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

• Published in: Automation and remote control Vol. 85; no. 1; pp. 68 - 78
• Main Authors: Danilov, M. I., Romanenko, I. G.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 2024; Springer Nature B.V
• Subjects: CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Computer-Aided Engineering (CAD; Control; Control in Technical Systems; Electric power systems; Mathematics; Mathematics and Statistics; Mechanical Engineering; Mechatronics; Nodes; Robotics; Systems Theory; static stability; regime existence subdomains; tropical geometry; electric power system
• ISSN: 0005-1179; 1608-3032
• DOI: 10.1134/S0005117924010028

The analysis of the known approach (Kirshtein, B.K. and Litvinov, G.L., Autom . Remote Control , 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.