**6. Conclusions**

In this paper, an analysis of the energy consumption of a pumping system consisting of three 4 kW pumps operating in parallel is carried out, considering the reliability constraints. One 4 kW variable frequency induction motor and two 4 kW fixed frequency induction motors are used in the drive of the pumping system.

Energy consumption of the system when three methods of flowrate control regulation are applied is compared: with minimum power consumption, with maximum reliability and trade-off regulation. Comparison of energy consumption in the considered cases shows that energy consumption is 18% higher with maximum reliability regulation compared to minimum energy consumption regulation without any reliability constraints. At the same time, when trade-off regulation is applied, the power consumption is only 2.3% higher. It can be concluded that the proposed trade-off regulation is promising in terms of minimizing the overall lifetime costs of the considered multi-pump single-drive system when both energy costs and maintenance and repair costs are considered.

In future works, it is planned to simulate the dynamics and select a controller for the multi-pump system under consideration when applying the proposed trade-off regulation principle.

**Author Contributions:** Conceptual approach, S.O. and V.P.; data curation V.D. and V.K.; software S.O. and V.K.; calculations and modeling, S.O., V.K. and V.P.; writing of original draft S.O., V.D., V.K. and V.P.; visualization, S.O. and V.K.; review and editing, S.O., V.D., V.K. and V.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work was partially supported by the Ministry of Science and Higher Education of the Russian Federation (through the basic part of the governmen<sup>t</sup> mandate, Project No. FEUZ-2020-0060).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is contained within the article.

**Acknowledgments:** The authors thank the editors and reviewers for careful reading and constructive comments.

**Conflicts of Interest:** The authors declare no conflict of interest.
