## 4 Result and Discussion
### Water Hammer Change Rule of End Valve Under Different Influencing Factors
As shown in Figure 8, the pressure peaks at the closed valve end (a1, b1, c1, d1) are generally higher than those at the open valve end (a, b, c, d), and after a rapid rise in the initial phase, the pressure gradually stabilizes. In Figure 9a,b, the pressure increase rate for pipelines with larger diameters (Condition 1) is higher than that for pipelines with smaller diameters (Condition 2), reaching a stable value in a shorter time, indicating that larger-diameter pipelines are more prone to high transient pressures. In Figure 9c,d, the pressure at the closed valve end (c1, d1) exhibits significant oscillations after reaching the peak, reflecting the more pronounced volatility of larger-diameter pipelines under the water hammer effect. Figure 10 magnifies the pressure variation details in the initial phase (0-2 s), further illustrating the effects of different pipeline diameters and monitoring point locations on the transient water hammer response. These results indicate that the selection of different diameters and monitoring point locations significantly affects the water hammer effect, thereby providing theoretical support for optimizing valve control strategies and mitigating water hammer impacts. 3.2 Analysis of the Effect of Different Distances from the Turnpike on the Change of Water Hammer Pressure  
Considering the influence of different branch pipe quantities and varying distances between branches on water hammer pressure variations, water hammer calculations were first conducted for four different distance scenarios. These scenarios correspond to Condi  
Figure 10: Pressure cloud of monitoring points before closing the valves of large-diameter units (2s). Figure 9: Variations in water hammer pressure for different branch pipe diameters: (**a**) Unit D1; (**b**) Unit D2; (**c**) Unit X1; (**d**) Unit X2. tions 3-6, 3-D1X1 closure, 4-D1X2 closure, 5-D2X1 closure, and 6-D2X2 closure, to assess the impact of different branch pipe distances on water hammer pressure variations at this power station. The valve closure strategy for both the large and small units was a 12 s single-stage linear closure. Based on the results under these four conditions shown in Figure 11, it was determined that the distance between the branch pipes in the Xinlongkou Power Station had little effect on the maximum water hammer pressure. Under the conditions involving the small and D1 unit valve closures, the maximum water hammer pressures at monitoring point a1 were 3416 and 3417 kPa, respectively. The corresponding maximum pressures at the small unit valve closure monitoring points c1 and d1 were 3393 and 3391 kPa, respectively. Under the conditions involving small and D2 unit valve closures, the maximum pressures at monitoring point b1 were 3405 and 3406 kPa, respectively, whereas the corresponding maximum pressures at the small unit valve closure monitoring points were 3399 and 3394 kPa, respectively. These results indicate that the varying distances between the small and large units at this power station had almost no effect on the maximum water hammer pressure in the pipeline. 3.3 Analysis of the Effect of Different Numbers of Turnouts on the Variation of Water Hammer Pressure  
Based on the previous analysis of the impact of branch pipe distances on the maximum water hammer pressure at the Xinlongkou Hydropower Station, it was concluded that the distance had a minimal effect. To investigate the influence of the valve closure quantities on the increase in water hammer pressure, only the maximum water hammer conditions for each valve quantity were considered. Therefore, when examining a branch pipe quantity of 2, only condition 1 is considered; for a branch pipe quantity of 3, only the water hammer pressure resulting from the closure of two large and one small unit is considered. The results for the maximum water hammer pressure during load shedding for all units were then compared.