Abstract
As of 2023, substantiation of the criteria for optimal load balancing of territorial energy islands in the face of uncontrolled power shortages due to unpredictable failure (destruction as a result of military bombardment) of the upper (trunk) level energy infrastructure is relevant. The research aims to substantiate approaches to ensuring the controlled operation of regional power systems under conditions of power shortages. The study applied the theory and methods of mathematical analysis of complex multicomponent systems in the form of mixed Boolean linear programming. A Mathematical Programming Language and modelling methods of the NEOS server based on the Gurobi solver were used to describe the modes of operation of power grids. A proportional power distribution method between load nodes of the post-emergency network configuration was used to determine the direction of electricity transit with the least losses. An algorithm and a program for solving the problem of addressing flows and power losses in multi-node regional power systems are proposed. The optimisation problem is formulated in the form of a mixed Boolean linear programming model with the criterion of minimising the power momentum, considering balance constraints and upper limits on the power between supply and load nodes. The developed transport matrix made it possible to find the optimal power distribution for emergency and post-emergency modes according to the criterion of minimum network losses. Algorithms and scenarios for the response of dispatching services were formed, considering the capacity of power grids and determining temporary power supply schemes, the configuration of which will ensure the “survivability” of energy islands. The levels of efficiency of the Boolean linear programming model associated with the connectivity of the cycles of the transport problem and the order of traversal of its vertices for test examples depending on the constraints imposed on the components of the network structure are established. The process of tracking electricity flows will allow for establishing routes connecting specific electricity supply nodes with load nodes and determining their shares in covering the energy island’s demand under conditions of power shortage