Two-Stage Dual Dynamic Programming With Application to Nonlinear Hydro Scheduling

We present an approximate method for solving nonlinear control problems over long time horizons, in which the full model is preserved initial part of horizon, while remainder horizon modeled using a linear relaxation. As this problem may still be too large to solve directly, we Benders decomposition-based solution algorithm that iterates between and parts horizon. This extends dual dynamic programming approach commonly employed optimization linearized hydro power systems. prove proposed converges after finite number iterations, even when stage are solved inexactly. also bound suboptimality split-horizon with respect original problem, terms properties map state-input trajectories. then apply case study concerning multiple reservoir system, approximating head effects second McCormick envelopes. demonstrate near-optimal solutions can obtained shrinking setting used only short section For example, shown more practical than both conventional multi-cell envelope approximation from literature.