Technology

Small wind turbines are really, really poor. You need to go high to access the good air-streams and wide to get useful efficiency out of the turbine. Any wind turbine you put on your roof will vastly under-perform for the cost spent on it.

they generate about 3,800kWh per year. We also use about 3,800kWh of electricity each year.

Holy shit. I think we used that much last month, which is higher than average but not that high for August around here.

Seems to me his panel capacity is to small anyway.
We have 11 kWh panels, and yes in the summer we routinely produce 4 times more than we use, and we have a 7.5 kWh battery But November December and January it's not even close to enough.

In the Winter you can easily have a week with near zero production:
Our Import / export from grid last year:
November 215 / 59 kWh
December 300 15 kWh
January 268 / 34 kWh

Despite we have almost 3 times the capacity, and produce more than twice what we use per year, and we have a decent battery and believe it or not, even the shortest day we can produce enough power for a whole 24 hour day if it's a clear day! But we can also have clouds for 14 days!
But for those months we imported 783 kWh and exported 108 that could have been used with bigger battery. But the net import was still 675 kWh!! For those 3 months, and that's the minimum size battery we could have managed with, and then we even need 10% extra to compensate for charge/discharge losses.

TLDR:
Minimum 740 kWh battery in our case, and that's without heating, because we use wood pellets.

That means it would require at least the equivalent of 10 high end fully electric car batteries. But also a very hefty inverter, which AFAIK ads about 50% the price of the battery.

PS: Already in February we exported more than we imported.

I recently got a solar system and came to the conclusion that if you can sell power back to the grid (not everyone can) for some reasonable percentage of what it costs to buy it, then it will always be worth it to be connected (assuming you already are).

Quite simply, if you have enough solar capacity to get you through the winter (no house is going to have months of battery storage), then you will always be creating far more than you need in the summer. Selling this excess will easily cover any costs associated to being on the grid.

Also at current prices batteries are good for backup power only, it's always cheaper to sell excess power to the grid in the day and buy it back at night than it is to have battery capacity to get through the night. I worked out it would take 40 years for our battery to pay for itself (assuming the battery kept a constant battery capacity for 40 years...) but less than 10 years for the rest of the system to pay for itself.