## 6 Conclusions  
The article provides a comprehensive comparison and analysis of energy consumption for the multi-pump system consisting of two pumps operating in parallel mode and the single-pump system:  
* The single-pump system is equipped with a single variable speed drive. The multi-pump system is equipped with one variable speed drive that is fed by a frequency converter and a non-adjustable drive connected directly to a grid;
* The comparison of energy consumption for both pump system configurations shows that the usage of a multi-pump system supplied with two low-power pumps instead of a high-power pump in the single-pump system can lead to 29.8% energy savings;
* The energy savings are achieved due to the application of pumps and variable speed drives with a lower rated power and, therefore, with low losses in the operation modes in which the flowrate can be provided by one of the two pumps.
* Despite a rather low efficiency of the multi-pump system at high flowrates, the gain in the efficiency at the most frequent low flowrates results in an increase in the overall efficiency and energy saving.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Pump System**} & \multicolumn{1}{c}{\(\mathbf{E_{day}}\)**, kWh**} & \multicolumn{1}{c}{\(\mathbf{E_{year}}\)**, kWh**} & \multicolumn{1}{c}{\(\mathbf{C_{year}}\)**, \(\mathbf{\xi}\)} & \multicolumn{1}{c}{\(\mathbf{S_{year}}\)**, \%} & \multicolumn{1}{c}{\(\mathbf{S_{year}}\)**, \(\mathbf{\xi}\)**} \\ \hline Two parallel pumps (FC-IM1) + IM2 & 12.37 & 4516 & 919 & 29.8 & 391.1 \\ System with one pump (FC-IM) & 17.63 & 6437 & 1310 & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of a system’s power consumption.  
Figure 10: Electrical power consumption of the pumping systems depending on the flowrate.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \(\mathbf{Q_{req}}\)**, \%** & **10** & **20** & **30** & **40** & **50** & **60** & **70** & **80** & **90** & **100** \\ \hline \multirow{4}{*}{\(P_{1}\), \(W\)} & \(Q_{req}\), m\({}^{3}\)/h & 2.40 & 4.80 & 7.20 & 9.60 & 12.0 & 14.4 & 16.8 & 19.2 & 21.6 & 24.0 \\  & Two parallel pumps & 213 & 272 & 347 & 453 & 599 & 812 & 1300 & 1465 & 1668 & 1928 \\  & One pump & 580 & 605 & 646 & 704 & 788 & 880 & 1012 & 1192 & 1454 & 1872 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Electric power consumption of pumping systems for various flowrate modes.  
* In future works, the optimization of the energy consumption of the considered configurations of multi-pump systems will be presented using mathematical optimization methods, considering the characteristics of motors and frequency converters.  
Conceptual approach, V.K. and V.P.; data curation L.G., and V.D.; software S.O. and V.K.; calculations and modeling, S.O, V.K., and V.P.; writing of original draft, L.G., S.O., V.D., V.K. and V.P.; visualization, L.G., S.O. and V.K.; review and editing, L.G., S.O., V.D., V.K. and V.P. All authors have read and agreed to the published version of the manuscript.  
The work was partially supported by the Ministry of Science and Higher Education of the Russian Federation (through the basic part of the government mandate, Project No. FEUZ-2020-0060).  
The authors thank the editors and reviewers for careful reading and constructive comments.  
The authors declare no conflict of interest.