Revealing synergistic regulation mechanisms of cascade reservoirs under competing hydrological objectives in the Upper Yellow River

Understanding how large regulating reservoirs alter the synergistic relationships among water supply, power generation, water–sediment regulation (WSR), and ecological protection is essential for adaptive water-resource management. This research investigates multi-objective synergy in the Upper Yellow River cascade reservoir system before and after the planned commissioning of the Heishanxia Reservoir. Based on synergetics theory, a multi-objective synergistic regulation framework was developed by establishing an order-parameter system, a multi-objective synergistic optimal operation model, and a Synergy Contribution Index (SCI) to quantify the relative contributions of different operational objectives to system synergy. The results show that commissioning the Heishanxia Reservoir increases the system synergy degree from 0.74 to 0.84. SCI analysis indicates that water supply and WSR remain the primary contributors to system synergy, while the contribution of power generation increases after reservoir commissioning, reflecting improved compatibility between energy production and other operational objectives. The SCI contributions of water supply, power generation, WSR, and ecological protection change by +0.3, +1.7, −0.9, and −1.0 percentage points, respectively, with power generation showing the largest increase. The optimized operation reduces agricultural water deficits during critical periods by approximately 54.0% and increases power generation reliability during the non-ice-flood-control period from 19.37% to 66.88%. These findings demonstrate that the Heishanxia Reservoir can improve operational benefits, enhance inter-seasonal water redistribution, and strengthen coordination among reservoir functions and multiple operational objectives. This study provides new insights into adaptive cascade reservoir operation and future reservoir planning in the Upper Yellow River.