Electrical – Equivalent electrical model for induction motor

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equivalent circuit model of induction motor

I'm trying to understand the model characteristics and from the image attached, I don't understand what the terms and where they came from:

V=-Np*V(w)sdt(V(Yr))
V=Np
V(w)*sdt(V(Xr))

The constants from the below parameters are hiding somewhere in the model and I couldn't find where they are.

.param N=475
+Bs=1.8 Br=0.5 Hc=40
+A=1m5 Lm=0.2 Lg=1m5

I'm designing power electronics for 3-phase 3KW SR motor and I'm trying to model an equivalent SR motor circuit that can be used in LTspice to simulate the results. For simplicity, I'm trying to first simulate only 1 phase of the motor. To do that I'm only using upper circuit model with input X and not considering the secondary phase with input Y(assuming this is right way) from the below image. But the equation V=-Np*V(w)sdt(V(Yr)) has parameters from the secondary phase. How to define the model without secondary phase?

Thanks in advance.

Best Answer

I don't think you're going to get far without finding the documentation on the motor model from which this electrical model was derived. Ultimately it is up to the author to decide on the model features.

The meaning of the symbols however can mostly be deduced, even if their impact on the model is not clear.

V=-Np*V(w)sdt(V(Yr))

V is the voltage of the behavioural source Bx. Np is the number of stator poles, V(w) is the voltage at the point w in the circuit, which in this case is meant to represent the angular speed (\$\omega\$) of the motor. sdt is the integral and V(Yr) is the voltage at the point Yr.

Similar deduction applies to V=NpV(w)*sdt(V(Xr)), the voltage of behavioural source By.

The directive

.param N=475
+Bs=1.8 Br=0.5 Hc=40
+A=1m5 Lm=0.2 Lg=1m5

gives a number of constants to be used somewhere hidden in the model. They look like magnetic properties of the motor. N would be the number of windings on the stator, Bs would be the magnetic flux density of the stator, Br of the rotor. Hc would probably be the magnetic field strength of the central magnetic path. A is likely to be the cross-sectional area, Lm the magnetising inductance and Lg the inductance of the air-gap.