My understanding of static inverters is that they work fine for loads within their rated range, but are not happy with loads that are too small. A 5.5KW inverter is pretty big and will probably have a correspondingly bigger minimum load. Generally I believe that they are happy with running multiple motors BUT the total load must be within the rated range. So, a big lathe might use one for the main drive motor and would be happy with lube/coolant pumps running at the same time but would probably not start aforesaid lube/coolant pumps without the main motor running.

I would have a look at the Transwave site to see if they give specs there for the permitted range of loads, including minimum load.