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 the reservoirs. The framework jointly models exogenous forecast errors and endogenous uncertainty propagation, explicitly characterizing the dependence between upstream releases and downstream inflow variability through a heteroskedastic variance model conditioned on past errors, variance, and control actions. We formulate a joint chance-constrained optimization problem to ensure reliable system operation under uncertainty and develop a tractable supporting hyperplane algorithm that enables explicit and adaptive risk allocation under DDU. We establish the convergence of the proposed method and show its risk allocation behavior under steady-state conditions. A randomized case study based on Columbia River data demonstrates that incorporating DDU reduces the constraint violations by up to 7.0\% and increases total generation by up to 0.5\% relative to decision-independent uncertainty (DIU). Sensitivity analyses of the dry-season streamflow conditions further highlight the value of adaptive risk allocation for resilient and risk-aware hydropower operations.