Electrical Load Resistance Research Articles

Performance analysis of functionally graded multifunctional piezoelectric energy harvesting microgyroscopes

Functionally graded materials (FGMs) are composite materials with varying material properties in one or more directions. These materials possess distinct characteristics compared to their constituent components. The ability to control material distribution and compositions in FGMs offers improved constraints over the natural frequencies of the system, making them highly suitable for energy harvesting applications. In this study, we focus on a piezoelectric FGM composed of Platinum (Pt) and Lead Titanate Zirconate (PZT). By utilizing FGMs for energy harvesting, we simplify the system from a multilayer structure to a single-layer system, thereby increasing power density by reducing volume. In this work, a power law distribution is used to model the material variation throughout the thickness of the single-layered beam. The governing equations of motion and boundary conditions for FG energy harvesting microgyroscope are derived using Euler-Bernoulli beam theory, the constitutive piezoelectric principle, and the extended Hamilton's principle. To simulate the nonlinear motion of the FG energy harvester, we employ the differential quadrature method (DQM). Subsequently, an investigation is carried out to examine the effects of various factors including material distribution, platinum percentage, base rotation, DC voltage, and electrical load resistance on the energy harvesting microgyroscope with functionally graded materials. The findings suggest that functionally graded energy harvesting gyroscopes can be adjusted to obtain effective energy harvesting and sensing capabilities by carefully selecting the material distribution, input voltage, and electrical load resistance.

Sensor Fusion for Power Line Sensitive Monitoring and Load State Estimation.

This paper deals with a specific approach to fault detection in transformer systems using the extended Kalman filter (EKF). Specific faults are investigated in power lines where a transformer is connected and only the primary electrical quantities, input voltage, and current are measured. Faults can occur in either the primary or secondary winding of the transformer. Two EKFs are proposed for fault detection. The first EKF estimates the voltage, current, and electrical load resistance of the secondary winding using measurements of the primary winding. The model of the transformer used is known as mutual inductance. For a short circuit in the secondary winding, the observer generates a signal indicating a fault. The second EKF is designed for harmonic detection and estimates the amplitude and frequency of the primary winding voltage. This contribution focuses on mathematical methods useful for galvanic decoupled soft sensing and fault detection. Moreover, the contribution emphasizes how EKF observers play a key role in the context of sensor fusion, which is characterized by merging multiple lines of information in an accurate conceptualization of data and their reconciliation with the measurements. Simulations demonstrate the efficiency of the fault detection using EKF observers.

Dynamic Behavior of Galloping Micro Energy Harvester with the Elliptical Bluff Body Using CFD Simulation

Energy extraction from flow-induced oscillations based on piezoelectric structures has recently been tackled by several researchers. This paper presents a study of the dynamic behavior analysis and parametric characteristics of a galloping piezoelectric micro energy harvester (GPEH) applied to self-powered micro-electro-mechanical systems (MEMS). The mechanical performance of a piezoelectric micro energy harvester cantilever beam with two layers of elastic silicon and piezoelectric (PZT-5A) attached to a tip elliptical cylinder is numerically simulated. Using size-dependent beam formulation on the basis of the modified couple stress theory and Gauss’ law, the coupled electro-mechanical non-linear governing equations of the energy harvester are obtained. The mode summation and Galerkin methods are used to derive the extracted power from the system. The study also models the flow field effect on the beam oscillations via CFD simulation. The effect of elliptical cylinder mass, damping ratio, beam thickness, and load resistance on the dynamic behavior and harvested power of the system is studied. Findings reveal that increasing the normalized tip mass from 0 to 0.5 and 1 increases the output power density from 0.12 to 0.2 and 0.22, respectively, and the corresponding electrical load resistance of maximum power increases from 175 to 280 kΩ and 375 kΩ, respectively. An approximately linear relation between the elliptical cylinder mass and the load resistance is observed. By increasing/decreasing the cylinder mass, the required electrical load resistance for maximum output power proportionally changes. The damping analysis shows that a higher damping ratio increases the onset velocity of galloping and decreases the extracted power.

Thermoacoustic hysteresis of a free-piston Stirling electric generator

A panorama of thermoacoustic hysteresis of a free piston Stirling electric generator (FPSG) was studied, where a thermoacoustic networks approach was proposed to model the corresponding process. Of the featuring nonlinear phenomena inherent in an FPSG, thermoacoustic hysteresis occurs during the onset and damping evolvement, representing irreversibility and pertinent loss characteristics to some degree. In order to unveil the underlying mechanism, onset and damping experiments were conducted, on a lab-developed 5 kW FPSG prototype, under multiple operating conditions. The experimental results show that the damping temperature is significantly higher than the onset temperature, and dynamic parameters all experience a similar hysteresis curve against heating block temperature. It is found that larger initial heating power leads to higher onset temperature, while charge pressure exerts an opposite impact. So far, as the electric load resistance is concerned, the larger one leads to both lower onset and damping temperature. Based on the experiments, a frequency-domain thermoacoustic networks model was developed and validated, with a maximum deviation within 2.79% in onset temperature and −0.96% in onset frequency at various load resistance. Although the dynamic damping process is not reproduced in the current model, it provides a good way to predict the onset characteristics promptly.

Performance investigation and parameter identification of inverse variable cross-section energy harvester

An important issue in traditional energy harvesters is that the best performance of the device is limited to the uneven longitudinal strain and electric displacement distributions. One solution to this challenge is to incorporate of variable cross-section design and rotational motion. In this study, we propose a new rotational inverse complex piezoelectric energy harvester featuring two beams for ultra-low-frequency rotation applications. A comprehensive electromechanical model is developed based on the extended Hamilton's principle, and the analytical models are extracted for vibration response and electric performance under ultra-low-frequency excitations. Closed-form analytical expressions of the rotational frequency, electrical load resistance, and centrifugal coefficient are derived to give in-depth insights into the influence mechanism of the centrifugal softening effect for the extreme conditions of RL→0 and RL→∞. Moreover, we propose a parameter identification method to recognize optimal electrical load resistance for ultra-low-frequency rotational scenarios in the absence case of experimental equipment. Based on the validated theoretical model, parametric studies are conducted to investigate the effects of the structural parameters on the dynamic behaviors and output electric performance, it can be concluded that the appropriation selection of the structural parameters can change the dynamic behaviors of the harvester and enhance the energy harvesting performance. Besides, the prototype of the proposed harvester was designed and fabricated and experiments were carried out. Both analytical simulation and experimental results show that the proposed inverse energy harvester has an excellent harvesting performance at the ultra-low-frequency rotational excitations, and the output voltage of the proposed inverse energy harvester is 12% larger than that of a traditional inverse energy harvester.

Development and applicability of low-fidelity solutions for electret-based microcantilever energy harvesters

An electrostatic energy harvester is investigated where the reduced-order model is developed accounting for the electrical and mechanical nonlinearities. To overcome the difficulty of dealing with such a nonlinear model, an analytical approach based on the method of multiple scales is employed to create analytical solutions for displacement, electrical charge, and power of this harvester. The reduced-order model with the analytical solutions makes this approach novel and unique. The limits of applicability of this approach is determined by comparing the analytical solutions with solutions obtained using numerical integration. The results show that with estimating the effective nonlinearity as suggested in this approach, it is possible to interpret the behavior of harvester for a variety of operating conditions. The effective nonlinearity decreases more for a particular electrical load resistance as the electret voltage increases. However, the effective nonlinearity increases for a particular electret voltage as the electrical load resistance increases. When effective nonlinearity becomes very small, the behavior of the harvester turns into almost linear, and the matching of solutions of method of multiple scales with solutions of numerical integration is perfect. But, when the effective nonlinearity is significant, the deviation between solutions of method of multiple scales and solutions of numerical integration becomes noticeable. Moreover, increasing acceleration amplitude of the base excitation for cases of significant effective nonlinearity creates a bounded motion with softening behavior.

Nonlinear modeling, characterization, and effectiveness of three-degree-of-freedom piezoaeroelastic energy harvesters

Modeling and performance investigation is conducted on a three-degree-of-freedom piezoaeroelastic system with freeplay and multi-segmented stiffness with and without impact. A piezoelectric transduction mechanism is considered in the plunge degree of freedom and the aerodynamic loading is modeled with the unsteady representation based on the Duhamel formulation, including the stall phenomenon. The typical aeroelastic section model is comprised of a pitching and plunging airfoil with a control surface containing freeplay and multi-segmented stiffness springs in the pitch and control surface motions. Nonlinear characterization is conducted on the response of the energy harvesting system when changing the nonlinear stall coefficient, freeplay gap size in the pitch and control surface springs, and the multi-segmented nonlinear stiffness to simulate impact. Results show that grazing and grazing/sliding bifurcations may be present, and the response is complex with several transitions as the wind speed is increased. Additionally, the presence of freeplay and multi-segmented nonlinearities allow for energy harvesting at speeds smaller than that of the linear flutter velocity. An effective design is determined for a three-degree-of-freedom wing-based energy harvester by selecting the freeplay gap size and multi-segmented nonlinear stiffness in the pitch and control surface and the electrical load resistance.

Experimental comparative analysis of hybrid energy harvesters exposed to flow-induced vibrations

In this study, hybrid energy harvesting based on electromagnetic induction (EM) and piezoelectric transduction (PZT) is experimentally investigated under different conditions of flow-induced vibrations. The energy harvesting performance of the system is examined when the electromagnetic and piezoelectric mechanisms are used both separately and simultaneously. In this regard, firstly, only electromagnetic induction harvesting structure is attached to a beam, and time-dependent voltage and displacement are experimentally investigated. Then, PZT has adhered to the beam, and voltage outputs are measured in both the PZT and EM circuits. The third scenario is based on removing the electromagnetic harvesting structure and only the piezoelectric energy harvesting performance is studied. The mentioned cases are investigated under different excitation circumstances, that is, distinct bluff-body geometries and flow velocities. While the square bluff-body geometry is connected to the structure, both PZT and EM harvested power are determined by considering different electrical load resistances. It is mainly revealed that the total energy amount is higher in the hybrid configuration. After determining the hybrid structure is the most effective, elements with different splitters geometry are attached to the bluff-body geometry of the harvesting structure. Finally, the vibration enhancement potential of these new types of splitters on the harvesting structure is experimentally investigated. For the solo electromagnetic harvester, the maximum power is obtained at an external load resistance value of 10 kΩ, while for the solo PZT harvester, the maximum power is observed at the resistance value of 330 kΩ. Among the three types of splitter geometries examined, the highest voltage was obtained from type-1 as 14.168 V.

Increasing the efficiency of a bistable cantilever beam energy harvester exploiting vibro-impact effects

In this paper, a novel energy harvester is proposed by adding a barrier to a typical bistable energy harvester, which is modeled exploiting an equivalent single degree of freedom. By using Euler-Lagrange equations, mass, structural stiffness, magnetic force and electromechanical coupling coefficient of the harvester, are converted to an equivalent SDOF model. The frequency bandwidth of the system and the level of harvested power in impacting and non-impacting conditions are obtained. According to the numerical results, it is found by adding a barrier to a typical bistable energy harvester, the working frequency bandwidth of the system is increased tangibly. In fact, by vibro-impact phenomenon, the working frequency bandwidth and extracted power of the system are increased about 42.95% and more than 7 times, respectively. Additionally, the effects of stiffness and initial gap of the barrier are shown on frequency bandwidth of the harvester. It is observed that the gap distance has more effect on widening frequency bandwidth of the system against barrier stiffness. Finally, the effect of the electrical load resistance on the harvested power is discussed at various barrier stiffnesses and initial gap distances and finally the optimum values of the electrical load are provided for each condition.

A generalized whole-cell model for wastewater-fed microbial fuel cells

A comprehensive mathematical modeling of wastewater-fed microbial fuel cells (MFC) demands an in-depth process understanding of the main electrical and bioelectrochemical interactions at both electrodes. In this study, a novel holistic simulation approach using a low-parameterized model was applied to predict pollutant transport, conversion, and electrical processes of mixed-culture single-chamber MFCs. The proposed whole-cell model couples the combined bioelectrochemical-electrical model with the well-established Activated Sludge Model No.1 (ASM1) and specific equations from ASM2. The cathodic gas–liquid mass transfer of oxygen and free ammonia nitrogen was described in terms of a diffusion film model, while the diminishing diffusivity due to salt deposits was considered via a fouling decline kinetic model. The predictive capacity of the model was validated using experimental data of three continuous-flow single-chamber MFCs operated with municipal wastewater for 150 days. Electrochemical parameters were estimated in real-time by pulse-width modulated connection of the external electrical load resistance. Following a sensitivity analysis, the most relevant model parameters were optimized through the Monte-Carlo Markov-Chain method using the adaptive Metropolis algorithm. All other parameters were adopted from benchmark simulation studies. The simulated relative contributions of aerobic carbon oxidation, denitrification, electrogenesis, and methanogenesis to the total COD removal rate were 21–22%, 44–45%, 21–25%, and 9–14%. Overall, the presented whole-cell model is able to successfully predict the evolution of electricity generation, methane production, and effluent concentrations (soluble COD and total ammonia nitrogen) under different hydraulic conditions and organic loading rates.

Nonlinear electro-elastic dynamics of a hub–cantilever bimorph rotor structure

Dynamics of a rotating mini hub–bimorph structure excited by periodic torque supplied to the hub is studied in this paper. The mathematical model of the system is formulated by means of the extended Hamilton’s principle. In the analysis the nonlinear constitutive behaviour of the piezoceramic material is adopted based on experimental results published in literature. Moreover, nonlinear inertia effects related to the system rotation are taken into account. The derived system of three integro-partial differential equations represents the electro-mechanical behaviour of the beam (transverse displacement and transducer output voltage) and the hub rotation coordinate. The state equations are discretized and solved numerically around the first resonance zone for the system excited by a periodic torque supplied to the hub. The obtained response curves reveal strong softening behaviour with additional unstable solutions identified out of the resonance zones. Within the framework of the performed numerical simulations the impact of torque excitation amplitude, torque mean value, hub inertia and electrical load resistance on system behaviour is discussed. Finally, the responses of the system with parallel vs series connected transducers are compared.

Matching and optimization for a thermoelectric generator applied in an extended-range electric vehicle for waste heat recovery

In a conventional fuel vehicle, it is always difficult to find design points for a thermoelectric generator (TEG) because of the variation in engine power seen in different driving cycles. In contrast, the engine of an extended-range electric vehicle (EEV) is decoupled from the road load and only works at a single operating point in most cases, making it particularly suited for a TEG optimization design. This paper describes a method to match an optimized TEG to an EEV based on two criteria: TEG protection and high net power density. The trade-offs for TEG performance from TEG weight, added electric pump power consumption and backpressure are all taken into consideration. On this basis, the electric load resistance and configuration of the TEG are optimized, achieving a 11.6% increase of net power density compared to a preliminary designed TEG. The fuel economy of the optimized TEG integrated in an EEV (EEV-TEG) is assessed against that of a conventional EEV. The comparison shows that a 1.7% reduction in equivalent fuel consumption is obtained by the EEV-TEG, which is higher than that of a TEG applied in conventional fuel vehicles. These results exhibit the crucial importance of the method of matching and optimization for a TEG applied to EEVs.

Duty Cycle-Rotor Angular Speed Reverse Acting Relationship Steady State Analysis Based on a PMSG d–q Transform Modeling

Multilevel converters have been broadly used in wind energy conversion systems (WECS) to set the generator angular speed to a certain value, which allows maximizing wind power extraction; nevertheless, power that is drawn out from WECS strongly depends on the power coefficient and the ability to operate at the optimal tip speed ratio that corresponds to the maximum power coefficient. This work presents a novel and formal steady-state analysis to demonstrate the reverse relationship between the duty cycle of a multilevel boost converter (MBC) and the angular speed of a permanent magnet synchronous generator (PMSG). The study was based on the d–q transformation using the rotor reference frame. It was carried out by employing a reduced order dynamic system that included an equivalent electrical load resistance as a representation for the subsystems that were cascade-connected at the terminals of the PMSG. The steady-state characteristic was obtained by using the definition of equilibrium point. The set of nonlinear equations that represents the steady state of this WECS was solved by using the Newton method; besides, an analysis that considers the equivalent load as a bifurcation parameter demonstrates that the number of equilibria never changes.

Experimental Investigation of Piezoelectric Energy Harvesters Applied in Concrete Pavement

This paper proposes the application and manufacturing of piezoelectric devices based on pile and arc-bridge transducers to harvest mechanical energy from concrete pavement. Multi-scale experiments are conducted to clarify the influence of electrical connection, load resistance, traffic speed, and loading times on the electrical properties of the harvesters. The reduced-scale test shows that the transducers should be connected to rectifiers before being connected as an array. Moreover, the output power of the arc-bridge transducer with resistance variations is unstable compared with that of the pile transducer. Accelerated pavement testing illustrates that the output power of the half pile array device increases to 1.7 mW with an optimal resistance of 10.0 MΩ; reducing the internal equivalent resistance is a potential way to increase the energy output. The results also show that the load speeds significantly influence the profile of the voltage and have a minor effect on the generated electric energy in the tested conditions. Furthermore, the electrical properties of the piezoelectric device exhibit no statistical degradation after the electrical fatigue test of 100,000 tire loads, indicating a novel electrical fatigue performance. The findings in this paper can further guide the application of such piezoelectric devices in concrete pavement.

Nonlinear modeling and efficacy of VIV-based energy harvesters: Monostable and bistable designs

In this effort, performance of a magnetoelastic multi-stability energy harvester is investigated in monostable and bistable configurations while working under combination of vortex-induced vibration (VIV) and base excitation. For this purpose, a mathematical model is developed that accounts for coupled lift force, magnetic force, cylinder’s motion, and generated voltage. First, a linear analysis is carried out to investigate the effects of electrical load resistance on the coupled natural frequency of the system and its impact on the synchronization region. Static and frequency analyses are performed to identify the point of buckling based on the distance between the magnets. Then, a reduced-order model based on the Galerkin discretization is derived to investigate the effects of various nonlinearities on the harvester’s response. A convergence analysis is examined up till seven modes and it is found that three modes are sufficient. To compare the efficacy of the energy harvester at same coupled frequency in monostable and bistable regimes, three pairs of datasets are selected. Various parametric studies are presented to investigate the impacts of distance between the magnets, electrical load resistance, frequency, and wind speed. This study not only presents one of its kind quantitative comparisons of performance of the energy harvester working in monostable and bistable regimes at same coupled frequency but also provides an insight to performance of the harvester under combined effect of VIV and base excitation. In this regard, quenching phenomenon is visible. In addition, performance trends in pre-synchronization region, synchronization region, hysteresis region, and post synchronization regions are explained by presenting four wind speed graphs together. Some phase portraits and time histories are included for further exploration. In nutshell, the study is very useful for understanding of monostable and bistable designs and their working under VIV as well as hybrid excitations.

Design and Experiments of a Galloping-Based Wind Energy Harvester Using Quadruple Halbach Arrays

This study aims to develop a device for harvesting electrical energy from low-speed natural wind. Four linear Halbach arrays are adopted to design a high-performance galloping harvester with the advantage of high durability and efficiency at low-frequency vibrations. The results of magnetic field analysis reveal that there are optimal sizes of the main and transit magnets of the Halbach arrays and coil to obtain the maximum magnetic flux density normal to the coil. The experimental and simulation results show that the electrical external load resistance significantly affects the vibration amplitude and the galloping onset velocity of the harvester. The results also reveal that the performance of the original design using the quadruple Halbach array was lower than that of the existing harvester because of the heavy magnet mass embedded in the tip prism. The modified design, reducing mass, improved the performance by four times compared to the original design.

A Multifunction Robot Based on the Slider-Crank Mechanism: Dynamics and Optimal Configuration for Energy Harvesting

An electromechanical robot based on the modified slider-crank mechanism with a damped spring hung at its plate terminal is investigated. The robot is first used for actuation operation and for energy harvesting purposes thereafter. Mathematical modeling in both cases is proposed. As an actuator, the robot is powered with a DC motor, and the effect of the voltage supply on the whole system dynamics is found out. From the numerical simulation based on the fourth-order Runge-Kutta algorithm, results show various dynamics of the subsystems, including periodicity, multi-periodicity, and chaos as depicted by the bifurcation diagrams. Applications can be found in industrial processes like sieving, shaking, cutting, pushing, crushing, or grinding. Regarding the case of the robot functioning as an energy harvester, two different configurations of the electrical circuit for both single and double loops are set up. The challenge is to determine the best configuration for the high performance of the harvester. It comes from theoretical predictions and experimental data that the efficiency of the robot depends on the range values of the electrical load resistance RL. The double loop circuit is preferable for the low values of RL50 Ohm) while the single loop is convenient for high values of RL ≥ 50 Ohm.

Predefined angle of attack and corner shape effects on the effectiveness of square-shaped galloping energy harvesters

Energy harvesting based on transverse galloping of a square cylinder has been widely studied while the effects of angle of attack and corner shape remain unclear. This study proposes to explore the impacts of these two parameters on the characteristics and effectiveness of square-based galloping energy harvesting systems using a coupled fluid–structure-electrical model. It is demonstrated that the onset speed of instability is dependent on the electrical load resistance. Additionally, the load resistance value corresponding to the maximum onset speed of galloping is inversely proportional to the natural frequency of the energy harvester. Further, the onset wind speed of instability and the dynamic response of the energy harvester are largely affected by the angle of attack and corner shape. The rounded corners make the onset velocity less sensitive to the angle of attack. The considered square cylinders with different corner shapes exhibit the largest transverse displacements at the angle of attack α0 = 0°, while the displacements at α0 = 2° are only slightly lower than those at α0 = 0°. In general, the rounded corners slightly decrease the displacements and power outputs of the harvester. However, the rounded corners enhance the robustness of the harvester by making its performance less sensitive to the angle of attack within α0 = 0° ~ 6°. It is also shown that the type of instability is strongly dependent on the angle of attack and corner shape which may result in the presence of unexpected bifurcations, such as the subcritical and saddle-node ones.

Effective design and characterization of flutter-based piezoelectric energy harvesters with discontinuous nonlinearities

A comprehensive study on the design and nonlinear characterization of a two-degree of freedom piezoaeroelastic energy harvesting system with freeplay and multi-segmented nonlinearities in the pitch degree of freedom is explored and discussed. The nonlinear governing equations of the considered piezoaeroelastic energy harvesting system are derived and the unsteady representation based on the Duhamel formulation is employed to represent the aerodynamic loads. Nonlinear piezoaeroelastic response analysis is carried out in the presence of freeplay and multi-segmented nonlinearities before and after the linear onset of flutter. Such nonlinearities can be introduced to piezoaeroelastic energy harvesters for performance enhancement through the possible existence of subcritical Hopf bifurcation and aperiodic responses due to the grazing and grazing/sliding bifurcations. It is shown that the existence of discontinuous effects result in the possibility of harvesting energy at lower speeds than the linear onset speed of instability due to the activation of the subcritical Hopf bifurcation. Additionally, the increase of the strength of the multi-segmented nonlinearities leads to the existence of aperiodic responses with the presence of several bifurcations limiting the system's dynamics at low pitch angles with limiting stall issues. It is proved that an effective design with harvesting energy at low wind speeds can be carried out for wing-based energy harvesters by carefully selecting the linear stiffness of the pitch degree of freedom, gap and type of the multi-segmented discontinuity, and electrical load resistance.

Energy harvesting from longitudinal and transverse motions of sea waves particles using a new waterproof piezoelectric waves energy harvester

This paper experimentally studied the energy harvesting from the longitudinal and transverse motions of sea waves using a waterproof piezoelectric wave energy harvester (WPWEH). Because of sealing and specific design type of the WPWEH, the piezoelectric cantilever beam was entirely placed inside the water to increase the harvested electrical power. Three orientations of O1,O2 and O3were considered for placing the piezoelectric cantilever beam inside the water channel. In O1orientation, the cantilever beam was vertical and perpendicular to the floor while in O2and O3orientations, it was horizontal and parallel with the floor. The cantilever beam was perpendicular to the flow in O1andO2 and vibrates due to the longitudinal motion of wave particles while it was parallel with the flow in O3 and vibrates due to the transverse motion of wave particles. The influence of orientation, wave rate, and resonant frequency of the cantilever beam on the root mean square of the voltage and harvested electrical power was studied. The O1 orientation was selected as the optimum orientation for energy harvesting, because of having harmonic oscillations with a maximum generated voltage. The optimum electrical load resistance was calculated for the maximum harvested power. The results showed that the maximum density of the harvested electrical power from the WPWEH was increased compared to the other similar works.