Model-based design of piezoelectric energy harvesting systems

In the design process of energy harvesting systems based on piezoelectric elements, achievable energy output is the most interesting factor. To estimate this amount a priori manufacturing of prototypes a mathematical model is very helpful. Within this contribution we will introduce a model based on electro-mechanical circuit theory. Its parameters are identified by measurements and the model is validated by comparison to experimental results. The model is designed to support the development-engineer in the dimensioning of energy harvesting units to specific application demands. Two main challenges in device design are investigated with the mathematical model: influence of the ambient excitation frequency, and influence of the load impedance. Typically, the equivalent model approach delivers models for piezoelectric elements that are driven in resonance by electrical excitation. In the case of energy harvesting the piezoelectric elements are excited mechanically and most often non-resonant. Thus, we first set up a mechanical equivalent model for base excited systems. In first approximation it represents an energy harvesting unit around one resonance frequency. The model is expandable for a wider frequency range using the superpositioning of multiple circuits. From the viewpoint of optimum energy transformation between mechanical and electrical energy it is favorable to drive piezoelectric elements at resonance or anti-resonance. Thus, an energy harvesting system should be tuned to the excitation frequency.