Analytical tools for investigating stability and power generation of electromagnetic vibration energy harvesters

This paper presents a general linear methodology for analyzing how the choice of electrical load affects stability and average power generation of an electromagnetic vibration energy harvester. Using bond graph techniques, the entire electromechanical harvesting system is modeled as a dynamically equivalent electrical circuit and ultimately recast as a feedback control system. This modeling approach enables the use of well-established linear control tools to assess the overall stability of the energy harvesting system. These tools are used to show: 1) why the load which would result in maximum power transfer from the harvester to the load, as established by the maximum power transfer theorem (MPTT), can only be achieved at a single frequency, and 2) how to ensure the system will always remain stable if the harvester is used in conjunction with an active load. Moreover, the presented modeling approach enables development of the power harvesting ratio - an analytical method for quantifying the harvester's power generation when multi-frequency excitation is involved. A custom harvester was constructed for experimental evaluation of the power harvesting ratio when varying: 1) the electrical load attached across the harvester leads and 2) the multifrequency vibrations used to excite the harvester.