Use the variable parameter model function to implement medium-fidelity model simulation of a permanent magnet synchronous motor (PMSM). Like the constant parameter model, the variable parameter model uses the voltage equations, flux linkage equations, and torque equation of the (d,q) rotor reference frame. Unlike the constant parameter model, the motor inductance in the variable parameter model is a variable due to magnet saturation. The variable parameter model can obtain real motor characteristics from an RTT file, an ANSYS motor model file, or an external model.

The variable parameter model uses the following discrete equations to calculate the current for a PMSM.

I d k = V d k + ω r L q k - 1 I q k - 1 d t + I d k - 1 L d k - 1 - λ f k - 1 - λ f k - 2 R d t + 2 L d k - 1 - L d k - 2

I q k = V q k + ω r L d k - 1 I d k - 1 + λ f k - 1 d t + I q k - 1 L q k - 1 R d t + 2 L q k - 1 - L q k - 2

where

ωr is electrical speed, in rad/s, which equals to rotor speed times the number of pole,

R is the resistance,

Vd is the voltage along the d axis,

Vq is the voltage along the q axis,

λd is the flux linkage along the d axis,

λq is the flux linkage along the q axis,

λf is the flux linkage in the rotor magnet,

λf is the flux linkage in the rotor magnet,

Ld is the inductance along the d axis,

Lq is the inductance along the q axis,

k, k-1, and k-2 are the simulation steps.

For example, Id(k) is the current along the d axis at the k step. Id(k-1) is the current along the d axis at the k-1 step. Lq(k-2) is the inductance along the q axis at the k-2 step.

External Model

An external model is a model function you create by using the Electric Motor Simulation Toolkit. You can import the external model to get motor characteristics for simulating a PMSM with the variable parameter model. Motor characteristics include number of poles, resistance, temperature correction parameters, direct inductance table, quad inductance table, flux table, and so on.