Fine-grained load distribution of cascade hydropower stations considering vibration-zone crossings: A spatiotemporal hierarchical decoupling framework

The large-scale integration of renewables has intensified the peak-shaving duties of hydropower stations, making frequent unit startup/shutdown operations and vibration-zone (VZ) crossings increasingly prominent challenges. To achieve fine-grained load distribution while ensuring dispatch reliability, the startup/shutdown count and the VZ-crossing count must be incorporated alongside the conventional economic operation objective. However, their inclusion causes an explosive growth in unit-level integer variables. The cascade hydraulic coupling and the unit-level nonlinearities further add to the modelling difficulty, rendering the conventional “station-unit” two-layer nested framework unable to balance solution efficiency and quality. To this end, a spatiotemporal hierarchical decoupling framework is proposed for fine-grained load distribution of cascade hydropower stations, decomposing the problem into three coupled sub-problems: inter-station load distribution, unit commitment, and intra-station fine-grained dispatch. Spatially, cascade hydraulic coupling is handled at the inter-station level, while unit commitment and unit-level nonlinearities are handled in the lower layers, with the cascade and plant power balances retained throughout the decomposition. Temporally, the intra-station layer is split into hourly unit commitment and 15-minute fine-grained dispatch, with each sub-problem solved at its native temporal scale and globally coordinated through closed-loop feedback of the water consumption coefficient. A case study on the Hongjiadu-Dongfeng-Suofengying cascade of the Wujiang River shows that the proposed three-objective model reduces VZ crossings by 59% and 76% relative to the single- and dual-objective models, respectively, at an additional water-energy cost of only 1% and without additional startup/shutdown operations. Compared with the conventional two-layer nested framework, the proposed framework reduces the measured solution time by 72.2% to 89.9% for the tested 10-, 20-, and 30-unit cases, corresponding to speedups of 3.6 to 9.9.