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-
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-