Optimum power and efficiency of piezoelectric vibration energy harvesters with sinusoidal and random vibrations

Abstract

Assuming a sinusoidal vibration as input, an inertial piezoelectric harvester designed for maximum efficiency of the electromechanical energy conversion does not always lead to maximum power generation. In this case, what can be gained by optimizing the efficiency of the device? Detailing an answer to this question is the backbone of this paper. It is shown that, while the maximum efficiency operating condition does not always lead to maximum power generation, it corresponds always to maximum power per square unit deflection of the piezoelectric harvester. This understanding allows better optimization of the generated power when the deflection of the device is limited by hard stops. This is illustrated by experimental measurements on vacuum-packaged MEMS harvesters based on AlN as piezoelectric material. The results obtained for a sinusoidal vibration are extended to random vibrations. In this case, we demonstrate that the optimum generated power is directly proportional to the efficiency of the harvester, thus answering the initial question. For both types of studied vibrations, simple closed-form formulas describing the generated power and efficiency in optimum operating conditions are elaborated. These formulas are based on parameters that are easily measured or modeled. Therefore, they are useful performance metrics for existing piezoelectric harvesters.