I'm not sure the anticorrleation has ever been proved. While it seems logical, the cloudy / stormy weather that sometime we experience in UK is too harsh for wind farms

Named storms often generate records for wind power generation. Even if a few turbines in the middle of the storm have to turn off, the rest of the country still gets lots more wind.

If you look at graphs of the wind and solar production in winter vs summer, the correlation is obvious. On a day-to-day basis, much less so, but on average low wind does tend to come along with higher sun.

It's complicated by the fact that the relationship between wind speed and power isn't linear - it's cubic - double wind speed - 8 times the power!

This only happens in the designed operating window ( too light you get nothing, too strong you need to shut down ).

So one question is what window have your tuned your farm for?

Air density matters as well - the denser the more power - ie the colder the more power.....

Isn't it the sun's energy that ultimately creates the wind - through differential heating?

So whether it's anti-correlated might a local feature depending on the local factors driving the weather?

Perhaps stronger correlation would be that air movement ( wind ) is the thing that drives the weather changing. ie no wind, means slow change ( though the opposite isn't necessarily true - if you are in the centre of a cyclic weather system which isn't moving you could have wind and not much change ).