Supercapacitor for Wind Energy
Comparing super-capacitors and batteries ...

Batteries store much more energy per size/cost/weight than capacitors.

Batteries will handle peaks and dips from 10 minutes to hours, typically.

Capacitors will handle peaks and dips from seconds to minutes, typically.

Capacitors have a larger terminal voltage swing than batteries during the charge discharge cycle, so need wider range converters to best make use of their storage capacity. You generally can't just 'drop them in' to some suitable point on a wind turbine schematic.

Both batteries and supercaps die if overcharged, you need a proper charge controller for either.