Fast Weak-Bus and Bifurcation Point Determination using Holomorphic Embedding Method

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 Stahl's theorem are satisfied. Sigma (σ) 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. This paper investigates the theoretical foundation of the σ method and shows that the σ condition proposed in [10] will not produce reliable results and that a modified requirement can be used to produce a tight upper bound on the SNBP. A new HEM-based method is then proposed that can be used to estimate the weak buses in a system (from a steady-state voltage stability perspective) at all operating points through to the SNBP, using a single power-flow solution. Numerical results for the proposed approach are compared to traditional modal analysis for the IEEE 14-bus and 118-bus systems.