Question about single phase to three phase conversion

[SunnyBoyNY]

The source is a 1-phase AC source, not a DC source.

I assume you will rectify the single phase AC source to DC and put an energy buffer to the link as 1 phase connection is not capable of delivering continuous power as the three phases are.

Simply, if you motor takes 3 kW, then it is 3 kW continuous. Torque is dependent on the rotor/stator flux linkage and stator current. With sinusoidal windings the equations will look like this:

$Va = X*sin(ωt)\\ Vb = X*sin(ωt+\frac{2 Pi}{3})\\ Vc = X*sin(ωt-\frac{2 Pi}{3})\\$

Current are:

$Ia = Y*sin(ωt)\\ Ib = Y*sin(ωt+\frac{2 Pi}{3})\\ Ic = Y*sin(ωt-\frac{2 Pi}{3})\\$

Thus the power to the rotor is:

$Pr = Va*Ia+Vb*Ib+Vc*Ic = \frac{3}{2}XY$

As you can see the rotor power is not dependent on phase.

On the other hand, provided that you want to pull power from a 1-phase connection with unity power factor, the available power is:

Pin = V*sin(wt)*I*sin(wt)=VI*sin^2(wt)=VI/2*(1-cos(2wt)).

Therefore you need an energy buffer.

I would strongly suggest you do some reading on the topic.

Excellent books are:

Principles of Power Electronics by Kassakian, Schlecht, Vergese from MIT
Fundamentals of Power Electronics by Erickson and Maksimovic from Colorado
Ac Electric Machines and Their Control by Torrey from Union