Convexity of the annualized cost of energy systems with usage-dependent component lifetimes

Pierre Haessig (), Elsy El Sayegh, Jean Fructhieu Armand Delwende Nikiema () and Nabil Sadou ()
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Pierre Haessig: CentraleSupélec, IETR - Institut d'Électronique et des Technologies du numéRique - UR - Université de Rennes - INSA Rennes - Institut National des Sciences Appliquées - Rennes - INSA - Institut National des Sciences Appliquées - CentraleSupélec - CNRS - Centre National de la Recherche Scientifique - Nantes Univ - EPUN - Nantes Université - Ecole Polytechnique de l'Université de Nantes - Nantes Université - pôle Sciences et technologie - Nantes Univ - Nantes Université
Elsy El Sayegh: EDF R&D
Jean Fructhieu Armand Delwende Nikiema: CentraleSupélec, IETR - Institut d'Électronique et des Technologies du numéRique - UR - Université de Rennes - INSA Rennes - Institut National des Sciences Appliquées - Rennes - INSA - Institut National des Sciences Appliquées - CentraleSupélec - CNRS - Centre National de la Recherche Scientifique - Nantes Univ - EPUN - Nantes Université - Ecole Polytechnique de l'Université de Nantes - Nantes Université - pôle Sciences et technologie - Nantes Univ - Nantes Université
Nabil Sadou: CentraleSupélec, IETR - Institut d'Électronique et des Technologies du numéRique - UR - Université de Rennes - INSA Rennes - Institut National des Sciences Appliquées - Rennes - INSA - Institut National des Sciences Appliquées - CentraleSupélec - CNRS - Centre National de la Recherche Scientifique - Nantes Univ - EPUN - Nantes Université - Ecole Polytechnique de l'Université de Nantes - Nantes Université - pôle Sciences et technologie - Nantes Univ - Nantes Université

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Abstract: An energy system optimization (joint sizing & dispatch) which accounts for the effect of component aging on the annualized cost of the system is proposed. Despite being nonlinear, the model is proved to be convex under a generalized "lifetime = size/usage" hypothesis. This assumption is shown to cover the classical energy counting model for battery cycling aging, while a linear approximation is needed to account for the operating hours of dispatchable generators. The convexity of the model allows for a piecewise linear approximation which is solved efficiently with linear programming solvers. On an illustrative open-source microgrid sizing test case, the proposed model significantly reduces the levelized cost of energy compared to the classical fixed-lifetime approaches. Solving time is kept within the same order of magnitude, thanks to the model convexity. The proposed model also compares favorably with the more advanced "usage penalty" approaches, even though an improved variant of these is formulated and used.

Keywords: Energy systems; Microgrids; Sizing; Aging; Convex optimization (search for similar items in EconPapers)
Date: 2026-02-19
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