Optimum load computation of a piezoelectric-based energy harvester

Abstract

Objective: Maximum power extraction from piezoelectric energy harvesters is of key importance in the development of various current technologies. However, direct use of the maximum power transfer theorem on this type of energy harvester produces unstable and non-causal load models, which prevent its synthesis through a power electronic circuit and reduce the power available for the application’s specific hardware. This article presents the computation of a causal and stable transfer function that approximates the maximum power extraction load of a linear piezoelectric harvester. Methodology: Such a model is obtained using the Particle Swarm Optimization (PSO) algorithm, selected due to the sim- plicity of its implementation. In this study, a variation of the original algorithm is used to include the stability constraints. Results: The algorithm was employed to obtain 7th, 8th, 16th, and 20th-degree models to evaluate the impact of model complexity on the obtained objective function values. The minimum cumulative square error resulted in an objective function value of approximately 6 · 10−7Ω−2, attained by the 7th-degree model. Conclusions: A stable and causal system model was obtained through a PSO implementation. Results suggest a low dependence of the minimum objective function value on increasing model degrees. Nevertheless, the best model matched the degree of the admittance transfer function. Finally, the implementation of the unconstrained PSO algorithm obtained better results, suggesting that a different optimization algorithm can attain better results. Financing: This study was funded by the Corporación Nacional de Educación Superior CUN.

Keywords

• maximum power transfer theorem
• optimum load
• piezoelectric energy harvesting
• particle swarm optimization