Analyzing stable regimes of electrical power systems and tropical geometry of power balance equations over complex multifields

We present a novel approach to estimating the region of existence for an electrical power system's regime. The approach is based on the so-called complex tropical geometry. In the domain of the regime's existence, we indicate subregions where it is easier to control and crossing whose boundaries precedes losing the power system's regime. Based on these results, a user can be presented with simple and clear information that characterizes the stability margin of a power system, and software implementation of the proposed approach is much easier both computationally and in terms of programming work than implementations of other known approaches.