Improving Numerical Stability and Accuracy in Partitioned Methods with Algebraic Prediction

TL;DR

This paper introduces an $O(h^2)$-accurate algebraic prediction scheme that enhances the numerical stability and accuracy of partitioned power system simulations, especially for large-scale systems, by reducing step rejections and solver iterations.

Contribution

The paper proposes a novel algebraic prediction scheme for partitioned methods that improves stability and accuracy without increasing computational cost.

Findings

Significantly reduces step rejections in simulations.

Fewer nonlinear solver iterations needed.

Improves solution accuracy in large-scale power system models.

Abstract

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.