A Study of an Array of Piezoelectric Energy Harvesters Connected in Series

本研究之目的為探討串聯壓電振子陣列，在標準與電感同步切換整流介面電路架構下全頻域之輸出功率，並透過 PSpice 電路模擬軟體，驗證推導之理論解析公式的正確性。最後，以中力電耦合振子陣列為例，運用本團隊先前導出之並聯陣列解析公式與本研究中之串聯陣列解析方程式，描繪出各種架構之頻率響應關係，並比較其性能之優劣。 壓電振子以雙壓電層懸臂梁為例，運用壓電力學與特徵模態分析，可將振子化為一個電壓源與一個靜態電容串聯而成之電壓型等效電路模型。運用直接積分法或等效阻抗法以及電荷守恆與能量守恆的概念，即可導出各陣列架構在穩態下之系統輸出功率方程式。在推導的過程中，我們發現將振子的外力向量與位移向量各別乘上特定常數後，即可類比為電荷向量與電壓向量，因此可以電容矩陣描述外力與位移之關係。 運用串聯陣列之輸出功率公式，我們繪製出中力電耦合振子在串聯架構下輸出功率之頻率響應關係，比較結果顯示：串聯S-SSHI 架構的寬頻效果最佳，但峰值較低；串聯P-SSHI 架構同時具有寬頻與峰值提升的效果，綜合性能最佳。若將串聯陣列與並聯陣列相比，則可發現串聯S-SSHI與並聯P-SSHI同屬寬頻型，串聯P-SSHI 與並聯S-SSHI 主要為峰值提升型。The thesis is to study the electrical response of a series connection of multiple piezoelectric oscillators endowed with different energy harvesting circuits, including the standard and parallel-/series-SSHI (Synchronized Switch Harvesting on Inductor) interface electronics. The proposed analytic estimates are validated numerically by PSpice circuit simulation. In addition, we make comparisons with the case of piezoelectric array connected in parallel, and make conclusions by performance evaluation of the frequency response of oscillators arranged in different kinds of configurations. Based on piezoelectric mechanics and modal analysis, the bimorph piezoelectric energy harvester is modeled as a voltage type equivalent circuit model. Using this model together with the concept of charge and energy conservation, we derive the DC output power of each configuration by either direct integration method or equivalent impedance method. Besides, it is found that the force and the displacement vectors of a series array are analogous to the charge and the voltage vectors. It is further shown that they are related by a generalized capacitive matrix. From the frequency response of multiple piezoelectric oscillators connected in different ways, it is observed that a series array with series-SSHI circuit has the better broadband effect but with lower peak power. On the other hand, a series array with parallel-SSHI circuit enjoys both the wideband effect and higher peak power response. Furthermore, the electrical response of a series array with series-SSHI interface is similar to that of a parallel array with parallel-SSHI interface: both exhibit broadband modes. In contrast to the previous case, a series array with parallel-SSHI interface and a parallel array with series-SSHI interface show similar performance in power boosting