My model is clearly a rough one, and is not entirely accurate to the performance of the average induction generator. However, I believe that it captures the basic relationships between the variables involved in the operation of a generator, and that the work I have done has the potential to be useful, albeit after some refinement.
Over the course of my work, I have looked into several of models of standard wind turbines, and they have generally focused on the mechanics of the wind and its interaction with the blades, rather than the generator itself. While the mechanics of this interaction is obviously important to consider when designing a wind turbine, I have been surprised by how little attention is paid to the design of the generator. It might be said that this is because an induction generator is an induction generator, regardless of where it is, and we already know the most efficient designs. However, some wind turbine manufacturers are switching to a new gearless design where in place of a gearbox to magnify the rotation rate of the rotor, there is a much larger rotor that can hold more magnets and thus generate more power. Clearly there are still advances to be made in generator design for wind turbines, and modeling is a good way to explore these potentialities in a cost-effective manner.
If I were to continue my work, the first thing that I would do is construct a more complicated model that accounts for the electromagnetic torque exerted on the stator by the rotor (I believe this to be the largest flaw in my current model). I would also attempt to look at not just the generator, but the various conversion processes that the generated current must go through before being fed into the grid, as this could inform my design.
I agree with you when you say the work you’ve done can be useful. At first glance, your model shows it’s possible to improve the efficiency of your wind turbine generator by simply adding more wire loops to your stator. I too was surprised when I saw that your plot of frequency difference versus induced emf was linear. It would be interesting to see if including the electromagnetic torque in your model changes the way that plot looks.
When you talk about integrating the Fourier-Transformed triangle wave and Mathematica failing at the absolute value integral, you could try integrating the function over a single half-period and multiplying by the number of them on the graph to get the total absolute area.
Your derivation was clear and easy to follow, and your Fourier Transform idea was a simple, effective strategy for getting your linear function. It’s curious that the number of wire loops in your stator has the same effect as the difference in rotation frequencies between the stator and rotor. That provides a definite advantage to anyone trying to optimize a wind turbine.
In the end, I think you did a good job achieving your initial goal of creating a rough model of emf generated in a wind turbine. Nice work thinking outside the gearbox!