Stochastic Modeling in the Frequency Domain for Energy Harvester With Switching Electronic Interface

Nonlinear techniques consisting in a switching device triggering on maximum and minimum displacements have demonstrated superior performance for piezoelectric harvesters excited with a monochromatic force allowing a harvested energy gain of 9 compared to the standard technique. However, until now the performance of switched-interface piezoelectric harvesters under broadband and/or random force excitations has barely been studied. In this study, we investigate a periodic switching strategy to simplify the problem, and derive a mathematical model based on cyclostationary stochastic theory and the concepts of self-sampling and self-aliasing. From this model, the harvester performance under a broadband force excitation can be obtained efficiently from the force spectral density. The model has been verified by experiments and applied to several force excitation cases in the form of model spectral functions. The harvester is found to have a better performance than for a resistive load when the switching frequency is slightly less than twice the harvester resonance frequency. The effect of the coupling factor k² and the mechanical quality factor QM is also discussed in detail to give a reference for the harvester design. An interesting result is that the harvester will perform differently for different choices of k² and QM even when the values of k²QM are the same.