Generator Design
The approach I've been taking in designing generators is to try and match the generator power curve to the peak power of wind turbine. Sometimes, one has the generator and has to match the turbine to it; that is just the opposite of what is done here. The first step is to estimate the shape of the turbine peak power curve. In this example, I've modeled the power curve for a 0.50 m diameter, 0.40 m^2 drag type turbine where the maximum power occurs at a tip speed ratio (TSR) of 0.6 and the turbine speed tops out at a TSR of 1.2. The orange curve passes through the peaks. The peak power curve is a cubic function while the generator power curve is quadratic. The characteristics of the generator cannot exactly match those of the wind turbine, but they will be designed to mimic this curve near the target range of wind speeds as discussed elsewhere.
| dragtypeturbinepowercurves.xlsx |
Generator Characteristics
In the example uses in the discussion on power availability, it was decided that the target wind speeds would be between 3 m/s and 8 m/s. The peak of that target range occurred at 5.2 m/s. Continuing with that example, generator characteristics (speed at which it starts to charge the battery etc.) were chosen such that the generator curve is tangent to the wind turbine peak power curve at 5.2 m/s.
| generatorcharacteristics.xlsx |
The equation for generator power works out to be the following in this example (N is the turbine speed in RPM).
I have two concerns about using this approach. The first is that the generator will end up with a fairly high resistance and that will adversely affect the power delivered to the battery. The second is that the generator does not do a good job of limiting the speed of the turbine. A steeper generator curve would result in a narrower range of turbine speeds. I would like to simulate power production using these generator characteristics. Then repeat those simulations for a generator with a lower resistance and see if power to the battery is increased. That process can be repeated until an optimum is found. I suspect that the optimum generator will also take care of limiting the turbine speed.
Generator Optimization
Here is a different approach to selecting the generator characteristics. The power delivered to the battery was calculated for wind speeds in the targeted range. Then the delivered power was multiplied by the typical amount of time at that speed to get energy. The energy was multiplied by the weighting function as before. The result was totalled over all the windspeeds to get a "Figure of Merit" that would be used for optimization. The process was a bit convoluted, but I think it worked okay.
Continuing with the example turbine (4.5 m/s average windspeed, 0.4 m^2, 0.5 m dia.) The results of the optimization can be seen in the figure above. It appears that lowering the stator resistance is always a good thing. But given a stator resistance, there is an optimum K factor for the generator (K is how much voltage the generator produces per RPM). I chose a stator resistance of 16 ohms for this example and a K factor of 0.18. The following figure shows how the generator power curve compares with the turbine power curve. The "P Delivered" is how much power is delivered to the battery. To determine how much power is delivered for a given wind speed, find the intersection of the "P Consumed" curve and the power curve for the given wind speed; that will give the operating RPM. Then go straight down from there to the "P Delivered" curve and read the value to the left. For instance, the turbine should spin at about 146 RPM when the wind is 7.0 m/s. The generator should deliver just over 10 Watts at that speed.
Continuing with the example turbine (4.5 m/s average windspeed, 0.4 m^2, 0.5 m dia.) The results of the optimization can be seen in the figure above. It appears that lowering the stator resistance is always a good thing. But given a stator resistance, there is an optimum K factor for the generator (K is how much voltage the generator produces per RPM). I chose a stator resistance of 16 ohms for this example and a K factor of 0.18. The following figure shows how the generator power curve compares with the turbine power curve. The "P Delivered" is how much power is delivered to the battery. To determine how much power is delivered for a given wind speed, find the intersection of the "P Consumed" curve and the power curve for the given wind speed; that will give the operating RPM. Then go straight down from there to the "P Delivered" curve and read the value to the left. For instance, the turbine should spin at about 146 RPM when the wind is 7.0 m/s. The generator should deliver just over 10 Watts at that speed.
The following excel file is quite crude. I've just included it here for the curious.
| genoptimizer.xlsx |
Comparison with tangent approach
The earlier approach to generator optimization where the generator curve was made tangent to the peaks of the turbine power curves results in a K factor of 0.235 and a stator resistance of 44.3 Ohms. Using the method above, this design results in a FOM of 625 compared to the FOM of 822 for a K factor of 0.18 and a resistance of 16 Ohms. So it appears that the tangent method does not produce the best results.
After looking at the results of some optimizations, it would appear that one could do quite well by simply choosing the lowest resistance that one thinks they could attain economically and then designing the generator curve to pass through the peak of turbine curve at the average windspeed.
The next step is to choose generator design parameters such as number of magnets, magnet dimensions, number of turns of wire etc. to cause the generator to function as desired in the most economical way.
The next step is to choose generator design parameters such as number of magnets, magnet dimensions, number of turns of wire etc. to cause the generator to function as desired in the most economical way.
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