Normally when the super capacitor voltage is smaller than the load (battery voltage) no charge occurs, so its impossible to harvast low wind energy that would otherwise be available, until the alternator output > battery voltage. Once this condition is met normal charge occurs trough rectification.
To use the low voltage stored on a capacitor one needs a boost converter whose output directly supplies the battery. So its possible to have 15 or 20V stored on the capacitor charging a 48V battery at reduced power, for example. When the capacitor voltage reaches 12V the DC-DC is stopped until the capacitor is once again charged. This is because efficiency drops and we dont want to go all the way down to zero to let the alternator gain speed (Otherwise it would stall).
I use a similar aproach to charge my EV altough the reason is to both to have PFC correction and step mains voltage to 440VDC, however I have thought about using a similar method to use the exixting hardware to charge from a 48V-72V solar array.
To do this basically one needs a DC-DC boost converter operating in constant current mode. This is better handled by an external circuit, such as an UC3842 based boost converter. Here's an example available on eBay which I have personally used for LVDC (up to 60V).
150W DC-DC Boost converter
The exact requirements will depend on the alternator/load voltages and power levels (altough 150W is plenty for "low wind operation")
The arduino keeps log of the super capacitor voltage and once the set point is reached enables the boost converter. The voltage will drop and the circuit will be switched off. The exact time the circuit remains on depends essentially on the alternator output. Programming wise this makes things simple, so any arduino could be used. If you wish to perform the duty cycle generation for the boost converter directly on the arduino things get more complex. Again I recomend using a dedicated analog IC for such purpose.
A top thereshold voltage disables the DC-DC if the capacitor voltage goes up rather than down. This is to ensure charge occurs normally trough rectification if the wind suddently starts blowing.
An interesting point:
One doesnt necessarily need super capacitors for this purpose. Any normal capacitor will work will this aproach. One can have a 20ms on 10S off duty cycle for example, without loss of efficiency. As the alternator power increases, the duty cycle also increases.
It should be without saying that this is a not a beginner project. There's not a lot of programming but there's a lot of hardware mods required.