Determination of fast battery-charging profiles using an electrochemical model and a direct optimal control approach

Julio Cesar Gonzalez-Saenz, Victor Becerra*

*Corresponding author for this work

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This paper describes an approach to determine a fast-charging profile for a lithium-ion battery by utilising a simplified single-particle electrochemical model and direct collocation methods for optimal control. An optimal control problem formulation and a direct solution approach were adopted to address the problem effectively. The results shows that, in some cases, the optimal current profile resembles the current profile in the Constant Current–Constant Voltage charging protocol. Several challenges and knowledge gaps were addressed in this work, including a reformulation of the optimal control problem that utilises direct methods as an alternative to overcome the limitations of indirect methods employed in similar studies. The proposed formulation considers the minimum-time optimal control case, trade-offs between the total charging time, the maximisation of the lithium bulk concentration, and energy efficiency, along with inequality constraints and other factors not previously considered in the literature, which can be helpful in practical applications.
Original languageEnglish
Article number2
Number of pages20
Issue number1
Publication statusPublished - 20 Dec 2023


  • lithium-ion batteries
  • battery charging
  • electrochemical battery models
  • optimal control
  • direct methods

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