Nonlinear Energy Harvester Research Articles

Investigation of Nonlinear Piezoelectric Energy Harvester for Low-Frequency and Wideband Applications.

This paper proposes a monostable nonlinear Piezoelectric Energy Harvester (PEH). The harvester is based on an unconventional exsect-tapered fixed-guided spring design, which introduces nonlinearity into the system due to the bending and stretching of the spring. The physical–mathematical model and finite element simulations were performed to analyze the effects of the stretching-induced nonlinearity on the performance of the energy harvester. The proposed exsect-tapered nonlinear PEH shows a bandwidth and power enhancement of 15.38 and 44.4%, respectively, compared to conventional rectangular nonlinear PEHs. It shows a bandwidth and power enhancement of 11.11 and 26.83%, respectively, compared to a simple, linearly tapered and nonlinear PEH. The exsect-tapered nonlinear PEH improves the power output and operational bandwidth for harvesting low-frequency ambient vibrations.

Wireless powered cognitive radio networks with multiple antenna sources and hardware impairments

In this paper, a radio-frequency (RF) energy harvesting enabled cognitive radio network (CRN) is considered in the presence of transceiver hardware impairments (HIs). Herein, one of the secondary nodes (SNs) exploits simultaneous wireless information and power transfer (SWIPT) technology to harvest energy from the primary signal and provides relay assistance for the primary transmission. We consider multiple antennas at the primary nodes (PNs) to ensure better link reliability and spectrum sharing to mitigate the spectrum scarcity. In the first phase, relaying SN uses non-linear energy harvester circuit to harvest energy from the RF signals received from PN using the power splitting approach. In the second phase, the same SN adds its own signal intended for the other SN along with the primary signal and broadcasts the combined signal. Assuming the network to operate in a Nakagami-m fading environment, the performance of the considered CRN is evaluated in terms of outage probability and system throughput. Also, we formulate two optimization problems to minimize the OP and maximize the system throughput. The Karush–Kuhn–Tucker conditions are used to obtain the closed-form solution of the constrained convex optimization. Numerical results are provided to examine the performance impact concerning different system and channel parameters.

Joint Subcarrier and Transmission Power Allocation in OFDMA-Based WPT System for Mobile-Edge Computing in IoT Environment

Mobile-edge computing (MEC) is expected to play an important role in the next-generation of Internet-of-Things (IoT) services with artificial intelligence (AI) by providing the sustainable computation capability of resource-constrained IoT devices. Since the finite battery lifetime has been a longstanding challenge of the MEC system for IoT services, the wireless power transfer (WPT) technology has been recently developed for the MEC system in order to support the perpetual operation of IoT devices. In this article, we introduce two resource allocation problems for OFDMA-based WPT-MEC systems: 1) a max–min energy fairness (MMEF) problem and 2) a power sum maximization (PSM) problem. These problems ensure high-performance computations for AI-based applications, where the network reliability and the tremendous power consumption may be required. Moreover, we incorporate a logarithmic nonlinear energy harvesting (EH) model into our formulated problems, which lead to nonconvex mixed-integer nonlinear programming (MINLP) problems. In order to resolve these NP-hard problems, we convert the proposed problems into their equivalent convex forms by applying the continuous relaxation method. The near-optimal solutions are thereby obtained in closed-form expressions by leveraging the Lagrangian duality method for each relaxed problem. Numerical results are presented to validate the merits of the proposed algorithms of MMEF&PSM over the alternative benchmark algorithm and provide significant insights on the effects of the key system parameters, including the number of IoT devices and power transmission subcarriers.

Performance Analysis of Dual-Hop AF Relaying with Non-Linear/Linear Energy Harvesting.

Massive device-to-device communication nodes and Internet of Things (IoT) devices are expected to be crucial components in next-generation wireless networks. However, the energy constraint of these nodes presents a challenge since the energy of the batteries is limited. Motivated by this, radio frequency energy harvesting (EH) has been developed as an efficient strategy to overcome the energy constraint of IoT devices and sensor networks. In this paper, a wireless-powered dual-hop amplify-and-forward relaying system, in the absence of a direct link between the source (S) and the destination (D), is considered. It is assumed that a dedicated power beacon (PB) transmits an energy-bearing signal from which the power-constrained S and relay (R) harvest energy. Theoretical derivations of bit error probability, outage probability, and throughput expressions are performed for both linear and non-linear energy harvesting models. Moreover, the theoretical results provided for different system parameters are validated via Monte Carlo simulations. The obtained results reveal the difference between the realistic non-linear EH model and the conventional linear EH model, which overestimates the system performance at high levels of harvested energy. Thus, it leads to misunderstanding the real performance of the EH systems. However, at low levels of harvested energy, both models behave similarly and provide realistic results.

Mutual Information Maximization for SWIPT AF MIMO Relay Systems With Non-Linear EH Models and Imperfect Channel State Information

In this paper, we investigate a two-hop simultaneous wireless information and power transfer (SWIPT) amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay communication system with an energy-limited relay node. The relay node harvests energy based on the radio-frequency (RF) signal transmitted from the source node through the time-switching (TS) protocol and fully uses the harvested energy to precode and forward the information to the destination node. The non-linear energy harvesting models are considered at the relay node. With the consideration of the channel estimation error, the joint optimization of the TS factor, source and relay precoding matrices is proposed with robustness against the channel state information (CSI) mismatch to maximize the mutual information (MI) between the source and destination nodes. The optimal structure for the source and relay precoding matrices is derived to simplify the transceiver optimization problem. Numerical simulations show that the system performance provided by the proposed algorithms with robustness is better than the non-robust algorithm.

Throughput Maximization for IRS-Aided MIMO FD-WPCN With Non-Linear EH Model

This paper studies an intelligent reflecting surface (IRS)-aided multiple-input-multiple-output (MIMO) full-duplex (FD) wireless-powered communication network (WPCN), where a hybrid access point (HAP) operating in FD broadcasts energy signals to multiple devices for their energy harvesting (EH) in the downlink (DL) and meanwhile receives information signals from devices in the uplink (UL) with the help of an IRS. Taking into account the practical finite self-interference (SI) and the non-linear EH model, we formulate the weighted sum throughput maximization optimization problem by jointly optimizing DL/UL time allocation, precoding matrices at devices, transmit covariance matrices at the HAP, and phase shifts at the IRS. Since the resulting optimization problem is non-convex, there are no standard methods to solve it optimally in general. To tackle this challenge, we first propose an element-wise (EW) based algorithm, where each IRS phase shift is alternately optimized in an iterative manner. To reduce the computational complexity, a minimum mean-square error (MMSE) based algorithm is proposed, where we transform the original problem into an equivalent form based on the MMSE method, which facilities the design of an efficient iterative algorithm. In particular, the IRS phase shift optimization problem is recast as an second-order cone program (SOCP), where all the IRS phase shifts are simultaneously optimized. For comparison, we also study two suboptimal IRS beamforming configurations in simulations, namely partially dynamic IRS beamforming (PDBF) and static IRS beamforming (SBF), which strike a balance between the system performance and practical complexity.

High order analysis of a nonlinear piezoelectric energy harvesting of a piezo patched cantilever beam under parametric and direct excitations

In this paper, the nonlinear dynamics of a piezoelectric beam under simultaneous parametric and external excitation is studied. The energy sensor considered is composed of a substrate and a piezoelectric layer used as a vibratory sensor located in the middle of the beam. The model thus constituted takes into account the electromechanical nonlinearities. Based on the Galerkin’s method, a strongly coupled nonlinear system is obtained. The multiple scales method is used to determine the analytical expressions of the deflection of the beam, the output voltage generated by the piezoelectric patch and the power harvested around the resonant frequency of the structure. The nonlinear characteristics of the energy harvester are explored under parametric and direct excitations. Analytical formulations of the deflection and the output voltage have been provided leading to investigate new insights into the effects of certain parameters such as the electromechanical coupling coefficient, the thickness and width of the elastic beam and the piezoelectric patch. In particular the position of the piezoelectric patch on the performance of the energy harvester is studied. The results show that for large values of the damping coefficient and thickness, the frequency-amplitude response curves of the energy harvester decrease. On the other hand, the frequency response curves of the displacement and voltage increase for large values of the excitation width and amplitude. We also note the fact that the length ratio influences not only the vibration amplitudes but also the output voltage. The deflection amplitudes and the output voltage obtained by the elaborated second-order multiple scale method are higher than those obtained by the first order, these results show the importance of nonlinearities in the dynamic study of vibrational energy harvesting systems by piezoelectric materials.

Nonlinear Piezoelectric Energy Harvester: Experimental Output Power Mapping

In this paper, the output power map of a nonlinear energy harvester (PEH) made of a console beam and the membrane of a resonant vibration speaker is analyzed experimentally. The PEH uses two large piezoelectric patches (PZT-5H) bonded into a parallel bimorph configuration. The nonlinear response of the deformable structure provides a wider bandwidth in which power can be harvested, compensating for the mistuning effect of linear counterparts. The nonlinear response of the proposed PEH is analyzed from the perspective of its electrical performance. The proposed experimental method provides novelty by measuring the effects produced by the nonlinearity of the deformable structure on the output power map. The objective of this analysis is to optimize the size of the PZT patch in relation to the size of the console beam, providing experimental support for the design. The presentation of the most significant experimental results of a nonlinear PEH, followed by experimental mapping of the output power, ensured that the proposed objective was achieved. The accuracy of the experimental results was determined by the high degree of automation in the experimental setup, assisted by advanced data processing.

An ultra-low frequency ball-impacted potential-variable nonlinear energy harvester

Efficient energy harvesting for ultra-low frequency vibrations remains a large challenge. An ultra-low frequency ball-impacted potential-variable nonlinear energy harvester (abbreviated as BPNEH) is proposed in this work to provide a new solution for the challenge. Upon excitation, a horizontal beam, which is magnetically coupled to a vertical one, vibrates back and forth with large amplitudes through ball-impacts, along with a variable potential energy due to the vibration of the coupled vertical one. A prototype of the proposed BPNEH is fabricated to demonstrate the effective contribution of both the ball-impact and the variable potential energy under an ultra-low frequency excitation. Compared to a conventional potential-variable nonlinear energy harvester (abbreviated as PNEH), the RMS voltage of the proposed BPNEH is increased by 78.4 % in 1–8 Hz, along with a sub-peak that appears to the left side of the main peak. This new finding of a double peak phenomenon is further observed and clarified by a theoretical model, where the output voltage of the proposed BPNEH is increased by 209.6 % in 1–10 Hz. In addition, the main factors affecting the sub-peak in the observed double peak phenomenon are also considered and discussed with respect to harvesting more energy. The proposed BPNEH along with the double peak phenomenon is believed to be applicable to ultra-low frequency scenes, especially with large amplitudes, of engineering fields such as wearable devices, structural health monitoring systems, etc.

Wide range tuning behavior of a new nonlinear energy harvester based on the beam–slider structure

Wide range tuning behavior of a new nonlinear energy harvester based on the beam–slider structure

Optimization for piezoelectric energy harvesters with self-coupled structure: A double kill in bandwidth and power

Vibration energy harvesting is promising to supply power autonomy for many electronic devices. This paper proposes a novel nonlinear piezoelectric energy harvester with a two-degree-of-freedom self-coupled structure. The operating frequency range and the power output of the new harvester is enhanced simultaneously compared with the conventional stopper-based nonlinear energy harvester. The dynamic model of the self-coupled structure is established, and then the bucket hat-like elastic potential energy function of the structure is obtained, which accounts for the superior performance of the harvester. Moreover, an optimization methodology for developing the nonlinear piezoelectric energy harvester was proposed. The conventional and novel energy harvesters were designed, optimized, and fabricated. Experimental results indicate that the maximum output power of the novel energy harvester can be enhanced to 3.54 times of that of the conventional energy harvester with a stopper structure. Besides, the working bandwidth is broadened from 4.7 Hz to 5.2 Hz. It is expected that this work is devoted to the future improvement of vibration energy harvesters in practical applications.

Energy-Balancing Resource Allocation for Wireless Cooperative IoT Networks With SWIPT

In this article, orthogonal frequency-division multiplexing (OFDM)-based downlink simultaneous wireless information and power transfer (SWIPT) is considered in the Internet of Things (IoT) wireless interference network, where one hybrid access point (HAP) performs both wireless power transfer (WPT) and wireless information transfer (WIT) to energy harvesting (EH) and information decoding (ID) nodes while multiple coexisting energy access points (EAPs) carry energy to EH nodes. As the transmission methodology for interference avoidance, we improve and refine the subcarrier separation (SS), which allocates the dedicated energy subcarrier set orthogonal to the information subcarrier set. Based on the modified SS, to enhance the harvested energy while minimizing the number of dedicated energy subcarriers, we design the cooperative WPT with transmit diversity and adopt the time-division multiple access scheme for multiple EH nodes. The optimal joint subcarrier, node, and power allocation problem is formulated based on the proposed transmission strategies to maximize the achievable sum rate for given energy requirement with a practical nonlinear EH model for low-power IoT nodes. However, it is difficult to obtain the global optimal solution due to the nonconvexity of the problem, so we investigate the cooperative resource allocation scheme. First, to solve the subcarrier allocation and node selection jointly, two basic methods for maximizing energy and minimizing rate loss are designed, and the additional scheme considering both energy requirement and rate-loss minimization is proposed by introducing a weighting factor for balancing the total transmit power into WPT and WIT. Then, the optimal power allocation on the allocated subcarriers and selected nodes is performed with the split transmit power. Simulation results show that the proposed schemes achieve superior rate–energy (R-E) region to conventional schemes. Our study provides useful insights on how to transmit signals for improving performance in IoT interference networks with SWIPT.

A parametric frequency domain approach to analysis and design of critical design parameters of nonlinear energy harvesting systems: Parametric output spectrum and power generation functions

Nonlinear energy harvesting systems have been extensively studied which usually involve quite a few critical design parameters to determine. However, a straightforward parametric design method for such a purpose is still far from developed. Traditional methods with harmonic balance or numerical simulation usually cannot reveal a straightforward relationship between the energy harvesting performance and system parameters, and in most cases face relatively large computational costs during parametric studies. To this aim, a novel Volterra series-based frequency domain method is established in this study with respect to a typical nonlinear harvesting system. A concise parametric characteristic approach, namely the linear and nonlinear characteristic output spectrum (lnCOS) method, is thus proposed to achieve parametric characteristic expression for the nonlinear output frequency response and power generation function (PGF) of the system, referred to as the lnCOS function and the Parametric-PGF respectively. Compared with the harmonic balance method, the vibration responses/power generation can be obtained in a more straightforward way without solving complex algebraic equations, and the lnCOS method directly links the power outputs to critical system parameters in a concise parametric way. It is for the first time to provide explicit expressions for vibration responses and power generations with respect to structural parameters of a nonlinear energy harvesting system, which cannot be achieved in a traditional way. Based on the obtained explicit expressions of the lnCOS function/Parametric-PGF, the sensitivity analysis of vibration response and power generation with respect to structural parameters can be directly performed. Our work provides an efficient way to characterize both the linear and nonlinear effects on a nonlinear energy harvesting system and demonstrates an efficient approach to the analysis and design of nonlinear energy harvesting systems.

A review of nonlinear piezoelectric energy harvesting interface circuits in discrete components

Piezoelectric energy harvesting is considered as an ideal power resource for low-power consumption gadgets in vibrational environments. The energy extraction efficiency depends highly on the interface circuit, and should be highly improved to meet the power requirements. The nonlinear interface circuits in discrete components have been extensively explored and developed with the advantages of easy implementation, stable operation, high efficiency, and low cost. This paper reviews the state-of-the-art progress of nonlinear piezoelectric energy harvesting interface circuits in discrete components. First, the working principles and the advantages/disadvantages of four classical interface circuits are described. Then, the improved circuits based on the four typical circuits and other types of circuits are introduced in detail, and the advantages/disadvantages, output power, efficiency, energy consumption, and practicability of these circuits are analyzed. Finally, the future development trends of nonlinear piezoelectric energy harvesting circuits, e.g., self-powered extraction, low-power consumption, and broadband characteristic, are predicted.

Coverage Performance of UAV-Assisted SWIPT Networks With Directional Antennas

This article studies the coverage performance of unmanned aerial vehicle (UAV)-assisted simultaneous wireless information and power transfer (SWIPT) networks under the nonlinear and linear energy harvesting (EH) models in the rich scattering scenarios, including smart farming and smart ranching, where the None-Line-of-Sight (NLoS) links are the dominate component of the wireless channel. Multiple UAVs are equipped with directional antennas to transfer information and energy to ground users (GUs). Power splitting (PS) or time switching (TS) architecture is employed at GUs. In order to evaluate the system performance in fading channels, the information and energy coverage probabilities of the system are discussed, and by using the stochastic geometry approach and the approximate scaling method, the general and lower bound explicit expressions of the coverage probabilities are derived. Numerical results show that the coverage performance of PS-based systems is superior to that of TS-based systems. Moreover, although the linear EH model yields better results than the nonlinear one, as the linear EH model is too ideal, its yielded results may mismatch practical EH circuits, and the ones yielded by the nonlinear EH model is much closer to practice, as the nonlinear EH model is based on real data measurement. Additionally, the nonlinear EH model has a relatively small effect on the harvested energy coverage probability, and the linear EH model introduces greater bias for the TS-based system than that for PS-based one.

Power expectation as a unified metric for the evaluation of vibration energy harvesters

Vibration energy harvesters (VEHs) allow the extraction of ambient mechanical energy. The proposed analysis focuses on bistable harvesters with Duffing nonlinearity. Bistable harvesters exhibit larger frequency bandwidth than linear monostable harvesters, but they exhibit complex behaviors (i.e., multiple periodic orbits and chaos), making their evaluation challenging. To assess the quality of a VEH, it is necessary to evaluate its energy performance generically. In this paper, we offer a new quantitative metric that can be used to evaluate bistable harvesters while taking into account the richness and diversity of their dynamics. This metric – called power expectation – is based on the average harvested power of each existing orbit weighted by its occurrence probability. The value of this power expectation depends on the harvester characteristics and potential orbit jump strategy implemented. Finally, we define a new figure of merit (FoM) based on the integral of the power expectation over all vibration frequencies. This FoM can be used for a generic evaluation of nonlinear vibration energy harvesters (NVEHs), by taking into account the various orbits and their respective probability of occurrence depending on the orbit jump strategy used. The proposed FoM also makes it possible to ensure a fair comparison with linear VEHs and quantitatively assess the effectiveness of orbit jump strategies for a given VEH.

Age of information and energy efficiency of amplify‐and‐forward relay‐assisted Internet of Things with nonlinear energy harvesting and imperfect channel state information over Nakagami‐ fading channels

AbstractThe emergence of the fifth generation of communication networks (5G) has paved the way for the fast development of Internet of Things (IoT) as well as many real‐time and mission‐critical applications. Because the status update required to be as timely as possible, a new metric termed as age of information (AoI) was born with the ability of capturing the timeliness. However, in practical implementation the sensor is energy constrained and transmits very low‐power signals, which yield high AoI so that the received status update can be stale or even outdated. To overcome this problem, this work proposes an IoT system model by integrating energy harvesting (EH), amplify‐and‐forward (AF) relay cooperation, and short packet communication (SPC) techniques. In the proposed scheme, the relay that is connected to fixed power grid, transfers energy radio frequency signals to charge the sensor and assists forwarding status update by using time switching scheme. The employment of SPC overcomes the freshness loss caused by relay cooperation and EH. Then, this work investigates the AoI and energy efficiency of the proposed scheme under finite block length communications over Nakagami‐ fading channels by specially considering channel state information (CSI) and nonlinear EH model. Under these practical constraints, the tractable AF relay transmission model and the end‐to‐end approximated signal‐to‐noise ratio are found. The end‐to‐end block error probability of finite block length transmission is derived, too. Third, under the simultaneous consideration of nonlinear EH and outdated CSI, the statistical descriptions of the time duration for the sensor fully charging its battery are derived as well as the ones of the time intervals of update packet delivery. As a result, the average AoI is achieved with closed‐form expression and the tradeoff model of AoI to energy efficiency is established by simultaneously exploiting outdated CSIs and nonlinearity of EH circuit. The presented numerical analysis exploits the impact of the outdated CSIs and nonlinear EH model and gives the insights of such model.

New Practical Nonlinear Energy-Harvesting Models for Wireless-Powered Communications

As a massive number of nodes are expected to be connected to each other in next-generation wireless networks, the power supply of such multiple-antenna nodes is a challenge and requires new and sustainable solutions. Radio frequency energy harvesting (EH) is among the promising approaches to solve this issue. In this paper, two new mathematically tractable nonlinear EH (NL-EH) models are proposed, for which the system performance is evaluated in terms of average harvested power, throughput, and bit error probability. The system consists of one multiantenna power-constraint source harvesting its power from a dedicated power beacon and transmitting its signal to a destination equipped with multiple antennas. For a comprehensive analysis of the system, closed-form expressions are derived for Nakagami- m fading channels and the special case of Rayleigh channels. For comparison purposes, the performance derivations in Nakagami- m fading channels are provided for linear and piece-wise linear EH models given in the literature. Besides, the simulation results are obtained by applying the Monte-Carlo method for NL-EH models existing in the literature. The results provide a broadening view of EH systems and thoroughly compare the proposed NL-EH models with linear, piece-wise linear, and NL-EH models available in the literature. Hence, these provide better insights towards the analyses and design of EH systems.

System-level modeling and design method of an array of piezoelectric energy harvesters under typical ambient vibration

Vibration-based piezoelectric energy harvesting has received significant attention recently due to its ability to convert vibration energy from the surrounding environment into electric energy to power wireless sensors. In this work, two typical types of vibration sources, that is, engine-induced floor vibration and train-induced bridge vibration, are considered. The array of piezoelectric energy harvesters (PEHs) is adopted to harvest the energy of vibration with different frequencies. The aim of this work is to give a stable system-level modeling method and present a method to select operating point for designing energy harvesters connected with nonlinear energy harvesting circuits under complex excitations. The system-level modeling method is based on Krylov’s subspace model order reduction algorithm. With the help of this method, the harvester can be modeled using conventional finite element software and co-simulated with nonlinear circuits at a system-level. The proposed method is validated using equivalent circuit method, equivalent impedance method and experiment results, and then employed to investigate the performances of harvesters under typical real vibrations. Finally, design suggestions for PEHs under different types of vibration sources are presented.

On the Coverage of UAV-Assisted SWIPT Networks With Nonlinear EH Model

Unmanned aerial vehicles (UAVs) with huge-capacity batteries could be employed to wirelessly charge the ground sensor users (GSUs) and enhance the coverage of aerial wireless networks in outdoor Internet of Things (IoT). This paper investigates the information and energy coverage of UAV-enabled simultaneous wireless information and power transfer (SWIPT) networks. Both power splitting (PS) and time switching (TS) receiver architectures are considered. By using stochastic geometry approach, the general and explicit expressions of the information coverage probability (ICP), the energy coverage probability (ECP) and the joint information and energy coverage probability (JIECP) are derived under the nonlinear and linear energy harvesting (EH) models, respectively. Particularly, the Laplace transform and the probability generating functional (PGFL) are used to derive the ICP. And, Campbell’s theorem and the maximum function are applied to obtain the ECP and the JIECP, respectively. To achieve the optimal UAVs’ deployment density, the maximization optimization problems are formulated for the PS-based and TS-based systems, respectively. By using the series expansion of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q(x)$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -function) with large <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula> , the closed-form approximating optimal solutions to the formulated problems are obtained. Monte Carlo simulations validate the correction of our obtained theoretical results, and numerical results show that the performance of the PS-based system is superior to that of the TS-based one. Moreover, when the energy requirement of GSUs or the transmit power of UAVs is relatively large, or when the information requirement of GSUs or the UAV deployment density is relatively small, compared with the nonlinear EH model, the analysis bias caused by traditional linear EH model is relatively large and in these cases, traditional linear EH model cannot be used to replace the nonlinear EH one for the system performance analysis or optimal system design.