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Two-stage dual dynamic programming with application to nonlinear hydro scheduling
Publikationstyp
Journal Article
Date Issued
2020-01-23
Sprache
English
Volume
29
Issue
1
Start Page
96
End Page
107
Article Number
8967158
Citation
IEEE Transactions on Control Systems Technology 29 (1): 8967158 96-107 (2021-01-01)
Publisher DOI
Scopus ID
Publisher
IEEE
We present an approximate method for solving nonlinear control problems over long time horizons, in which the full nonlinear model is preserved over an initial part of the horizon, while the remainder of the horizon is modeled using a linear relaxation. As this approximate problem may still be too large to solve directly, we present a Benders decomposition-based solution algorithm that iterates between solving the nonlinear and linear parts of the horizon. This extends the dual dynamic programming approach commonly employed for optimization of linearized hydro power systems. We prove that the proposed algorithm converges after a finite number of iterations, even when the nonlinear initial stage problems are solved inexactly. We also bound the suboptimality of the split-horizon method with respect to the original nonlinear problem, in terms of the properties of a map between the linear and nonlinear state-input trajectories. We then apply this method to a case study concerning a multiple reservoir hydro system, approximating the nonlinear head effects in the second stage using McCormick envelopes. We demonstrate that near-optimal solutions can be obtained in a shrinking horizon setting when the full nonlinear model is used for only a short initial section of the horizon. For this example, the approach is shown to be more practical than both conventional dynamic programming and a multi-cell McCormick envelope approximation from the literature.
Subjects
Dual dynamic programming (DDP)
hydro optimization
nonlinear model predictive control (NMPC)
optimal control
DDC Class
004: Informatik
600: Technik
More Funding Information
This work was supported by the SCCER FEEB&D Project, as well as by the European Research Council under the Project OCAL, ERC-2017-ADG-787845.