Vandermonde Interpolating as Nonlinear Predictor Applied to Continuation Method

Abstract

The electricity sector, especially in emerging countries, has experienced several transformations, mainly resulting from the increase of electricity demand. This encourages more investment in the generation sector and causes increasing concerns with the development and improvement of tools for static voltage stability analysis of electrical power systems. In this paper the results of the use of the nonlinear predictor for the tracing of the P-V curves are presented. The predictor is based on Vandermonde interpolating polynomial of second degree allowing to reconstruct a function passing through three known points on the P-V curve. The main benefit of using this predictor occurs in the most heavily loaded part of the P-V curve, i.e., near the maximum loading point. In this region, the nonlinear predictor resembles the curve of solutions trajectory and provides a smaller number of iterations and CPU time in the corrector step compared to some linear predictors. In the corrector step, the magnitude of the nodal voltage is used as a continuation parameter. The tests are performed for a two bus system, IEEE-14 bus system and real large systems, 787 buses, corresponding to parts of South-Southeast Brazilian system. Comparisons are presented, in terms of numbers of iterations and robustness, between the methods that use linear predictors and the nonlinear predictor.