Mathematical model for the representation of the electrical behaviour of a lithium cell

Lithium ion systems have emerged as a promising technology for energy storage in space applications with a high energy density reaching up to 150 Wh/kg associated with a better charge retention than conventional systems. The prediction of the electrical performances is a must in the design of a satellite power system as the environmental conditions affect them strongly. The approach which has been considered consists of giving priority to a modular model, representative of the lithium ion systems where a reduced number of parameters reflects the dependence with environmental conditions while being able to integrate ageing effects. The Zimmerman model has been shown to be very suitable for the modelling of the lithium systems due to its ability to associate electrochemical and statistical representations of cell operations. Its definitive advantage is its feature to represent the cell by an electrical network where branch currents and node voltages describe the internal processes of the cell while remaining compatible with the electrical system of a spacecraft. This model has been set up in the case of the G4 cell from SAFT. It consists of representing the behavior of the cell in all conditions by an equivalent nonlinear electrical circuit submitted to the electrical stimuli of the spacecraft power system. The influence of the internal temperature is introduced by an another electrical network representing the thermal model of the cell in its environment.