Single Phase Induction Motor, Capacitor-Start Capacitor-Run Equivalent Circuit Diagram

[JustinME]

I have created a circuit diagram for a single phase CSCR induction motor, but only for the purpose of calculating start-up current (i.e. motor speed is at, or very near, zero RPM). I have created this diagram because: 1) I do not have the tools & knowledge required to generate the Steinmetz equivalent circuit with the capacitors included; and 2) The values for each of these circuit elements can be measured using an LCR meter (except for my beta term).

Please review the attached circuit diagram and let me know if you find anything incorrect. Or, if it looks like this is a reasonable approximation for near zero speed currents then please give me a confirmation.

The beta term I have in the diagram is something I conjured to represent the magnetic flux that the roto bars consume. My idea is that the measured inductance of each stator coil will be greater than the actual stator coil inductance during the start-up event because the LCR meter does not pass a sufficiently large current that a significant portion of the resulting magnetic field would pass through the rotor bar loops. For one motor tested on one power supply, I have found that my calculated start-up current is within 3% of the measured start-up current when I set beta = 50%. Does it make sense that, during the start-up event, the rotor would consume half of the magnetic flux generated by the stator coils?

Thank you in advance for your help!

Link to attachment:

http://files.engineering.com/getfil...nduction_Motor_Equivalent_Circuit_Diagram.pdf

 

[electricpete]

Let's forget about the complexities of CSCR motor with two windings and just talk about simple three-phase motor per-phase diagram.

You can't determine the inductive parameters by LCR measurement.
1 - The terminal measurement is L1 in series with parallel combo of L2 and Lm (all parameters referred to primary). I'd have no problem assuming L1~L2, but now you've still got 2 equations with three unknowns and nothing else reliable to assume (ratio L1/LM very variable).
2 - With LCR meter, the measurement is taken at completely different flux level than operating… iron is highly non-linear throughout the range (not just near saturation as you might think).


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(2B)+(2B)' ?

 

[JustinME]

I cut the wires to the capacitors so that I measured the inductance for each coil without the capacitors in the circuit.

Is there any known relationships for the magnetic permeability for steel? If so, then a scalar could be identified by dividing mu for very low current over mu for very high current.

 

[Parchie]

Your representation of the equivalent circuit for a single-phase induction motor is wrong. What you're showing is a per phase representation of a three-phase IM.
Please research more on "forward rotor impedance" and "backward rotor impedance"--> all referred to the primary of the single-phase IM (stator).

 

[electricpete]

Is there any known relationships for the magnetic permeability for steel? If so, then a scalar could be identified by dividing mu for very low current over mu for very high current.

Again there is not a single value. You have to know the flux density during your test.
And even if you somehow knew that, you still cannot distinguish effects of magnetizing and leakage reactances.

And as I said that is only sticking with simple three-phase motor per-phase circuit.///
Parchie points out that single phase motor is another complication.

Many hurdles, already. There are more that would run into if you really analysed it but it has already been shown as a hopeless cause with single measurement as you are suggesting.

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(2B)+(2B)' ?