How can I properly convert two phase AC supply to three phase using capacitors?

Question

I have an AC 3 phase delta connected submersible induction motor with specifications 440 V, 10.5 A, 5 HP, 2800 RPM which is already fitted with a 3 phase PF correcting capacitor in parallel. The capacitor specification is 415 V, 3 kVAR, 4.2 A, 3×18.5 uF, ∆ connection.

The 3 phase AC supply system has a supply voltage range between 380-440 V and a frequency of 50 Hz. This motor is used to pump water from a depth of 45 ft inside a well, so it is always a loaded motor. The operating current at this load when there is 3 phase supply is 7 A approximately at each phase.

Currently, I am trying to implement the 2 phase to 3 phase conversion using capacitors when there is a phase failure. In this process, I used a 50 uF capacitor for starting and 2 parallel connected 36 uF capacitors for running the motor. As a result, I get the phase currents as 15 A, 8 A, 6 A which is not a balanced currents. Moreover I get 15 A which will damage the coil of the motor.

My requirement is that I need a formula to calculate the capacitance of the capacitors that will properly convert 2 phase AC supply to 3 phase supply. That is, how much MFD must be used to start the motor and how much MFD must be used to run the motor with atleast a nearly balanced current in every phase.

Note:

1. I don't want to use VFD or something similar to that. I have to achieve the conversion only through capacitors currently.

2. Is it mandatory to use a separate start capacitors to start the motor every time why it is not possible to achieve the same by using run capacitors alone? Currently, I will disconnect the start capacitors using a switch every time after the motor has started. The reason why I am asking this is that I don't want an extra task to start the motor other than switching on the motor starter.

3. Currently, I am connecting capacitors only between the failed phase and one of the available phases. Do I need to connect capacitors between the two available phases, too?

It's a pretty urgent need so I need a speedy solution.

Answer 1

I made a simulation of a static phase converter, but I have not built it or tested it on an actual motor. The inductors shown are actually a 220-78 VAC transformer, and this simulation is for 220 VAC. It might be good to use a "Variac" for the transformer, so performance might be adjustable.

Here is a simulation using 440 VAC 50 Hz and a 3 phase 5 HP load, showing voltages and supply current for a 480-120 V transformer, and various values for capacitor C1. Better balance can be achieved with different transformer ratios, and the phase loads can be adjusted as well, but connecting a three phase induction motor should bring the voltages and phase angles into better alignment. The capacitor needs to be adjusted for different loads. For 100 ohms per phase, an 80 uF capacitor works well.

Note that there is approximately 90 degrees phase shift between V(ac1,ac2) to V(ac3), as expected.

========================= Edit 11/17/22 =========================

I have a little 60 watt 3 phase induction motor that is rated for 220 VAC and 0.43 A, which is an impedance of 523 ohms. It reads 57 ohms between phases. A capacitor with this reactance at 60 Hz is 5 uF. I used a 4.7 uF film capacitor between the red and black wires, and I connected a variable AC source from white to red. The motor starts and runs (no load) at 101 VAC W-R, and shows 113V R-B and 115V B-W.

Based on this experiment, the corresponding capacitor for the OP's motor (440V 10.5A 50 Hz) would have a reactance of 42 ohms, which would be a 76 uF capacitor.