Mathematical Modeling and Optimization for the Power Density of the Free-Standing Magnetic Field Energy Harvester

The free-standing magnetic field energy harvester (FSMFEH) offers a potential solution for powering sensors in the power grid. However, designing the FSMFEH through finite element simulations and experiments is time-consuming and difficult to summarize generalized design guidelines. To address this issue, a mathematical model relating the power density to the coil and core parameters is developed in this article. A correction term is introduced to reflect the aggregation of the H-shaped core to the external magnetic field. The experimental results show that the model error is less than 4%. Based on this model, the core geometry, core material, coil turns, and wire radius are optimized to enhance the power density of the FSMFEH. It is found that the coil has a significant impact on the power density, which deviates from previous studies that solely focus on the core volume. The induced voltage of the coil is also considered in the optimization procedure. The optimized FSMFEH attains an output power of 6.33 mW with a magnetic field of 200
μ
T/50 Hz. Compared to previous studies, the FSMFEH designed in this work can achieve high power and power density with a smaller size and weaker external magnetic field.