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This paper aims at providing an uptodate review of nonlinear electronic interfaces for energy harvesting from mechanical vibrations using piezoelectric coupling. The basic principles and the direct application to energy harvesting of nonlinear treatment of the output voltage of the transducers for conversion enhancement will be recalled, and extensions of this approach presented. Latest advances in this field will be exposed, such as the use of intermediate energy tanks for decoupling or initial energy injection for conversion magnification. A comparative analysis of each of these techniques will be performed, highlighting the advantages and drawbacks of the methods, in terms of efficiency, performance under several excitation conditions, complexity of implementation and so on. Finally, a special focus of their implementation in the case of low voltage output transducers (as in the case of microsystems) will be presented.
The increasing growth in terms of autonomous devices, promoted both by industrial fields (aeronautics and transports, civil engineering, biomedical engineering,
Several energy sources can achieve this purpose, for instance solar or thermal [
Nevertheless, the energy that can be harvested using Piezoelectric Electrical Generators (PEGs) is still limited to the range of a few tens of microwatts to a few milliwatts, as the mechanical source features limited power and because the coupling coefficient of piezoelectric materials is quite low and localized at particular frequencies, especially when using the elements in flexural solicitation (which is the most common approach to match the input vibration spectrum and increase the input mechanical energy). In order to address this issue, several approaches have been proposed, such as the use of intrinsic mechanical nonlinearities [
Apart from the mechanical approach, nonlinear electronic interfaces have also been proposed in order to increase the conversion abilities of piezoelements, and therefore to harvest more energy. The purpose of the present study is to provide an uptodate view of such systems. In this field, Guyomar
This paper aims at highlighting the specificities, advantages and drawbacks of each of the nonlinear electronic interfaces that have been proposed in the literature (in terms of performance, load independency and so on). A particular focus will be placed on the implementation issues of these techniques for microscale devices (for example performance under low voltage output or scalability of the control circuit).
The paper is organized as follows: Section 2 aims at briefly introducing the basics of energy harvesting, exposing the energy conversion chain in microgenerators, as well as the modeling of the structure and the possible options for increasing the conversion abilities. Then the principles of the nonlinear switching approach and its application to energy harvesting is outlined in Section 3. The performance and implementation issues of these techniques derived from the nonlinear approaches will then be discussed in Section 4. Finally, Section 5 briefly concludes the paper, recalling the main observations and tentatively classifying the techniques considering several criteria.
Generally speaking, a vibration energy harvester can be represented using the schematic depicted in
Therefore, there are three steps in the conversion process:
Conversion of the input energy into mechanical energy.
Electromechanical conversion.
Electrical energy transfer.
However, it is important to note that the conversion processes are affected by the next stage, due to backward coupling. Hence, converting mechanical energy leads to a modification of the properties of the global structure, therefore changing the input energy, and extracting electrical energy from the piezoelectric element changes the amount of mechanical energy converted into electricity. Therefore the design of an efficient microgenerator has to consider:
The maximization of the input energy.
The maximization of the electromechanical energy (coupling coefficient).
The optimization of the energy transfer.
Nevertheless, as stated previously, these design considerations cannot be performed independently because of the backward coupling. At this stage it can be noted that the scope of this paper is to review nonlinear electronic interface for the optimization of the conversion. Hence, only the last two items will be considered. Efficient energy harvesters that consist of taking advantage of mechanical nonlinearities (and in particular nonlinear compliance) to ensure a maximization of the input energy [
In the following, particular attention will therefore be placed on the last two points: optimization of the energy conversion and energy transfer. Considering that the electromechanical system can be modeled by a coupled springmassdamper system depicted in
The energy analysis of such a system over a time range
From
Increase of the voltage.
Reduction of the time shift between speed and voltage (approximating the voltage and speed by monochromatic functions (
Increase the coupling term (
The last option implies the change of the material itself. In this domain, single crystals have recently been investigated [
As the principles of energy harvesting enhancement have been described, the aim of this section is to present the various electronic interfaces that have been proposed in the literature, and to discuss the performance of each. Basically, the approaches can be divided into two categories, whether the piezoelectric element is directly connected to the storage stage, or not.
Nevertheless, whatever the considered case, the operation principles are quite similar and consist of using the two possibilities for enhancing the conversion (
Such a processing of the voltage inversion can be implemented in a really simple way, by briefly connecting the piezoelectric element to an inductor (
However, because of the losses in the switching device (especially resistive losses in the inductor), the voltage inversion is not perfect and characterized by the inversion coefficient
Finally, it can be noted that the concept of the nonlinear operation is independent from the physical phenomenon (as long as one quantity is continuous), allowing its application to other conversion effects [
The first class of nonlinear electronic interfaces for conversion enhancement consists of performing the previously described switching concept with a direct connection of the piezoelectric element to the storage stage.
In this case, starting from the standard implementation of an energy harvester as depicted in
The first and simplest one consists of connecting the switching element in parallel (
The principles of operations of the parallel SSHI [
Open circuit phase
Harvesting phase
Inversion phase
Open circuit phase
Harvesting and inversion phase
It can also be noted that the series SSHI harvesting approach may be obtained by replacing the switching inductance by a transformer, which actually allows an artificial change in the load seen by the piezoelectric element (by a factor
As the SSHIMR also permits an electrical decoupling of the storage stage from the extraction stage, it is possible to combine it with the parallel SSHI, leading to the concept of hybrid SSHI (
Using typical components, the gain, in terms of harvested energy of the SSHI techniques, can reach up to 10 compared to the classical implementation under constant displacement magnitude. The SSHI also permits increasing the effective bandwidth of the microgenerators [
In [
The last possibility for performing the switching process, consists of assisting the voltage inversion through the use of an inverter, using pulsewidth modulation (PWM) approaches (
The previously exposed approaches consisted of directly connecting the piezoelectric element to the storage stage (possibly through an inductor). However, because of this connection, the extracted energy and, therefore, harvested powers are closely dependent on the connected load. In realistic applications, however, the load may not be fixed in advance, and can even change with time according to the state of the connected system (e.g., sleep mode, RF communication,
Hence, in order to counteract this drawback, using the switching concept in a slightly different way has been proposed. In these techniques, the inductance is used as an energy storage element. The energy harvesting process is therefore performed in two steps. First, the energy available on the piezoelement is transferred to the inductance. Then the piezoelement is disconnected from the circuit, and the energy stored in the inductor is transferred to the storage capacitor. This therefore prevents the direct connection of the piezoelectric element to the load, and thus leads to a harvested energy independent of the connected system.
The direct application of this concept leads to the
In order to be able to control this tradeoff, it is possible to combine the series SSHI with the SECE, leading to the Double Synchronized Switch Harvesting (DSSH) technique [
Another approach consists of using the SECE technique but adding an energy feedback loop from the energy storage stage to the piezoelectric element itself that permits applying an initial voltage to the active material [
Extracting the energy from the piezoelectric element (using the SECE interface  S1 and L1).
Providing energy to the piezoelectric insert, from the storage stage (S21, S22 and L2).
Let the voltage increase by leaving the active material in opencircuit condition.
Such an energy injection technique therefore permits bypassing the limits of the unidirectional standalone techniques presented so far (this excludes the case of the active energy harvesting scheme), and features a harvested energy gain of up to 40 (typically 20 using offtheshelf components) compared to the classical system when considering constant displacement magnitude. When the damping effect cannot be neglected, the energy feedback loop, by a particular “energy resonance” effect, allows bypassing the power limit of the previously exposed techniques.
This section outlines the performances of the considered energy harvesting schemes as well as their implementation issues.
Here the performance of the energy harvesting systems will be compared. For the sake of simplicity, it is assumed that the input force is monochromatic (broadband excitation will be discussed in Section 4.2). When considering that the system features a constant displacement magnitude
This figure clearly demonstrates the ability of the nonlinear processing to significantly enhance the conversion enhancement (and thus the power generation ability) of microgenerators when the backward coupling can be neglected (high mechanical damping coefficient and/or low coupling). When using the SSH approach, the harvested power gain is typically 10 compared to the classical technique. However, it will be further shown that the two schemes feature the same power limit for highly coupled, weakly damped systems. The particular principles of the active energy harvesting scheme also permit an outstanding power output (theoretically infinite), but it has to be noted that the switching and driving losses have not been taken into account in the figure. A full analysis of the energy transfer and energy balance would show the limits of this technique. The damping effect (in the constant displacement magnitude case, the input energy is neither fixed nor bounded) not taken into account here, would also decrease the power harvested by the active scheme.
Although the series SSHI features a power slightly less than the parallel SSHI, it permits a decrease of the optimal load, which may be beneficial for realistic systems, as the dielectric behavior of piezodevices associated with the low frequencies of vibration leads to relatively high optimal resistance (usually several hundreds of kiloohms in standard case). Hence the series SSHI may be more adapted to electronic devices whose input impedance is less than this value, which is generally the case. However, although they permit a high power gain, the SSHI approaches are strongly dependent on the connected load, which would be problematic if the connected system would have an input impedance varying with time (corresponding, for example, to a change in state, e.g., from active transmission to sleep mode). An additional stage aimed at providing a constant load seen by the piezoelectric element would therefore be required [
Such an case does not occur when using the SECE, DSSH or ESSH approaches, as these techniques provide a natural load adaptation, although providing lower power output (it can however be noted that the global output of SSHI generator with load adaptation stage is similar to the harvested power of the DSSH and ESSH; the latter requiring less components as well). To a lesser extent, the SSDCI also permits an independent harvested power from the load as long as the rectified voltage (or equivalently the load) is less than a critical value.
Finally, using a part of the harvested energy to allow a bidirectional energy transfer (energy injection technique) allows outperforming all the previously exposed techniques, with a typical energy gain of 20 using typical offtheshelf components. Such an energy harvesting magnification may be explained by a particular “energy resonance” effect that occurs at the optimal load. As the power output increases, the injected energy increases as well; this leads to an increase of the harvested energy and so on. It can be seen on
The associated energy cycles for each technique are depicted in
When considering that the converse piezoelectric effect may not be neglected (low damping and high electromechanical coupling), harvesting electrical energy decreases the amount of mechanical energy in the structure, leading to a damping effect that limits the conversion. In this case, when considering that the system is driven by a constant force magnitude, the harvested powers as a function of normalized loads and powers, as well as of the figure of merit
In this case, it can be shown that the use of nonlinear approaches permits harvesting the same amount of energy than the standard approach but using much less volume of active materials (
However, the most efficient technique among the unidirectional energy transfer approaches remains the active scheme, which permits reaching the power limit for very low value of
From
When designing systems that aim at scavenging energy from environmental sources, particular attention has to be placed on the design in terms of realistic implementation (e.g., the energy balance between harvested energy and required energy should be positive).
In terms of implementation issues, several architectures have been proposed to make the switch control autonomous [
Although the previous analysis has been done considering sine excitation, realistic solicitation would more likely be random. Although few analyses have been conducted in this domain for nonlinear systems [
In the particular case of smallscale systems and microsystems (e.g., MEMS devices), some considerations occur with respect to the implementation of the control systems [
However, the main limitations of piezoelectric generators at microscale are due to the electronic command, and particularly discrete components (such as diodes and transistors) that feature voltage gap whose values which are typically a few hundreds of millivolts [
This paper proposed a comprehensive review of nonlinear energy harvesting interfaces for performance enhancement of vibration energy harvesters featuring the piezoelectric element. The principles of each scheme have been presented and main results summarized, and the specificities of each of them emphasized, in terms of output power, load dependency and performance under low piezoelectric output voltage. From the analyses done though the paper, it is possible to classify the techniques according to several criteria. As a conclusion,
General schematic of a vibration energy harvester.
Electromechanically coupled springmassdamper system.
(
Standard energy harvesting interface.
Synchronized Switch Harvesting on Inductor (SSHI): (
Hybrid SSHI.
SSDCI.
Active energy harvesting scheme.
Synchronous Electric Charge Extraction (SECE).
Double Synchronized Switch Harvesting (DSSH).
Energy harvesting, featuring energy injection.
Normalized harvested powers under constant vibration magnitude.
Normalized energy cycles (converted and transferred) for different energy harvesting interfaces: (
(
Principles of the selfpowered switching device.
Diodeless Series SSHI.
Classification of the harvesting techniques.
Standard 






Parallel SSHI 






Series SSHI (diodeless) 






SSHIMR 






Hybrid SSHI 






SSDCI 






Active Scheme (Ericsson) 






SECE 






DSSH/ESSH 






Energy injection 






The “happy face”relates the maximum power greater than all the other techniques for moderate value of