Windmills are supported by steel cylinder towers which are very sturdy already, why not close them shut and use them as giant canisters to hold compressed air?
The pressurized air can run a pneumatic motor housed in the nacelle and attached directly to the generator or gearbox. Reusing these components keeps initial and maintenance costs down. No additional land or infrastructure is needed.
This approach would help flatten the output curve: when wind blows strong part of the kinetic energy could be used to fill the tank, when it dies down the motion of the turbine can be assisted by the pneumatic motor (both driving the generator together).
More constant output would help wind better compete with traditional on-demand energy sources. It also would make more efficient use of transmission infrastructure. In the end, it would reduce the price per kwh.
UPDATE 1
I found the white paper below which indicates some trials are being done in this area, but apparently only storing the air either underground or in special vessels rather than in the tower. Also, they use a turbine instead of a pneumatic motor so the air needs to be heated, usually by burning natural gas.
I like the idea of using compressed air since it's not flamable, it's readily available all around the turbines, can be discharged into the atmosphere for maintenance without damage to the environment, and it does not damage the internal parts of the assembly.
What about using the energy to also heat up the air so that you can get more output out of the compressed air whenever needed?
What about using the energy to also heat up the air so that you can get more output out of the compressed air whenever needed?