Multi-Objective Optimization of Nozzle Closing Strategies for High Head Pelton Turbines to Shorten the Nozzle Closing Time and Mitigate Water Hammer Effects

The rapid shutdown of high-head and large-capacity Pelton turbines equipped with long penstocks often induces severe water hammer effects, threatening the structural safety of the diversion system. Traditional linear or simple piecewise nozzle closing laws struggle to achieve an optimal balance between shortening the nozzle closing time and suppressing the maximum transient pressure. To address this issue, this study proposes a multi-objective optimization framework for the non-linear nozzle-closing strategy of a large-capacity six-nozzle Pelton turbine. A one-dimensional transient flow model of the complex diversion system was established and solved using the Method of Characteristics (MOC). Subsequently, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was coupled with the model to globally optimize the discretized 10-segment nozzle-closing trajectory. The optimization objectives were to minimize both the total closing time and the maximum pressure before the nozzle. The results demonstrate that the NSGA-II algorithm autonomously converges to a “Fast-Slow-Fast” non-linear closing pattern. Compared to the baseline linear closing strategy, the optimized trajectory reduces the total shutdown time by 7.22% (from 18.15 s to 16.84 s) and decreases the maximum pressure before the nozzle by 7.61 m, effectively mitigating the net water hammer pressure rise by 13.40%. Physical mechanism analysis reveals that the intermediate “slow” phase effectively staggers the constructive superposition of reflected positive water hammer waves, achieving an active peak-shifting effect. This study can provide a theoretical reference for the safe and efficient shutdown control of large-capacity Pelton turbines.