BrookesNews.Com
Monday 01 September 2003

The US government has spent hundreds of million of dollars on wind energy but most US wind farms use turbines purchased from Danish companies. It’s our way of subsidizing a poor little anti-nuclear country whose economy is smaller than Atlanta, Georgia’s.

Early wind turbines had very poor capacity factors. They produced barely 15 percent of the nameplate power, when averaged over a year. Now they are achieving much higher capacity factors, in some cases, 30 percent. However, there is a lot less here than meets the eye.

The power in the winds is easy to calculate. Take the wind speed in meters per second, and cube it. Divide the result by it, and you have the wind power density in watts per square meter, at least within a percent or so. Of course, the wind speed is a variable quantity, so it is a good idea to calculate the average power over thousands of readings extending over several years.

(As a reminder, the average power density is not equal to the power density calculated from the average wind speed. For two days when the wind speed is zero and 10 meters per second respectively, the average power density is (1000/n +0/n)/2, or 159 watts per square meter. The power density calculated from the average wind speed is (125/n), or 40 watts per square meter.)

The correctly calculated average power density, however, is misleading. To explain why, I will refer to a table having nothing to do with wind, the alumni contributions to a certain university in a recent campaign. There were about 92,000 gifts of $99 or less, amounting to about $2.7 million. There were 25,000 gifts of between $100 and $250 that totaled $3.0 million. On the other hand, a mere 47 gifts of more than $1 million resulted in $141 million in contributions. That is, the overwhelming majority of alumni money comes from a numerically negligible number of contributors. (The same is undoubtedly true of campaign contributions.)

The average power density of wind is similarly highly biased by the rare occurrences of high-speed winds. Suppose, for example, that the wind speed for 29 days in a month is 5 m/s (power density = 40 W/m2), and on one day the wind speed is 25 rn/s (power density = 5000 W/m2). The average power density is 205 W/m2.

Now imagine having a windmill at that site whose efficiency is 50 percent. How much average power would it produce during those 30 days for every square meter swept out by the turbine blades? Answer: 20 W. The wind turbine (of any body’s manufacture) has to be shut off in high-speed winds to keep from blowing apart. In other words, the largest contributions to the average wind power density are of no value (but of some danger) to wind turbines. It’s as if a university could not accept contributions of more than (say) $20,000. Fortunately, universities are not as fragile as wind turbines.

The Arbitrary Capacity of Wind Turbines

Design an excellent wind turbine of 50 percent efficiency, and there are still some constraints. You could design it so that it could withstand the highest wind likely in the next 1000 years, when it would produce 100,000 kW, for example. It would be vastly over-designed for more normal winds. Most of the time, it would be producing 50 kW.

Instead, manufacturers design with a much lower wind speed in mind, knowing that the machine will have to be shut down in high winds. For example, a machine might have a capacity of 100 kW, rated at a wind speed of (say) 25 m/s above which the machine must be shut off. Suppose that in one month, during which the wind speed never got up above 20 rn/a, the average power was 15 kW. Then the capacity factor would be given as 15 percent.

The very same machine could be made to operate under different rules. For example, the blades could be automatically “feathered” (rotated on their axes) so that the turbine’s efficiency steadily decreased as the wind speed increased between 20 rn/s and 25 rn/s. Throughout that range, the turbine would produce 50 kW instead of 100 kW. The capacity of the wind turbine would then be given as 50 kW. During the very same month when the average power was 15 kW, the very same machinewould have a capacity factor of 30 percent instead of 15 percent.

In short, the capacity, or nameplate power, of a wind turbine is a bit arbitrary. By extension, the capacity factor is also a bit arbitrary. The recent increases in capacity factor are partly due to improved reliability, but mostly due to the re definition of capacity.

Chasing Frequency

There is considerable merit in operating wind turbines at power levels well below what one would predict from the diameter of the fan, People talk of steady winds in some place, but that is always a poor description. Many sites are always windy, but the wind speed is minute-by-minute variable at all of them. Therefore, the power density in the wind is also highly variable.

When either a large load is connected to the power line or a large source of power on the line goes off-line, the voltage drops, but the more evident change is a drop the rotation rate of the generators. This in turn is immediately sensed as a de crease in the frequency of the AC electricity. Similarly, when a large load is disconnected from the power line, or a power plant comes on line, the frequency increases. Electric clocks that are plugged into the power line rely on the frequency of the power to be exact. If the frequency — 60 cycles per second — is low by 1 part in 100,000, the clocks will be off by about an intolerable one second in one day. The fre quency must be very tightly controlled.

There are control stations staffed by engineers and techm cians that monitor the power lines. If the frequency varies ever so slightly, they must respond by calling for more (or less) power from the power stations whose power levels are easiest to vary (hydro stations, when possible, otherwise “spinning reserve”). When the wind is gusty at a wind farm, the power fluctuates all over the map, and in short order. The engineers get very exasperated “chasing frequency,” trying to hold the line frequency constant while the wind causes the input power to fluctuate wildly.

When wind turbines produce essentially constant power over a wide range of wind speed, it is much easier — nay possible — to control frequency. The only way for this nice situation to occur is for the wind turbines to reduce their efficiency for all speeds in excess of some given wind speed.

Whereas they might be capable of 100 kW at (say) 25 m/s wind speed, they must produce only 50 kW, and do so for a large range of wind speed. For lower wind speed, it would not be necessary to reduce the efficiency, because the wind turbines produce precious little power anyway; fluctuations amount to a fraction of precious little.

Dr. Howard Hayden runs The Energy Advocate in which this article was originally published.