This really is pretty basic stuff and should be obvious
And also is wrong
Once steady state is achieved (the condition in which the inverter unit winds down), the air conditioning unit output, averaged over time, equals the heat loss (or gain, if we are in the summer) through the room walls. This heat loss depends linearly and exclusively on the temperature difference between the room (chosen by the user) and outside (determined by the weather), and insulation resistance of the room walls
The air conditioning unit has no effect on the heat loss. In case of an on/off switching unit, the hysteresis beween the on and off temperatures is way less than the temperature difference between indoors and outdoors, so in average it still has no effect on the heat loss
The air conditioning unit then must pump the same quantity of heat/time unit in or out to maintain the temperature difference constant. Heat is energy, heat per time unit is power
Consider 2 compressors with identical COP but different power. One is of the exact power required to counter the heat loss, and the other is 2x the power. The 1x one will work continuously, the 2x one will work with 50% duty cycle. Twice the power for half the time is the exact same energy
So no, thermodynamics absolutely don't confirm this basic stuff
Now let's look at the electrics :
The on/off unit has a simple induction motor. There is no principal limit on the efficiency of such motor. Having to work only in a single set of conditions (same power, same refrigerant pressures, ...) it seems obvious to optimize this motor for working at this exact set of conditions
Limiting the efficiency of such motor is only cost - If using a bigger motor with room for thicker winding, Using lowloss steel in the laminations, etc. The motor can be made to any desired efficiency
The inverter unit has a similar induction motor. It is basically a plain 3 phase motor, though most of them are not for 50/60 Hz but for somewhat higher frequency
Higher frequency allows for smaller cores and less turns in each winding (which means thicker wire can be used in the same motor size), same as in lighting ballasts. However, there are few parts that can pull efficiency down as well :
- The stator is still made of laminations, which dont behave well above few 100s Hz. (Eddy currents, hysteresis losses, increasing loss in general)
- The motor must work efficiently in a broad range of speeds and pressures. Is it optimised for the exact ones at which it'll run in your case ?
- The inverter itself also got losses
Considering that 50/60Hz induction motor efficiency is typically 85%..90%, this gives the theoretical upper limit of energy you might save if the inveter and inverter powered motor would be 100% efficient
In reality, the motor is probably closer to the same 85..90% as the other motor, and the inverter has a few % left behind as well
And at the mechanics :
Running at higher speed (due to higher RPM motor) allows pumping the gas faster, or at the original speed but with smaller pistons
Smaller pistons and all the other mechanical bits have less friction surface, however they work faster for the same output, so the friction loss happens more times
Similar considerations would apply to other compressor types as well (Scroll, vane, etc)
I am not sure how the less surface vs. faster running exactly balance vs each other
Same as with the electrics, the mechanics are the same in principle and only differ in size. Both have losses of the same order of magnitude
At this point, it is no longer about any significant energy savings, but other things :
- Cost cutting. We have reached the point where a complete inverter circuit cost is cancelled out by the savings on smaller and cheaper motor and mechanics which have to work faster. (And question remains whether the mechanics will last as long as the bigger slower running ones)
- Blatant shoving of advanced technology everywhere it is not needed