This article presents the idea and mathematical model of a pumped storage power plant. PSPS Porąbka Żar was selected as the real object for modelling. Due to the specificity of the operation of an intervention-regulatory and scheduled nature related to the coverage of power demand in the power system, the possibility of different modes of operation was taken into account in the model. Porąbka-Żar power plant is a pearl of hydro-engineering on the global stage. It is the first underground and the second largest pumped storage power plant in Poland. It is located in Międzybrodzie Bialskie, in the Silesian province. The short distance between the upper reservoir of the power station, located on Mt. Żar, and the lower reservoir of the międzybrodzkie lake, the high average head of the power station of 432 m above sea level, create great opportunities for accessibility and interference in the operation of the power station. It is equipped with four reversible Francis turbine sets, which operate simultaneously with a total capacity of 500 MW in the generator mode and 542 MW in the pumping mode. Due to its high potential and short turn-on and turn-off times of the turbine sets, it plays an important role in the national power system. The mathematical model was made in Matlab - Simulink software. An important role in the control process of the facility is played by the forecast of both power demand and contingencies. The forecasting model is equipped with elements of artificial intelligence. In addition, the article shows the possibility of supplementing an operating power plant with hybrid elements. The analysis is supported by commentary and a number of charts
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