I’ve been reading up on these and I wondered if anyone here has had experience with ones big enough to power a generator, or are they just not powerful enough.

When you say generator, how large are you referring to?

The Stirling engine is large and heavy for its equivalent output compared to an IC engine. And while about 8 percent more efficient than the IC engine, it's power is only developed at HIGH speed. In generator applications (low speed applications), it would require a speed reducer between the power plant and the generator.

Being an external combustion engine, cooling needs to be many times larger than a comparable IC engine. In stationary application, such as large generators; the size of the cooling system, needed speed reducer, and the extra size and weight of the engine may not be direct disadvantages. However, the increase in costs to build bigger must be weighed against the savings in operating costs. In portable or mobile applications, the disadvantages out weigh any increase in efficiency the engine may provide.

In a side note, the Swiss have experimented and developed a Stirling/air-independent propulsion powerplant for use in submarines. But for direct propulsion the Stirling is only capable of moving the vessel at a quarter the speed developed when using battery power. The Stirling AIP powerplant advantage (using liquid O2) is its ability for the sub to remain submerged for weeks rather than days before having to resurface to recharge batteries.