Theoretical and experimental study of a bi-stable piezoelectric energy harvester under hybrid galloping and band-limited random excitations

In the practical environment,it is very common for the simultaneous occurrence of base excitation and crosswind.Scavenging the combined energy of vibration and wind with a single energy harvesting structure is fascinating.For this purpose,the effects of the wind speed and random excitation level are investigated with the stochastic averaging method(SAM)based on the energy envelope.The results of the analytical prediction are verified with the Monte-Carlo method(MCM).The numerical simulation shows that the introduction of wind can reduce the critical excitation level for triggering an inter-well jump and make a bi-stable energy harvester(BEH)realize the performance enhancement for a weak base excitation.However,as the strength of the wind increases to a particular level,the influence of the random base excitation on the dynamic responses is weakened,and the system exhibits a periodic galloping response.A comparison between a BEH and a linear energy harvester(LEH)indicates that the BEH demonstrates inferior performance for high-speed wind.Relevant experiments are conducted to investigate the validity of the theoretical prediction and numerical simulation.The experimental findings also show that strong random excitation is favorable for the BEH in the range of low wind speeds.However,as the speed of the incoming wind is up to a particular level,the disadvantage of the BEH becomes clear and evident.

Theoretical Analysis of the Galloping Energy Harvesters under Bounded Random Parameter Excitation

In this paper,the response properties of galloping energy harvesters under bounded random parameter excitation are studied theoretically.The first-order approximate solution of the galloping energy harvester is derived by applying the multi-scales method.The expression for the largest Lyapunov exponent that determines the trivial solution is derived,and the corresponding simulation diagrams,including the largest Lyapunov exponent diagrams and time domain diagrams,verify our results.Then the steady-state response moments of the nontrivial solution are studied using the moment method,and the analytical expressions for the first-order and second-order moments of the voltage amplitude are obtained,respectively.The corresponding results show that wind speed enhances the steady-state response moments of the voltage amplitude.Meanwhile,the voltage output can be controlled by adjusting the cubic coefficient.To further verify the response characteristics of the galloping energy harvester,the stationary probability density functions of the displacement and velocity are obtained by the Monte-Carlo simulation method.The results show that the wind speed enhances the displacement of the bluff and the damping ratios should be reduced asmuch as possible to improve the performance.What’smore,the piezoelectric materials also impact the performance of the energy harvester.

Incident flow effects on the performance of piezoelectric energy harvesters from galloping vibrations

In this paper, we investigate experimentally the concept of energy har- vesting from galloping oscillations with a focus on wake and turbulence effects. The .harvester is composed of a unimorph piezoelectric cantilever beam with a square cross-section tip mass. In one case, the harvester is placed in the wake of another galloping harvester with the objective of determining the wake effects on the response of the harvester. In the second case, meshes were placed upstream of the harvester with the objective of investigating the effects of upstream turbulence on the response of the harvester. The results show that both wake effects and up- stream turbulence significantly affect the response of the harvester. Depending on the spacing between the two squares and the opening size of the mesh, wake and upstream turbulence can positively enhance the level of the harvested power.

Tracking Galloping Profile of Transmission Lines Using Wireless Inertial Measurement Units

Galloping of power transmission lines might bring about huge damage such as massive power outage and collapse of the transmission towers. To realize forecast of the galloping and provide data for study on the galloping mechanism, this paper proposes an online monitoring system for tracking galloping profile of power transmission lines based on wireless inertial measurement units (WIMUs). The system is composed of three modules: wireless inertial measurement nodes, monitoring base station, and remote monitoring station. After detailing the hardware system, the corresponding software which positions and displays galloping profile of the transmission line in real-time is outlined. The feasibility of the proposed on-line monitoring system is demonstrated through a series of experiments at the State Grid Key Laboratory of Power Overhead Transmission Line Galloping (Zhengzhou, China) by taking into account different vibration patterns.

MODES COMPUTATION AND ANALYSIS FOR LONG MULTI-SPAN BUNDLE CONDUCTORS OF POWER TRANSMISSION LINES WITH GALLOPING CONTROL DEVICES

A new type of element which is suitable for solving the modes of thegalloping long multi-span bundle conductor structures is presented. The element is composed of allsub-conductor segments between two spacers. Based on the linearized governing differential equationsof the conductors, the mass matrix and stiffness matrix of the element in consideration of theconstrained relations imposed on the conductors by spacers are derived. The dynamic characteristicsof the galloping control devices can be directly added to the element. The modes for an actual powerline structure are computed by using the element formula and FEM procedures, where seven cases ofdifferent galloping control device allocations are considered. Compared with the measured data, themethod is shown to be reliable and effective. Analysis and discussions of the computational resultsare given. Some hints that are helpful to further investigation of galloping are also obtained .

On the formation and wind enhancement mechanisms of a Mongolian cyclone that caused a transmission line galloping trip in Gansu province

Influenced by strong winds associated with a southeastward-moving Mongolian cyclone,a severe transmission line galloping occurred in Baiyin City,Gansu Province,on 14 April 2020.This caused a tripping incident of the transmission line in this region.Based on the hourly,0.5°×0.5°,ECMWF ERA5 reanalysis data,this study investigated the formation mechanisms of the Mongolian cyclone and its associated strong winds.Results from the vorticity budget indicate that the convergence-related vertical stretching and the upward transport of cyclonic vorticity governed formation of the Mongolian cyclone in this event;whereas,tilting and export of cyclonic vorticity from the central region of the cyclone mainly decelerated the cyclone’s formation.The kinetic energy(KE)budget shows that the wind associated with the Mongolian cyclone was mainly enhanced by the positive work of the pressure gradient force.Unlike some typical strong wind events in Northwest China,during this event,no significant downward momentum transportation from the upper troposphere was found.The vertical transport of KE exerted a slightly favorable effect on the KE increase around the location where the transmission line galloping trip appeared.In contrast,the horizontal transport mainly caused an export of KE from this region,which applied an overall negative effect on the wind enhancement associated with the Mongolian cyclone.

Enhanced galloping energy harvester with cooperative mode of vibration and collision

The low power and narrow speed range remain bottlenecks that constrain the application of small-scale wind energy harvesting.This paper proposes a simple,lowcost,and reliable method to address these critical issues.A galloping energy harvester with the cooperative mode of vibration and collision(GEH-VC)is presented.A pair of curved boundaries attached with functional materials are introduced,which not only improve the performance of the vibration energy harvesting system,but also convert more mechanical energy into electrical energy during collision.The beam deforms and the piezoelectric energy harvester(PEH)generates electricity during the flow-induced vibration.In addition,the beam contacts and separates from the boundaries,and the triboelectric nanogenerator(TENG)generates electricity during the collision.In order to reduce the influence of the boundaries on the aerodynamic performance and the feasibility of increasing the working area of the TENG,a vertical structure is designed.When the wind speed is high,the curved boundaries maintain a stable amplitude of the vibration system and increase the frequency of the vibration system,thereby avoiding damage to the piezoelectric sheet and improving the electromechanical conversion efficiency,and the TENG works with the PEH to generate electricity.Since the boundaries can protect the PEH at high wind speeds,its stiffness can be designed to be low to start working at low wind speeds.The electromechanical coupling dynamic model is established according to the GEH-VC operating principle and is verified experimentally.The results show that the GEH-VC has a wide range of operating wind speeds,and the average power can be increased by 180%compared with the traditional galloping PEH.The GEH-VC prototype is demonstrated to power a commercial temperature sensor.This study provides a novel perspective on the design of hybrid electromechanical conversion mechanisms,that is,to combine and collaborate based on their respective characteristics.

A Numerical Study on Piezoelectric Energy Harvesting by Combining Transverse Galloping and Parametric Instability Phenomena

This paper aims to numerically investigate the effects of parametric instability on piezoelectric energy harvesting from the transverse galloping of a square prism. A two degrees-of-freedom reduced-order model for this problem is proposed and numerically integrated. A usual quasi-steady galloping model is applied, where the transverse force coefficient is adopted as a cubic polynomial function with respect to the angle of attack. Time-histories of nondimensional prism displacement, electric voltage and power dissipated at both the dashpot and the electrical resistance are obtained as functions of the reduced velocity. Both, oscillation amplitude and electric voltage, increased with the reduced velocity for all parametric excitation conditions tested. For low values of reduced velocity, 2:1 parametric excitation enhances the electric voltage. On the other hand, for higher reduced velocities, a 1:1 parametric excitation(i.e., the same as the natural frequency) enhances both oscillation amplitude and electric voltage. It has been also found that, depending on the parametric excitation frequency, the harvested electrical power can be amplified in 70% when compared to the case under no parametric excitation.

Nonlinear numerical simulation method for galloping of iced conductor

Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In numerical simulation, a three-node isoparametric cable element with three translational and one torsional degrees-of-freedom at each node is used to discretize the transmission line. The nonlinear dynamic system equation is solved with the Newmark time integration method and the Newton-Raphson nonlinear iteration. Numerical examples demonstrate the efficiency of the presented method and the developed finite element program. A new possible galloping mode, which may reflect the saturation phenomenon of a nonlinear dynamic system, is discovered under the condition that the lowest order of vertical natural frequency of the transmission line is approximately two times of the horizontal one.

Study on Galloping Stability Mechanism of Conductor and Its Application to Anti-Galloping of Transmission Lines

Galloping of conductor is a major hazard to safe operation of transmission lines. This paper introduces the basic galloping stability mechanism of conductor, design method of anti-galloping and the application of anti-galloping double pendulum and integral eccentric pendulum in China. Galloping stability mechanism of conductor was established based on vertical galloping mechanism developed by Den Hartog and torsional galloping mechanism developed by O. Nigel. A design method of anti-galloping was derived and anti-galloping double pendulum and integral eccentric pendulum were developed. Applications to several transmission lines including a 500 kV transmission line of large span indicated that they have played important roles in anti-galloping.

Numerical Analysis of the Influence of Turbulence Intensity on Iced Conductors Gallop Phenomena

Turbulence is expected to play a relevant role in the so-called conductor gallop phenomena,namely,the high-amplitude,low-frequency oscillation of overhead power lines due to the formation of ice structures and the ensu-ing effect that wind can have on these.In this work,the galloping time history of a wire with distorted(fixed in time)shape due to the formation of ice is analyzed numerically in the frame of afluid-solid coupling method for different wind speeds and levels of turbulence.The results show that the turbulence intensity has a moderate effect on the increase of the conductor’s aerodynamic lift and drag coefficients due to ice accretion;nevertheless,the corresponding changes in the torsion coefficient are very significant and complicated.A high turbulence intensity can affect the torsion coefficient in a certain range of attack angles and increase the torsion angle of the conductor.Through comparison of the galloping phenomena for different wind velocities,it is found that the related amplitude grows significantly with an increase of the wind speed.For a relatively large wind speed,the galloping amplitude is more sensitive to the turbulence intensity.Moreover,the larger the turbulence intensity,the larger the conductor’s vertical and horizontal galloping amplitudes after icing.The torsion angle also increases with an increase in the wind speed and turbulence intensity.

柱体流激振动能量俘获理论与技术研究若干进展

潮流能分布广泛,且储量巨大,具备巨大的规模化开发利用价值.流激振动是一种常见的流固耦合现象,通过柱体流激振动能够在流速较低时实现有效的能量转换,基于柱体流激振动的能量俘获技术在未来具备广阔的工程应用前景.近年来,针对柱体结构流激振动特性和能量俘获性能,出现了大量的实验和数值仿真研究工作.文章全面阐述了多种截面形式的单个柱体、柱群结构流激振动能量俘获理论与技术方面的研究进展:对于单个圆柱流激振动能量俘获,目前已基本揭示了被动湍流控制器参数、系统阻尼、雷诺数和边界条件等因素对能量俘获性能的影响规律,基本完成了理论和技术积累;对于非圆截面柱体流激振动能量俘获,已初步明确特定来流攻角、系统质量比、系统阻尼、系统刚度和雷诺数条件下三角形、四边形、多边形与异形等多种截面形式柱体的流激振动作用机理和能量俘获能力;对于柱群的流激振动能量俘获,各柱体振子之间存在流场干涉,需要合理设计柱体排布形式、柱体间距和系统阻尼等参数,实现流体能量俘获最大化.通过综述国内外流激振动能量俘获理论和技术方面的研究进展,对今后该问题的研究进行了力所能及的展望,期望促进流激振动能量俘获理论的发展和流激振动能量转换装置的工程应用.

磁力调控驰振压电-电磁复合俘能器设计与研究

为避免驰振俘能器高流速下PZT损坏,使其能在复杂工作环境中具有稳定的输出特性,该文提出了一种利用磁力控制悬臂梁振动幅值的压电-电磁复合俘能器(GPEEH)。引入的非线性磁力可以调控钝体的振幅,提高驰振压电俘能器(PEH)的输出稳定性,改善其对高风速环境的适应性,且能够增加复合俘能器的输出电压。在搭建风洞实验平台和制作实验样机的基础上,研究不同负载电阻、风速、关键结构参数d 0和d 1对俘能器输出特性的影响规律。实验结果表明,当PEH钝体的振幅被磁力限制在一定区间时,钝体的振动频率和速度随着风速的升高而逐渐增加。风速为11.5 m/s时,PEH振动主频率(6.3 Hz)是风速为8.4 m/s时PEH振动主频率(4.3 Hz)的1.4倍。当风速为12 m/s,GPEEH的输出功率为6.18 mW,相较于单一驰振压电俘能器的输出功率提高了47%。其中当风速达到10.5 m/s时,PEH和电磁俘能器(EEH)的输出功率均趋于稳定。

基于柔性套管悬臂梁式压电能量采集器的实验研究

为了提高压电能量采集器的使用寿命,保证内部发电部件的稳定运行,提出了一种柔性套管悬臂梁式压电能量采集器收集能量的盾形截面的钝体,通过实验研究该结构的输出性能。分析了外接负载、风速、钝体质量对能量采集器的输出功率的影响。结果表明:能量采集器的输出功率随着负载阻值的增大呈现先增大后减小的趋势,存在最佳负载使得能量采集器的输出功率达到最大;同时输出功率会随流速的增大而增大,符合驰振现象;在实验所考虑的质量范围内,最大输出功率随着质量的增大而减小。实验中,能量采集器在钝体质量为70 g,最佳负载为10^(5)Ω,流速为8.0 m/s时达到最大输出功率5.22 mW。

大风区接触网线路参数对附加导线舞动的影响

针对大风环境下兰新高速铁路接触网附加导线发生剧烈舞动以及线间放电的现象,依据接触网附加导线结构特点,建立了附加导线有限元计算模型,并对附加导线进行找形计算。采用谐波叠加法模拟接触网附加导线处的随机风场,并对导线模型施加风荷载,利用无条件稳定Newmark法以及荷载增量法,分析接触网线路参数对附加导线舞动及线间距离的影响规律,并给出相应的舞动防治措施。结果表明:40 m及更小档距对导线在低风速及高风速下的舞动均有明显的抑制效果;将附加导线运行张力提高至6.5 kN,导线阻尼比提高至1.5%及以上能有效降低两条导线的舞动剧烈程度;接触网附加导线的档距过大,运行张力及阻尼比过小,将导致导线舞动时悬挂点张力过大,易引起导线掉线、断线等事故;随附加导线档距减小、运行张力及阻尼比增大,线间最小距离呈递增趋势;不同线路参数下(档距、运行张力及阻尼比)附加导线舞动时线间最小距离均随风速增大出现减小趋势。本研究可为兰新高铁大风区段接触网附加导线舞动及线间放电的防治提供有效的理论依据。

大跨长挑臂钢箱组合梁桥抗风性能试验研究

为了解大跨长挑臂钢箱组合梁桥抗风性能及选取合适的声屏障形式,以挑臂长7.5 m的钢箱组合梁桥——临猗黄河大桥为背景,基于有限元计算的施工及成桥阶段桥梁动力特性指标,制作1个缩尺比1∶50的最大悬臂施工状态钢箱梁、2个缩尺比1∶60的成桥状态不同声屏障设置形式(直线形、折线形,高度均为2.5 m)钢箱组合梁节段模型进行风洞试验,分析施工和成桥状态主梁断面的涡振、颤振和驰振性能。结果表明:施工状态的钢箱梁抗风稳定性良好,涡振、颤振和驰振性能均满足设计要求;常遇风攻角为0°、±3°时,成桥状态下,设置2.5 m高折线形声屏障可有效抑制主梁涡振响应,且颤振与驰振稳定性均满足规范要求;设置2.5 m高直线形声屏障的主梁发生明显的竖向涡振现象。该桥主梁最终采用2.5 m高折线形声屏障。

高雷诺数下串列粗糙三圆柱的流致振动试验研究

通过试验研究了高雷诺数下串列粗糙三圆柱的流致振动,分析与探讨了刚度、间距比对各个圆柱振幅响应、频率响应、位移频谱的影响,并与串列粗糙双圆柱的结果进行对比,揭示了干扰圆柱数量的增加对受扰圆柱流致振动的影响规律。研究结果表明:在初始分支,上游圆柱对下游圆柱有强烈的屏蔽作用,而在上端分支,出现下游圆柱振幅超过上游圆柱的现象;在上端分支和过渡区域,低刚度条件下,下游圆柱干扰数量的增加可以明显降低上游圆柱的振动频率;在涡激振动区域,下游干扰圆柱数量的增加几乎不影响上游圆柱的振幅;在驰振区域,上游圆柱干扰数量的增加降低了下游圆柱的振幅,并随着刚度的增加对下游圆柱振幅的降低程度下降;间距比对串列粗糙三圆柱的流致振动响应具有显著影响。

基于IPSO-BP神经网络的导线舞动预警方法

为确保输电线路在易舞气象条件下的正常运维,根据线路舞动与气象条件之间的复杂映射关系,采用改进粒子群算法(improved particle swarm optimization,IPSO)对BP神经网络进行优化,提出一种基于改进粒子群算法优化BP(IPSO-BP)神经网络的导线舞动预测方法。利用文本挖掘技术分析舞动影响因素,确定以档距、覆冰厚度、温度、风速、风向、相对湿度及风向与线路走向夹角为特征输入的IPSO-BP神经网络模型,通过舞动历史数据训练模型以达到预测的功能。对比IPSO-BP神经网络模型与其他算法模型的精度和稳定性,结果表明该方法具有一定的优越性。最后采用该方法预测河南谢庄地区的导线舞动,验证该方法的准确性和实用性。