An Variable Step-size 2S-DIRK Algorithm for Electromagnetic Transients Simulation With Arbitrary Events

PANG Bohan; LIU Wenzhuo; TANG Yong

doi:10.13334/j.0258-8013.pcsee.242476

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An Variable Step-size 2S-DIRK Algorithm for Electromagnetic Transients Simulation With Arbitrary Events

更新时间：2026-10-12

- An Variable Step-size 2S-DIRK Algorithm for Electromagnetic Transients Simulation With Arbitrary Events
- Vol. 46, Issue 4, Pages: 1431-1442(2026)
- 作者机构：
  
  中国电力科学研究院有限公司，北京市海淀区,100192
- 作者简介：
- 基金信息：
- DOI：10.13334/j.0258-8013.pcsee.242476
  CLC：
- Published：2026
- 稿件说明：
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PANG Bohan, LIU Wenzhuo, TANG Yong. An Variable Step-size 2S-DIRK Algorithm for Electromagnetic Transients Simulation With Arbitrary Events[J]. 2026, 46(4): 1431-1442.
DOI：

PANG Bohan, LIU Wenzhuo, TANG Yong. An Variable Step-size 2S-DIRK Algorithm for Electromagnetic Transients Simulation With Arbitrary Events[J]. 2026, 46(4): 1431-1442. DOI： 10.13334/j.0258-8013.pcsee.242476.

摘要

在非线性电路的电磁暂态仿真中，梯形法面临数值振荡问题。2级对角隐式龙格-库塔法(2-stage diagonally implicit Runge-Kutta，2S-DIRK)虽具有L-稳定性，不会产生数值振荡，但存在数值尖峰和难以处理开关事件的问题。针对上述问题，该文提出了一种改进2S-DIRK(modified 2S-DIRK，M2S-DIRK)数值积分方法。该文首先分析了2S-DIRK的数值积分过程，阐述了2S-DIRK产生数值尖峰的原因；然后，给出了M2S-DIRK的数值积分格式及伴随模型，并设计了事件定位算法和可变步长方案；最后，通过仿真算例验证了M2S-DIRK的正确性和有效性。仿真结果表明，M2S-DIRK继承了2S-DIRK的L稳定特性，从根本上解决了数值振荡问题，且有效避免了数值尖峰，能够灵活准确地处理开关事件。与过零点插值、临界阻尼调整、特性补偿法算法相比，M2S-DIRK方法更加简便，具有更高的数值稳定性，适用于非线性电路的电磁暂态仿真。

Abstract

The trapezoidal method faces numerical oscillation problems in electromagnetic transients (EMT) simulation of nonlinear circuits. Although the 2-stage diagonally implicit Runge-Kutta method (2S-DIRK) is L-stable and does not produce numerical oscillations

it has the problems of numerical spikes and difficulty in handling switching events. To address these problems

this paper proposes a modified 2S-DIRK (M2S-DIRK) numerical integration method. The paper first analyzes the numerical integration process of 2S-DIRK and explains the causes of numerical spikes. Then

the numerical integration formulas and companion model of M2S-DIRK are given

along with the design of an event location algorithm and a variable step-size scheme. Finally

the correctness and effectiveness of M2S-DIRK are verified by simulation examples. The simulation results show that the M2S-DIRK method inherits the L-stability of 2S-DIRK

fundamentally solves the numerical oscillation problem

effectively avoids numerical spikes

and can flexibly and accurately handle switching events. Compared with algorithms such as zero-crossing interpolation

critical damping adjustment

and characteristic compensation method

the M2S-DIRK method is simpler and has higher numerical stability

and is suitable for EMT simulation of nonlinear circuits.

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