Energy Harvesting Model Research Articles

Dynamic responses of a two-degree-of-freedom bistable electromagnetic energy harvester under filtered band-limited stochastic excitation

This study investigates the dynamic responses of a two-degree-of-freedom (2DOF) nonlinear bistable electromagnetic energy harvester under filtered band-limited stochastic excitation. The mathematical model of the 2DOF bistable energy harvester is derived, and its fidelity is experimentally verified. A comprehensive numerical investigation is conducted under filtered band-limited stochastic excitation (which is the white Gaussian noise filtered by a second-order filter). Comparative studies are performed between the 2DOF bistable energy harvester, the 2DOF equivalent linear energy harvester, and the single-degree-of-freedom (SDOF) linear energy harvester when subjected to white Gaussian noise and the exampled band-limited stochastic excitation. The comparative results show that the 2DOF bistable energy harvester can significantly improve the average power compared to the equivalent 2DOF and SDOF linear energy harvesters. The study reveals the insights of the excitation strength, bandwidth, and center frequency into the system performance. Finally, structural parametric studies demonstrate that the bigger frame mass and the larger spring stiffness coefficient will increase the oscillation velocity which has great significance for energy harvester.

Geometrical investigations of piezoelectric microcantilever coupled with square/circular shaped micromembrane designs for an energy harvesting application

The Finite element analysis (FEA) plays a vital role for the design and development of microdevices, which provides the solutions to understand the behaviour virtually for the optimization of specific device. In the present work, we designed two different energy harvesting (EH) models with variable dimensions and analyzed the EH performance for wide range of pressure. The proposed models consist of four piezoelectric microcantilevers coupled with square (Design-I) and circular (Design-II) shaped micro-membranes. The piezoelectric material PZT-5H was used as transduction material and the gold electrodes were used as charge collector. The EH designs (I & II) were modelled with variable membrane thickness viz., 1 µm and 0.5 µm and their output performances like total displacement, von Mises stress, volumetric strain and electric potential were studied for the pressure range of 200–2000 Pa. The EH design-I generated the maximum output potential of 167 µV (1 µm) and 186 µV (0.5 µm) for the applied pressure of 2000 Pa. Similarly, EH design-II generated the maximum output potential of 138 µV (1 µm) and 174 µV (0.5 µm) for the applied pressure of 2000 Pa. Relatively, the EH designs I & II with 0.5 µm thickness exhibited best output performance for the maximum applied pressure of 2000 Pa, which generated maximum output potential of 186 µV and 174 µV, respectively. In comparison with the other designs, the piezoelectric microcantilever coupled with square shaped micro-membrane (Design-I) of 0.5 µm thickness exhibited better EH performance than the circular shaped micro-membrane (Design-II).

A Survey of Energy Modeling and Efficiency Techniques of Sensors for IoT Systems

Sensors power the entire internet of things applications. Sensors are one of the major power consuming devices of IoT networks while transmitting and receiving data. Optimizing power is one of the approaches to solve this problem. This paper surveys various power modeling techniques of sensors that are applicable to the internet of things and sensor networks applications. Various techniques and strategies have been studied in this paper. Some of the techniques that are studied and surveyed are transmission power modeling, power modeling of the sensor for sensor subsystems and IoT systems, clustered approach, energy harvesting models and transmission distance modeling. Our survey proposes that there exists a valid and feasible model for a given application that satisfies the power constraints of the sensor devices.

Manifestation of Flexible p–i–n Solar Cells Fabricated Using HWCVD in WSN Application

The wireless sensor network (WSN) consist of battery-powered sensor nodes which are self-configured and are deployed for monitoring several physical or environmental conditions such as temperature, pressure, humidity, vibration, pollutants etc. The major constraint in most of the WSN applications is the replacement/recharging of the battery contained by the node once it gets exhausted. This limitation reduces the lifetime of WSN. The placement of energy harvesting device within the sensor node may be the best probable solution to recharge the exhausted battery. In this paper, the integration of low cost, light weight and foldable flexible solar cells with WSN has been focused. The aim of this paper is to fabricate the flexible solar cells and showing the potential use of them in WSN. Moreover, the use of flexible solar cell is the better selection for emerging wearable WSN. This paper also describes the various issues in the already developed energy harvesting models and suggested a self-powered model for energy management based on finite state machine (FSM). The proposed models completely avoid the overcharging and the frequent charging of the batteries. This optimal utilization of the battery maximizes the lifetime of WSN network. In the proposed model, the flexible p–i–n solar cells are used to convert solar energy into electrical energy that can charge the battery of the WSN node. Finally, it can be concluded that the node will continue to function actively till the battery lifetime i.e. approximately 25–30 years.

Self-Powered Smart Beehive Monitoring and Control System (SBMaCS).

Beekeeping in Africa has been practiced for many years through successive generations and along inherited patterns. Beekeepers continue to face challenges in accessing consistent and business-driven markets for their bee products. In addition, the honeybee populations are decreasing due to colony collapse disorder (CCD), fire, loss of bees in swarming, honey buggers and other animals, moths, starvation, cold weather, and Varoa mites. The main issues are related to un-controlled temperature, humidity, and traditional management of beekeeping. These challenges result in low production of honey and colony losses. The control of the environmental conditions within and surrounding the beehives are not available to beekeepers due to the lack of monitoring systems. A Smart Beehive System using Internet of Things (IoT) technology would allow beekeepers to keep track of the amount of honey created in their hives and bee colonies even when they are far from their hives, through mobile phones, which would curtail the challenges currently faced by the beekeepers. However, there are challenges in the design of energy-efficient embedded electronic devices for IoT. A promising solution is to provide energy autonomy to the IoT nodes that will harvest residual energy from ambient sources, such as motion, vibrations, light, or heat. This paper proposes a Self-Powered Smart Beehive Monitoring and Control System (SBMaCS) using IoT to support remote follow-up and control, enhancing bee colonies’ security and thus increasing the honey productivity. First, we develop the SBMaCS hardware prototype interconnecting various sensors, such as temperature sensor, humidity sensor, piezoelectric transducer—which will work as a weight sensor—motion sensor, and flame sensor. Second, we introduce energy harvesting models to self-power the SBMaCS by analyzing the (i) energy harvested from adult bees’ vibrations, (ii) energy harvesting through the piezoelectric transducer, and (iii) radio frequency energy harvesting. Third, we develop a mobile phone application that interacts with the SBMaCS hardware to monitor and control the various parameters related to the beehives. Finally, the SBMaCS PCB layout is also designed. SBMaCS will help beekeepers to successfully monitor and control some important smart beekeeping activities wherever they are using their mobile phone application.

Energy-Efficient Power Allocation in Non-Linear Energy Harvesting Multiple Relay Systems

In this paper, to maximize the energy efficiency (EE) in the two-hop multi-relay cooperative decoding and forwarding (DF) system for simultaneous wireless information and power transmission (SWIPT), an optimal power allocation algorithm is proposed, in which the relay energy harvesting (EH) adopts a nonlinear model. Under the constraints, including energy causality, the minimum transmission quality of information and the total transmission power at the relays, an optimization problem is constructed to jointly optimize the transmit power and power-splitting (PS) ratios of multiple relays. Although this problem is a nonlinear fractional programming problem, an iterative algorithm is developed to obtain the optimal power allocation. In particular, the joint power allocation at multiple relays is first decoupled into a single relay power allocation, and then single-relay power allocation is performed by the Dinkelbach iteration algorithm, which can be proven that it is a convex programming problem. Its closed form solutions for different polylines of EH models are obtained by using mathematical methods, such as monotonicity, Lagrange multipliers, the KKT condition and the Cardan formula. The simulation results show the superiority of the power allocation algorithm proposed in this paper in terms of EE.

Generalized Selection in Wireless Powered Networks With Non-Linear Energy Harvesting

The rapid growth of the so-called Internet of Things is expected to significantly expand and support the deployment of resource-limited devices. Therefore, intelligent scheduling protocols and technologies such as wireless power transfer, are important for the efficient implementation of these massive low-powered networks. This paper studies the performance of a wireless powered communication network, where multiple batteryless devices harvest radio-frequency from a dedicated transmitter in order to communicate with a common information receiver (IR). We investigate several novel selection schemes, corresponding to different channel state information requirements and implementation complexities. In particular, each scheme schedules the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -th best device based on: a) the end-to-end (e2e) signal-to-noise ratio (SNR), b) the energy harvested at the devices, c) the uplink transmission to the IR, and d) the conventional/legacy max-min selection policy. We consider a non-linear energy harvesting (EH) model and derive analytical expressions for the outage probability of each selection scheme by using tools from high order statistics. Moreover, an asymptotic scenario in terms of the number of devices is considered and, by applying extreme value theory, the system’s performance is evaluated. We derive a complete analytical framework that provides useful insights for the design and realization of such networks.

Stochastic analysis of a galloping-random wind energy harvesting performance on a buoy platform

A new concept of a galloping-random wind energy harvester, which is a galloping-based piezoelectric harvester mounted on a buoy platform is proposed. The galloping-random wind energy harvester can concurrently harvest galloping energy due to the aero-instability and stochastic vibration energy due to the ocean wave. The harvester performance is comprehensively investigated through wind tunnel experiments and theoretical investigation. The mathematical model of the system is formulated, and its aerodynamic galloping is then validated with wind tunnel experimental measurements. Based on the verified mathematical model of the galloping-random wind energy harvester, the stochastic average method is applied to analytically obtain the probability density functions of the system’s stochastic responses and the average harvested power. The fidelity of the analytical solution is also verified by the numerical integration using the Euler-Maruyama algorithm. The results show that a unique crater phenomenon is discovered in the joint PDF of the responses, owing to the concurrent galloping and stochastic vibrations. In this case, the energy harvester exhibits a periodic galloping response with a fluctuating amplitude. The annulus range is wider when the galloping response is dominant and becomes stronger. In addition, this study investigates the average power output in terms of the stochastic excitation intensity, structural natural frequency, aerodynamic mass ratio, and normalized electrical term, to provide the useful design guidelines. The results show that the strong stochastic excitation intensity is beneficial to broadband energy harvesting and especially provides a high advantage for the low wind speed. The low structural natural frequency and large aerodynamic mass ratio can improve the performance. The parametric study also uncovers the optimal electrical term that can significantly improve the broadband average power output.

Performance Analysis of SWIPT for Intelligent Reflective Surfaces for Wireless Communication

The performance of simultaneous wireless information and power transfer (SWIPT) is investigated for an intelligent reflective surface (IRS)-aided wireless system. Tight bounds for the achievable rate and harvested energy are derived in closed-form for the time-switching (TS) and power-splitting (PS) protocols by adopting linear/non-linear energy harvesting models. The achievable rate-energy trade-off of IRS-aided SWIPT is quantified, and the effects of phase-shift quantization at the IRS are investigated. The impact of TS/PS factors, the number of reflective elements, reflective coefficients, and linear versus non-linear energy harvesting models is also investigated through analytical results and Monte-Carlo simulations.

Joint Transceiver Optimization for DF Multicasting MIMO Relay Systems With Wireless Information and Power Transfer

In this article, we investigate a two-hop decode-and-forward (DF) multicasting multiple-input multiple-output (MIMO) wireless relay communication system. Different to conventional systems, the radio frequency (RF) energy from the source node is harvested at the relay node and used for forwarding signals to a group of receivers. Considering the structure of the energy harvesting (EH) relay node, we present a power splitting (PS) based protocol and a novel time switching (TS) based protocol by introducing two additional TS factors. For both protocols, we maximize the system mutual information (MI) of the multicasting MIMO relay system by jointly optimizing the source and relay covariance matrices under the constraints of the source energy and the relay harvested energy. In addition, a practical nonlinear EH model is adopted, where the energy harvested by the relay node is bounded as the incident RF signal power increases, and the harvested power is zero when the input power is below the minimum power for harvesting. For the TS based protocol, we also consider peak transmission power constraints at both the source and relay nodes. The performance of the proposed algorithms is verified via numerical simulations. The results demonstrate that the novel TS based protocol achieves a larger MI than the conventional TS protocol. The PS and TS based protocols achieve tradeoffs at different source power levels. In particular, compared with the PS based protocol, the proposed novel TS based protocol can reach a higher system MI when the EH bound is not reached, while the former protocol reaches a higher MI when the EH circuit is saturated. We show that the peak harvested energy constraint plays an important role in selecting the optimal location of the relay node.

Optimal Resource Allocations for Statistical QoS Provisioning to Support mURLLC Over FBC-EH-Based 6G THz Wireless Nano-Networks

One of most important techniques for enabling the sixth-generation (6G) mobile wireless network lies in how to efficiently guarantee various stringent quality-of-service (QoS) performance-metrics to support the emerging massive Ultra-Reliable Low-Latency Communications (mURLLC) in 6G. Correspondingly, finite blocklength coding (FBC) has been developed as an effective technique to significantly improve various QoS indices for mURLLC through implementing short-packet communications. On the other hand, Terahertz (THz) band wireless nano-communications have been widely envisioned as a promising 6G technique to efficiently support utra-high data-rate (up to 1 Tbps). One of the major constraints over THz-band nano-networks is the severely limited energy that can be accessed by nano devices. Towards this end, various novel energy harvesting (EH) mechanisms have been proposed to remedy the energy scarcity problem. However, how to accurately characterize the relationships among THz wireless channels, energy consumption, and EH models for FBC based nano communications remains a challenging problem to support statistical delay and error-rate bounded QoS provisioning over FBC based 6G THz wireless nano-networks. To overcome these challenges, in this paper we propose optimal resource allocation policies to achieve the maximum ε-effective capacity in the THz band over FBC-EH-based nano-networks. Particularly, we establish nano-scale system models and characterize wireless channel models in the THz band using FBC. In order to support statistical delay and error-rate bounded QoS provisioning, we formulate and solve the ε-effective capacity maximization problem under several different EH constraints for our proposed schemes. Simulation results are included, which validate and evaluate our proposed schemes in the finite blocklength regime.

Benefiting wireless power transfer scheme in power domain based multiple access: ergodic rate performance evaluation

Power domain based multiple access scheme is introduced in this paper, namely Non-orthogonal multiple-access (NOMA). We deploy a wireless network using NOMA together with a wireless power transfer (WPT) scheme for dedicated user over Nakagami-$m$ fading channel. When combined, these promising techniques (NOMA and WPT) improve the system performance in term of ergodic performance at reasonable coefficient of harvested power. However, fixed power allocation factors for each NOMA user can be adjusted at the base station and it further provide performance improvement. We design a new signal frame to deploy a NOMA scheme in WPT which adopts a linear energy harvesting model. The ergodic capacity in such a NOMA network and power allocation factors can be updated frequently in order to achieve a fair distribution among NOMA users. The exact expressions of ergodic capacity for each user is derived. The simulation results show that an agreement between analytic performance and Monte-Carlo simulation can be achieved.

Energy Harvesting in Sub-6 GHz and Millimeter Wave Hybrid Networks

Dense deployment of sub-6 GHz BSs not only enhance the network capacity but also improve the energy efficiency of wireless power transfer (WPT). Millimeter wave (MMW) technology features large antenna arrays with high directional beamforming gain and dense base station (BS) deployment that is also beneficial for WPT. This paper focuses on the hybrid deployment of sub-6 GHz and MMW networks, where the user equipment (UE) can simultaneously receive information and harvest energy from either sub-6 GHz or MMW BSs. By using a stochastic geometry framework, we develop analytical expressions for the energy coverage probability (ECP) and signal-to-interference-plus-noise coverage probability (SCP) of a typical user, where the BS and UE locations are modeled by either a Poisson point process (PPP) or a Poisson cluster process (PCP). We further incorporate the unique characteristics of MMW communications in the analysis and study the impact of the practical energy harvesting model on the system performance. Numerical results are provided to validate the accuracy of the analytical models. The results demonstrate that the ECP depends on the considered UE models, where for the PPP model, as the cluster size of BS increases, the ECP increases. In contrast, for the PCP model, the ECP decreases with the increasing of BS cluster size. The results also show that the energy coverage probabilities for both PPP and PCP users converge to the PPP model as the cluster size tends to infinity.

Achievable Computation Rate in NOMA-Based Wireless-Powered Networks Assisted by Multiple Fog Servers

This article investigates a multifog server (FS)-assisted nonorthogonal multiple access (NOMA)-based wireless powered network, where an energy-limited wireless device (WD) first harvests energy from a power transmitter (PT) and multiple helping FSs and then uses the harvested energy to partially offload its computing task to the FSs with NOMA for computing. To explore the WD's performance limit in terms of achievable computation rate, an optimization problem is formulated by jointly optimizing the time assignment, the power allocation, and the computation frequency under multiple system constraints. Since the problem is nonconvex with no known solution, an efficient solution approach is designed to achieve the ε-optimal solution, in which the transmit power vector and the computation frequency are jointly optimized with fixed-time assignment, and then, a golden section search (GSS)-based algorithm is designed to find the optimal time assignment. For the case when the FS is with sufficiently strong computation capability, some semiclosed-form results are derived. Numerous results show that our proposed design achieves much higher computation rate than benchmark schemes. Moreover, with the increment of the helping FSs, the achievable computation rate increases while the increasing rate is decreased. Besides, by employing NOMA, the WD's computation rate is also improved compared with orthogonal multiple access (OMA)-based scheme. Additionally, in such a system, with nonlinear energy harvesting (EH) model adopted, the more the helping FSs are deployed, the more the performance loss caused by the traditional linear EH model can be reduced.

Energy harvesting in variable stiffness composite piezolaminated plates

Harnessing ambient vibrational energy to power small and medium power electronic devices has been greatly explored in the past decade. Most of the available energy harvester models use straight fibers. Use of curvilinear fiber in bimorph energy harvester is explored in this computational study and its effect on tailoring the resonance frequency and extracted power is also investigated. The variable stiffness composite laminate (VSCL) bimorph energy harvester is modelled using first order shear deformation theory (FSDT) and equations are derived using a nine noded isoparametric finite element. Curvilinear fiber based composite and PZT-5A materials are utilized for the analysis of harvester. Curvilinear fiber model is validated by comparing the natural frequency of VSCL plate with the already published results. Power frequency response function (PFRF), voltage frequency response function (VFRF) and relative tip motion frequency response function are plotted for a fixed curvilinear fiber orientation. Effects of plate aspect ratio on the peak power is also investigated.

Modeling of a Rope-Driven Piezoelectric Vibration Energy Harvester for Low-Frequency and Wideband Energy Harvesting.

In this work, a mechanical model of a rope-driven piezoelectric vibration energy harvester (PVEH) for low-frequency and wideband energy harvesting was presented. The rope-driven PVEH consisting of one low-frequency driving beam (LFDB) and one high-frequency generating beam (HFGB) connected with a rope was modeled as two mass-spring-damper suspension systems and a massless spring, which can be used to predict the dynamic motion of the LFDB and HFGB. Using this model, the effects of multiple parameters including excitation acceleration, rope margin and rope stiffness in the performance of the PVEH have been investigated systematically by numerical simulation and experiments. The results show a reasonable agreement between the simulation and experimental study, which demonstrates the validity of the proposed model of rope-driven PVEH. It was also found that the performance of the PVEH can be adjusted conveniently by only changing rope margin or stiffness. The dynamic mechanical model of the rope-driven PVEH built in this paper can be used to the further device design or optimization.

Finite Element Modeling and Performance Evaluation of Piezoelectric Energy Harvesters with Various Piezoelectric Unit Distributions.

The piezoelectric energy harvester (PEH) is a device for recycling wasted mechanical energy from pavements. To evaluate energy collecting efficiency of PEHs with various piezoelectric unit distributions, finite element (FE) models of the PEHs were developed in this study. The PEH was a square of 30 cm × 30 cm with 7 cm in thickness, which was designed according to the contact area between tire and pavement. Within the PEHs, piezoelectric ceramics (PZT-5H) were used as the core piezoelectric units in the PEHs. A total of three distributions of the piezoelectric units were considered, which were 3 × 3, 3 × 4, and 4 × 4, respectively. For each distribution, two diameters of the piezoelectric units were considered to investigate the influence of the cross section area. The electrical potential, total electrical energy and maximum von Mises stress were compared based on the computational results. Due to the non-uniformity of the stress distribution in PEHs, more electrical energy can be generated by more distributions and smaller diameters of the piezoelectric units; meanwhile, more piezoelectric unit distributions cause a higher electrical potential difference between the edge and center positions. For the same distribution, the piezoelectric units with smaller diameter produce higher electrical potential and energy, but also induce higher stress concentration in the piezoelectric units near the edge.

Theoretical modeling and experimental verification of rotational variable reluctance energy harvesters

Energy harvesting has great potential for powering low-power wireless sensor nodes by converting environmental energies into the electricity. It can be widely used for real-time online industrial monitoring. Among different transducers, the variable reluctance energy harvester (VREH) has attracted much attention due to the great performance for the low-speed rotations. However, there is a lack of precise models for performance prediction. In this paper, a new modeling method for VREH is proposed to predict the output voltage. A combined Substituting Angle - Magnetic Field Division modeling method is presented to accurately model the magnetic permeance of the air–gap for the VREH. Then, the magnetic flux change in the magnetic circuit is derived to calculate the voltage response of the coil. The numerical and experimental results of voltage responses verify the effectiveness of proposed model with the maximum error of 4%. The influence of some key factors on voltage response is investigated, including the thickness of air–gap and tooth height. Moreover, power analysis demonstrates that the output power increases from 5.06 mW to 46.7 mW with the rotational speed from 100 rpm to 300 rpm.

Computational EE Fairness in Backscatter-Assisted Wireless Powered MEC Networks

In this letter, we study the computational energy efficiency (EE) fairness in a backscatter-assisted wireless powered mobile edge computing (MEC) network, where multiple edge users (EUs) can offload tasks to the MEC server via passive backscatter communications (BackComs) and active transmissions (ATs) under the guidance of the harvest-then-transfer protocol. Specifically, with the practical non-linear energy harvesting (EH) model and the partial offloading scheme considered at each EU, we propose a max-min computational EE-based resource allocation scheme to ensure the fairness among multiple EUs by jointly optimizing the reflection coefficient, transmit power, local computing frequency and execution time of each EU, as well as EUs' time sharing between BackComs and ATs, and then develop a Dinkelbach-based iterative algorithm to obtain the optimal solutions. We further employ the Lagrange duality method to obtain instrumental insights on the max-min computational EE-based resource allocation scheme. Simulation results verify the superiority of the proposed scheme over benchmark schemes in terms of computational EE fairness.

Optimizing Computation Efficiency for NOMA-Assisted Mobile Edge Computing With User Cooperation

In this article, we investigate the application of user cooperation (UC) and non-orthogonal multiple access (NOMA) schemes for a wireless powered mobile edge computing (MEC) system under the non-linear energy harvesting model, in which two single-antenna mobile users first harvest energy from a multi-antenna access point (AP) integrated with an MEC server. Then, during the computation offloading phase, both mobile users simultaneously offload tasks to the MEC server with the harvested energy, by performing NOMA protocol. To better enhance the system performance, UC scheme is carried out, where the near user acts as a relay to help the far user offload computation tasks to the AP. To obtain energy efficient MEC design, our objective is to maximize the computation efficiency (i.e., the total computation bits divided by the consumed energy) by jointly designing the energy beamforming, time and power allocations, which yields a challenging nonconvex optimization problem. To deal with it, the original problem is first transformed into a more tractable formulation by applying the semidefinite relaxation (SDR) technique and then solved by utilizing the sequential convex approximation (SCA) method. Numerical results demonstrate that UC has a great impact when two users are close, while NOMA makes effect when two users are relatively far. Combining both NOMA and UC, the proposed scheme, named NOMA-UC MEC, yields better system performance than the benchmark schemes.