Framework for extracting multi-objective operation rules for cascade reservoirs based on causal features and physical mechanisms

The cascade reservoirs in the middle and lower Yalong River, China Coordinated optimal operation of cascade reservoirs can improve hydropower benefits. Deep learning models can extract reservoir operation rules by mapping known conditions to outflow discharge decisions. However, the “black-box” nature of these models and challenges associated with high-dimensional inputs impede simulation of reservoir operations. To overcome these issues, this study proposes a rule extraction framework. Based on this framework, a Bidirectional Long Short-Term Memory network enhanced with Multi-Head Self-Attention Mechanism and Bayesian Optimization (BO-MHSAM-BiLSTM) is developed for extracting operation rules. To reduce high dimensionality, Convergent Cross Mapping (CCM) quantifies causal relationships between features and decision variables. Moreover, embedding physical constraints into the model’s loss function further enhances interpretability. Applied to three reservoirs in the middle and lower Yalong River, the framework achieved Nash-Sutcliffe Efficiency (NSE) values of 0.81, 0.95, and 0.96 and Water Balance Index (WBI) values of 1.00, 1.00, and 0.99. By applying the simulated operation rules with relevant constraints to the cascade reservoir system operation model, the annual average power generation of the cascade reservoirs increased by 3.39 billion kWh compared to design values. Moreover, CCM-based feature screening improved simulation accuracy, and physical constraints strengthened rule practicality. These findings demonstrate strong applicability and offer valuable guidance for cascade reservoir operation rule extraction. • Using CCM to reduce model input dimensions improves simulation accuracy. • Physics-mechanisms loss improves the physical directiveness of simulations. • Framework rules enhance cascade reservoir performance and improve interpretability.