A Novel Lagrangian Multiplier Update Algorithm for Short-Term Hydro-Thermal Coordination

P. M. R. Bento, S. J. P. S. Mariano, M. R. A. Calado and L. A. F. M. Ferreira
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P. M. R. Bento: IT—Instituto de Telecomunicações, University of Beira Interior, 6201-001 Covilhã, Portugal
S. J. P. S. Mariano: IT—Instituto de Telecomunicações, University of Beira Interior, 6201-001 Covilhã, Portugal
M. R. A. Calado: IT—Instituto de Telecomunicações, University of Beira Interior, 6201-001 Covilhã, Portugal
L. A. F. M. Ferreira: Instituto Superior Técnico and INESC-ID, University of Lisbon, 1049-001 Lisbon, Portugal

Energies, 2020, vol. 13, issue 24, 1-19

Abstract: The backbone of a conventional electrical power generation system relies on hydro-thermal coordination. Due to its intrinsic complex, large-scale and constrained nature, the feasibility of a direct approach is reduced. With this limitation in mind, decomposition methods, particularly Lagrangian relaxation, constitutes a consolidated choice to “simplify” the problem. Thus, translating a relaxed problem approach indirectly leads to solutions of the primal problem. In turn, the dual problem is solved iteratively, and Lagrange multipliers are updated between each iteration using subgradient methods. However, this class of methods presents a set of sensitive aspects that often require time-consuming tuning tasks or to rely on the dispatchers’ own expertise and experience. Hence, to tackle these shortcomings, a novel Lagrangian multiplier update adaptative algorithm is proposed, with the aim of automatically adjust the step-size used to update Lagrange multipliers, therefore avoiding the need to pre-select a set of parameters. A results comparison is made against two traditionally employed step-size update heuristics, using a real hydrothermal scenario derived from the Portuguese power system. The proposed adaptive algorithm managed to obtain improved performances in terms of the dual problem, thereby reducing the duality gap with the optimal primal problem.

Keywords: hydro-thermal coordination; Lagrangian relaxation; Lagrangian dual problem; Lagrange multipliers; subgradient methods; step-size update algorithm (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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