Analytical Model of a Vibrating Electromagnetic Harvester Considering Nonlinear Effects

In this paper, an analytical model of a vibrating electromagnetic harvester, taking into account nonlinear effects, is presented. Knowing the acceleration applied to the harvester system, the model is able to predict the performance of the harvester in terms of induced voltage on the load. The energy transducer consists of four magnets, two movable and two fixed, arranged in a way such that both fixed magnets repel the moveable one. The model was implemented in Simulink and exploits the results of a finite element method (FEM) solver (Flux2D) to estimate the non-linear electromagnetic repulsion force and the flux linkage by the coil. To evaluate the effect of a load applied to the harvester, the effect of the Lorentz's force, caused by the interaction of the current that flows in the coil and the flux density of the moveable magnet, was taken into account. As a consequence, the error in the estimate of induced voltage, at resonance, is reduced from about 80% to 7%. Finally, at resonance, the maximum power that could be delivered by the harvester and dissipated on a resistive load was estimated to be about 6 mW.