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View Full Version : Watt vs. kilo-Watt-hours, and instantaneous vs. average wind speed


Rob Beckers
3rd May 2007, 09:12
Just a little post of something I'd like to point out because I see it getting confused by so many people. First one up is Watt or kW (kilo-Watt = 1000 Watt) and Wh or kWh (kilo-Watt-hour = 1000 Watt-hours). I was talking to an electrician last week, and even he was consistently talking about "kilo-Watt" when he meant "kilo-Watt-hours".

Watt is a measure of power. Watt is not energy, it is energy-per-second. Horsepower is another way to measure power, and the two are readily convertible, where 1 hp is just about 746 Watt. Take a 100 Watt light bulb, its power is, as it says on the bulb, 100 Watt. So how much energy does it use? Depends on how long you let it burn; After one hour it used up 100 Wh, two hours makes 200 Wh, and after 10 hours we're at 1000 Wh, or 1 kWh. Likewise, a light bulb with a power rating of 1 kW would only need to burn for 1 hour to use up 1 kWh in energy.

The other one is wind speed, where an instantaneous wind speed gets confused with the average wind speed for a site. The former is just that, the wind speed you measure if you stick an anemometer up in the wind. The wind speed at that instant. Average wind speed for a site is what you get if you measure the instantaneous wind speed frequently and regularly (say every minute or so), add them all up, and divide by the number of measurements. So, a storm can be blowing at your site, and you measure an instantaneous wind speed of 21 m/s (= 47 mph), while that same site has an annual average wind speed of only 5 m/s (= 11 mph) because the wind doesn't blow all the time, or not that hard at least.

So how does all this relate to wind turbines? Instantaneous wind speed is coupled to power. If the wind blows with a constant wind speed of, say, 5 m/s your wind turbine may be producing 1000 Watt or 1 kW. This is not energy, this is power. Because the power in the wind follows the cube of the wind speed, wind turbine output tends to go up very rapidly when the wind speed increases. Not quite with the cube of the wind speed, because wind turbines usually get less efficient at increased power levels. So, at 8 m/s (= 18 mph, which has 4 times the power in the wind vs. 5 m/s) that same wind turbine may be producing, say, 3 kW. Measure wind turbine power output for a range of wind speeds, and you get a power curve.

Power is nice, but what most people are more interested in is how much energy, in kWh, their wind turbine produces per month or per year. You could of course measure power every minute, multiply it by one minute (to get energy), keep doing that for a few years, and divide to get average annual production in kWh. The easier way to get at production is to use average (annual) wind speed for a site. All that's needed is a way to relate average wind speed to the various instantaneous wind speeds and how often (and how long) those occur. Some physics whiz did just that, and found that for the average site on land the average wind speeds relates to instantaneous wind speed through something called a Weibull distribution. There's a constant in that distribution that determines its shape, and for most situations over land a factor of k = 2 seems to be just about right.

The Weibull distribution says how strong the wind blows (wind speed), for how much of the time (frequency). So now it's a matter of using the power curve to get power for each wind speed, then use the Weibull distribution for our average wind speed to look up how often this happens (duration), multiply the two, and we have production (energy).

To make life easier I've created a spreadsheet does the heavy lifting for you (see http://www.greenpowertalk.org/showthread.php?t=7 to download it). Replace the power curve for the turbine you want to calculate production for, set the average wind speed, tower and anemometer heights, and you're off to the races. Honesty compels me to tell you that I didn't create this spreadsheet. It comes from a commercial turbine, and I modified it to be a bit more versatile and provide more information than the original. The other disclaimer is that production from the spreadsheet is only an approximation. It all hinges on how closely the wind speed distribution at your site follows a Weibull distribution. My understanding is that over land it's pretty close, but as they say, your mileage may vary.

Now if someone says "1 kW at 11 mph" we'll hopefully all know what was meant by that! ;)

-Rob-

Stewart Corman
3rd May 2007, 12:36
Rob,
Good post.
I might add the the Weibull distribution with a factor of 2 has an intrinsic turbine design parameter associated with it.

What is is basicly saying is that average WS is "average", but that smaller amount of WS just over the avg has a lot more power in it by the cubic relationship ....therefore, if you design your turbine's pitch angle, cord widths, etc to be maximized at this slightly higher WS, you are getting the most you can out of the turbine over time. As an example, if your avg WS is really 10mph, then design your rotor/generator for a 12.5mph maximum efficiency. Furl it at the capacity of the generator to deliver w/o self destructing.
If it's 12mph, then design for 15mph .

You don't care if efficiency falls off at even higher WS, BECAUSE by definition of Weibull the turbine won't be seeing those WS very often at all. You can't get power from WS that you never see. You wouldn't design for that 47mph gust would you? Another benefit is that falling efficiency at high WS is feathering by airfoil parameter w/o using any mechanical gismo, it is also the force that pushes against the tail furling mechanism to steer it out of the wind.

Unfortuneately, most if not all of the commercial two or three blade high TSR units function at max efficiency in the low 20mph WS range with rated specs at 26 ->29mph for advertising claims. How this affects your purchase is that when run at low WS like 10mph which is way below optimum, you only get a fraction of the efficiency where you need it, so a 1.8KW rated (at 26mph) unit only delivers 300 watts for you (if you are lucky).

Stew Corman from sunny Endicott

Rob Beckers
3rd May 2007, 13:07
To add to what Stew brought up: If you take the spreadsheet I attached and plug in your average wind speed (for your turbine site), you can actually see from it what wind speed range will contribute the most to your energy production.

For example, the default setting of the spreadsheet is 5.5 m/s (12.3 mph) average @ 10 m. For a tower of 30 meters (100') this translates to a wind speed of 6.4 m/s (14.3 mph) at hub height. When one scrolls down in that spreadsheet there's a section labeled 'net kW @ V'. This tells us what contribution each wind speed 'bin' makes to the energy production. In our example it turns out that the largest contribution is around 9 and 10 m/s (20 - 22 mph).

Note that the contribution to energy production already has the turbine's power curve figured into it. So a different turbine, with a different power curve, might have a different wind speed that contributes most to production.

-Rob-