Energy Systems

, Volume 9, Issue 1, pp 59–77 | Cite as

Continuous optimal control approaches to microgrid energy management

  • Benjamin Heymann
  • J. Frédéric Bonnans
  • Pierre Martinon
  • Francisco J. Silva
  • Fernando Lanas
  • Guillermo Jiménez-Estévez
Original Paper


We propose a novel method for the microgrid energy management problem by introducing a nonlinear, continuous-time, rolling horizon formulation. The method is linearization-free and gives a global optimal solution with closed loop controls. It allows for the modelling of switches. We formulate the energy management problem as a deterministic optimal control problem (OCP). We solve (OCP) with two classical approaches: the direct method and Bellman’s Dynamic Programming Principle (DPP). In both cases we use the optimal control toolbox Bocop for the numerical simulations. For the DPP approach we implement a semi-Lagrangian scheme adapted to handle the optimization of switching times for the on/off modes of the diesel generator. The DPP approach allows for accurate modelling and is computationally cheap. It finds the global optimum in less than one second, a CPU time similar to the time needed with a Mixed Integer Linear Programming approach used in previous works. We achieve this result by introducing a ‘trick’ based on the Pontryagin Maximum Principle. The trick reduces the computation time by several orders and improves the precision of the solution. For validation purposes, we performed simulations on datasets from an actual isolated microgrid located in northern Chile. The result shows that the DPP method is very well suited for this type of problem.


Energy management system (EMS) Microgrid Optimal control Direct method Pontryagin Maximum Principle (PMP) Semi-Lagrangian scheme 

Mathematics Subject Classification

93C15 90C39 49L20 49J15 



This work is product of collaboration between the COMMANDS (INRIA, France) and Centro de Energía teams (Universidad de Chile, Chile), it was also supported in part by CONICYT/FONDAP/15110019. FJS was supported by project iCODE: “Large-scale systems and Smart grids: distributed decision making” and from the Gaspar Monge Program for Optimization and Operation Research (PGMO). JFB was supported by the laboratory Dauphine CREST EDF R&D Finance des Marchés d’Energies.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.CMAP, Inria, Ecole polytechnique, CNRSUniversité Paris-SaclayPalaiseauFrance
  2. 2.Institut de recherche XLIM-DMI, UMR-CNRS 7252, Faculté des sciences et techniquesUniversité de LimogesLimogesFrance
  3. 3.Energy Center, Faculty of Mathematical and Physical Sciences, School of EngineeringUniversidad de ChileSantiagoChile

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