I have a small, hobby machine shop with a bunch of woodworking and metalworking equipment. Some of it runs on 120v AC, some on 240v AC, and some on 240v 3-phase AC. On the border of my farm runs a high voltage 3-phase distribution line, so it looks like it would be easy for me to get 3-phase to the building, but I was quoted about $12,000 to install a couple of poles, a transformer, and connect to my barn. So I started thinking about rotary 3-phase convertors. My brother Joe got me a great deal on a big, 25 hp, 20 kVA 3-phase motor. And I started reading about convertor circuits.

Here's the best example I found from a great online forum 10hp_rotary_phase_convertor.pdf
I ended up with this circuit.

Circuit description

The 25hp idler motor (which incidentally is waaaay oversized for my application) is driven by single phase 240v connected directly to two legs of the motor. Then there are 4 capacitors: Run capacitors Cp and Cs, Start capacitor Cstart, and Power Factor correction capacitor Cpf. Cstart is connected only momentarily to start the 3-phase idler motor turning. If you turn it on without pushing the start button, it just humms for about 3 seconds before blowing the 50amp breaker. And, if you leave Cstart connected for more than about half a second, the lights go down in the shop ;-). So the starting process is close the start switch, then one-two, close the main switch and open the start switch. The big Cstart drives motor leg C with current that leads the L1 voltage by 90°. The spinning motor then generates voltage at terminal C. But this voltage is a little weak, so we add Cp and Cs to help it be stronger. There's a bit of an art to tuning these capacitor values. It goes like this, all while the motor is idling with no loads connected:
  1. Measure Vab to get your nominal RMS AC voltage, say it's 240v.
  2. Measure Vac and you'll find it is a bit low, like 210v. So add capacitance to Cp until Vac comes up to about 8% larger than Vab or about 260v.
  3. Now measure Vbc and add capacitance to Cs until Vbc comes up to about 3% over Vab or 247v.
There, you are done with the big run capacitors. Last step is to add capacitance to Cpf to minimize the input current measured at L1 or L2. This power factor correction capacitor compensates for the inductive load of a motor and keeps things a bit cooler.

Circuit performance

So what does the output look like?

I measured the RMS volts at T1, T2, and T3 relative to ground with a Fluke multimeter. It doesn't look like 3-phase 240v does it? I see 118.8, 117.5, and 212.6 volts. The two 118 volt legs make sense. They are the input phases L1 and L2 and between them is 240v. And L3 is close to 240 volts, but that's not what I expected. I thought I'd see something that looks like 3 equal phases, each something like cos(60°) * 240 or 208v from ground. But a circuit like this cannot do that. A and B are connected directly to L1 and L2. They can't suddenly be a lower voltage or a different phase. Not unless the supply leeds from the power company are very long and have significant inductance. And in this case they don't. The power company supply is "very stiff". But when I measure the phase-to-phase voltages on the 3-phase outputs T1-T2, T1-T3, and T2-T3, the voltages are well behaved, all near 240v. I got 237, 245, and 242 volts. All good, right? No, the problem is this is not 120° 3-phase 208. It's 90° 3-phase 240. Fine, 3-phase motors are happy enough with this that all the machines run just fine. My 3 hp Accra knee mill is fine, my 5 hp Grob bandsaw is fine, my 1 hp Boyer Schultz surface grinder is fine, my 1 hp Baldor pedastal grinder is fine, and my 7.5 hp monster dual 30" disc sander is fine (acutally I haven't powered that last one up yet, but I'm sure it will OK too). Here's a little experiment I ran while watching the phase-to-ground voltages with an oscilloscope. You clearly see the 90° relationship while the system is powered up, but the moment I open the input switch, the phases snap to 120° as the three motors coast down.

Three phase motors are wound with equally spaced windings that work best with 120° separated power phases. When they are supplied with 90° phases, the motor pole pieces don't line up right and the motor performance is slightly degraded. What this means in practice is that if I was doing a maximum-performance cut for an extended period of time, the motor would overheat. Or more practically, the motors will all run a bit warmer than they would if I had perfect, utility-supplied, 3-phase power. For these machines, I'll never notice the difference. There's another consideration, and that is mixed phase equipment. For example, the Boyer-Schultz surface grinder has a magnetic chuck which runs off a nominal 120v AC supply. It is wired to use one of the 3-phase input phases to power the chuck and returns that current to ground. If I connect the chuck supply to L1 or L2 (A or B) but not C it will work perfectly. But if I were to use C, it would be getting 212 volts. Not a nice thing to do to a 120 volt device. So watch out when connecting things like 120v work lights, or DRO, or the X-axis power-feed on the mill.

Tweaking performance

This is bugging me, so I got to thinking... you know how that goes.... How can I get the input phases to not be separated by 180°? If the power lines had some inductance, the voltage could be pulled off of 180° What if I add some inductance, or better yet the right ratio of inductance and capacitance to pull the phase back 60°? Then maybe the motor would start easily, maybe even without a start capacitor bank and a start switch. And the three phases would be much closer to 120° separated. I've forgotten most of the EE math I did freshman or sophomore year about 40 years ago. You know, that Laplace trasnform stuff with the s-variable and reactive impedances like s×C. But I do know how to write differential equations and solve them with numerical integration.

Doing it right with a VFD

So I searched for a while for a big transformer core that I could re-wind into an inductor sufficient to fix the rotary phase convertor. And while I was on eBay, I found this

7.5KW 10HP 220V Variable Frequency Drive Inverter CNC VFD VSD Single To 3 Phase
for $167.90 including shipping

It cost about the same as the set of large run capacitors I bought for my hinky 3-phase convertor. I can't believe how fast power electronics prices are falling. I guess modules made for EVs are making things like this and welders really cheap.

I set this up to spin the 25 HP idler motor with real 3-phase, and the inertia in that system can handle surge loads. I programmed it to ramp up for a gentle start (3 seconds) that doesn't cause all the barn lights to flicker. For turn off, I have it ramp down in 5 seconds. It doesn't like to ramp all the way down to zero without an over-current fault. But so far, that seem innocuous. Just hit stop/reset before restarting.

So my recommendation is forget about lame-ass 3-phase synthesis circuits and buy a VFD. They are cheaper than capacitors and produce real, 120 degree, 3-phase power. If you want some inertia for doing things like quick-reversing your milling machine when backing out a tap, then turn on another machine with some inertia like a band saw or a lathe with a chuck on it or a disc sander. Or, what I did, and kept my 25 HP idler motor in the circuit.