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The emergence of piezoelectric functionally graded materials (PFGMs) has sparked the present research interests toward their energy harvesting behaviors. This paper theoretically investigates the optimized energy harvesting characteristics of PFGM cantilever beams under harmonic excitation. The electromechanical coupling governing equations are formulated based on Euler–Bernoulli beam theory, and utilizing the Galerkin discretization yields the frequency-response relations of the voltage, current, and power parameters, and the analytical optimal resistance as well. The present theoretical model is validated by comparing with the experimental results in literature, and parametric studies are addressed to discuss the effects of the damping ratio, the inhomogeneous parameter of PFGMs and the electrical resistance on the structural responses. More importantly, the optimized energy harvesting characteristics of PFGM cantilever beams are captured during discussions on the optimal conditions of the frequency-ratio and the electrical resistance. Results reveal that the superiority of PFGM energy harvesters over the conventional piezoelectric laminate ones, basically, lies in the design toward constituent distribution of PFGMs enabling the control over the energy harvesting efficiency. Specifically, provides that both the optimal frequency-ratio and the optimal resistance hold simultaneously, there would be a critical value for the inhomogeneous parameter, which can be utilized to maximize the energy harvesting efficiency for PFGM beams. The present work may support the prospective material gradient design of piezoelectric energy harvesters.

A broad bandwidth is considered to be one of the most important characteristics of vibrational energy harvesters (VEHs) in order to enhance energy efficiency. To this end, an axially compressive load is applied to the VEHs of a conventional bimorph piezoelectric cantilever beam by pre-tensile cables. The theoretical framework is based on Euler-Bernoulli beam theory and the von Kárman nonlinear kinetic relation, and the electromechanical coupling governing equations are derived by using the Hamilton variational principle of the total potential energy. Treatments by Galerkin discretization and the perturbation method of multiscales give the asymptotically analytic solutions of the displacement amplitude, the voltage amplitude and the average output power, which are validated by the experimental datum in the literature. With the aid of COMSOL Multiphysics, the parametric studies are addressed to explore the mechanisms of the axial preload, the harmonic excitation, the resistance, etc, acting behind the energy harvesting characteristics. The results show that the preload does improve the bandwidth characteristic significantly, specifically, a 64% reduction in the first natural frequency and 196.6% increase of the bandwidth. The present work provides fundamental theoretical support and guides the design of potential preloaded VEHs.

In order to improve the efficiency of photovoltaic generation as well as the power quality, grid-connected inverters for PV generation research was carried out for photovoltaic maximum power point tracking. Based on some current studies on the incremental conductance method, an advanced incremental conductance control algorithm was proposed, which can track maximum power point rapidly and accurately. The oscillation phenomenon, which exists near the maximum power point, was improved at a great extent, so to the efficiency of photovoltaic cells generation electricity. The inverter control system has an advantage in its high speed and flexibility by applying advanced control algorithm. And the source harmonic current is remarkably reduced. In addition, the power factor is enhanced and the power quality is improved. Finally, according to the principle of inverter control system and based on the analysis on the mathematical model of photovoltaic inverter, a simulation model of that is established based on MATLAB/SIMULINK.

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