  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.

Systems and Control