## 4 Optimization of Unit Operation in the Station
### Total Water Inflow--70 m\({}^{3}\)/s  
When the water intake of the pump station is 70 m\({}^{3}\)/s and the working head of each operating unit is ensured to be within the head constraint conditions, six units are started, of which five have a flow rate of 11.5 m\({}^{3}\)/s. The total input power of the pump station is at minimum when the other unit has a flow rate of 12.5 m\({}^{3}\)/s. The corresponding working flow of each operating unit of the pump station, combined with the results of flow distribution, is determined by adopting a full combination scheme. Six flow distribution combination schemes are evaluated and shown in Table 4, with the uniformity of flow velocity at the inlet section of the pump and the average deviation angle of the section as indicators (such as in Equations (4) and (5)). Compared with other cases, when the axial flow velocity uniformity and the average deviation angle of the section are closer \begin{table}
\begin{tabular}{c c} \hline \hline
**Total Water Intake of Pump Station** & **Inlet Water Level** \\ \hline
70 m\({}^{3}\)/s & 450 m \\
60 m\({}^{3}\)/s & 448.57 m \\
50 m\({}^{3}\)/s & 447.14 m \\
40 m\({}^{3}\)/s & 445.71 m \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Water level of intake pool of pumping station. Figure 6: Grid independence verification. Figure 7: Water level diagram of different flow intakes into the pool. to 0\({}^{\circ}\), more water flow can enter the pump unit vertically, which is conducive to the safe and stable operation of the pump unit. Figure 8 shows the calculation results of the full combination scheme when the total water intake of the pump station is 70 m\({}^{3}\)/s. Uniformity of water pump cross-sectional flow rate \(\lambda\):  
\[\lambda=\left[1-\frac{1}{\overline{v}_{\mathrm{a}}}\sqrt{\frac{\sum\left(v_{ ai}-\overline{v}_{\mathrm{a}}\right)^{2}}{m}}\right]\times 100\% \tag{4}\]  
where: \(\lambda\)--Uniformity of axial flow velocity at the inlet section of the water pump, %;  
\(\overline{v}_{\mathrm{a}}\)--Average axial velocity of water pump inlet section, m/s;  
\(m\)--Number of calculation units for the inlet section of the water pump;  
\(v_{ai}\)--The \(i\)th calculation unit axial velocity of the water pump inlet section, m/s;  
Average deviation angle of water pump cross-section \(\theta\):  
\[\theta=\frac{\sum v_{ai}\Big{[}\arctan(\frac{v_{ii}}{v_{ai}})\Big{]}}{\sum v_{ ai}} \tag{5}\]  
where: \(\theta\)--Average deviation angle of water pump cross-section;  
\(v_{ii}\)--The \(i\)th calculation unit lateral velocity of the water pump inlet section, m/s;  
\(v_{ii}=\sqrt{v_{wi}^{2}+v_{ri}^{2}}\) (\(v_{wi}\), \(v_{ri}\) is tangential velocity and radial velocity of the \(i\)th calculation unit of pump inlet section). Figure 8 shows that, under different schemes, the flow velocity uniformity and average deviation angle at the inlet section of the water pump have no significant variation amplitudes. In the full combination scheme, the maximum average deviation angle of the water pump inlet section is 15.15\({}^{\circ}\) and the minimum is 14.84\({}^{\circ}\), with a difference of 0.31\({}^{\circ}\), while the maximum value of flow velocity uniformity is 66.28% and the minimum is 65.59%, with a difference of 0.69%. Thus, the changes are not significant. Considering the uniformity of flow velocity and average deviation angle at the inlet section of the water pump, the results show that when the total water intake of the pump station is 70 m\({}^{3}\)/s, the sixth group of combination schemes is selected; that is, the operating unit of the pump station and its corresponding working flows are 12.5 m\({}^{3}\)/s for Unit 1 and 11.5 m\({}^{3}\)/s for Units 2-6. This scenario achieves the minimum input power of the pump station and the maximum overall efficiency.