On the optimal energy harvesting from a vibration source using a piezoelectric stack

Abstract

The modeling of an energy harvesting device consisting of a piezoelectric based stack is presented. In addition, the optimization of the power acquired from the energy harvester is considered. The harvesting device is a piezoceramic element in a stack configuration, which scavenges mechanical energy emanating from a 1D-sinusoidal-base excitation. The device is connected to a harvesting circuit, which employs an inductor and a resistive load. This circuit represents a generalization of the purely resistive circuit, which has received considerable attention in the literature. The optimization problem is formulated as a nonlinear programming problem, wherein the Karush-Kuhn-Tucker (KKT) conditions are stated and the various resulting cases are treated. One of these cases is that of a purely resistive circuit. For resistive circuits, researchers usually neglect the effect of mechanical damping in their optimization procedures. However, in this chapter, we specifically explore the role of damping and electromechanical coupling on the optimization of circuit parameters. We show that mechanical damping has a qualitative effect on the optimal circuit parameters. Further, we observe that beyond an optimal coupling coefficient, the harvested power decreases. This result challenges previously published results suggesting that larger coupling coefficients culminate in more efficient energy harvesters. As for the harvesting circuit, the addition of the inductor provides substantial improvement to the performance of the energy harvesting device. More specifically, at the optimal circuit parameters, optimal power values obtained through a purely resistive circuit at optimal excitation frequencies can be obtained at any excitation frequency. Moreover, simulations reveal that the optimal harvested power is independent of the coupling coefficient (within realistic values of the coupling coefficient); a result that supports our previous findings for a purely resistive circuit. © 2009 Springer US.