solarnovice

An RCD (earth leakage) works on a difference in current. If 1A is going in on the live wire, 1A has to come back on the neutral wire. A small mismatch is allowed, usually around 15mA (your typical 30mA RCD starts to trip somewhere between 15mA an 20mA).
The trouble is that many RCDs don't distinguish between a transient leakage (small sharp spike in energy that dissipates in microseconds) and a real sustained leakage. And this causes nuisance tripping.
Furthermore, many appliances have a small leakage (by design), often because there are filtering components that pass a small amount of current to ground. For example, many computer power supplies have a small amount of leakage, which is why large amounts of computers on the same RCD can lead to nuisance tripping. Ask anyone who's run a university lab full of computers.
So the first thing to figure out is what kind of leakage you are dealing with, and the only way I have found to do that is a clamp meter around the conductors. It is possible that you have a standing leakage that is close to the tripping limit, and that other factors push you over at night.
Why only on inverter? Well, because inverters usually don't make a perfect sine wave. They get close, but there is a bit of harmonic distortion in it. Maybe this is acting up in some of the filters.
Here, for example, is the standing loss I had before I split things up a bit. Almost 7mA.