On the optimal energy harvesting from a vibration source

The optimization of power acquired from a piezoelectric vibration-based energy harvester which utilizes a harvesting circuit employing an inductor and a resistive load is described. The optimization problem is formulated as a nonlinear program wherein the Karush-Kuhn-Tucker (KKT) conditions are stated and the resulting cases are treated. In the first part of the manuscript, the case of a purely resistive circuit is analyzed. While this configuration has received considerable attention in the literature, previous efforts have neglected the effect of damping on the optimal parameters. Here, we explore the impact of damping on power optimality and illustrate its quantitative and qualitative effects. Further, we analyze the effect of electromechanical coupling demonstrating that the harvested power decreases beyond an optimal coupling coefficient. This result challenges previous literature suggesting that higher coupling coefficients always culminate in more efficient energy harvesters. In the second part of this work, the effect of adding an inductor to the circuit is examined. It is demonstrated that the addition of the inductor provides substantial improvement to the performance of the energy harvesting device. It is also shown that within realistic values of the coupling coefficient, the optimal harvested power is independent of the coupling coefficient; a result that supports previous findings for the purely resistive circuit.