Improving Numerical Stability and Accuracy in Partitioned Methods with Algebraic Prediction

TL;DR

The paper tackles stability and accuracy challenges in partitioned power-system DAEs caused by delays between state $\mathbf{x}$ and algebraic $\mathbf{y}$ variables. It introduces an $O(h^2)$ algebraic prediction within a predictor-corrector scheme, deriving how algebraic-error propagates to the state and proposing a backward-difference-based estimate for $\mathbf{y}_{n+1}$ to reduce this error. The approach is validated on a poorly damped SMIB and a 140-bus NPCC network with adaptive time stepping, showing reduced step rejections, fewer nonlinear solver iterations, and accuracy comparable to implicit simultaneous methods. The results indicate that the proposed method enhances stability and efficiency for large-scale dynamic simulations, offering a practical improvement over conventional partitioned approaches.

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.

Figures (4)

• Figure 1: Comparison of Generator 1 speed for the SMIB system.
• Figure 2: Step size used by the integration scheme. (a) ITM (b) PC approach with no prediction (unstable case) (c) PC approach with prediction, (d) PC with no prediction (stable case)
• Figure 3: Absolute difference in the simulation results. (a) PC approach with no prediction, (b) PC approach with prediction
• Figure 4: Step size used in numerical integration for the simulation of NPCC.