Real-time Coordination of Cascaded Hydropower under Decision-Dependent Uncertainty

Abstract

This study proposes a real-time control framework for cascaded hydropower systems that incorporates decision-dependent uncertainty (DDU) to capture the coupling of streamflow uncertainties across reservoirs. The framework jointly models exogenous forecast errors and endogenous uncertainty propagation, characterizing the dependence between upstream releases and downstream inflow variability through a heteroskedastic variance model conditioned on past forecast errors and releases. We formulate a rolling-horizon joint chance-constrained optimization under DDU to ensure reliable cascade hydropower dispatch, with storage-reference tracking to address the future water value and a McCormick relaxation of the nonconvex head. We develop a tractable supporting hyperplane algorithm that decouples uncertainty from decisions across time steps and directly enforces the joint chance constraint under DDU at the prescribed risk level. We establish the convergence of the proposed method and characterize its adaptive risk allocation behavior. Case studies on the Lower Columbia River demonstrate that incorporating DDU reduces the integrated violation index by up to 34.2% and increases total generation by up to 12.8 GWh over a year relative to decision-independent uncertainty (DIU). Sensitivity and scalability analyses across Monte Carlo inflow scenarios further demonstrate the value of the framework for reliable real-time cascaded hydropower operations.