A novel method to converge to the unstable equilibrium point for a two-bus system

This paper presents a novel method for calculating the unstable equilibrium point (UEP) for a two-bus system using holomorphic embedding (HE). The method is guaranteed to find the UEP solution. The focus of this paper is to prove mathematically that if a UEP solution exists, the method is guaranteed to arrive at that and only that solution and if no solution exists, then such is indicated by the oscillations is the series form of the solution. While there is limited interest in the solution to a two-bus problem, this is hopefully a first fruitful step that can eventually be generalized to the multi-bus problem and, possibly, other non-linear equations.