This could use a different thread.... see last sentences below.
Actually not. The currents in the manufactured leg *look* a lot different than those in the utility leg. Sorry if that's confusing.
If readers are confused by: "it's tough to measure currents in a rotary converter and make sense of them, unless you look at the power factor in them" then yes, it's a confusing
situation. How about if I sugar-coat it and say, 'there be dragons here' and that might not be so confusing?
This topic comes up again and again. Simple hand-waving apparently does not work. Sometimes ya just gotta whip it out. Complex plane, that is.
You did not read/comprehend, unfortunately.
What I WROTE was that the currents in the LOAD MOTOR are going to be similar on all legs IF the SOURCE is similar on all.
Point being that the better the idler motor simulates the power company (this is the part you missed), the more similar the current in the generated leg is to the current in the "pass thru" legs. The "balance" will be better.
The inverse of this (it IS a "linear" system so that's fair) is that if the currents are similar in all three legs, the RPC is balanced and effectively simulating the power company output.
The load motor will draw current in the same way on all legs if provided with a similar impedance source of the same voltage on all legs.
So, it is now up to you to justify the statement that the currents "look a lot different" on the manufactured leg. It appears that you are really criticizing the less effective converters, rather than establishing a principle that applies to all of them regardless. But it is not clear just what you are saying.
Perhaps you are referring to a slight phase difference on the manufactured leg. I say slight, because the voltage is the same back EMF on all, and it is substantially in-phase with the source. It is generated by the rotor field cutting the windings of all the phases. There may be a slight phase difference, but if the voltages were not substantially the same phase and close to the same voltage, then currents would be very high. They are not, so that condition is well satisfied (the inductive impedance of the motor is low, as is the resistance, most of the opposition to current comes from the back EMF). Your own often-posted scope traces support this.
There is a higher harmonic content in the back EMF, as shown by the slight flattening of the sine wave visible in your 'scope traces. That will slightly affect generated voltages, and thus current.
There is an effect of resistance in the generated leg, which is not present in the pass-thru legs. That would be phase-neutral, except that the load is inductive, so there is some effect, which changes with load. The larger the idler compared to the load, the less effect there will be, as your own large idler shows.
There is an effect of inductance as well, also not present in the pass-thru legs. That DOES tend to be phase-neutral if the load is inductive, and will change with load because the load motors change their characteristics as they are loaded, becoming more resistive. This is also reduced by a larger idler.
The usually used capacitors can counteract inductance, and somewhat eliminate these effects. Phase changes are dependent on the amount of capacitance added, and on the split of that capacitance between the two incoming (pass-thru) legs (which are 120 degrees ahead of, and behind, the generated leg, and so can provide currents at different phase angles).
Part of the "balancing" process is to adjust those factors of phase and voltage (which are related), so as to minimize bad effects, although an RPC does not need any balancing to actually operate, as your own simple converter shows.
So, please provide a more detailed impression of what you are talking about, and the mechanisms you feel are causing the effects you claim.
I suggest we have a different thread to do it in, and if you are interested enough to start one, I will move the somewhat off-original-topic discussions from this thread to that thread.
If not, then I think I will clean this thread up to just remove them.