分数阶电路的仿真计算研究
发布时间：2018-07-15 19:00
【摘要】：随着分数阶微积分理论的发展,电气工程领域涌现出很多分数阶模型及应用,如变压器绕组、传输线、电缆线路、超级电容器等分数阶模型。这些模型不仅降低了模型的复杂度,而且提高了仿真精度,使仿真结果更加符合实际。分数阶电路理论是研究这些分数阶模型的基础,所以分数阶电路元件、分数阶电路的性质以及分数阶电路的仿真计算研究对于电气工程的发展具有重要意义。传统整数阶电路元件可以用电磁场知识加以描述,分数阶电磁场作为传统电磁场的拓展,也可以很好地解释分数阶电路元件。本文将分数阶Maxwell方程进行泰勒级数展开得到各阶次Maxwell方程,利用特定阶次的电场、磁场组合时的分数阶波阻抗对分数阶元件加以描述,从电磁场角度印证了分数阶元件的存在。分数阶电路的性质研究是分数阶电路理论发展的基础,分数阶微积分的引入使电路产生了许多新的性质。本文根据已有研究,归纳总结了分数阶RL_βC_α电路的相关性质,并提出和证明了分数阶电路的振荡条件,为分数阶电路理论的发展奠定了基础。分数阶电路性质研究离不开分数阶电路的仿真计算,本文选取L1插值离散逼近法建立了分数阶元件的伴生模型,基于MATLAB语言采用稀疏表格法编写分数阶电路分析程序。通过仿真计算验证了分数阶元件伴生模型和仿真程序的正确性。为分数阶电路的计算机辅助分析提供了有效的辅助工具,一定程度上弥补了当前电路分析软件的不足。
[Abstract]:With the development of fractional calculus theory, many fractional order models and applications have emerged in the field of electrical engineering, such as transformer windings, transmission lines, cable lines, supercapacitors and other fractional order models. These models not only reduce the complexity of the models, but also improve the accuracy of simulation, and make the simulation results more realistic. The theory of fractional circuit is the basis of studying these fractional order models. Therefore, the study of fractional circuit elements, properties of fractional order circuits and simulation of fractional order circuits is of great significance for the development of electrical engineering. Traditional integral order circuit elements can be described by electromagnetic field knowledge, fractional order electromagnetic field as an extension of the traditional electromagnetic field, but also a good explanation of fractional circuit elements. In this paper, the fractional Maxwell equation is expanded by Taylor series to obtain the Maxwell equation of each order. The fractional order element is described by the fractional wave impedance when the electric field and magnetic field are combined, and the existence of the fractional order element is confirmed from the point of view of electromagnetic field. The study of the properties of fractional order circuits is the basis of the development of fractional order circuits. The introduction of fractional calculus makes the circuit produce many new properties. In this paper, the related properties of fractional order RL尾 C伪 circuits are summarized, and the oscillation conditions of fractional order circuits are proposed and proved, which lays a foundation for the development of fractional order circuit theory. The properties of fractional circuit can not be studied without the simulation of fractional circuit. In this paper, we select L1 interpolation discrete approximation method to establish the associated model of fractional component, and use sparse table method to compile the program of fractional order circuit analysis based on MATLAB. The simulation results verify the correctness of the fractional component companion model and the simulation program. It provides an effective assistant tool for the computer aided analysis of fractional circuit, and to some extent makes up for the deficiency of the current circuit analysis software.
【学位授予单位】：华北电力大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TM13
本文编号：2125081
[Abstract]:With the development of fractional calculus theory, many fractional order models and applications have emerged in the field of electrical engineering, such as transformer windings, transmission lines, cable lines, supercapacitors and other fractional order models. These models not only reduce the complexity of the models, but also improve the accuracy of simulation, and make the simulation results more realistic. The theory of fractional circuit is the basis of studying these fractional order models. Therefore, the study of fractional circuit elements, properties of fractional order circuits and simulation of fractional order circuits is of great significance for the development of electrical engineering. Traditional integral order circuit elements can be described by electromagnetic field knowledge, fractional order electromagnetic field as an extension of the traditional electromagnetic field, but also a good explanation of fractional circuit elements. In this paper, the fractional Maxwell equation is expanded by Taylor series to obtain the Maxwell equation of each order. The fractional order element is described by the fractional wave impedance when the electric field and magnetic field are combined, and the existence of the fractional order element is confirmed from the point of view of electromagnetic field. The study of the properties of fractional order circuits is the basis of the development of fractional order circuits. The introduction of fractional calculus makes the circuit produce many new properties. In this paper, the related properties of fractional order RL尾 C伪 circuits are summarized, and the oscillation conditions of fractional order circuits are proposed and proved, which lays a foundation for the development of fractional order circuit theory. The properties of fractional circuit can not be studied without the simulation of fractional circuit. In this paper, we select L1 interpolation discrete approximation method to establish the associated model of fractional component, and use sparse table method to compile the program of fractional order circuit analysis based on MATLAB. The simulation results verify the correctness of the fractional component companion model and the simulation program. It provides an effective assistant tool for the computer aided analysis of fractional circuit, and to some extent makes up for the deficiency of the current circuit analysis software.
【学位授予单位】：华北电力大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TM13
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