Modeling magnetic saturation and saliency effects via Euler-Lagrange models with complex currents for three-phase permanent magnet machines

Permanent magnet machines with both magnetic saturation and saliency effects can be directly described via Euler-Lagrangian formulation with complex currents. The Lagrangian is the sum of a mechanical kinetic energy and a magnetic Lagrangian. This second term is expressed in terms of rotor angle, complex stator and rotor magnetizing currents. Via simple modification of magnetic Lagrangian we derive a non-trivial dynamical model describing permanent-magnet machines with both saturation and saliency. We propose an experimental validation of such models on a customized torque machine of 1.2 kW. This first validation relies on injections of high frequency oscillations on the stator voltage. According to the proposed saturation model, the resulting amplitudes of the current-ripples is an increasing function of the current offset. Such dependance is effectively observed experimentally and confirmed by simulations.