基于任意代数精度的电路微分方程数值积分算法  

Numerical Integration Algorithm of Circuit Differential Equations Based on Arbitrary Algebraic Precision

作　　者：杜金鹏 王康 汪光森[1] 刘著 Du Jinpeng;Wang Kang;Wang Guangsen;Liu Zhu(National Key Laboratory of Electromagnetic Energy,Naval University of Engineering,Wuhan,430033,China)

机构地区：[1]电磁能技术全国重点实验室(海军工程大学),武汉430033

出　　处：《电工技术学报》2025年第7期1995-2006,共12页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金面上项目资助(51477179)。

摘　　要：数值积分是求解电路微分方程的经典方法之一,但传统数值积分形式固定、积分精度不可调节,且精度、计算量与积分的定量关系不明确。针对此问题,该文提出一种基于任意代数精度的显隐式数值积分算法。首先,给出显隐式数值积分的构造方法,以任意代数精度为条件确定积分系数,并分析证明所提积分算法的精度与稳定性;其次,定义单位时间计算量,补充传统数值积分评价指标,并研究单位时间计算量随方程维度、积分精度等因素的变化规律;最后,通过实时仿真验证所提积分算法与指标的有效性。仿真结果表明,与传统高阶积分相比,所提积分算法的准确度可提高33%~72%,计算量可减小9%~42%,单位时间计算量可减小16%~61%,且单位时间计算量能够定量描述精度、计算量与积分的关系,对数值积分的选择具有指导意义。The circuit differential equation is the foundation of electrical engineering,spanning various fields such as circuit principle analysis,topology design,and power system engineering applications.However,with the increasing scale of the power system and the widespread application of high-frequency semiconductor switches,solving circuit differential equations quickly and accurately has become increasingly challenging.Numerical integration is one of the classic methods for solving circuit differential equations,but traditional numerical integration methods are fixed in form,with non-adjustable integration accuracy,and the relationship between accuracy,computation effort,and integration is not well-defined.Moreover,traditional indicators such as stability,accuracy,and calculation effort only allow for qualitative comparisons of numerical integration,making it difficult to accurately evaluate integration accuracy and computation efficiency.To address these problems,an explicit or implicit numerical integration algorithm based on arbitrary algebraic precision is proposed.Meanwhile,the computational effort per unit time is defined to supplement the traditional integral evaluation indicators.Firstly,the construction method of explicit and implicit numerical integration is given.By independently selecting the differentiation items and their orders to construct a new type of integration,the structure of the integration is simplified,thereby enhancing the efficiency of the integration calculation.Secondly,a method for determining integral parameters based on arbitrary algebraic precision is proposed to improve integration accuracy,and the accuracy and stability of the proposed algorithm are proved.Finally,computational effort per unit time is defined to clarify the quantitative relationship between accuracy,computational effort,and numerical integration.And the patterns of variation with respect to the scale of circuit equations and factors like accuracy are investigated.Using classic RLC circuits and a two-level converter

关 键 词：电路微分方程 数值积分 代数精度 计算量 

分 类 号：TM133[电气工程—电工理论与新技术]