I LIKE your style.
You took what was stated to you, and repeated it back clearer than it was said to you.
Have you studied Stephen Covey?
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Let me add another detail to this -- it is called "slip."
The nominal RPMs you listing -- 1800 for a 4 pole motor -- are not what actually come out of the shaft.
(and let me add for other readers, 3600 rpm for a 2 pole, and 1200 for a 6 pole motor)
The real RPMs under load are closer to 1725 (or so).
The difference is the lag. In that lag field is where power transfer from the electrical and magnetic energy are transferred to the mechanical domain.
Maybe think of this like wind on sailboat that is just running with the wind, with the big spinnaker parachute sail up. It does not go quite as fast as the wind, but it is dragged along by the wind. That is what the electromagnetic field does to the shaft. It drags it along, but there is some slip.
Now when it comes to our area of interest, we are going to push it faster. As we go faster than the field the power is pushed and dragged by us. So ideally we should be able to speed up the rpm of the motor by the difference of full load slip added to the nominal no-load speed and it should produce the same of amount of current being pumped back up the system as the motor would consume at full load.
So putting that into our sample model of an 1800 rpm motor, which has a full rpm of 1725 (means slip = 75 rpm) -- gives if we are connected to the grid to energize the field and we turn it at 1800 + 75 rpm, we should be pushing the full load current up the grid.
The overall system voltage stays about the same, the frequency stays the same, it is just we are a "source" of current rather than a "sink" or consumer
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Let me re-state, that I have never personally done this in the real world.
But that is my understanding (and I am not particularly a stooge in this field ) and it seems reasonable.
A couple of cautions are that the motor was not designed or built to be such a generator (which does not mean it will not do it just fine), and many motors are not built to do their job continuously, and/or at full load. So doing this may violate warranties, and UL listings -- as well as possibly toast some things while we sort it all out.
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About your application -- 20 hp systems are big enough to real exciting (in a not so good way) if something does not work well, as well the components tending to be expensive.
My end goal is to run a few parallel 10hp units at about 70% of capacity.
I would propose we try this with some 1 to 5 hp sized equipment to get started and see how that does before we blow-up some big stuff.
I have some of that type stuff, along with pulleys, belts, relays, motor starters, breakers, mounting frames, and I think about everything we will need for some low power tests.