How's this for a theory? Shoot it down in flames if you like...
The spinning magnetic field inside the motor (be it a spinning electromagnet in a brushed motor or a spinning solid-state magnet in a BLDCM) induces an alternating electric field into the metal body of the motor. The average potential of this field is zero, but the instantaneous potential could be quite high. The capacitors are there to leech this electric field away from the body before it can radiate out from the body, thus reducing the possibility of it interfering electromagnetically with the surrounding delicate electronics.
I'm understanding this question to mean that you're trying to run a three-phase motor off a single-phase line. If you're trying to run the motor directly off the AC line, the phase angles involved will make it difficult to get the motor started, which is part of the reason three-phase exists in the first place. Single-phase motors usually have motor start caps for just that reason. That sounds like what you're describing.
The simple answer to your question is that to get three-phase AC from single-phase AC, you need to rectify the single-phase AC line into DC, then run the DC back through an inverter to get controlled three-phase AC. There are other electronic approaches, but they're less common in my (limited) experience. There are also mechanical approaches, which may be more convenient if you have the parts.
I'd suggest using a drive to operate your three-phase motor. Typical variable-frequency three-phase drives are exactly what I described above: a rectifier, followed by an inverter. I can't speak as to what's on the market in a given power class, but larger three-phase drives typically have terminals for the three-phase AC line input, the DC bus, and the three-phase motor output. If you have those terminals, you have two options.
One is to run single-phase AC through the three-phase input of the drive. If the voltages are correct, the drive should operate fine. The caveat is that you'll have to derate the drive somewhat. The input diodes are spec'd assuming that the drive's constant-power load will be distributed among three legs of the rectifier. If you distribute that same load over just two legs, those diodes will get hotter. The internal bus capacitors will also get hotter, because they'll see more ripple current without the third phase. Check with the drive manufacturer for the derating info.
If your drive has DC bus terminals, your other option is to skip it's internal rectifier and use an external one. Rectify the single-phase AC, then use that DC as the input to the drive. This will let you avoid derating the drive. My company makes something exactly for that purpose, though its power range may be larger than is cost-effective for your application. You'd have to price both options out to find out for sure. Read this for more details.
![[2]](https://i.stack.imgur.com/DU7Eg.jpg)
Best Answer
Motor capacitors are not plain electrolytics, because the voltage across them reverses at the mains frequency.
The larger value ones are start capacitors - usually bipolar electrolytic, and rated to the peak mains voltage - but not for continuous operation. They are usually disconnected by a centrifugal switch in the motor, which operates when the motor is up to speed. Consider that not only is the voltage high, and continually reversing, but the ripple current is high too (especially when the motor is still at low speed) and you'll see the apacitor has to handle unusually high power.
Smaller value ones (10s of uF) are used as run capacitors in smaller (less than 1hp) motors. These phase shift the current to the start winding, but remain connected during operation, so must be rated for continuous operation. These are usually film capacitors (or, if old enough, paper in oil) which are much larger per microfarad than an electrolytic.