Two-bus holomorphic embedding method-based equivalents and nose-point determination

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. Two-bus reduced-order equivalents obtained using HELM-based models, involving 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. Further, determining the relationship between the buses judged to be weak using sigma indices and the weak buses obtained using traditional modal analysis remains an open problem.