摘要
分数阶元件作为分数阶电路的基本单元,其构建和实现方法是研究分数阶电路系统的基础。然而,目前单组件分数阶元件未见商业应用,分数阶元件仍以多元件的集成方式为主。与单组件分数阶元件相比,分数阶元件的多组件实现方法在构成元件种类、数量和参数选择方面更加灵活,且分数阶元件的阶数和阻抗系数可以调节,具有更强的实用性。为了能够根据具体应用需求选择合适的多组件分数阶元件,该文在总结现有大部分多组件分数阶元件构造方法的基础上,按照构成器件种类将其构造方法分为基于无源元件、基于运算放大器和基于电力电子变换器三类,重点介绍一些典型构造方法的工作原理,并对这些构造方法进行分析和比较。最后,该文探讨了多组件分数阶元件在电网功率补偿场合的应用,为拓展多组件分数阶元件的应用提供了参考。
Fractional-order elements(FOEs)serve as fundamental components in fractional-order circuits,forming the cornerstone of research into fractional-order circuit systems.Unlike single-component counterparts,the multi-component method offers greater flexibility in selecting constituent elements,enabling the adjustment of order and impedance coefficients for enhanced practicality.This paper provides a comprehensive overview of prevailing construction methods to facilitate the selection of appropriate multi-component FOEs for specific application needs.These methods are classified into three categories based on the type of constituent devices:passive devices,operational amplifiers,and power electronic converters.In the construction method based on passive devices,two approaches involving Foster RLC ladder circuits are discussed.Passive RLC networks are used to create circuits that match the impedance characteristics of the transfer function.Reducing phase error requires increasing the order and using numerous components,leading to complex structures and cumbersome calculations.When standard off-the-shelf components cannot be used,replacing analytical parameters with standard ones increases the phase angle deviation.Adjusting the FOE order or impedance coefficients requires replacing all circuit components.This method is most suitable for fixed FOE order and impedance coefficients,which are effective in medium to low-frequency scenarios.Next,the paper introduces the construction method based on operational amplifiers.The method of constructing FOEs based on generalized impedance converter(GIC)circuits can realize FOEs with orders varying from-2 to 2.However,the limited open-loop gain and gain instability of operational amplifiers often result in significant deviations of the obtained FOE performance from its ideal characteristics.Therefore,exploring how to use other active devices,such as operational transconductance amplifiers(OTA)and current feedback operational amplifiers(CFOA),to construct FOEs is an exploration direction.GIC circuits offer great integration and functionality,making them suitable for applications where precise impedance and phase characteristics are crucial.The construction method based on power electronic converters is also discussed in detail.Multi-component FOEs based on power electronic converters have wide applications because their power level depends on the inverter,and their order and impedance can be adjusted by changing the control parameters.However,different structures of filters affect the operating performance of fractional-order elements.Therefore,exploring the application of different filter structures on multi-component FOEs and optimizing the parameters of the filters become the direction of development for power electronic converter-based FOEs.Power electronic converters provide the advantage of handling higher power levels and dynamic adaptability.The ability to digitally control the fractional order and impedance in real-time makes these elements highly versatile.Lastly,this paper proposes a three-phase fractional-order electrical spring(TPFES).TPFES controls the order of the equivalent fractional-order capacitance of each phase and the pseudo-capacitance.The effect of stabilizing the load voltage is realized,the power factor is improved,and the power is balanced.The application in grid power compensation demonstrates that multi-component FOEs can effectively enhance the performance of practical circuit systems.This work provides a reference for future applications of fractional order components in electrical engineering.
作者
王佳豪
丘东元
张波
陈艳峰
Wang Jiahao;Qiu Dongyuan;Zhang Bo;Chen Yanfeng(School of Electric Power Engineering South China University of Technology,Guangzhou 510641 China)
出处
《电工技术学报》
北大核心
2025年第8期2365-2379,共15页
Transactions of China Electrotechnical Society
基金
国家自然科学基金资助项目(52277177,52077085)。
关键词
分数阶电路
分数阶电容
分数阶电感
逆变器
Fractional-order circuit
fractional-order capacitor
fractional-order inductor
inverter
