# Equivalent electrical model for induction motor

For those people who are looking for induction induction motor SPICE model, please follow the link LT SPICE tools and applications

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=NpV(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?

• Hi Andy,I have changed the title now. The link I attached above has the spice models for 3 phase induction motor and simplified 2 phase induction motor. Sorry for the confusion I should have clarified it in the beginning itself. – lomesh pudipeddi Jan 29 '18 at 12:55
• The diagram indicates it is a three-phase motor represented by a "2-Ph simplified model." That seems like a rather unusual model. Three-phase motors are normally analyzed using a per-phase, line-to-neutral equivalent circuit. The model shown makes more sense as a model for a single-phase motor. As suggested by @Heath Rafferty, you probably need to find this approach described in a research paper. – Charles Cowie Jan 29 '18 at 16:03
• You've now added a very different question from your original question, which makes this Q&A confusing. Many people confuse this site with a forum - it is not, it is a Q&A site. If you have another question, then ask it in another question. But take the time to make it a well-contained, standalone question. And pre-warning - the answer is probably "don't create a 1-phase model by removing a phase from a 2-phase model - they are no where near the same thing. With respect, you've got a long learning curve ahead of you - start reading or get a tutor". – Heath Raftery Feb 4 '18 at 5:41

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.

• I suspect that V(w) may be V as a function of angular speed (ω) – Charles Cowie Jan 29 '18 at 15:55
• Possible, but I'm convinced otherwise because of Erpm. It is equal to V(w)*60/2/PI. Since $RPM = \omega *60 / 2 / \pi$, it's highly likely that V(w) is equal to $\omega$. – Heath Raftery Jan 29 '18 at 19:47
• I don't exactly understand the simulation diagram and notations. I know that the back emf is influenced by slip frequency, rotor saturation and the change in effective rotor-bar resistance due to the non-homogeneaty of current density in the rotor bars. Somehow that must be handled by the equation for the dependent source, but I don't know how. – Charles Cowie Jan 29 '18 at 22:54

Thanks for the explanation and also thanks for the time you put into answering this question. 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 above 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. It's first time I'm using the stack exchange. But the comments has only limited number of characters. – lomesh pudipeddi Jan 29 '18 at 16:08
• You may also edit your question. – Janka Jan 29 '18 at 16:12