基于指数项有理分式拟合的网络差分化算法及其适用性分析

摘要

In the power system electromagnetic transient(EMT)simulations,the conventional method will produce sustainable numerical oscillations (chatters) when circuit breakers and switches are operated repeatedly.In order to further solve the chatter problems, this paper developes a new high-order algorithm with variable parameters based on the rational approximation of exponential function.This method itself can eliminate chatters,while making up for the shortage of conventional methods by reducing complexity and changing parameters adaptively to improve accuracy and numerical stability. By deriving impedance error coefficients,it has been proved that the simulation accuracy of the proposed algorithm with appropriate parameters is better than conventional methods.At the same time,the algorithm possesses L-stability when appropriate parameters are chosen and its advantages on eliminating chatters are even more prominent.Simulation results show the accuracy and numerical performance of the algorithm,which provides a better solution for off-line/real-time simulations of power systems.%电磁暂态仿真中，断路器和电力电子开关反复动作时会出现数值振荡问题，文中提出了一种基于有理多项式的可变参数指数拟合法。该算法自身可以消除数值振荡，同时可以弥补传统算法及其改进方法实现复杂且无法根据算法精度和数值稳定性的要求自适应改变参数的不足。通过推导阻抗误差系数，证明了所提算法在选取合适参数的情形下，仿真精度优于传统算法。同时，该算法在选取合适参数情形下具有L稳定性，抑制数值振荡优点更加突出。实际算例表明所提算法在提高计算精度和抑制数值振荡上具有明显优势，为实现含有开关网络的电力系统离线/实时仿真提供了更有效的解决方案。