Why do you think there is a 40% loss?
Probably because the inverter uses up energy to turn DC to AC. Those watts (assuming it was properly measuring watts) have to end up as heat. At the low end I could believe it. Just think it's got to run the fan, that's a "loss". On say a 2kW inverter though, I'd be concerned if it was losing 400W when feeding a 600W load. It would be getting bloody hot...
something I'm still not quite clear about:
if a load has a 0.5 PF and V=230V, P=230W then I=2A
If I had an inverter with a 230V DC battery, what would the current drawn from the battery be?
So the DC end would be 1A with perfect efficiency. Or at a more reasonable 90% efficiency would be 1.11A
Power factor is not efficiency. (The volts and amps are not energy... They match it when PF is 1. See linked article below)
Those V are different. One is "230V AC"... I.e. a wave going from 315 to 0 then to -315. Work is done along that wave form depending on how the device pulls the energy -- e.g. a heating element, all the time -- a switch mode PSU in microsecond pulses.
For the the heating element the power factor is 1. I.e. it takes the energy all along the wave form; for the switch mode psu which is snipping but of energy here and there, it can be 0.3 or 0.1... but that doesn't mean you don't need the amps, and it doesn't mean you use more watts.
Why inverters make this much complicated is when they aren't pure sine waves. So most stuff is built to not be too bad power factor with a sine wave -- is going to be all over the place with a square wave.
(Not for efficiency but for not needing too many amps to do the same work)
Btw this is advanced electrical stuff guys, so don't expect it to be simple. It's literally about sine waves (so trigonometry) and work done by electricity etc. You need to use complex maths (using sqrt of minus 1) to do calculations with it.
This is a better explanation than what I can give.
Answer to What's the physical meaning of reactive power? by William Beaty
https://www.quora.com/Whats-the-phy...id=22200627&share=7c4299db&target_type=answer