Real-time Coordination of Cascaded Hydroelectric Generation under Decision-Dependent Uncertainties

This paper proposes a real-time control policy for cascaded hydropower systems that incorporates decision-dependent uncertainty (DDU) to capture the coupling of streamflow uncertainties across the network. 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 convergence of the proposed method and show that it recovers the Bonferroni approximation under steady-state conditions. A randomized case study based on Columbia River data demonstrates that the proposed framework improves both energy generation and reservoir reliability by accounting for DDU. Sensitivity analyses on drought severity and model parameters further highlight the value of adaptive risk allocation for resilient hydropower operations.