一类分数阶电力电容器动力学建模与数值分析

刘凌 1; 庞霞 1; 刘崇新 1; 李锐海 2

doi:10.7652/xjtuxb201408018

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一类分数阶电力电容器动力学建模与数值分析

更新时间：2025-07-09

- 一类分数阶电力电容器动力学建模与数值分析
- Dynamical Modeling and Numerical Analysis for Fractional-Order Power Capacitor System
- 西安交通大学学报 2014年48卷第8期页码：104-108
- 作者机构：
  
  西安交通大学电气工程学院,西安,710049
- 作者简介：
- 基金信息：
  
  : 2014-03-11。作者简介: 刘凌(1980—),男,博士,讲师,硕士生导师。基金项目: 国家自然科学基金资助项目(51307130);特高压工程技术(昆明、广州)国家工程实验室开放基金资助项目(NEL201304)
- DOI：10.7652/xjtuxb201408018
  中图分类号： TM461
- 网络首发：2014-08-10，
  
  纸质出版：2014
- 稿件说明：
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刘凌 1, 庞霞 1, 刘崇新 1, 等. 一类分数阶电力电容器动力学建模与数值分析[J]. 西安交通大学学报, 2014,48(8):104-108.

Dynamical Modeling and Numerical Analysis for Fractional-Order Power Capacitor System[J]. 2014, 48(8): 104-108.
刘凌 1, 庞霞 1, 刘崇新 1, 等. 一类分数阶电力电容器动力学建模与数值分析[J]. 西安交通大学学报, 2014,48(8):104-108. DOI： 10.7652/xjtuxb201408018.

Dynamical Modeling and Numerical Analysis for Fractional-Order Power Capacitor System[J]. 2014, 48(8): 104-108. DOI： 10.7652/xjtuxb201408018.

摘要

针对整数阶电力电容器绝缘设计中电场分布不均匀的问题

提出了一种分数阶电场优化模型。该模型基于分数阶微积分算子理论

设计了含10 kV并联电力电容器的分数阶链型等效分抗电路拓扑结构

进而采用ABM(Adams-Bashford-Moulton)预估校正算法对模型进行了频域转换。当分数阶阶次取0.1～0.9且最大误差分别为2 dB和3 dB时

通过数值模拟得到等效电路中电容内部各等效点的电位值。仿真结果表明

当确定了波特图的最大误差时

随着分数阶阶次的增加

电容内部的电场分布趋于均匀

各点电压的相位值在同一时间逐渐增大

并展现出良好的空间关联性。

Abstract

An optimized fractional-order electric field model is proposed to deal with non-uniform electric field distribution in integer-order form of power capacitor design. Following fractional derivative theory

the model for chain type fractional-order circuit topology containing a 10 kV parallel power capacitor is established. Then the frequency domain conversion is performed by Adams-Bashford-Moulton(ABM)predictor-corrector algorithm

the model is simplified and the potential distribution characteristics of fractional-order power capacitor is analyzed by adjusting the parameters. The potential internal capacitance in fractional equivalent circuit can be obtained by taking the fractional order within 0.1-0.9 and the maximum error as 2 dB and 3 dB respectively. The simulation result demonstrates that the electric field inside the capacitor tends to distribute uniformly and the voltage phase value at each point gradually increases as the maximum Bode plot error is determined and the fractional order is heightened.

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references

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