Would one large wind turbine be more efficient than many small wind turbines in theory?
closed as off topic by Kevin Vermeer Jun 1 '12 at 3:02
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The proper answer to this would take several days to write and would cost you money.Please advise if you wish to proceed :-).
However, the answer is "no", BUT there are factors that could bias the result either way.
Assuming you are dealing with air, (yes, I know you said wind) which is compressible, the theoretical maximum efficiency for an unshrouded isolated turbine is known as the Betz limit and is about 59%.If you shroud the turbine fully (infinite duct) you can get much closer to 100%.
Turbine's in arrays in certain arrangements tend to act as partial shrouds for others near them and efficiencies in very special cases can be slightly higher than stand alone.
BUT arrays of turbines spread out across an area tend to steal wind from others (put simplistically) and reduce efficiency of nearby ones.
The industry trend is to larger and larger turbines with time. 1 MW has become common, 5 MW is big and 10 MW will come. This suggests there are commercial advantages in increased size per unit BUT commercial driver is most return per expenditure and while efficiency is important, if you can make something 5% less efficient but produce 10% more $ % return then the most efficient design will lose out. If you think that is a questionable statement it show that you are an engineer and not an accountant :-).
Turbines at the bottom end may be drag type or a drag/lift mix but these are usually used for DIY or where unusual construction is favored (has 100,000 oildrums in warehouse), or in very niche applications. High efficiency is achieved my maximizing lift and eliminating drag. Lift allows blades to move through the air faster than wind speed. Tip speed to wind speed ratio (= TSR) is the measure of how fast the rotor turns in a given wind. Efficiency rises with tip to wind speed ratio but at very high TSRs other losses set in. As TSR rises blade count drops to keep shaft RPM down. TSR's of 10+ can be achieved using SINGLE blade machines (not double). There are Russian examples around but I have seen few others mentioned.
Wind speed increases with altitude and power available increases with velocity cubed so making tall towers and large rotors allows higher faster winds to be utilized. Technically getting more and faster wind is not increasing efficiency per se BUT it allows more energy out per some parts of your investment so looks like efficiency to an accountant. To this extent the large turbine may appear "more efficient".
Efficiency depends on blade shape ...
More later ...
If the turbines were small, they would have less mass and hence would require less wind energy to spin. So the same wind force striking a large and small turbine would cause the small turbine to turn faster. A faster spinning turbine cause a larger current to be induced in the generator. This is assuming we could build a small, light turbine and generator that could handle the currents.
However, with a smaller turbine, I would think Lenz's Law would come into effect far sooner then with a larger turbine with greater momentum as it spins. Forces due to Len's Law would build up and oppose the spinning of the smaller turbine, in effect slowing it down.
Did any of that stuff I just typed make sense?