## 5 Conclusions  
This study takes the pump station with seven water pump units as an example and combines the external characteristic curves of the units to establish a mathematical model with the objective function of minimizing input power. The regulation schemes of the pump station are examined under the constraints of flow and head. The specific conclusions are as follows:  
1. Based on the external characteristic curve of the pump unit, under the premise of a certain total water intake of the pump station, with the goal of minimizing the input power of the pump station and the constraints of flow and head, a mathematical model for flow distribution in the pump station system was established. A genetic algorithm was used to optimize the number of operating units and flow distribution of the pump station under different water intake volumes. The flow optimization results indicate that, when there are multiple pump units operating in parallel in the pump station, the total input power of the pump station is the highest when the water intake is constant and the working head of each operating unit is within the operating area of the pump unit, and the working flow distribution of each operating unit in the pump station is the same. The greater the difference in the assigned working flow of each operating unit, the smaller the total input power of the pump station. 2. Based on the preliminary determination of the optimal pump station startup combination plan, combined with the optimal results of flow distribution, using the uniformity of flow velocity at the pump inlet section and the average deviation angle of the section as evaluation indicators, the optimal control plan for the pump station system was determined through the optimization combination of units in the station, under the premise of a certain total water diversion volume. When the total water intake is 70 m\({}^{3}\), the working flow of Unit 1 is 12.5 m\({}^{3}\)/s and the working flow of Units 2-6 is 11.5 m\({}^{3}\)/s. When the total water intake is 60 m\({}^{3}\), the working flow of Units 1, 5, and 7 is 11.5 m\({}^{3}\)/s; the working flow rate of Unit 3 is 13.5 m\({}^{3}\)/s; and the working flow rate of Unit 4 is 12 m\({}^{3}\)/s. When the total diversion volume is 50 m\({}^{3}\), start Units 1, 3, 5, and 7, and the corresponding working flow rates are 13.5 m\({}^{3}\)/s, 11.5 m\({}^{3}\)/s, 11.5 m\({}^{3}\)/s, and 13.5 m\({}^{3}\)/s. When the total water intake is 40 m\({}^{3}\)/s, the starting units are Units 1, 3, and 5, and the corresponding working flow rates are 13.5 m\({}^{3}\)/s, 13.5 m\({}^{3}\)/s, and 13 m\({}^{3}\)/s. When these conditions are met, the pump station has the smallest input power and the best efficiency under the corresponding operating conditions. 3. This study has a good guiding effect on the operation of pumping stations, providing a reference for the same type of pumping station based on a genetic algorithm for starting combination and flow distribution methods. It can determine the number of starting units with the entire operating cost of the pumping station as the target, and enable the pumping station to achieve the goal of minimizing energy efficiency and maximizing benefits, creating economic and social benefits to the greatest extent. [PERSON] and [PERSON] carried out the construction of the optimization system, numerical simulations, and data analysis. [PERSON] and [PERSON] conducted the experiment and wrote the first draft of the manuscript. [PERSON] and [PERSON] conceived and supervised the study and edited the manuscript. [PERSON]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Total Water Inflow** & & & & & \\
**(m\({}^{3}\)/s)** & & & & & \\ \hline
70 & 1\#, 12.5 & 2\#, 11.5 & 3\#, 11.5 & 4\#, 11.5 & 5\#, 11.5 & 7\#, 11.5 \\ \hline
60 & 1\#, 11.5 & 3\#, 13.5 & 4\#, 12 & 5\#, 11.5 & 7\#, 11.5 \\ \hline
50 & 1\#, 13.5 & 3\#, 11.5 & & 5\#, 11.5 & 7\#, 13.5 \\ \hline
40 & 1\#, 13.5 & 3\#, 13.5 & & 5\#, 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Control scheme in the pump station system.