Ben Colla
16th October 2010, 22:51
I can't answer that for you. For three very good reasons.
1. I don't know where you are
2. I don't know what diameter turbine you are asking about.
3. I don't know how tall your tower is
But, with some thinking we can come up with a reasonably good answer.
I’ll refer to the following web sites and or pages
1. http://www.talentfactory.dk/en/tour/wres/index.htm
2. http://www.talentfactory.dk/en/tour/wres/calculat.htm
3. http://www.reuk.co.uk/Calculate-kWh-Generated-by-Wind-Turbine.htm
4. http://www.solacity.com/SiteSelection.htm
5. http://www.solacity.com/Economics.htm
6. http://www.sustainability.vic.gov.au/www/html/2123-wind-map.asp
7. http://www.otherpower.com/bottom_line.shtml
8. http://www.talentfactory.dk/en/tour/wres/enrspeed.htm
Everything here is aimed at personally owned turbines. So probably no bigger than 10 kW (or about a 7 meter diameter). Though it probably holds true for the commercial sized turbines as well.
Those three things I listed are the most important list of things, for wind turbines. They are listed in order of importance. The most important, sadly, is the one you can do the least about. *Sigh*.
1. Location Location Location. If you are not in a windy location, nothing else matters. You may as well stop reading now, and flick over to the solar panel section. There are numerous places to find wind maps online. The one relevant to me is link 6. But of course, that only helps if you are in Victoria, Australia. So, go find a wind map for your area. If the average wind is less than 4 m/s (8mph or 14 kph) you are not going to get much out of a turbine. The power in wind goes up with the cube of the speed of the wind. So you need wind. You need wide, flat open windy terrain, in general.
2. Diameter. Bigger is better, but big is more expensive. How big can you afford? How big can you legally go? How big can you handle (big = heavy). The power you can generate goes up with the square of the diameter. So, wind speed is better than turbine size. (besides, wind is free, big turbines are not)
3. The higher you go, the higher the wind speed. And as wind power increases with the cube of the speed, you need to go up to get power. But bigger towers cost a lot more and need a bigger area around them. Also better foundations and probably decent guy wires. Tall towers get expensive.
Let us pick my (proposed) site for a turbine for my example.
From the Victorian wind map (link 6), I know that my average wind speed is 7.3 – 7.4m/s. This is truly awesome. I am looking at a turbine rated at 5kw with a diameter of 5 meters. So if you use link 3 you get somewhere around 24,000 kWh/year (I’ll explain this page in a bit). Holy smokes batman!!! But, there is a problem. That sounds too good to be true. So let’s check the fine print on that wind map. Hmmm ... O here it is. Wind speed measured at 65meters above ground level.
65 meter tower. Ummm, I don’t think the local council would like that, the neighbours certainly won’t, and the bank manager is just going to laugh at me. You cannot directly translate wind speed at 65 meters altitude to the wind speed at ground level. It slows down the closer you get to the ground, until it’s zero at ground level.
You’ll have the same problem. Wind speed measured at a different height to your tower height.
But link 2 lets you estimate the ‘wind shear’ factor. That is, how much the wind speed varies depending on altitude.
So open it up in a different tab. I’ll use the ‘1.5’column (the middle one) as it’s a reasonable one to use. Read up on ‘roughness’ on the same site to find out why. I put 7.2 in the 1.5 column at 60 meters altitude and hit ‘calculate’. There it is, nice and easy, the height at 10, 20, 30 .... and so on meters. This will also spit out a pretty graph. So plot one.
Look at that graph. It shows you the wind speed depending on the altitude.
Notice how above 20 meters, it’s a lot more vertical, and below 10 meters it’s a lot more horizontal. You want to go as high as possible, but there are diminishing returns. Going from 100 to 150 meters gets you 1 m/s speed, and so it’s probably not worth the money to add the extra 50 meters height to a 100 meter tower. Going from a 10 meter tower, to a 20 meter tower gets you only ½ m/s. But the extra tower cost is marginal and may well be worth it. The cost/benefit ratio changes somewhere in this range, for small turbines. Higher is always better, but the cost adds up. (Unsubstantiated thought ... you want your tower height to be at the 45 degree part of this graph. Lower, means you are leaving easy picking’s wind speed on the table, and higher makes the tower to costly, while adding little to wind speed. Discussion?)
Anyway, we have converted wind speed at X height, to wind speed at your tower height. Now we can calculate how much power you’ll actually get.
Open up link 3 again.
OK excellent.
It asks for 6 numbers. Some of these are simple.
Rotor diameter, is the blade diameter. Put in your blade diameter.
Mean wind speed. Or the average. We figured that out just a little bit ago. So put it in. Better to round down than up, so as to not inflate your generated power.
Cut in speed. This is the minimum wind speed that your turbine will make any power at. If you’re unsure use 3.5 (there is bugger all power in wind below 3.5m/s anyway).
Cut out speed. Is the highest wind speed that your turbine will make more power at. Surprisingly, it makes very little difference if you change this from 15 to 25.
Turbine effiency. This is tough to get an accurate answer to. It relates to how much power there is in the wind, to how much electricity your turbine can actually make. This CAN NEVER exceed 60%, no matter how magically awesome your turbine is, and probably won’t exceed 30%. Use 30% unless you know better, and if someone is telling you that their turbine they are trying to sell to you is better than 40%, they are probably lying to you.
Weibull Shape Parameter. Tough to explain. Go hit Wikipedia. OK. Good, your back. Leave it at 2. That was easy.
Hit calculate.
And you have your answer.
For me, it’s somewhere around 10,000 kWh’s / year, with a 5 meter diameter set of blades.
Fiddle with some of the numbers. I find it especially interesting how the ‘cut out’ speed makes very little difference. Even though the power in the wind increases with the cube, you’d think that a high cut out factor would be critical. But, very high wind speeds are very uncommon, so they add very little to total power generated. With these high wind speeds, you don’t want the turbine to blow up trying to capture the power, you just want it to survive.
Cut in is also interesting. There is so little power in very low winds, it’s not worth even trying to capture it. You can ignore wind below about 3m/s because there is no power there anyway. Hit up link 7, and read down until you see the chart. At 6 mph even 6meter blades will only be generating just over 100w. Link 8 also shows this. Low wind is low energy, and there is nothing you can do to fix this.
Changing the mean wind speed by even 0.2m/s makes a significant difference. There is that cube power increase working again. Varying the wind speed from 5.5 m/s to 5.7 m/s (5 meter diameter) adds 1,100 kWh/year
Now, you’re probably asking, how do I know those figures are correct?
Well, .... I don’t have a good answer. I have several tolerable answers though.
1. The Australian Government has a Renewable Energy Certificate scheme. Each REC is worth 1 mWh of generated electricity. If you visit https://www.rec-registry.gov.au/sguCalculatorInit.shtml and put in a 5 meter wind turbine at the default 2000 hours, is spits out 47 RECs, or 47 mWhs, over a 5 year period. Pretty close enough.
2. Rob Beckers has a spread sheet available, that does the same sort of calculations, and it spits out similar results. With luck he'll link it for us. [edit] He doesn't have to. It's right at http://www.greenpowertalk.org/showthread.php?t=7 in the first post.
3. http://www.solacity.com/Economics.htm has some charts, and if you follow them through, you also get similar results. However, both 2 & 3 here refer back to the same person eventually, so it’s slightly suspect. Not that I’m claiming that Rob is lying, just that using the same person twice for the same task inherently has a ‘they ain’t completely independent’ problem.
If I've made a mistake, let me know, and I'll correct it, but I think it's generally correct.
1. I don't know where you are
2. I don't know what diameter turbine you are asking about.
3. I don't know how tall your tower is
But, with some thinking we can come up with a reasonably good answer.
I’ll refer to the following web sites and or pages
1. http://www.talentfactory.dk/en/tour/wres/index.htm
2. http://www.talentfactory.dk/en/tour/wres/calculat.htm
3. http://www.reuk.co.uk/Calculate-kWh-Generated-by-Wind-Turbine.htm
4. http://www.solacity.com/SiteSelection.htm
5. http://www.solacity.com/Economics.htm
6. http://www.sustainability.vic.gov.au/www/html/2123-wind-map.asp
7. http://www.otherpower.com/bottom_line.shtml
8. http://www.talentfactory.dk/en/tour/wres/enrspeed.htm
Everything here is aimed at personally owned turbines. So probably no bigger than 10 kW (or about a 7 meter diameter). Though it probably holds true for the commercial sized turbines as well.
Those three things I listed are the most important list of things, for wind turbines. They are listed in order of importance. The most important, sadly, is the one you can do the least about. *Sigh*.
1. Location Location Location. If you are not in a windy location, nothing else matters. You may as well stop reading now, and flick over to the solar panel section. There are numerous places to find wind maps online. The one relevant to me is link 6. But of course, that only helps if you are in Victoria, Australia. So, go find a wind map for your area. If the average wind is less than 4 m/s (8mph or 14 kph) you are not going to get much out of a turbine. The power in wind goes up with the cube of the speed of the wind. So you need wind. You need wide, flat open windy terrain, in general.
2. Diameter. Bigger is better, but big is more expensive. How big can you afford? How big can you legally go? How big can you handle (big = heavy). The power you can generate goes up with the square of the diameter. So, wind speed is better than turbine size. (besides, wind is free, big turbines are not)
3. The higher you go, the higher the wind speed. And as wind power increases with the cube of the speed, you need to go up to get power. But bigger towers cost a lot more and need a bigger area around them. Also better foundations and probably decent guy wires. Tall towers get expensive.
Let us pick my (proposed) site for a turbine for my example.
From the Victorian wind map (link 6), I know that my average wind speed is 7.3 – 7.4m/s. This is truly awesome. I am looking at a turbine rated at 5kw with a diameter of 5 meters. So if you use link 3 you get somewhere around 24,000 kWh/year (I’ll explain this page in a bit). Holy smokes batman!!! But, there is a problem. That sounds too good to be true. So let’s check the fine print on that wind map. Hmmm ... O here it is. Wind speed measured at 65meters above ground level.
65 meter tower. Ummm, I don’t think the local council would like that, the neighbours certainly won’t, and the bank manager is just going to laugh at me. You cannot directly translate wind speed at 65 meters altitude to the wind speed at ground level. It slows down the closer you get to the ground, until it’s zero at ground level.
You’ll have the same problem. Wind speed measured at a different height to your tower height.
But link 2 lets you estimate the ‘wind shear’ factor. That is, how much the wind speed varies depending on altitude.
So open it up in a different tab. I’ll use the ‘1.5’column (the middle one) as it’s a reasonable one to use. Read up on ‘roughness’ on the same site to find out why. I put 7.2 in the 1.5 column at 60 meters altitude and hit ‘calculate’. There it is, nice and easy, the height at 10, 20, 30 .... and so on meters. This will also spit out a pretty graph. So plot one.
Look at that graph. It shows you the wind speed depending on the altitude.
Notice how above 20 meters, it’s a lot more vertical, and below 10 meters it’s a lot more horizontal. You want to go as high as possible, but there are diminishing returns. Going from 100 to 150 meters gets you 1 m/s speed, and so it’s probably not worth the money to add the extra 50 meters height to a 100 meter tower. Going from a 10 meter tower, to a 20 meter tower gets you only ½ m/s. But the extra tower cost is marginal and may well be worth it. The cost/benefit ratio changes somewhere in this range, for small turbines. Higher is always better, but the cost adds up. (Unsubstantiated thought ... you want your tower height to be at the 45 degree part of this graph. Lower, means you are leaving easy picking’s wind speed on the table, and higher makes the tower to costly, while adding little to wind speed. Discussion?)
Anyway, we have converted wind speed at X height, to wind speed at your tower height. Now we can calculate how much power you’ll actually get.
Open up link 3 again.
OK excellent.
It asks for 6 numbers. Some of these are simple.
Rotor diameter, is the blade diameter. Put in your blade diameter.
Mean wind speed. Or the average. We figured that out just a little bit ago. So put it in. Better to round down than up, so as to not inflate your generated power.
Cut in speed. This is the minimum wind speed that your turbine will make any power at. If you’re unsure use 3.5 (there is bugger all power in wind below 3.5m/s anyway).
Cut out speed. Is the highest wind speed that your turbine will make more power at. Surprisingly, it makes very little difference if you change this from 15 to 25.
Turbine effiency. This is tough to get an accurate answer to. It relates to how much power there is in the wind, to how much electricity your turbine can actually make. This CAN NEVER exceed 60%, no matter how magically awesome your turbine is, and probably won’t exceed 30%. Use 30% unless you know better, and if someone is telling you that their turbine they are trying to sell to you is better than 40%, they are probably lying to you.
Weibull Shape Parameter. Tough to explain. Go hit Wikipedia. OK. Good, your back. Leave it at 2. That was easy.
Hit calculate.
And you have your answer.
For me, it’s somewhere around 10,000 kWh’s / year, with a 5 meter diameter set of blades.
Fiddle with some of the numbers. I find it especially interesting how the ‘cut out’ speed makes very little difference. Even though the power in the wind increases with the cube, you’d think that a high cut out factor would be critical. But, very high wind speeds are very uncommon, so they add very little to total power generated. With these high wind speeds, you don’t want the turbine to blow up trying to capture the power, you just want it to survive.
Cut in is also interesting. There is so little power in very low winds, it’s not worth even trying to capture it. You can ignore wind below about 3m/s because there is no power there anyway. Hit up link 7, and read down until you see the chart. At 6 mph even 6meter blades will only be generating just over 100w. Link 8 also shows this. Low wind is low energy, and there is nothing you can do to fix this.
Changing the mean wind speed by even 0.2m/s makes a significant difference. There is that cube power increase working again. Varying the wind speed from 5.5 m/s to 5.7 m/s (5 meter diameter) adds 1,100 kWh/year
Now, you’re probably asking, how do I know those figures are correct?
Well, .... I don’t have a good answer. I have several tolerable answers though.
1. The Australian Government has a Renewable Energy Certificate scheme. Each REC is worth 1 mWh of generated electricity. If you visit https://www.rec-registry.gov.au/sguCalculatorInit.shtml and put in a 5 meter wind turbine at the default 2000 hours, is spits out 47 RECs, or 47 mWhs, over a 5 year period. Pretty close enough.
2. Rob Beckers has a spread sheet available, that does the same sort of calculations, and it spits out similar results. With luck he'll link it for us. [edit] He doesn't have to. It's right at http://www.greenpowertalk.org/showthread.php?t=7 in the first post.
3. http://www.solacity.com/Economics.htm has some charts, and if you follow them through, you also get similar results. However, both 2 & 3 here refer back to the same person eventually, so it’s slightly suspect. Not that I’m claiming that Rob is lying, just that using the same person twice for the same task inherently has a ‘they ain’t completely independent’ problem.
If I've made a mistake, let me know, and I'll correct it, but I think it's generally correct.