Optimal power, power limit and damping of vibration based piezoelectric power harvesters

Abstract

Power harvesting describes the process of acquiring the ambient energy surrounding a system and converting it into usable electrical energy. Much of the work over the past two decades has focused on the conversion of ambient vibration energy sources using piezoelectric, electromagnetic and electrostatic transduction. Attempts were made to obtain a general model that could be applied to any transduction mechanism. Of the most interest is an electromagnetic generator model that was used by many researchers to model piezoelectric power harvesters. Two major results from the model are the power limit expression and the equal relationship between the electrically induced damping and the mechanical damping to reach the power limit. However, piezoelectric power harvesters cannot be accurately modeled by this electromagnetic model due to the essential difference in physics. There have also been attempts to obtain the power limit expression based on piezoelectric relationships, but they either neglect the piezoelectric backward coupling to the structure, or assume the power limit occurs at the resonance of the system. This paper obtains the power limit expression based on the piezoelectric coupled equations without those assumptions. In addition, the relationship between the electrically induced damping and mechanical damping at the power limit is studied. Furthermore, a closed-form criterion is derived and proposed to define strongly and weakly coupling power harvesters, whose differences in power characteristics are explained through analytical and numerical analysis. While most of the discussion is focused on linear power harvesters connected to a resistive circuit, the aim of this paper is to provide a comprehensive and deep understanding of this simple configuration, answers to important questions, and a starting point to develop a more general theory on power harvesters because similar system characteristics are observed in power harvesters with more complexities.

Maximum power point of piezoelectric energy harvesters: a review of optimality condition for electrical tuning

“…For example, it reports a system from the literature that surpasses the theoretical limit [8] [9]. A recent study has summed up the main theoretical results to achieve optimal impedance matching but does not study the particular circumstances of the numerous existing architectures [10]. The aim of our paper is to propose a structured overview of existing techniques for piezoelectric energy harvesting (PEH) and reconcile PEH circuits and theory in terms of optimal operating conditions -taking into account the bidirectional electromechanical coupling.…”

Experimentally validated model and analytical investigations on power optimization for piezoelectric-based wireless power transfer systems

“…However, this power is less than the maximum achievable power when k 2 ø k 2 cr . See Shu et al (2007), Arroyo et al (2012), and Liao and Sodano (2018) for an example. Note that the corresponding optimal load is computed by substituting the optimal frequency back into equation ( 26).…”

Uncertainty Analysis of Piezoelectric Vibration Energy Harvesters Using a Finite Element Level-Based Maximum Entropy Approach

“…Depending on the amount of coupling in the system, this limit may or may not be reached. The minimum coupling to reach the power limit, i.e., critical coupling, for energy harvesters of a resistive interface circuit is given [26,48] as…”

“…On the other hand, to enhance the power or energy conversion performance of the system and provide design guidance for energy harvesters, optimization studies have been conducted on the geometrical parameters [19][20][21][22] or the electrical parameters [23][24][25][26]. Additionally, topology optimization methods have also been applied [27][28][29].…”