Piezoelectric Energy Harvesting System Research Articles

Modeling and Characteristic Analysis of Combined Beam Tri-Stable Piezoelectric Energy Harvesting System Considering Gravity

The emergence of the vibration energy harvesting system makes it possible for wireless monitoring nodes in coal mines to realize self-power supply. In order to reveal the influence of gravity effect on the response characteristics of the combined beam tri-stable piezoelectric energy harvesting system (CTEHS), the system’s nonlinear magnetism is calculated according to the principle of point magnetic charge dipole, and the system’s nonlinear resilience is obtained through experimental measurements and nonlinear fitting methods. Based on the Lagrange equation, the system’s electromechanical coupling motion model considering gravity is established. The system’s motion equation is solved numerically based on the Runge–Kutta algorithm, and the effects of the end magnet mass and the initial vibration point on the bifurcation behavior, potential energy, and system output performance are investigated by emulation and experiment. The research shows that the magnet’s gravity effect causes a change in the stable equilibrium position and the system’s motion state and also causes the system to generate additional gravitational potential energy, which leads to a potential asymmetric well of the system. Under the consideration of magnet gravity, the appropriate end magnet mass and initial vibration point can not only reduce the system’s requirements for external excitation strength but also effectively improve the system’s response and output. This research provides a new theoretical basis for the optimal design of the tri-stable piezoelectric energy harvesting system.

Statistical linearization for random vibration energy harvesting with piezoelectric material nonlinearity

Due to piezoelectric softening and dissipative nonlinearities, the piezoelectric cantilever energy harvester exhibits nonlinear hysteresis when subjected to large excitation. These nonlinearities have brought significant challenges to the modeling and response prediction of randomly excited piezoelectric energy harvesting systems. In this study, the voltage responses of the nonlinear piezoelectric cantilever energy harvester under random excitation are initially assumed to follow the Gaussian distribution which is experimentally validated later. The equivalent linear transfer function are derived from the approximate linearization of the stiffness and damping using the statistical linearization (SL) technique. The mathematical expectations of the voltage responses are calculated from the multivariate normal distributions. Frequency sweep experiments are conducted to a cantilever energy harvester to identify the nonlinear piezoelectric material properties. The statistically linearized model was experimentally validated under random base acceleration excitation by comparing the probability density function of the predicted voltage responses and average power against the experimental measurements. The advantage of the SL technique lies in allowing one to use an iterative procedure to estimate the equivalent linear terms while the analytical expressions are unattainable because of the complex nonlinearity in the governing equations. The results show that the prediction of the SL model to the random base acceleration excitation agrees with experimental measurements with a broadband frequency range, although only the fundamental mode of the beam is considered.

Nonlinear piezoelectric energy harvesting induced through the Duffing oscillator.

In this paper, nonlinear piezoelectric energy harvesting induced by a Duffing oscillator is studied, and the bifurcation trees of period-1 motions to chaos for such a piezoelectric energy-harvesting system are obtained analytically. Distributed-parameter electromechanical modeling of a piezoelectric energy harvester is presented first, and the electromechanically coupled circuit equation excited by infinitely many vibration modes is developed. The governing electromechanical equations are reduced to ordinary differential equations in modal coordinates, and eventually an infinite set of algebraic equations is obtained for the complex modal vibration responses and the complex voltage responses of the energy harvester beam. One single mode case is considered in this paper, and periodic motions with bifurcation trees are obtained through an implicit discrete mapping method. The frequency-amplitude characteristics of periodic motions are obtained for the nonlinear piezoelectric energy-harvesting systems, which provide a better understanding of where and how to achieve the best energy harvesting. This study describes about how the nonlinear oscillator induces piezoelectric energy harvesting through a beam system. The nonlinear piezoelectric energy harvesting is presented through a nonlinear oscillator. Due to the nonlinear oscillator, chaotic piezoelectric energy-harvesting states can get more energy compared to the linear piezoelectric energy-harvesting system.

Simulation and performance analysis of self-powered piezoelectric energy harvesting system for low power applications

<span lang="EN-US">Energy harvesting is a process of extracting energy from surrounding environments. The extracted energy is stored in the supply power for various applications like wearable, wireless sensor, and internet of thing (IoT) applications. The electricity generation using conventional approaches is very costly and causes more pollution in the environmental surroundings. In this manuscript, an energy-efficient, self-powered battery-less piezoelectric-based energy harvester (PE-EH) system is modeled using maximum power point tracking (MPPT) module. The MPPT is used to track the optimal voltage generated by the piezoelectric (PE) sensor and stored across the capacitor. The proposed PE system is self-operated without additional microarchitecture to harvest the Power. The experimental simulation results for the overall PE-EH systems are analyzed for different frequency ranges with variable input source vibrations. The optimal voltage storage across the storing capacitor varies from 1.12 to 1.6 V. The PE-EH system can harvest power up to 86 µW without using any voltage source and is suitable for low-power applications. The proposed PE-EH module is compared with the existing similar EH system with better improvement in harvested power.</span>

Design and analysis of piezoelectric energy harvester for laser pointer

Obtaining energy from human body activities to power electronic equipment has broad application prospects. In this study, a piezoelectric energy harvesting system is designed to harvest energy from human finger rapping. The harvested energy can drive a laser lamp group to operate. The piezoelectric energy harvester uses a piezoelectric cantilever beam with a spring-mass block at the free end to obtain the kinetic energy of the finger operating a laser pen. The structure can produce considerable bending deformation under finger movement. At the same time, a dual-input synchronized switch harvesting on inductor circuit is designed to extract the charge generated by the piezoelectric beam when the spring-mass block at the free end is rapped and store it in the energy storage element. The charge and discharge of the energy storage element are controlled by a DC-DC management circuit. Experimental results show that the average harvesting power of the piezoelectric energy acquisition system is 169 μW, and its power density is 388.5 μW/cm3. When the spring-mass block is rapped for 8 s, the energy generated by the piezoelectric energy harvester lights the laser pen for 0.35 s.

Parametric Analysis of Nonlinear Bi-Stable Piezoelectric Energy Harvester Based on Multi-Scale Method

Given the geometric nonlinearity of the piezoelectric cantilever beam, this study establishes a distributed parameter model of the nonlinear bi-stable cantilever piezoelectric energy harvester, following the generalized Hamilton variational principle. The analytical expressions of the dynamic response were obtained for the energy harvesting system using Galerkin modal decomposition and the multi-scale method. The investigation focuses on how the performance of the energy harvesting system is influenced by the gap distance between magnets, external excited amplitude, mechanical damping ratio and external load resistance. The calculation results were compared with those obtained neglecting the geometric nonlinearity of the beam. The results show that the system responses contain jump and multiple solutions. The consideration of the geometrical nonlinearity significantly amplified the peak displacement and peak output power of the intra-well and inter-well motions. There is an evident hardening effect of the inter-well motion frequency response curve. By reasonable adjusting the parameters, it is possible to improve the output power of the piezoelectric energy harvesting system and broaden the operating frequency of the system.

A self-powered H-Bridge joule theory circuit for piezoelectric energy harvesting systems

• A self-powered HBRJT is proposed for energy harvesting. • The proposed circuit rectifies, boost the low voltage into high DC voltage. • A novel application can be developed using the proposed circuit. In this paper, investigation of high direct current/voltage (DC) and power gains using H-Bridge joule theory (HBRJT) circuit with an input voltage of alternating current/voltage (AC) is carried out by avoiding higher switching frequency and additional switches for piezoelectric energy harvesting (PEH) systems. The interventions of the proposed HBRJT circuit delineate the boost conversion topology from AC that is generated by the piezoelectric generator (PG) as a result of the excitation into DC and eliminates the usage of additional switches, inductors, capacitors, duty cycles that result in higher output DC voltage. The proposed topology integrates the implications of both the H-Bridge and joule theory circuits. One additional feasibility of the proposed circuit is that it does not require an additional power supply to trigger the switches. In order to validate the effectiveness of the HBRJT circuit, both simulation and experimental results were presented. In the experiment, a series of testing scenarios were carried out, namely varying the frequency with fixed input voltage and cold start-up at a high frequency. The outcome of the proposed circuit is compared with the conventional H-Bridge, Dual-stage H-Bridge (DSHBR) and literature circuits. When contrasted to H-Bridge DSHBR circuits, the proposed circuit significantly boosts the input low AC voltage into high DC voltage. In addition, compared to structures with an H-Bridge, DSHBR, and literature circuits, the HBRJT circuit is more feasible to achieve supposed voltage and power gains without duty cycles and auxiliary circuits.

Output optimization of piezoelectric monitoring system considering loss impedance and spatial arrangement under traffic load

A widely adoption of stacked piezoelectric transducers in roads or railways health monitoring is limited by a lack of matching quantitative impedance analysis and optimal spatial arrangement. This paper proposes an equivalent circuit model of the stacked piezoelectric transducer considering loss impedance to quantify the output electrical energy. Assisted by laboratory tests, variation in loss impedance as loading amplitude and frequency is obtained, and then, is incorporated into the proposed model to calculate output of piezoelectric transducers. A numerical model is further established to assess effect of spatial arrangement on output of piezoelectric transducers combining with theoretical model and laboratory tests. It is observed that energy output of layered arrangement increases by 300% than that of flat arrangement. An increase in the transducers number not only reduces the matching impedance but also the corresponding output of piezoelectric transducers under the same traffic load. Moreover, a field test is carried out to study the external impedance output power of a stacked piezoelectric energy harvesting system. A closed comparison between theoretical and test results verifies that the proposed model with special consideration on the loss impedance can predict the output of piezoelectric transducers reasonably well, which provides a reference for optimizing the self-power health monitoring system used in roads or railways.

Experimental study of a two-degree-of-freedom piezoelectric cantilever with a stopper for broadband vibration energy harvesting

This paper presents a two-degree-of-freedom (2-DOF) piezoelectric energy harvesting (PEH) system with a stopper for wideband operation. The proposed system consists of a folded piezoelectric cantilever with a stopper integrated. Two cases are considered where the stopper is placed at the free end of the outer beam and inner beam, respectively. It is shown experimentally that with the proper parametric combination we can move the anti-resonance point outside the two resonant peaks and widen the frequency responses of both the peaks. Large amplitude voltage output over 11 Hz can be obtained when we focused on the dynamics of the inner beam. In addition, it is demonstrated that arranging the stopper at the free end of the inner beam yields better performance than that with the stopper placed at the outer beam. Detailed parametric studies are performed to investigate the influences of the stopper distance, amplitude of base movement, and frequency sweep directions on the voltage output. A maximum power output of 713μW is obtained.

Circuit Techniques for High Efficiency Piezoelectric Energy Harvesting.

This brief presents a tutorial on multifaceted techniques for high efficiency piezoelectric energy harvesting. For the purpose of helping design piezoelectric energy harvesting system according to different application scenarios, we summarize and discuss the recent design trends and challenges. We divide the design focus into the following three categories, namely, (1) AC-DC rectifiers, (2) CP compensation circuits, (3) maximum power point tracking (MPPT) circuits. The features, problems encountered, and suitable systems of various AC-DC rectifier topologies are introduced and compared. The important role of non-linear methods for piezoelectric energy harvesting is illustrated from the perspective of impedance matching. Energy extraction techniques and voltage flipping techniques based on inductors, capacitors, and hybrid structures are analyzed. MPPT techniques with different features and targets are discussed.

Foot Drop Stimulation via Piezoelectric Energy Harvester

The design and implementation of a piezoelectric energy-harvesting system, aimed at stimulating the Tibialis anterior muscle to aid patients struggling with a foot drop disability, are investigated. A physical prototype designed to be installed inside a shoe sole, consisting of an energy-harvesting unit along with a power-management circuit and a functional electrical-stimulation circuit, is fabricated. The piezoelectric energy harvester (PEH) incorporated six layers of Polyvinylidene-Fluoride sheets to achieve a mean-charge generation of 65.25 μC/step and a peak power of 10.76 mW/step. A peak voltage of +80.0 V generation was achieved during a stomping motion. The electrical systems store, convert, and deploy 60 mA electric pulses at the desired frequencies to the target muscle. The finalized prototype is best-suited to prolong the duration of the charged batteries whilst in use. In a practical sense, it should be used alongside external-power sources to recharge the batteries installed in a foot drop stimulation device. The PEH in its current state is fully capable of solely powering blood pressure sensors, glucose meters, or activity trackers.

L-shape triple defects in a phononic crystal for broadband piezoelectric energy harvesting

This study proposes a phononic crystal (PnC) with triple defects in an L-shape arrangement for broadband piezoelectric energy harvesting (PEH). The incorporation of defects in PnCs has attracted significant attention in PEH fields owing to properties such as energy localization and amplification near the defect. Several studies have been conducted to enhance output electric power of PnC-based PEH systems with single defects. However, it is susceptible to the limitations of narrow bandwidth. Recently, double-defect-incorporated systems have been proposed to widen the PEH bandwidth via defect-band splitting. Nevertheless, the PEH performance rapidly decreases in the frequency range between the split defect bands. The limitations of single- and double-defect-incorporated systems can be resolved by the incorporation of the proposed design concept, called the L-shape triple defects in a PnC. The isolated single defect at the top vertex of the letter ‘L’ compensates for the limitations of double-defect-incorporated systems, whereas the double defects at the bottom vertices compensate for the limitations of the single-defect-incorporated systems. Hence, the proposed design can effectively confine and harvest elastic-wave energy over broadband frequencies while enhancing the application of single and double defects. The effectiveness of the proposed design concept is numerically validated using the finite element method. In the case of a circular hole-type PnC, it is verified that the PnC with L-shape triple defects broadens the bandwidth, and improves the output voltage and electric power compared with those of single- and double-defect-incorporated systems. This study expands the design space of defect-incorporated PnCs and might shed light on other engineering applications of the frequency detector and elastic wave power transfer.

Application of the meta-substrates for power amplification in rotary piezoelectric energy harvesting systems: Design, fabrication and testing

In this paper we numerically and experimentally investigate a new proposal of utilizing the auxetic meta-structure concepts to enhance the efficiency of piezoelectric energy harvesters in rotating systems. The proposed energy harvester is designed to be installed on the freight train axel to provide necessary power for the self-powered sensors. The harvester is a resonator consists of a cantilever beam with a tip mass and a piezoelectric patch mounted on its latticed substrate. Three various auxetic patterns are suggested and implemented on the base of the cantilever in order to enhance the harvested powers. The efficiency enhancement of the suggested concepts is compared with a conventional plain resonator. In order to optimize the geometrical parameters of the auxetic patterns and investigate the efficiency of various resonator’s output power, the finite element modeling (FEM) is employed. Maximum output powers according to the optimum electrical resistance and resonance frequency are achieved. Also, the effects of different PZT types on the extracted energy are taken into investigation. Two different substrate materials (aluminum and steel) are used in the fabrication of resonators. The​ numerical models are validated by experimental results in the rotating speed at the range of 6–7 Hz, which is tuned to the operational rotational frequency of the freight train axles. It is shown that for Auxetic-I, Auxetic-II, and Auxetic-III, the magnification factors are 3.28, 2.5, and 2.14 are achieved for the aluminum substrate. These factors are 3.0, 2.6, and 2.3 for the steel resonator, respectively. The experimental results show that the auxetic resonators are able to considerably enhance the efficiency of rotary energy harvesting systems.

Piezoelectric and thermoelectric energy harvesting system based on a self-triggered flyback converter topology

Piezoelectric and thermoelectric energy harvesting system based on a self-triggered flyback converter topology

Multicriteria Approach for Design Optimization of Lightweight Piezoelectric Energy Harvesters Subjected to Stress Constraints

In this work a multicriteria optimization approach to minimize weight and maximize power output in piezoelectric energy harvesting systems for aerospace applications is studied. The design variables are the geometric and electric circuit parameters of the vibration-based piezoelectric energy harvester (PEH). A finite element model is developed to model the dynamic behavior of the composite plate-type harvester with embedded piezoelectric layers. The cantilever PEH structure is subjected to constraints in the bending stresses which must be lower than or equal to the tensile yield strength of the piezoelectric material. For solving the multi-objective optimization problem, the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the Non-dominated Sorting Genetic Algorithm III (NSGA-III) and the Generalized Differential Evolution 3 (GDE3) algorithm are employed. It is shown that the proposed algorithms are effective in developing optimal Pareto front curves for maximum electrical power output and minimum mass of the PEH system. A comparative assessment of the solutions generated on the Pareto Front show that GDE3 achieved solutions that generate higher maximum power output and performs better compared to the two other algorithms.

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 article extends the equivalent impedance analysis from single harmonic to multiple harmonics for describing the complex dynamics and harvested power of a PEH system under nonharmonic 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.

Non-Linear Switching Circuit for Active Voltage Rectification and Ripples Reduction of Piezoelectric Energy Harvesters

This paper describes an improved non-linear switching circuit (INLSC) for active rectification of voltage and reduction of ripples in the voltage waveform for the piezoelectric energy harvesting (PEH) system. The proposed converter controls the alternating current (AC) generated by the piezoelectric device (PD) under mechanical vibration. The proposed circuit combines the boost and buck-boost processes through a switching process, which functions in both positive and negative cycles. In addition, it controls the voltage and frequency of the load capacitor. In this process, the passive components in the circuit are energised by being short with the AC voltage using switching signals, which facilitates the active rectification of ultra-low AC voltage. Design considerations, theoretical analysis, simulations and experimental results are presented. It was shown that the circuit was able to control the switching signal and to convert low AC voltage (0.44 Vi) to high direct current (DC) voltage (6.5 Vdc) while achieving an output power of 469 µW which outperforms the existing similar circuits and synchronous rectifier circuit. The ripples in the rectified voltage were also comparatively less. Application-wise, the proposed circuit could power a manually connected 7-segments display, commonly used for traffic applications.

Performance analysis of nonlinear vibration energy harvesting system with inelastic barrier under colored noise excitation

The vibro-impact structures are introduced into the piezoelectric vibration energy harvesting (VEH) systems, which can broaden the operating bandwidth of the piezoelectric VEH systems and thus improve the harvesting efficiency. The process of vibro-impact not only causes energy loss during the impact process but also causes the local deformation between two impact bodies. Therefore, this manuscript proposes a class of stochastic non-classical inelastic impact VEH models, whose non-classical impact processes are described by Hertz contact forces. Firstly, the relationship between the total energy of the unperturbed system and the potential energy of the system at the barrier position is used to determine whether the impact phenomena have occurred or not, then used to derive the period and frequency of the system. Secondly, using the quasi-conservative stochastic averaging method, the averaged drift term and the averaged diffusion term of the piecewise smooth averaged Ito^ equation are derived. The stationary probability density functions (PDFs), the mean square output (MSO) voltage and the root mean square (RMS) voltage of the system response can be obtained from solving the corresponding Fokker-Planck-Kolmogorov (FPK) equation for averaged Ito^ equation. Finally, an example is provided to verify the effectiveness of the proposed method, and the effects of the model parameters on the MSO voltage and power conversion efficiency (PCE) are analyzed. The relationship between the MSO voltage and the PCE is also analyzed. It is of great significance for the design and optimization of stochastic VEH systems.

Uncertainty analysis of galloping based piezoelectric energy harvester system using polynomial neural network

This paper deals with the impact of uncertain input parameters on the electrical power generation of galloping-based piezoelectric energy harvester (GPEH). A distributed parameter model for the system is derived and solved by using Newmark beta numerical integration technique. Nonlinear systems tend to behave in a completely different manner in response to a slight change in input parameters. Due to the complex manufacturing process and various technical defects, randomness in system properties is inevitable. Owing to the presence of randomness within the system parameters, the actual power output differs from the expected one. Therefore, stochastic analysis is performed considering uncertainty in aerodynamic, mechanical, and electrical parameters. A polynomial neural network (PNN) based surrogate model is used to analyze the stochastic power output. A sensitivity analysis is conducted and highly influenced parameters to the electric power output are identified. The accuracy and adaptability of the PNN model are established by comparing the results with Monte Carlo simulation (MCS). Further, the stochastic analyses of power output are performed for various degrees of randomness and wind velocities. The obtained results showed that the influence of the electromechanical coefficient on power output is more compared to other parameters.

On Theoretical and Numerical Aspects of Bifurcations and Hysteresis Effects in Kinetic Energy Harvesters

The piezoelectric energy-harvesting system with double-well characteristics and hysteresis in the restoring force is studied. The proposed system consists of a bistable oscillator based on a cantilever beam structure. The elastic force potential is modified by magnets. The hysteresis is an additional effect of the composite beam considered in this system, and it effects the modal solution with specific mass distribution. Consequently, the modal response is a compromise between two overlapping, competing shapes. The simulation results show evolution in the single potential well solution, and bifurcations into double-well solutions with the hysteretic effect. The maximal Lyapunov exponent indicated the appearance of chaotic solutions. Inclusion of the shape branch overlap parameter reduces the distance between the external potential barriers and leads to a large-amplitude solution and simultaneously higher voltage output with smaller excitation force. The overlap parameter works in the other direction: the larger the overlap value, the smaller the voltage output. Presumably, the successful jump though the potential barrier is accompanied by an additional switch between the corresponding shapes.