The partitioned approach for the numerical integration of power system differential algebraic equations faces inherent numerical stability challenges due to delays between the computation of state and algebraic variables. Such delays can compromise solution accuracy and computational efficiency, particularly in large-scale system simulations. We present an $O(h^2)$-accurate prediction scheme for algebraic variables based on forward and backward difference formulas, applied before the correction step of numerical integration. The scheme improves the numerical stability of the partitioned approach while maintaining computational efficiency. Through numerical simulations on a lightly damped single machine infinite bus system and a large-scale 140-bus network, we demonstrate that the proposed method, when combined with variable time-stepping, significantly enhances the numerical stability, solution accuracy, and computational performance of the simulation. Results show reduced step rejections, fewer nonlinear solver iterations, and improved accuracy compared to conventional approaches, making the method particularly valuable for large-scale power system dynamic simulations.

翻译：电力系统微分代数方程数值积分的分区方法，由于状态变量与代数变量计算之间的延迟，面临固有的数值稳定性挑战。此类延迟可能损害求解精度与计算效率，在大规模系统仿真中尤为显著。本文提出一种基于前向与后向差分公式的代数变量$O(h^2)$精度预测方案，该方案在数值积分校正步骤前执行。该策略在保持计算效率的同时，显著提升了分区方法的数值稳定性。通过对弱阻尼单机无穷大系统及大规模140节点网络进行数值仿真，证明所提方法结合变步长策略后，能显著增强仿真的数值稳定性、求解精度与计算性能。结果显示，与传统方法相比，该方法减少了步长拒绝次数，降低了非线性求解器迭代次数，并提升了计算精度，使其在大规模电力系统动态仿真中具有重要应用价值。