On the efficacy of charging a battery using a chaotic energy harvester

Introduction of stiffness nonlinearities to broaden the frequency bandwidth of vibratory energy harvesters has the adverse influence of complicating the response behavior of the harvester. As such, unlike linear energy harvesters, for which direct performance metrics can be easily developed, it is not always easy to develop metrics to assess the performance of nonlinear energy harvesters. One particular issue arises when the harvester operates in its chaotic regime resulting in an unpredictable response, under which the harvester's performance is hard to assess. In this paper, we present a statistical technique to estimate the charging time of a battery being charged by a chaotic vibratory input. The proposed approach, which accounts for the presence of a rectifier circuit, a buck converter, and the dependence of the battery voltage on the state of charge, only requires the knowledge of the probability density function of the open-circuit voltage of the harvester. Using the proposed technique, it is also possible to obtain the optimal duty cycle of the buck converter. Results of the proposed methodology were compared to numerical data generated using MATLAB's Simscape toolbox demonstrating excellent agreement. Not only does the proposed technique provide a valuable tool to assess performance of a chaotic energy harvester, but it can also be easily applied to other chaotic and random energy sources.