## Wind Power Curves

by Ian Woofenden

What's Wrong, What's Better

If you're baffled by a wind turbine's power curve, here's how to interpret wind generator manufacturers' data to choose a turbine that will give you the best performance at your site.

Power Curves for Three Turbines

Power curves are frequently presented by turbine manufacturers in their marketing literature, and interpreting these curves is at best a complicated exercise even for the mathematically inclined. Few wind turbine buyers know how to use this information to determine what they really need to know—how much energy a wind generator will produce at a given site. Let's look at why power curves are not a useful tool for most of us, and what to use instead.

What's the Curve?

Any alternator or generator produces electricity at varying levels, depending on its rotational speed (rpm). When we plot the output against the speed, we get a curve. If the original motive force is wind, we can plot the generator output against wind speed, which gives us what is typically called a "power curve" for the wind generator (see the "Power Curves" graph). It shows wind speed in miles per hour (mph) or meters per second (m/s), and power in kilowatts (KW).

It's important to remember that power in its technical sense means "watts." This is an instantaneous measure of the rate of electricity generation (or transfer or use), and not a measure of energy (watt-hours), a quantity.

What's Wrong with the Curve?

Misinterpreting wind generator power curves is common and can happen in a variety of ways. First, the untrained eye is naturally drawn to the top of the curve—the peak power. If we were looking at a gasoline-powered generator, this would be useful information. As long as it's supplied with gasoline and a load, it continues to produce at or near its rated output.

Peak power for a wind generator is very different—at most sites, the wind speed at which a turbine generates its peak power occurs only a very small percentage of the time. So focusing on the peak may lead you to wildly exaggerated energy expectations.

Trying to compare one wind generator to another using power curves is another common mistake. While there is some useful comparative information in the curves, it's not a simple comparison, and people too often scrutinize turbines poorly, looking primarily at the peak. For example, I've lived with two turbines that shared about the same peak on their power curves—yet one produced 2.3 times more energy than the other in similar conditions.

If (and that's a big "if") power curves accurately predicted energy production, it might make sense to compare turbines by looking at the low end of the curve. Good performance at low wind speeds is most important in a wind turbine, since that is where it will spend most of its time (see "Wind Speed Distribution" graph).

Next, applying an average wind speed to a power curve can be an impossible and illogical task. A power curve demonstrates instantaneous production (watts), while a focus on average wind speed points toward overall energy potential (watt-hours).

All these misconceptions or misunderstandings of power curves become clearer as we look at the physics of wind and the reality of how wind works at a typical site.

### Velocity Cubed

Wind is variable. This we know intuitively. We feel it blow lightly on our face one moment, not at all the next moment, and maybe a few minutes later it'll be blowing us down the street. Wind is rarely constant, and it's a myth that there are sites where "it always blows at 15 mph." When you start

Wind Speed Distribution

Wind Speed (mph)

i i i i i i i i i i 0 5 10 15 20 25 30 35 40 45 Wind Speed (m/s)

looking at measured wind data, it's hard to find groups of consecutive data points that are the same in one minute, let alone for hours.

The most crucial fact to understand about wind energy is that the power available in the wind is related to the cube of the wind speed. Humans are fairly comfortable with linear functions: Spend twice as much money and you'll get twice as much coal; double the rainfall will result in doubling the catchment water into your tank.

Cubic functions are not as intuitive. You might think that when you double the wind speed (velocity, or V), you double the power. But in fact, doubling the wind speed gives eight times the power (2 V x 2 V x 2 V = 8 V). A 20 mph wind has eight times the energy (20 x 20 x 20 = 8,000) of a 10 mph wind (10 x 10 x 10 = 1,000). It doesn't always play out precisely this way with wind energy capture, since different turbines have different efficiencies. But the principle remains vital to understanding wind electricity.

The V3 law can be worked both ways— up and down the power curve. If a "perfect" turbine produces 100 watts at 10 mph, it has the potential to produce 800 watts at 20 mph. If the machine produces 1,000 watts at 24 mph, it will produce 125 watts or less in a 12 mph wind. Understanding the V3 law helps you look at power curves—and wind energy—differently.

### Wind Distribution

The other major factor that comes into play is wind distribution. When we start to study the way the wind varies, we find out that every site has a different wind distribution profile. A wind "distribution" plots the frequency of each wind speed. Typically, it's shown in a wind distribution curve (see "Distribution" graph). For example, one site may experience 15 mph winds 4% of the time, and another site may see winds of 15 mph only 3% of the time. The distribution curve

Instantaneous power means nothing for wind energy.

—Mike Klemen

Perfect Turbine or Pipe Dream?

Wind turbines operate within the limits of Betz' Law. Simply put, if you try to capture 100% of the energy available in the wind, the wind is stopped—it cannot move the blades. On the opposite end of the scale, the wind just goes around a fixed obstruction. In either case, the result is the same—no energy is extracted.

The Betz limit says that capturing 59.6% of the energy in the wind is the best compromise between stopping the air and letting it pass through the turbine unaffected. Maintaining the flow of air is the compromise any wind machine must make, whether it is a horizontal-axis (a traditional-style turbine) or a vertical-axis turbine; with many blades or few. All turbines are subject to the Betz limit.

The "Energy Output" table shows the amount of energy you can reasonably capture per rotor swept area at several average wind speeds. You can multiply by the swept area of the turbine you're considering to see if the manufacturer's claims are even possible!

However, comparing the "model" wind turbine columns with manufacturers' claimed production data from four reputable manufacturers' turbines, none are as good as claimed. Numbers in the "Model Turbine" column are based on an average efficiency of 35%. It is not terribly likely that you'll find a wind turbine that is more efficient than this. Remember: If it's too good to be true, it may very well be!

The table shows the energy (KWH) per month that a "perfect" turbine designed to Betz' law could produce, and what a real-world model turbine could produce, taking inefficiencies and design into account. The table assumes a Rayleigh wind distribution at sea level.

Let's try an example. If you have a turbine with a swept area of 10 square feet in a 10 mph wind, you'll find that the "model" turbine value per square foot of rotor is 2.08. Multiply it by 10 because you have 10 square feet of rotor. If the manufacturer is claiming that the turbine can put out more than 20.8 KWH per month, the turbine is probably too good to be true. Next, multiply the Betz limit value of 3.5 by 10. If the manufacturer claims you can generate more than 35 KWH per month, then they are claiming to have broken the laws of physics.

—Mike Klemen

Monthly Energy Output Per Sq. Ft. of Swept Area

## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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