Published date: Jun 02 2020

Journal Title: KnE Engineering

Issue title: International Congress on Engineering — Engineering for Evolution

Pages: 728–742

DOI: 10.18502/keg.v5i6.7093

Pedro Bentopedro.bento@lx.it.ptInstituto de Telecomunicacoes and University of Beira Interior

Filipe PinaUniversity of Beira Interior

Sílvio MarianoInstituto de Telecomunicacoes and University of Beira Interior

Maria do Rosario CaladoInstituto de Telecomunicacoes and University of Beira Interior

For decades, researchers have been studying the unit commitment problem in electrical power generation. To solve this complex, large scale and constrained optimization (primal) problem in a direct manner is not a feasible approach, which is where Lagrangian relaxation comes in as the answer. The dual Lagrangian problem translates a relaxed problem approach, that indirectly leads to solutions of the original (primal) problem. In the coordination problem, a decomposition takes place where the global solution is achieved by coordinating between the respective subproblems solutions. This dual problem is solved iteratively, and Lagrange multipliers are updated between each iteration using subgradient methods. To tackle, time-consuming tuning tasks  or user related experience, a new adaptative algorithm, is proposed to better adjust the step-size used to update Lagrange multipliers, i.e., avoid the need to pre-select  a set of parameters. A results comparison against a traditionally employed step-size update mechanism, showed that the adaptive algorithm manages to obtain improved performances in terms of the targeted primal problem.

Keywords: Hydro-Thermal coordination, Lagrangian relaxation, Lagrangian dual problem, Lagrange multipliers, Subgradient methods

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