Assumptions...
Your spreadsheet shows current based on the unloaded voltage, however once the current applies a load, the voltage across the output of the alternator will drop. The Aurora will actively, or with a look-up table, find the optimum load to apply so that the voltage doesn't fall too much, seeking the maximum power point.
That is correct.
My spreadsheet is a simple first-order approximation that bases current on unloaded voltage and power extracted from the rotor (the inverter needs to load the rotor in such a way that it match the power extracted from the wind, so the rotor doesn't speed up nor slow down). That breaks down for higher phase resistance values. To do it right means taking the whole circuit into account and solving the equations for all parts concurrently. Maybe I'll do that if I have some spare time on my hands. For the most part the simple approach is good enough.
The usual for these spreadsheets is that they get made spur-of-the-moment when they are needed, and there is no time for refinement...
You cannot calculate the maximum power point without knowing what the slope of the torque versus rpm graph looks like, how much it differs between various blade profiles i have no idea.
Actually it turns out that by far the best predictor of power from a rotor vs. wind speed is simply by using the equations for kinetic energy in the wind and a fixed, reasonable, efficiency. A really good blade profile may do a few percent more, a bad one a few percent less, overall the effect of blade profile seems to be quite limited (especially when compared to the other approximations). This assumes 'normal' blade profiles that are common for wind turbines; they tend to have a wide 'optimal TSR' area. In practice you don't want a blade that has to be run 'just right' to work, since any wear, insects, dirt, or ice will make the output drop like a brick.
The optimal TSR is determined by the angle-of-attack that the blades are fixed at to the hub, and the blades optimal angle for lift-to-drag or Cp (not quite true but close enough). So this is a design parameter, different for different turbines even if they run the same blade profiles.
The Aurora probably interpolates between the points in the table you give it (Yes Rob's input is necessary here).
Correct. You have 16 points for the table, it interpolates between (probably just first-order interpolation, but I don't know that for sure). I've written a note about MPPT for wind turbines, how inverters do this, and why it works.
You can read it here (scroll down a bit). Hopefully that will help explain the concept.
unless the resistance of the alternator is negative, then you will always operate above optimal tsr to reach the maximum power point.
write that down a few times if you have to.
Correct. But if this starts to make a large difference in voltage you're really pushing that alternator (and generating lots of heat!), probably more than you should. At that point the solution could be to increase the TSR (for the higher power levels), so the alternator puts out a higher voltage, the current goes down, and losses too. Even if that is above optimal TSR; the high end of the TSR vs. efficiency curve is even more flat than the low end, and at that point you got plenty of wind anyway (if obtaining maximum power output is your goal).
Truth is that a 'theoretical' MPPT curve will only get you so far no matter what. Still, it has value, and more than likely will get you in the ballpark (the many commercial turbines that I've made MPPT curves for seem to run just fine on them, despite the approximations). If you want to get to the real MPPT curve for your turbine you need an anemometer at hub height. Start with the best-guess MPPT curve, run it, log wind speed vs. power output (ie. make a power curve for the turbine). Then increase all the output values of the MPPT curve by 15% and repeat. Do the same a few times for higher and lower power values vs. voltage, and you will get a set of power curves that show where best output power vs. wind speed is headed. The anemometer doesn't even have to be calibrated, as long as the wind speed measurements are repeatable.
Menelaos, what are the parameters for your turbine? I'll run 'm in my spreadsheet and tell you what I get.
-RoB-
