Hi Milo, 

I have been researching this topic for a long time, and am convinced it is possible to run a reverse cycle air conditioner from an invertor, however the roof top RV units are not very well suited as they are old style non inverter units.

The roof top RV units I am aware of control the temperature by running the compressor until the temperature drops, then stopping the compressor (fans keep running), then when the temperature rises again they repeat the cycle. The motors only run at one speed (controlled by mains frequency), and are typically hard to start. As an example the Air Command Ibis that I am optioning out of my caravan has a running current of 5.9A, and a quoted starting current of 20 amps. At this sort of drain it would need a huge inverter, and battery to run it.

I am going to run a Fujitsu Split system with inverter drive. What the inverter means here is that the incoming 240V power is rectified to DC, then inverted back to AC but at the frequency the motor needs to run at to maintain the required temperature. Yes it means the motor basically runs all the time but often at a very low speed, and with a very low current drain. It also means the motor can be started gradually, thus reducing the current required to start it. The unit I am going to run requires 2.8A running current, with a maximum current requirement of 6A.

I will be feeding my unit from a low frequency pure sine wave inverter. It is important that it is low frequency as they have a physical transformer, and can handle much higher overloads for longer periods, this means you can reduce the basic size of the inverter. I will be feeding my inverter with DC from a large lithium battery, which I will charge using a number of light weight solar panels glued to the roof.

I hope this vastly simplified explanation helps.