The object of the study is a pumping station with four parallel-connected centrifugal pump units driven by asynchronous electric motors. The problem to be solved is that modern stations, partially equipped with variable frequency drive (VFDs), allow only maintaining the head without observing allowable modes, failing to ensure reliability and energy efficiency. This leads to rapid wear and efficiency reduction. The solution lies in optimizing energy consumption and keeping operating points within the POR (preferred operating region), to prevent accelerated wear. The essence of the results obtained lies in the development of a method for energy-efficient control based on the CMA-ES strategy integrated with a model in MATLAB (California, USA). Experiments showed that the balanced strategy reduces energy consumption by 7% while maintaining equipment in the POR zone for 95.8% of the time. Comparative analysis showed that a configuration with two VFDs is a rational compromise, limiting energy overconsumption to 25% relative to systems fully equipped with VFDs. These results allowed to solve the specified problem due to the introduction of a block performing an analytical express assessment of the required number of units based on affinity laws, using adaptive penalty functions and CMA-ES tuning. This allowed excluding combinatorial enumeration and reducing the search time for the optimal solution to 60–80 seconds, ensuring speed unavailable to standard genetic algorithms. The conditions under which they can be used on practice involve the application of the developed method as a supervisory control (SCADA) for water supply pumping stations to generate control setpoints with a periodicity of 1–2 minutes without the need for complete equipment replacement.
Bulatbayeva et al. (2026) studied this question.