Determining fast battery charging profiles using an equivalent circuit model and a direct optimal control approach

Julio Cesar Gonzalez-Saenz, Victor Becerra

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This work used an electrical equivalent circuit model combined with a temperature model and computational optimal control methods to determine minimum time charging profiles for a lithium–ion battery. To effectively address the problem, an optimal control problem formulation and direct solution approach were adopted. The results showed that, in most cases studied, the solution to the battery’s fast-charging problem resembled the constant current–constant voltage (CC-CV) charging protocol, with the advantage being that our proposed approach optimally determined the switching time between the CC and CV phases, as well as the final time of the charging process. Considering path constraints related to the terminal voltage and temperature gradient between the cell core and case, the results also showed that additional rules could be incorporated into the protocol to protect the battery against under/over voltage-related damage and high-temperature differences between the core and its case. This work addressed several challenges and knowledge gaps, including emulating the CC-CV protocol using a multi-phase optimal control approach and direct collocation methods, and improving it by including efficiency and degradation terms in the objective function and safety constraints. To the authors’ knowledge, this is the first time the CC-CV protocol has been represented as the solution to a multi-phase optimal control problem.
Original languageEnglish
Article number1470
Number of pages26
Issue number6
Publication statusPublished - 19 Mar 2024


  • battery charging
  • optimal control
  • equivalent circuit models
  • lithium-ion batteries
  • CC-CV protocol

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