适用于电磁暂态仿真的变阶变步长3S-DIRK算法  

Variable Order/Step Integration by 3-stage Diagonally Implicit Runge-Kutta Method for Electromagnetic Transient Simulations

作　　者：叶小晖 汤涌 宋强[2] 刘文焯 吕广宪 陆一鸣 YE Xiaohui;TANG Yong;SONG Qiang;LIU Wenzhuo;Lü Guangxian;LU Yiming(China Electrical Power Research Institute,Haidian District,Beijing 100192,China;Dept.of Electrical Engineering,Tsinghua University,Haidian District,Beijing 100084,China)

机构地区：[1]中国电力科学研究院有限公司,北京市海淀区100192 [2]清华大学电机工程与应用电子技术系,北京市海淀区100084

出　　处：《电网技术》2020年第11期4047-4054,共8页Power System Technology

基　　金：国家重点研发计划项目(2016YFB0900601)。

摘　　要：电磁暂态仿真在计算过程中将产生数值振荡现象,现有算法切换到低阶数值积分算法将导致较大的数值误差。文章利用布彻矩阵和龙格库塔理论对数值临界阻尼CDA算法的准确性和稳定性进行了分析,提出一种三级半角隐式龙格库塔(3-stagediagonallyimplicitRunge-Kuttaformula,3S-DIRK)算法,该算法具有4个分算法,分算法具有不同的优点,可以用在电磁暂态的不同计算情形。文章给出了算法应用于电磁暂态的仿真策略,在切换算法时可以保证元件的等值导纳不变,整个仿真过程中计算精度不低于2阶,且故障期间具有L稳定可以消除数值振荡,支持变步长计算。文章利用该算法推导了线性元件的等值电路,对该算法的使用方法进行了说明。最后使用2个算例验证3S-DIRK算法的有效性和优点。When dealing with the numerical oscillation in electromagnetic transient simulation,a lower order numerical integration switched may lead to a larger numerical error.Based on the butcher tableau,firstly,the accuracy and stability of the critical damping adjustment method are studied and a 3-stage diagonally implicit Runge-Kutta(3S-DIRK)formula is proposed.This formula is composed of 4 methods with different advantages suitable for different electromagnetic transient situations.Then the simulation strategies are given by switching among these 4 methods to solve the electromagnetic simulation problems.The accuracy of the proposed 3S-DIRK is no less than 2 nd order during the whole calculation,and its L-stable property can eliminate the numerical oscillation and moreover can calculate in variable steps.The equivalent circuit of the linear components is derived,illustrating the application of the 3S-DIRK method.Finally,2 cases are listed to verify the effectiveness and advantages of the 3S-DIRK method.

关 键 词：电磁暂态仿真 半角隐式龙格库塔算法 数值振荡 布彻矩阵 算法切换策略 

分 类 号：TM721[电气工程—电力系统及自动化]