Wind turbines generate electricity which has to be used immediately or converted to some other form of energy to be stored, most usually as chemical energy in a battery. On a large scale there are options to convert the electricity back into some form of potential energy, such as pumping water into a high level reservoir or compressing air in a vessel, which can then be released later through another generator system to make electricity once more. Pumped storage hydro electricity and mine compressed air storage are both used by electricity supply companies to balance differences between supply and demand. But the additional cost and complexity of such systems is unlikely to make them any cheaper than batteries at the small scale. Also you are converting energy three times in total with system losses at each stage so this is not an efficient means of storage.
Converting electricity to hydrogen for storage and then back to electricity in a fuel cell has great potential, but at the present the technologies are still in development and expensive so are not widely used. Also hydrogen is an explosive gas and so is probably not suitable for a small energy storage system.
Most generators ship their surplus energy to the grid when their demand is low and then buy back electricity when the wind fails. Over the course of a year you then generate as much electricity as you use, but at any one time you might be shipping electricity to someone else or buying it back from them.

Pumped water storage is one way. Batteries are definitely another.
Here’s a suggestion for a third alternative, though I haven’t seen this one used for an application like storing wind turbine power yet. I suspect friction losses, etc. probably upset the energy equation so that pumped water or batteries are going to prove more economical, but here goes…
It would be possible to use a flywheel storage generator set such as those that are becoming more common battery alternatives in data center UPS applications. Excess energy from the windmill would drive a motor that would spin flywheels to full velocity, converting electricity to kinetic energy. When the wind doesn’t blow, the flywheels would spin generators to convert their kinetic energy back into electricity.
Most of these systems are smaller in size and are designed only to carry an electrical load for a few minutes during an outage while backup motor generators or turbines are being brought online. I suspect your wind power application needs runtimes measured in hours or days, and I’m not sure the technology exists to run that long.

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