On the determination of the region border prior to the limit steady modes of electric power systems by the analysis method of the tropical geometry of the power balance equations

The analysis of the known approach (Kirshtein, B.K. and Litvinov, G.L., Autom. RemoteControl, 2014, vol. 75, no. 10, pp. 1802–1813.) in which tropical geometry over complex multifields of active power balances is used to estimate the region of existence of the electric power system mode. Its limitations are shown and a new approach is proposed, a criterion is also represented for determining the boundary that precedes the violation of the stability of the energy system due to the restructuring of the tropical set of solutions. The developed approach allows to determine the approach of the power system mode to the limit by the known parameters of the lines and the dynamics of changes of the nodes voltage modules and the nodes load.