A Lagrangian-Informed Long-Term Dispatch Policy for Coupled Hydropower and Photovoltaic Systems

This paper presents a long-term dispatch framework for coupled hydropower and floating photovoltaic systems. We introduce a temporal decomposition algorithm based on partial Lagrangian relaxation to address long-term water contract constraints. We derive a real-time, non-anticipatory dispatch policy based on water contract pricing. Our framework is evaluated with a case study using real-world hydrology and power system data from Lake Mead and Lake Powell, on the Colorado River, demonstrating competitive performance against commercial solvers for both linearized and nonlinear reservoir models. We conduct a sensitivity analysis on transmission capacity, electricity price and uncertainty scenarios, showing that the operational performance is significantly impacted by the transmission capacity and electricity prices while remaining relatively robust under uncertainty scenarios.