I. C. Lien

Analysis of power output for piezoelectric energy harvesting systems

Power harvesting refers to the practice of acquiring energy from the environment which would be otherwise wasted and converting it into usable electric energy. Much work has been done on studying the optimal AC power output, while little has considered the AC–DC output. This article investigates the optimal AC–DC power generation for a rectified piezoelectric device. In contrast with estimates based on various degrees of approximation in the recent literature, an analytic expression for the AC–DC power output is derived under steady-state operation. It shows that the harvested power depends on the input vibration characteristics (frequency and acceleration), the mass of the generator, the electrical load, the natural frequency, the mechanical damping ratio and the electromechanical coupling coefficient of the system. An effective power normalization scheme is provided to compare the relative performance and efficiency of devices. The theoretical predictions are validated and found to be in good agreement with both experimental observations and numerical simulations. Finally, several design guidelines are suggested for devices with large coupling coefficient and quality factor.

An improved analysis of the SSHI interface in piezoelectric energy harvesting

This paper provides an analysis for the performance evaluation of a piezoelectric energy harvesting system using the synchronized switch harvesting on inductor (SSHI) electronic interface. In contrast with estimates based on a variety of approximations in the literature, an analytic expression of harvested power is derived explicitly and validated numerically for the SSHI system. It is shown that the electrical response using an ideal SSHI interface is similar to that using the standard interface in a strongly coupled electromechanical system operated at short circuit resonance. On the other hand, if the SSHI circuit is not ideal, the performance degradation is evaluated and classified according to the relative strength of coupling. It is found that the best use of the SSHI harvesting circuit is for systems in the mid-range of electromechanical coupling. The degradation in harvested power due to the non-perfect voltage inversion is not pronounced in this case, and a new finding shows that the reduction in power is much less sensitive to frequency deviations than that using the standard technique.

Efficiency of energy conversion for a piezoelectric power harvesting system

This paper studies the energy conversion efficiency for a rectified piezoelectric power harvester. An analytical model is proposed, and an expression of efficiency is derived under steady-state operation. In addition, the relationship among the conversion efficiency, electrically induced damping and ac–dc power output is established explicitly. It is shown that the optimization criteria are different depending on the relative strength of the coupling. For the weak electromechanical coupling system, the optimal power transfer is attained when the efficiency and induced damping achieve their maximum values. This result is consistent with that observed in the recent literature. However, a new finding shows that they are not simultaneously maximized in the strongly coupled electromechanical system.

Revisit of series-SSHI with comparisons to other interfacing circuits in piezoelectric energy harvesting

SSHI (synchronized switch harvesting on inductor) techniques have been demonstrated to be capable of boosting power in vibration-based piezoelectric energy harvesters. However, the effect of frequency deviation from resonance on the electrical response of an SSHI system has not been taken into account from the original analysis. Here an improved analysis accounting for such an effect is proposed to investigate the electrical behavior of a series-SSHI system. The analytic expression of harvested power is proposed and validated numerically. Its performance evaluation is carried out and compared with the piezoelectric systems using either the standard or parallel-SSHI electronic interfaces. The result shows that the electrical response of an ideal series-SSHI system is in sharp contrast to that of an ideal parallel-SSHI system. The former is similar to a strongly coupled electromechanical standard system operated at the open circuit resonance, while the latter is analogous to that operated at the short circuit resonance with different magnitudes of matching impedance. In addition, the performance degradation due to non-ideal voltage inversion is also discussed. It shows that a series-SSHI system avails against the standard technique in the case of medium coupling, since its peak power is close to the ideal optimal power and the reduction in power is less sensitive to frequency deviation. However, the consideration of inevitable diode loss in practical devices favors the parallel-SSHI technique, since the frequency-insensitive feature is much more pronounced in parallel-SSHI systems than in series-SSHI systems.

Array of piezoelectric energy harvesting by the equivalent impedance approach

This article proposes to use the idea of equivalent impedance to investigate the electrical response of an array of piezoelectric oscillators endowed with distinct energy harvesting circuits. Three interface electronics systems are considered including standard AC/DC and parallel/series-SSHI (synchronized switch harvesting on inductor) circuits. Various forms of equivalent load impedance are analytically obtained for different interfaces. The steady-state response of an array system is then shown to be determined by the matrix formulation of generalized Ohm’s law whose impedance matrix is explicitly expressed in terms of the load impedance. A model problem is proposed for evaluating the ability of power harvesting under various conditions. It is shown first that harvested power is increased dramatically for the case of small deviation in the system parameters. On the other hand, if the deviation in mass is relatively large, the result is changed from the power-boosting mode to wideband mode. In particular, the parallel-SSHI array system exhibits much more significant bandwidth improvement than the other two cases. Surprisingly, the series-SSHI array system shows the worst electrical response. Such an observation is opposed to our previous finding that an SSHI technique avails against the standard technique in the case based on a single piezoelectric energy harvester and the explanation is under investigation.

Analysis of an array of piezoelectric energy harvesters connected in series

This paper investigates the electrical response of a series connection of piezoelectric energy harvesters (PEHs) attached to various interface electronics, including standard and parallel-/series-SSHI (synchronized switch harvesting on inductor) circuits. In contrast to the case of parallel connection of multiple oscillators, the system response is determined by the matrix formulation of charging on a capacitance. In addition, the adoption of an equivalent impedance approach shows that the capacitance matrix can be explicitly expressed in terms of the relevant load impedance. A model problem is proposed for performance evaluation of harvested power under different choices of interface circuits. The result demonstrates that the parallel-SSHI array system exhibits higher power output with moderate bandwidth improvement, while the series-SSHI system delivers a pronounced wideband at the cost of peak harvested power. The standard array system shows a mild ability in power harvesting between these two SSHI systems. Finally, comparisons between the series and parallel connection of oscillators are made, showing the striking contrast of these two cases.

Array of piezoelectric energy harvesters

This article analyzes the electrical behavior of an array of piezoelectric energy harvesters endowed with several interfacing circuits, including the standard AC/DC circuit and parallel/series SSHI (synchronized switch harvesting on inductor) circuits. The harvesters are classified according to the connection to a single or multiple rectifiers. The analytic estimates of harvested power are derived explicitly for different cases. The results show that DC power output changes from the power-boosting mode to the wideband mode according to various degrees of differences in the parameters of harvesters. In particular, the system with multiple rectifiers exhibits more bandwidth improvement than that with a single rectifier. Finally, it is shown that the electrical performance of an SSHI array system enjoys both power boosting and bandwidth improvement.

Piezoelectric array of oscillators with respective electrical rectification

This article reports the modeling of the parallel connection of multiple piezoelectric oscillators with respective electrical rectification. Such an array structure offers advantages of boosting power output and exhibiting broadband energy harvesting. The theoretical estimates are proposed for different choices of electronic interfaces, including the standard and parallel-/series-SSHI (synchronized switch harvesting on inductor) circuits. It is shown that the electrical response is governed by a set of simultaneous nonlinear equations with constraints indicating blocking by rectifiers. Finally, the validation is carried out by circuit simulations and shows good agreement.

Multiple piezoelectric energy harvesters connected to different interface circuits

The electrical response of multiple piezoelectric oscillators connected in parallel and endowed with various energy harvesting circuits is investigated here. It is based on the idea of equivalent load impedance of piezoelectric capacitance coupled with harvesting circuits. The main result is the matrix formulation of generalized Ohms law whose impedance matrix is explicitly expressed in terms of load impedance. It is validated numerically through standard circuit simulations.

A comparison between the standard and SSHI interfaces used in piezoelectric power harvesting

This article provides an analysis for the performance evaluation of a piezoelectric power harvesting system using either the standard or SSHI electronic interfaces. Instead of using the un-coupled and in-phase assumptions, an analytic expression of harvested power is proposed for the SSHI circuit based on the improved analysis. It is shown that the behavior of an ideal SSHI system is similar to that of strongly coupled electromechanical system using the standard interface operated at the short circuit resonance. In addition, the performance evaluation of a SSHI circuit is classified according to the relative magnitudes of electromechanical coupling coefficient and the mechanical damping ratio. It is found that the best use of the SSHI harvesting circuit is for the system with the medium range of electromechanical coupling. The performance degradation due to the non-perfect voltage inversion is not pronounced in this case, and a new finding shows that the average harvesting power is much less sensitive in frequency compared to that using the standard interface.