Causal PMSM model: fast, accurate, robust

Abstract:
Electromagnetic actuators and motors are central for electric drives of all types. For the appropriate application the simulation in several mutually coupled physical domains is essential. If the coupling is realised on system level instead on fields level several advantages can be exploited: fast transient simulations, co-operation via model exchange, early analysis of side effect like NVH. A description of the actuator or motor should be available in different degrees of accuracy to model different physical effects. Here we’ll concentrate on a detailed model including saturation and position dependent effects like torque/force ripple to be able to include NVH effects. A typical approach to generate a system model of an electric actuator or motor is to generate a lookup table that allows to find force/torque and magnetic flux linkage as the function of position and electric current. Force/torque and flux linkage are the main entries in the mechanical and electric equations of motion. The equations of motions are typically solved in system simulation tools capable of handling conservative models like Simcenter, AMEsim, Dymola, Ansys TwinBuilder or MathWorks Simscape. In this presentation we follow a different path. Instead of describing the electromechanical system with the derivatives of the magnetic co-energy, namely flux and generalised force as functions of position and current we utilise the derivatives of the magnetic energy, namely current and generalised force as functions of position and flux. The resulting equations of motion can be solved simply, directly, and robustly in a causal system simulation because the feedback loops do not contain derivatives of signals or matrix inversions. To realize this in a numerically effective manner for a PMSM several steps have to be executed: - Flux table creation using transient winding voltages - Parallel computations of flux variations for different positions - Numerical separation of fluxes into position dependent initial flux and voltage dependent flux increments - Appropriate table combinations for Y winding connections - System model in d,q space - Smooth multidimensional table interpolation based on spatial Fourier representations The resulting system model is shown to represent the transient behavior via comparison with full transient field calculations. Its efficiency and stability is demonstrated. As an example, the causal PMSM model is used to calculate NVH of an accelerating motor under PWM3 excitation. The structure borne sound is generated and played.