Two-Bus Holomorphic Embedding Method-based Equivalents and Weak-Bus Determination

Abstract: A new method of solving the power-flow problem, the holomorphically embedded load-flow method (HELM) is theoretically guaranteed to find the high-voltage solution, if one exists, up to the saddle-node bifurcation point (SNBP), provided sufficient precision is used and the conditions of Stahls theorem are satisfied. Sigma indices, have been proposed as estimators of the distance from the present operating point to the SNBP, and indicators of the weak buses in a system. In this paper, it is shown that the sigma condition proposed in [2] will not produce reliable results and that a modified requirement can be used to produce a tight upper bound on the SNBP. Introduced is an approach to estimate the weak buses in the system using the HEM power series with numerical results compared to traditional modal analysis for a 14-bus system.