# Modelling 3-phase induction motor and filter for inverter output in LTspice

I am designing an inverter in Ltspice and am looking to have a simple circuit to represent the motor load and filter out the PWM harmonics in order to obtain outputs. The motor characteristics are:

Synchronous Inductance: 500 uH

Resistance (line-neutral): 500 mohms

Will a RLC filter circuit similar to the image shown below work? If so what values should I use for the components (the PWM frequency I am trying to remove is 20kHz, will this use f=1/2*pi*RC)

I think I could do it for single phase however I am struggling with a 3 phase motor especially because of both resistor and inductor when calculating the values required for the filter.

Here is the overall circuit

• What do you call synchronous inductance ? What is the corresponding inductance on this figure ? And where is the motor connected in your schematic ? – Charles JOUBERT Dec 7 '18 at 12:33
• @CharlesJOUBERT the synchronous inductance is a property of the motor I am modelling. That is what I am trying to understand, would I need to make the sum of 'Lmot' in parallel equal to 500 uH to simulate the motor. The 3 inputs on the left are coming from the inverter (I have added a picture of the total circuit). – scouseydaniel Dec 7 '18 at 12:46

The term synchronous inductance (or reactance) is applied to synchronous motors and generally not to induction motors. The equivalent circuit of an induction motor has been the subject of many questions on this site, for example this one and this one. The motor is usually modeled as the line-to-neutral equivalent circuit of one phase. The capacitance from windings to ground is ignored for motor performance models, but is probably needed for your purpose. You may need that capacitance at the input side of the motor circuit. There is also a high-frequency path from stator to rotor and through the shaft bearings to ground.

Any added capacitance must be on the input side of the motor. Filter reactance may be needed on the input side also. You should not need to remove the carrier frequency entirely. You only need to be concerned about voltage stress on the winding insulation due to high dv/dt. Motor bearing currents probably need to be mitigated by other means. EMI probably needs to be mitigated at the controller and by shielding the motor leads.

I agree with Charles Cowie: the term synchronous inductance is for synchronous motors. Maybe, for your simulation, a phase of the motor could be modeled by an inductance $$\ L_{mot} \$$ in series with a resistance $$\ R_{mot} \$$ (and also a capacitor in parallel as wrote Charles Cowie). But the values of the elements are not easy to guess. I would say a first approximation of the impedance of this combination could be:

$$Z_{approx} = \frac{V}{I_{starting}}$$

where $$\{I_{starting}}\$$ is the starting current of your motor, and V the rated voltage.

I think the first schematic you give is a little misleading. I feel like you're mixing the filter with the equivalent circuit of the motor. Maybe the following one is closer to what you want to simulate?

simulate this circuit – Schematic created using CircuitLab

In this schematic, Rmot and Lmot represent the motor (see above). Lfilter, Cfilter and Rfilter belong to the filter. The purpose of Rfilter is to damp the filter. Values are arbitrary. The structure of the filter is close to the one presented in figure 3 of this document.