Optimization of Francis turbine runner based on analytic hierarchy process – entropy weight method and multi-objective Lichtenberg algorithm

In multi-energy complementary systems, the inherent randomness and volatility of renewable energy generation necessitate hydropower units with rapid start-up and flexible regulation capabilities to operate as energy-regulation units, ensuring grid stability and effective renewable energy integration. Consequently, hydraulic turbines are compelled to operate for prolonged periods in low-load regions characterized by low efficiency, severe cavitation, and intense vibrations, which significantly jeopardize operational safety and stability. To address these issues, this study develops a multi-condition, multi-objective optimization platform for a Francis turbine runner based on the Analytic Hierarchy Process-Entropy Weight (AHP) method and the Multi-Objective Lichtenberg Algorithm (MOLA). Bézier curves parameterize the runner blades, whereas the AHP-Entropy Weight method determines the optimal weight coefficients for operating conditions across the full load range (20%–100%Pr). The optimization objectives combine weighted efficiency across all conditions and weighted minimum pressure values with MOLA implementing multi-objective design optimization. The results demonstrate that the optimized runner reduces the high-entropy production zones in both the runner and draft tube, thereby lowering the energy losses and enhancing the efficiency throughout the full load range. Specifically, the turbine efficiency increased by 5.4% at 20% Pr and by 2.83% at 50% Pr. The optimized blade geometry significantly shrinks the low-pressure regions, thus improving cavitation resistance. Furthermore, passage vortices, flow separation vortices, and draft tube vortex rope under low-load conditions are effectively suppressed, reducing the pressure pulsation amplitudes by 85% at 0.20fn (20% Pr) and 32% at 0.20fn (50% Pr) while maintaining the rated-load performance. These findings provide critical insights for optimizing the turbine stability and runner design in multi-energy complementary systems.