Quantification of Loss of Lithium Inventory and Loss of Active Material for Li-ion Batteries

Lithium-ion batteries (LIBs) are earning an increasing attention for the decarbonisation of the industry as in the energy and the automotive sectors. As energy storages they are applied as energy and power source; therefore, the prediction of the battery life is fundamental. In this way the understanding of the batteries aging and the monitoring of the degradation on-board are good strategies. In this thesis work this purpose was pursued by studying the aging mechanisms and their consequences from a more global perspective. That was done by understanding and quantifying dominant cell degradation modes (DMs) such as Loss of Lithium Inventory (LLI) and the Loss of Active Material on both electrodes (LAMn & LAMp). Firstly, a search was done in literature to explore proposed methods for the quantification, then a comparison in terms of pros, cons and available data. The chosen method is based on the analysis of measured near-equilibrium (slow-rate) full cell voltage curve, i.e. pseudo-open circuit voltage (pOCV); that allows to consider negligible kinetic effects. The pOCV was modelled then with the fundamental state equation that reflects the voltage conservation between the electrodes near-equilibrium potentials and the full cell near-equilibrium potential. Electrode potentials are functions of lithium stoichiometries, that can be expressed as functions of full cell capacity and electrode state of health (eSOH) parameters, such as lithium electrode stoichiometries in fully charged/discharged state and total electrode capacities; since the full cell capacity is known from data, it is not considered as a modelled parameter. Thus, since they bear physical meanings, the knowledge of these parameters allows a complete description of the model and they can be used to derive electrochemical features such as degradation modes. This is why the model was applied to fit the measured pOCV, optimizing the eSOH parameters; by comparing the parameters of an aged cell to those one of a pristine cell, the DMs of the aged cell were quantified. At last, an attempt was made to identify the individual contributions of the DMs to the cell capacity loss; a correlation was detected, but it could be confirmed only by improving the accuracy of the fitting. The goodness of the fit was evaluated by the Root Mean Square Error (RMSE) between the estimated and measured voltage curve, so the optimization problem was solved minimizing the RMSE; the nonlinear solver fmincon in Matlab was used. Furthermore, since the problem becomes a non-convex optimization problem due to the nonlinearity of the OCV model, local minima could exist and optimization solution depends strongly by initial guess; in order to find an optimum solution, multiple initial guesses were generated within feasible bounds using multistart tool of Matlab. Feasible bounds were determined by assumptions and knowledges of cell parameters from the literature. In addition, to improve the accuracy and reliability of the results, differential curves analysis was integrated, i.e. differential voltage (DVA) and incremental capacity (ICA). The available data consisted of RPTs of calendar and cycle aged cells, used to extract the experimental OCV curves and the full cell capacities; electrode OCP data was collected from the literature and provided for different chemistries. Since the chemistry of the analysed cells was unknown, it was supposed by considering the best fitting results and by consulting the literature.