In the second half of the twentieth century, a cascade of reservoirs was constructed along the Angara: Irkutskoe, Bratskoe, Ust-Ilimskoe and Boguchanskoe, which were intended for producing renewable hydroelectric energy for providing transportation through the Angara and Yenisei Rivers, and for avoiding floods. The upper reservoir (Irkutsk Dam) is used to regulate the level of Baikal Lake. The cascade of Angarsk reservoirs is managed using the dispatch schedules developed in 1988. This article contains a multi-criteria analysis of the “Lake Baikal–Irkutsk Reservoir” operating modes in a changing climate, based on statistical summaries of performance criteria: reliability, resilience, vulnerability. Studies have shown that dispatch schedules need to be developed on the historical series of recent years, updated more often and optimization methods should be used for real-time management. This article discusses mathematical methods, algorithms and their implementations for the formation of reservoir operation modes based on dispatch schedules (DS) and optimization methods. Furthermore, mathematical methods, algorithms and programs have been developed for the formation of reservoir operation modes in real time, based on optimization approaches and long-term series of observed inflows, taking into account a given hierarchy of priorities of water users’ requirements. To solve the integer nonlinear large-dimensional task of performing water resource calculations, a special optimization algorithm was developed that allows decomposition of the task into a series of two-year dimensional independent subtasks.
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