At a lower power level , I used a 12 to 300 V DC/DC converter and a commercial VFD controller supplied with 300 V DC instead of single phase 230 V AC. You may want to build your own VFD controller, but it doesn't pay for low quantities.
It's not particularly a problem to build a 1kW/12V input DC/DC with todays MOSFET transistors, but battery live will be rather short, of course. The power consumption is in the range of a car starter. I guess you have an idea how long it can be operated from a single car battery. Most people would use at least a 24V battery supply for a high power UPS or similar applications, simply for the more handy wire gauges and higher DC/DC efficiency.