We know that there's T equivalent circuit and inverse Γ-equivalent circuit for 3 phase induction motor(IM). When the IM is operating under normal situation, the windings are symmetrical, so all 3 phases equivalent circuit should be the same, but when a fault occur to it—e.g., inter turn short circuit(ITSC) of phase A, the windings become asymmetrical. Is it okay to use equivalent circuit to reprensent each winding? Which means, same structure of equivalent circuit while the value of the parameters are different.
If it's okay, what should the input voltage to the equivalent circuit is? phase to phase voltage or phase to neutral point voltage?
Actually, per phase equivalent circuit of three phase induction motor can be used only under balanced operating conditions and symmetrical three phase windings. In case of unbalanced operation or unsymmetrical winding, fault conditions (per phase equivalent circuit will be not useful ) we should used thee phase mathematical model and therefore be able to represent any fault type, internal or external fault.
Amr Refky Abd Elwhab Thanks for the answer. Could you please elaborate more why per phase equivalent circuit of three phase induction motor is not eligible for unsymmetrical winding? I found a PhD thesis(https://theses.ncl.ac.uk/jspui/bitstream/10443/3232/1/Alturas%2c%20A.M.%202016.pdf Check chapter 7 out if you are interested) which use the per phase equivalent circuit for each phase condition monitoring, and the author detect short circuit of the induction motor.
Dear Ray Wang,
For unsymmetrical windings there are differences between phases parameters (phase resistances, phase inductances and mutual inductances ) so, single per phase equivalent circuit will not suitable for simulating unsymmetrical and fault conditions. only complete three phase model or three per phase complained equivalent circuits can simulate the fault and asymmetrical windings conditions.
Return to the 4th paragraph in the abstract of the A/M PhD thesis "A diagnosis scheme to detect stator winding faults in induction machines is also proposed in this thesis. The scheme uses time domain features derived from 3-phase stator currents in conjunction with particle swarm optimization algorithm to check characteristic parameters of the machine and detect the fault accordingly. The validity and effectiveness of the proposed technique has been evaluated for different common faults including interturn short-circuit, stator winding asymmetry (increased resistance in one or more stator phases) and combined faults, i.e. a mixture of stator winding asymmetry and interturn short-circuit. Results show the accuracy of the proposed technique and it is ability to detect the presence of the fault and provide information about its type and location."
The author scheme the 3-phase stator currents, which means he used 3-phase model, for different common faults including interturn short-circuit, stator winding asymmetry (increased resistance in one or more stator phases) in the 3-phase model. also in Chapter 7 three per phase equivalent circuit was used.
Amr Refky Abd Elwhab Thank you for the detailed elaboration. I might not express my self clealy. What I want to say is to represent each phase with their own equivalent circuit—i.e., per phase equivalent circuit A with A parameters to represent phase A, per phase equivalent circuit B with B parameters to represent phase B, per phase equivalent circuit C with C parameters to represent phase C. The input voltage is the corresponding stator phase voltage. That's like with one phase staor voltage and current, we can determine this phase corresponding parameters. Actually I verify the validity of this when the motor is under normal situation, but it doesn't perform well when it's under fault state—i.e, ITSC fault.
That's way I want to ask if it's okay to use equivalent circuit under asymmetric winding(one equivalent circuit for one phase with their own unique parameters).
After these day's research I had a conclusion but I'm not so sure. We can use equivalent circuit under asymmetric windings, but the input voltage should be the dostorted voltage under the configuration of 3 wires without neutral line, if it's 4 wires, the stator phase voltage is the same as supply voltage, which is what I use in simulation, and this might be the issue.
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