Multi-objective Optimization of Deep Peak Regulation Process for Francis Turbine Unit Based on the EMOGWO

The integration of high-penetration wind and solar power intensifies grid regulation demands, elevating the role of hydroelectric units, particularly large Francis turbine generating units (FTGUs), in deep peak regulation (DPR). However, DPR operation exposes FTGUs to significant safety risks, including vibration and water hammer pressure, especially during traversals of vibration-sensitive zones. To address the conflicting objectives of minimizing vibration amplitude and spiral case pressure rise during large load transients, this paper proposes a multi-objective optimization framework for DPR load regulation strategies. We establish a high-fidelity hydro-mechanical-electrical-vibration coupling transient model solved using the Method of Characteristics (MOC). Optimization objectives are formulated as minimizing pressure surge and minimizing vibration entropy. To solve this constrained, highly nonlinear problem, an Enhanced Multi-Objective Grey Wolf Optimizer (EMOGWO) is developed, incorporating Tent chaotic mapping for initialization, a weighted encircling strategy, and elite-guided Lévy mutation to improve population diversity, convergence, and escape local optima. Numerical experiments on a validated “single-penstock-single-unit” FTGU model demonstrate that EMOGWO effectively generates a superior Pareto front compared to the original MOGWO, enabling the identification of DPR strategies that simultaneously enhance operational safety by reducing both vibration severity and hydraulic transients while respecting critical constraints.