多组件分数阶元件的实现方法及其应用  

Realization Approach of Multi-Component Fractional-Order Element and Its Application

作　　者：王佳豪 丘东元[1] 张波[1] 陈艳峰[1] Wang Jiahao;Qiu Dongyuan;Zhang Bo;Chen Yanfeng(School of Electric Power Engineering South China University of Technology,Guangzhou 510641 China)

机构地区：[1]华南理工大学电力学院,广州510641

出　　处：《电工技术学报》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)。

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 dire

关 键 词：分数阶电路 分数阶电容 分数阶电感 逆变器 

分 类 号：TM502[电气工程—电器]