In this post I derive the electrical, torque and mechanical equations for a 3-phase star wound BLDC PMSM motor. The assumptions are the impedance of each leg is the same and the rotor flux is sinusoidal. The motivation is to develop the equations for a FOC controlled motor, which will be a follow-on blog.
Derivation of the Equations for 3-Phase BLDC PMSM Motor — Part 1b
This provides enough information such that the 3-phase BLDC PMSM motor can be simulated in engineering software such as MATLAB Simulink. Specifically, a MATAB S-Function can be used to solve the differential equations above given the terminal voltages as inputs and then output the phase currents, velocity and position. An alternate choice is to use a Colab Notebook and do the simulation in Python.
Closing
In a follow on blog I will introduce the topic of Space Vector Modulation (SVM) and field oriented control (FOC) and discuss how to simulate a BLDC PMSM motor using FOC control.