Knowing the true state of the battery such as the Loss of Active Material (LAM) in the anode and cathode along with the Loss of Lithium Inventory (LLI) allows us to push the cells to their true limit instead of a conservative terminal voltage limit, without inducing more degradation or hazardous shorts from lithium plating. In this work, the electrode-specific SOH parameters are estimated by utilizing the cell expansion and relating it to the intrinsic shift of the phase transition of the battery material as it ages. This shift creates an “aging signature” like a wrinkle that we can observe in the measured expansion more clearly than in the measured voltage, especially at relevant discharge ranges and rates. [2-5]

The peaks in the voltage derivative curve and the second derivative of the expansion curve correspond to the same phase transitions in the material. Unlike the differential voltage, the peaks are observable up to 1C rate in the differential expansion curve, which makes the differential expansion an excellent method for capacity estimation during fast charging scenarios (above C/2). To understand why that is the case, and at the same time develop a model-based estimator a reduced ordered electrochemical/mechanical model is developed. The electrochemical model is primarily based on the well-known Doyle Fuller Newman (DFN) model. The reduced ordered model is similar to the single particle model (SPM), where the molar flux and solid concentration are independent of location. However, the model also includes a particle expansion model. Furthermore, the energy balance and the electrolyte dynamics are considered in the model. [1]