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there's a question that has been annoying me for a while ,consider the follwoing (power,rotor speed) diagram for different wind speeds

wind rotor speed

at some wind speed(6m/s for example)how could a turbine running fast(15rpm) produce less energy than a turbine running slower(12rpm)?

and at some constant rotor speed(say 15rpm) ,if the wind speed is 7m/s the turbine would produce more power than 6m/s how is that possible?

i mean if they are both connected to the same gear box and generator shouldn't the one moving faster make the generator run faster hence produce more energy?

and if the rotor speed is constant shouldn't the turbines produce the same energy even at different wind speeds?

i know that the peak is caused by betz law,but my question isn't about that,its more of a mechanical question i think

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  • $\begingroup$ Most motors (and therefore most generators, since a generator is just a motor in reverse) do not output the same power for every speed. There tends to be a dropoff in the power provided by a motor (and therefore the efficiency of a generator) as a function of speed. $\endgroup$ – probably_someone Jun 15 '18 at 14:08
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Current produced by a generator tends to be proportional to the torque on its shaft, Voltage tends to be proportional to its speed, and output power is the product of current and voltage.

It's no coincidence BTW, that input power is the product of torque and speed.

If you disconnect the output of the generator, then in theory, the shaft can spin freely at any speed (e.g., you can spin it fast). There will be no electrical power output because the open circuit forces the current to zero, and there can be no power in the shaft because when the current is zero the torque also is zero.

If you short out the output of the generator, then you've forced the voltage to zero. Again there can be no output power, and in theory at least, you should be unable to turn the shaft, and so the input power must also be zero. (In practice, there are some power losses within the machine, and you will be able to slowly turn the shaft.)

In between those two extremes, there is significant voltage, and significant current and also, significant speed and significant torque. Therefore, significant power can be converted from mechanical to electrical.

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  • $\begingroup$ but isn't the peak in the curve caused by betz limit? and i know for sure that betz didn't work from an electrical perspective. $\endgroup$ – hakam zoubi Jun 16 '18 at 9:21
  • $\begingroup$ @hakamzoubi, You are right: It can be explained entirely by the mechanics. My mistake was to think that "wind turbine" == "electrical generator". For a given wind speed, the shaft can spin fastest if nothing resists it (i.e., if there's no torque), but with no torque, there is no power transmitted. If you lock the shaft so that it can not turn at all, then there's lots of torque, but no power transmitted because there is no rotation. In between those two extremes, the shaft can transmit power. $\endgroup$ – Solomon Slow Jun 16 '18 at 14:25
  • $\begingroup$ Sigh! I guess I never even looked at the label on the chart. It clearly says, "mechanical power." $\endgroup$ – Solomon Slow Jun 16 '18 at 14:38

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