Admittance-based equivalent circuit modeling of multi-patch piezoelectric energy harvesting plate

Harvesting energy from mechanical vibration using piezoelectric material is a common method to power small electronics and batteries. Implementation of multiple piezo-patches to plate-like structures increases the power capacity and frequency bandwidth of the energy harvester since multiple patches can capture more vibrational modes of the dense plate dynamics. To optimize the harvested electrical output using advanced harvesting circuits, equivalent circuit modeling (ECM) is a useful technique for representing the entire electromechanical system in circuit- simulator-software (LTspice). The ECM technique based on finite-element (FE) simulation has been used for plate-like structures with only one single-piezo-patch-harvester in the literature. However, when multiple patches are integrated into a plate-like structure, their coupling can cause charge cancelation, resulting in complex dynamics that cannot be handled by the existing ECM methods. This paper presents three new methodologies for extracting a multi-mode ECM of the harvesters (e.g.: multi-patch piezo-harvesters integrated into a plate), using an admittance-based system identification approach utilizing FE results. The first method incorporates the ECM of multi-patch harvester into a single ECM, so called OGC. It includes a circuit branch where multiple patches have only one ECM branch for each vibration mode, which requires less equivalent circuit elements and hence less computational cost. The second and third so-called respective ground uncoupled (RGU) and respective ground coupled (RGC) ECM methods generate circuit branches for each piezo-patch and for each vibration mode, whereby their electrical connection (e.g. parallel or series) is later configured in LTspice. The RGU method provides a general multi-patch modeling approach while RGC method provides ECM parameters for each patch simultaneously when they are all connected which is the case in network harvester analysis. The ECMs of parallel multi-patch harvesters are validated by system-level FE simulations. The proposed admittance-based ECM methods are reliable for deriving the system parameters of multi-patch harvesters.