Not a narrowboat owner myself but I've dealt with similar tripping issues on my motorhome when I upgraded my inverter, so hopefully some of this is useful.
First thing I'd check — what size fuse or breaker do you have between the battery bank and the inverter? A lot of people undersize this when fitting a new, larger inverter. Even if the inverter isn't pulling full load, the inrush current on startup can be massive and enough to trip a breaker that should theoretically be fine.
Also worth asking:
- What inverter did you fit? Pure sine or modified sine? Some motors and pumps on narrowboats react badly to modified sine and draw more current as a result.
- What's the cable run length and gauge? Long runs with undersized cable cause voltage drop, which makes the inverter work harder and draw more amps.
- Is your battery bank up to the job? If you're running AGM or older lead acid, they might not be delivering the peak current the inverter needs. What are you running — lithium?
On my motorhome I was running Fogstar lithium with a Victron MultiPlus and still had weird trips until I realised my BMS was set too conservatively for inverter loads. Might be worth checking your BMS settings if you've gone lithium.
What does the trip point appear to be — is it the breaker on the inverter itself, or upstream somewhere? That'll narrow it down quite a bit.