Multiple Harmonics Extended Impedance Model of Piezoelectric Energy Harvesting Systems

In a piezoelectric energy harvesting (PEH) system, the dynamics and harvested power vary with different base excitation. Accurately predicting the energy harvesting capability under different types of excitation is of importance for the analysis and design of PEH systems. Many studies started the modeling and analysis of such an electromechanically coupled system under harmonic excitation. However, in real-world scenarios, environmental vibration might be irregular and impulsive. This paper extends the equivalent impedance analysis from single harmonic to multiple harmonics for describing the complex dynamics and harvested power of a PEH system under non-harmonic base excitation. The proposed multiple harmonic analysis is based on the extended impedance method (EIM), which uniforms the impedance expressions of both linear and nonlinear components in a matrix form. The modeling principle and procedures of EIM are provided in detail. The power flow in the steady-state PEH systems and energy flow in the transient PEH systems are numerically discussed. Experiments based on a base-excited piezoelectric cantilever, as the energy harvester, and a full-wave bridge rectifier, as the power conditioning circuit, validate the EIM based analysis, in terms of harvested power/energy prediction and dynamics description.