This thesis focuses on the modeling and identification of lithium-ion batteries by integrating advanced approaches based on fractional calculus. The primary objective is to more accurately represent complex electrochemical phenomena, aging mechanisms, and to refine the equivalent circuit models traditionally used to describe their dynamic behavior.
A major contribution lies in the explicit consideration of non-zero initial conditions, directly linked to relaxation effects observed during experimental testing of Li-ion batteries. Two original time-domain identification algorithms are proposed to estimate the parameters of fractional-order models, with validation performed on both simulated data and different Li-ion cell chemistries.
In parallel, the estimation of the state of charge (SOC) is addressed through a hybrid method that combines a fractional equivalent circuit model with fuzzy logic, enabling reliable evaluation based on experimental data. This same fractional model is further used for the estimation of the state of health (SOH), by applying principal component analysis (PCA) to the model parameters in order to monitor their evolution throughout the aging process. Extensive experimental campaigns, involving 36 cells subjected to a calendar aging protocol, confirm the ability of fractional-order models to accurately reflect the real state of batteries. This opens promising perspectives for diagnostic and prognostic applications in energy management systems.
