How about small enough to never possibly provide more power than the load on the grid?
I don't think any inverter could support the load on the grid. Even in little UK, the generation capacity into the grid is over 50,000 MW.
And if the load was less than the generating capacity? Aye, there's the rub. I'm sure you had some sort of protection to prevent the inverter from putting out it's full capacity when that capacity had nowhere to go.
It isn't really a rub. The generating system doesn't have to put out its full capacity.
For the alternators there were AVRs that alter the excitation so their 6MW capacity didn't have to be fully utilised. This usually how these things, the alternators, even at utility level work. Their output has to match demand even if their capacity exceeds that demand.
Similarly with the inverter powered from from the water turbine. The turbine has a governor to regulate speed and thus the generator output. In this particular case the governor is mechanical, remember that it is very old, and it closes turbine inlet vanes. The excess water tumbles over the weir. Pretty to watch.
And the grid supplied what was required of it.
Now with your mill maybe it typically had a constant large load so this would rarely be a problem.
It wasn't.
But a couple of points.
That paper mill, like many others, routinely had what they call a summer shut. All the production machinery is shut down for annual maintenance. There used to be a joke, a wry view maybe, that we shut for a couple of weeks to fix everything then spend the next two months sorting out the new problems....
Levity aside, the required power was vastly reduced. Process steam wasn't required. The water turbine carried on as usual, still grid connected.
But with a typical residence with a net-metered solar system the load will almost always be lower than the solar system capacity.
You don't have to run the solar system at rated capacity.