A unified modeling and analysis framework for galloping piezoelectric energy harvesters

Abstract

Galloping-based piezoelectric energy harvesters (GPEH) connected with various interface circuits are usually analyzed by treating their advanced structures and circuits separately, and a general model is missing to gain insights at a system level. To tackle this issue, this paper proposes a unified framework that enables an integrated view of the physics of linear GPEHs in multiple domains at the system level. In addition, it elucidates the similarities and differences among power behaviors of GPEHs connected with various interface circuits. It is based on two major elements: an equivalent circuit representing the entire system, and an equivalent impedance representing the interface circuit. Firstly, the electromechanical system is linearized and modeled in the electrical domain by an equivalent self-excited circuit with a negative resistive element representing the external aerodynamic excitation, and a general load impedance representing the interface circuit. Then, a closed-form, analytical expression of the harvested power is obtained based on the Kirchhoff’s Voltage Law, from which the optimal load, maximum power, power limit, and critical electromechanical coupling (minimum coupling to reach the power limit) are determined. In this unified analysis, the exact type of energy harvesting interface circuit is not assumed. After that, the power characteristics of a GPEH connected with five representative interface circuits are analytically derived and discussed separately, by using the particular equivalent impedance of the interface circuit of interest. It is shown that they are subjected to the same power limit. However, the critical electromechanical coupling depends on the type of circuit.