Turbine Input vs Output Power

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Turbine Input vs Output Power

Postby Greystoke on Fri Jul 24, 2009 12:09 pm

Image
trying to design a turbine that will power a geyser seems fraught with pitfalls. Here's another one:
The power input follows a 3rd order polynomial curve of the windspeed. The resulting rpm is more like a linear curve.
The output voltage is proportional to the rpm, so - since P = Volt²/R, in which R = the resistance of the heating element - the output power follows a second order curve of the windspeed, and there is no way these two curves can be matched (as illustrated by the picture)
In this case, the output curve lies above the input curve. That's - of course - impossible, since you cannot get more out than was put in. So, what will happen?
What will happen is that this turbine wont even get out the starting blocks. Any bit of electricity is consumed by such a power hungry element that nothing is left to turn the turbine.

The only way this turbine will start is when we can get the yellow curve BELOW the blue curve for all windspeeds,(see the red dotted line) which puts a severe restraint on the usefulness of this design
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Cor
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Re: Turbine Input vs Output Power

Postby Greystoke on Sun Jul 26, 2009 10:32 am

Image
I found a way to match the power input curve, but only through selectively engaging the coils in and out of circuit. At higher outputs more coils get connected. Standing idle, only three coils are engaged. The windspeed indicates how many coils must be engaged.

This is very difficult the realise, and that just for an average of 100 Watt.Image Wonder if I'm on the right track :?:
Regards
Cor
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Re: Turbine Input vs Output Power

Postby windgat on Sun Jul 26, 2009 10:51 am

I think you are right, in that you want the converted wind power to exceed the generator power at that RPM. You can also affect this by altering the TSR.

Switching coils on and off is tempting, but will increase vibration, and adds one more potential point of failure. At low wind speeds there is so little power in the wind its not worth much, so I would say aim to optimise for medium to strong winds. In very strong winds, of course, that means you get runaway speeding up, which is why you need a furling/braking mechanism.
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Re: Turbine Input vs Output Power

Postby Greystoke on Sun Jul 26, 2009 2:38 pm

There's one alternative which looks a bit more promising, ie: to reduce the output voltage by means of an electronic attenuator.
I am going to investigate that option.
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Cor
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Re: Turbine Input vs Output Power

Postby windgat on Sun Jul 26, 2009 5:07 pm

Now that is a great idea! :clap: Basically what is needed is a programmable/variable DC-DC high efficiency convertor.
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Re: Turbine Input vs Output Power

Postby Greystoke on Wed Jul 29, 2009 6:23 am

Found a promising design. Need to study it a bit more.
Image
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Cor
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Re: Turbine Input vs Output Power

Postby Greystoke on Wed Jul 29, 2009 12:45 pm

Well, I've got one thing sorted out.
The reference voltage has to be proportional to the rpm, as per the first graph.
There's a bit of a bend in that curve close to zero, so its not that easy to reproduce.
However, the curve can be approximated with a straight line (but kep at zero below 100 rpm). So the "bend" is approximated by two straight line: one line at zero going from 0 to ±100rpm, and another going up proportionately to the rpm.
This way the power output will be closely approximated to the wind power input, as shown in the second graph

Image
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Cor
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Re: Turbine Input vs Output Power

Postby windgat on Sat Aug 01, 2009 1:07 pm

I don't quite follow exactly what the graphs are. Have you taken into account generator efficiency? Blade efficiency? etc? Intuitively it seems a bit close, i.e. the available power should be more above the output power.
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Re: Turbine Input vs Output Power

Postby Greystoke on Sat Aug 01, 2009 1:37 pm

The wind power has been derated to 80%. In other words: 20% is required to turn the blades at the designed rpm.
(I'm still trying to work-out the theoretical efficiency, meanwhile I thought 80% is a good bet. :thumbup: )

The "required output voltage" is the voltage to be applied to the 2kW element of the geyser, based on the available (converted) power, or: Power = Volt²/R, or Volt = sqrt(Power/R). (R= resistance of element)

The "approximation" represents how close we can get to representing the "required output voltage", while in the second graph we see how close we get to the "available power" using the "approximation".
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Cor
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Re: Turbine Input vs Output Power

Postby windgat on Sat Aug 01, 2009 5:07 pm

Ok... not sure I quite get the overall design you are looking at. And what happens in a 12 or 15m/s gust?
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Re: Turbine Input vs Output Power

Postby Greystoke on Sun Aug 02, 2009 6:49 am

OK, This is the general design. Not sure yet what to do with windgusts. Was thinking of using DC current to brake the turbine.


Series: 1X statorX18 coils + (2X18) 40X20X10 (N42)
Overall diameter 400
Pitch circle diam 260
Magnet length 40
Magnet width 20
Magnet depth 10
Magnets average fieldstrength ( 2-14mm) 3930
Nr of coils 18
Coil bunch Thickness (turns) 5
Coil height 50.0
Coil width 30.0
Coil Length (turns on 12mm) 12
Wiresize mm 1.00
Nr of turns per coil 60
wire length per coil (m) 8.40
Coil resistance [ohm] 0.1844
Max Coil amps @ ±1 kW input into a 2kW element 4.92
Total heat loss @ max amp [Watt] 80.3

Blade length [m] 1.35
windspeed [m/s] 8.5
Available mechanical Power (Watt) (80% of theoretical max) 895.39
Suggested Tip Speed Ratio (2 blades) 6
Estimated propellor rpm 361
magnet linear speed (m/s) 4.91
Output frequency (Hertz) 66
Estimated Total (Open) Peak Voltage (V) 166.9
Estimated Total Peak Voltage (V) into a 2kW element. 149.6
Required total Peak Voltage 169.6
Power into a 2kW element 777.30
Regards
Cor
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Re: Turbine Input vs Output Power

Postby windgat on Sun Aug 02, 2009 11:11 am

Ok, thanks. I was asking more about how this circuit fits in to the picture. And particularly what would happen in strong winds, when mechanical power will probably exceed electrical power?
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