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In our research, we focus on the reliability of the interconnected electricity supply system of three countries of the Eurasian Economic Union (EAEU)—Russia, Kazakhstan, and Kyrgyzstan. We apply a mathematical model to evaluate the reliability of the electricity supply system under the threat of earthquakes. Earthquakes can damage elements of electricity grids and, considering the interconnectivity of electricity supply systems in the EAEU, effects in the aftermath of earthquakes can be far-reaching and even transboundary. This necessitates the development of coordinated policies and risk management strategies to deal with electricity outage risks in the EAEU. In our study, the earthquake probability is derived from seismic zone maps, while damage events are computed using maps of energy power systems. In addition, we determine which elements of the system are susceptible to failure due to an earthquake of a given magnitude. We conduct a scenario analysis of earthquakes and their impacts on the reliability of the power supply system, considering potential energy losses and threats to energy security. An analysis of the resilience of electricity transmission grids allows us to determine the critical interconnection lines in terms of exposure to earthquake risk, as well as exposure to total systemic loss. We also identify the most critical interconnection lines where power outages can lead to the destabilization of the entire power supply system. Some examples of such lines are at the border of Kazakhstan and Kyrgyzstan, where power outages can lead to serious economic costs and electricity outages.

Based on the experience of domestic and foreign researchers, it is known that there are various mathematical models, software systems, and optimization methods used to solve the set tasks for assessing the resource adequacy of electric power systems (EPS). However, the continuous development of EPS leads to the complication and integration of systems against the background of which it becomes necessary to take into account an increasing number of its elements and parameters in one task. Thus, for more effective (in terms of speed and accuracy) solutions of modified models, it is required to analyze and search the most appropriate set of optimization methods. In this connection, the purpose of this study is to analyze the applicability and the effectiveness of applying the method of differential evolution and gradient optimization methods for the model of minimizing the power deficit, which should be also compared. The article considers the analysis of the results of the work that optimization methods, studies were conducted on a test isolated EPS, with various tuning parameters. As a result, it was confirmed that these methods could be used to solve the problem. From the point of view of accuracy and resources expended on calculations, the most efficient among the implemented methods was the method of differential evolution, which was confirmed by numerical experiments on the small systems.