Generated voltage is internal to the alternator. It is proportional to RPM.
The voltage you see at the output terminals of the alternator is the generated voltage minus the resistive voltage drop - which is current times series resistance.
The current produces a magnetic field in the coils that causes a drag between the rotor and the stator. This drag is directly proportional to the current.
If the alternator is hooked to a resistive load the current (and its resulting drag) will go up in proportion to the generated voltage (and the RPM). The voltage at the output terminals is a fixed fraction of the generated voltage. Everything rises in step. Power delivered is current times voltage (and power pulled from the wind is drag time RPM). These go up with the square of the RPM.
However if the alternator is hooked to a battery-charging load something very different happens.
First, up to the "cutin" RPM the generated voltage is below the battery voltage (plus the diode drops). No current flows, there's no drag on the turbine shaft (except for things like bearing friction), and the voltage at the alternator terminals is the open circuit voltage. The mill starts easily and spins up with the wind speed.
But once you reach cutin the current starts flowing. The battery is a pretty good approximation of a fixed voltage. So the voltage driving the current is the EXCESS of the generated voltage over the battery voltage (plus the diode drops, which are also approximately a constant), and the resistance this is driving current through is not the load resistance, but just the resistance of the coils and transmission lines. So current climbs very steeply with the EXCESS of the RPM above the cutin RPM. And so does drag.
Power is still current times voltage. But the power delivered to the battery is the current times the BATTERY voltage, while the power dissipated in the wiring is the current times the DIFFERENCE voltage (generated - (battery plus diodes)). You see the battery+diode voltage at the rectifier input, that plus the transmission line's portion of the voltage drop at the alternator terminals. But most of your resistive drop is proabably inside the coils (unless you used really wimpy transmission wiring).
Just as the current climbs steeply with above-cutin RPM, so does the drag. And that means so does the "slip" of the turbine versus the wind. If the alternator, transmission wiring, battery internal resistance, etc. were all superconductors, the RPM would track the wind speed up to the cutin RPM, then never exceed that RPM no matter how hard the wind blows. Because there's nontrivial resistance the RPM continues to rise, but more slowly, once the RPM is above cutin. You get a straight line with a kink in it: Rising steeply with windspeed up to cutin, rising more slowly afterward.
Now the amount of power available from the wind goes up with the CUBE of the wind speed. (Energy in a particular mass of air goes up with the square of the speed, but the amount of mass goes up with the speed as well. m * v^2 * v = m v^3) To extract that power optimally you'd want to keep the angle-of-attack of the blades constant. So the RPM (and generated voltage) would go up with the wind speed and the drag (and current drawn) with its square. Resistive loads have the current going with the first power of RPM leading to collected power going with the square - a not-too-bad approximation for a while, until the cube function gets away from it at higher RPMs - by which time you probably want to furl anyhow. For battery-charging loads the kink of the line goes the right way, but it's a single segment linear approximation.
In both cases the failure to track the available power means the angle-of-attack of the blade versus the apparent wind - and thus the efficiency of the blades - changes with RPM. In the case of the resistive load the current, and the drag, rises too slowly. But that lets the RPM climb more rapidly than the wind speed, giving a bit of compensation. (It also puts a stronger load on the turbine relative to the available torque at startup than during normal operation and a weaker one at high wind speeds, leading to both starting difficulties and runaways if furling is absent.)
In the battery-charging case startup is easy because there's no load up to cutin. But then the load starts rising steeply. You want to "match" the load to the blades so the slope is about tangent to the ideal cube function in the common operating region. Get it too high and you'll stall the blades at low wind speeds. The airflow detaches, you lose torque, and you never get up to proper RPM at the typical operating range wind speeds. Too low and you don't get the current you could have gotten. Within the "ok" range you can balance it to get that stall when the wind speed gets excessive (though this means you're not getting all the power you could have below stall). But that's a critical tuning to hit. Easier to tune it to pull the best power during operation at the cost of being subject to runaway at high winds, then prevent runaway with a separate furling mechanism.
Now "maximum power point tracking", as stated above, would have the voltage go up with the wind speed, the current with its square. But coil heating goes up with the square of the current, so it would go up with the FOURTH POWER of the wind speed (mitigated somewhat by the increased cooling with the first power of the wind speed and the first power of the temperature difference). This makes it critical to limit the current when you're approaching the burnout threshold of the alternator.
