Analysis of Convergence Behavior and Derivation of Divergence Indicator in Continuation Power Flow Iterations

Abstract

This research aims to achieve the following objectives: an analysis of the convergence behavior of the correction step within the iterations of the Continuation Power Flow (CPF), and the development of a divergence indicator. Specifically, the research delves into examining the numerical stability and convergence properties of the Continuation Power Flow Method (CPFM). Subsequently, a defined convergence area for the correction iterations is established. This definition enables an early estimation at the onset of the correction step regarding the likelihood of convergence. Additionally, it helps determine whether actions to enhance convergence (such as reducing the predictor step size) are necessary. The practical applications of the convergence area are exemplified using a few practical examples. The introduced convergence area concept proves effective in identifying potential divergence of the correction process, particularly during the critical phase of CPF analysis - even as early as the first iteration. Hence, if the corrector demonstrates a tendency to diverge, corrective actions can be implemented in advance before expending unnecessary computational time on iterations that diverge. Critical phase of CPF analysis involves the lower PV curve processing at the Lambda continuation parameter. Here, the concept of "area of convergence" serves as a valuable tool for stabilizing the corrector.