Journal of Optimization Theory and Applications

, Volume 179, Issue 3, pp 1043–1053 | Cite as

Optimal Battery Aging: An Adaptive Weights Dynamic Programming Algorithm

  • Benjamin HeymannEmail author
  • Pierre Martinon
Technical Note


We present an algorithm to handle the optimization over a long horizon of an electric microgrid including a battery energy storage system. While the battery is an important and costly component of the microgrid, its aging process is often not taken into account by the energy management system, mostly because of modeling and computing challenges. We address the computing aspect by a new approach combining dynamic programming, decomposition and relaxation techniques. We illustrate this adaptive weight’ method with numerical simulations for a toy microgrid model. Compared to a straightforward resolution by dynamic programming, our algorithm decreases the computing time by more than one order of magnitude, can be parallelized, and allows for online implementations. We believe that this approach can be used for other applications presenting fast and slow variables.


Control Aging Dynamic programming Energy management system 

Mathematics Subject Classification

93A13 93C15 90C39 49L20 49M27 49M29 



Benjamin Heymann acknowledges support from the Siebel Scholar Program. The authors wish to thank Frédéric Bonnans for his advice and comments on the paper. Thanks also to Hanyun Huang for her English suggestions.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CMAP, Inria, Ecole Polytechnique, CNRSUniversité Paris-SaclayPalaiseauFrance
  2. 2.CMMUniversidad de ChileSantiagoChile

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