I am reluctant to get into this as there are traps and pitfalls all the way.
Things are different in Europe compared with N America because the supply systems are different and if you want to comply with the countries laws and regulations it becomes a minefield.
It helps if you understand what happens in the inverter and what happens to the grid supply. Few seem to understand either but you should be able to understand your grid supply. Whether you can deduce what happens in a cheap inverter is another issue.
In Europe one side of the supply is grounded ( neutral ) for single phase and it is nominal 230v. Simple and no problem if you understand the inverter.
In N. America you have a 220v supply with centre tap grounded. You have no problem with 110v inverters ( similar to Europe). With 220v single phase you have a real problem as the cheap inverters are not designed to have any form of ground at half supply volts and grounding them on the American system usually destroys them.
Forgetting the regulations, they are isolated via the transformer and will work perfectly well as long as you don't ground them. There is little danger as it is a fully isolated system but I wouldn't want to argue that with the rule makers.
On the European system it is perfectly possible to ground one side of the inverter output if you want to but it may not be possible to do it if there is a ground on the dc supply side ( you need to know what is in the inverter). In nearly all cases the metalwork of the inverter can be grounded and should be so.
I generally ground the dc supply negative and the inverter case. I am happy to let the supply float. You have to watch it if the neutral ground is already present from grid wiring unless you know the inverter will take battery negative ans one mains out commoned.
As boB said there can be issues with filter circuits and where they are grounded and you will probably never know what the manufacturer has done. I have never been able to get even a basic block diagram let alone a proper circuit diagram for a cheap inverter. The present world seems happy to live in ignorance and just use things rather than understand anything.
Perhaps the modern world is to complex to understand everything and we have to accept it, but in a time of increasing regulation ans safety consciousness the idea seems self defeating.
For systems not connected to the grid in any way then I would ground battery negative and inverter case and leave it at that. If you can change over from the grid and isolate completely you can still do this but if you just break into circuits wired for grid connection with just a change over switch then you need top grade inverters designed for this in mind or you will have fun and probably smoke.
That is my opinion, now forget all I said, don't act on it or say that I said it and all will be ok. I doubt any of this would satisfy an inspector.
Flux
