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Optimized calibration of P2D lithium ion battery physical model following sensitivity-based multi-measurement protocol
Cell characterization
Characterization methods

Pseudo-2D Doyle-Fuller-Newman (P2D-DFN) is a state-of-art physical model for the simulation of lithium ion (LIB) battery, unravelling inaccessible quantities and local heterogeneities determined both during steady and dynamic operation. LIB operation, however, due to its complexity involving electrochemical redox and intercalation-deintercalation reactions together with mass and energy transport in both porous solid and liquid matter, is extremely complex to be reliably simulated, despite its fully commercial development stage. Moreover, despite its wide adoption and physical consistency, DFN model calibration requires complex and time-consuming experimental procedures, while risking overfitting issues due to the extremely large number of physical parameters, many of which are unconsolidated in the literature or not directly measurable.
Hence, an extensive sensitivity analysis has been performed on discharge curve, electrochemical impedance spectroscopy and voltage relaxation techniques (an example is reported in Attachment 1) to highlight the sensitivity of each physical parameter as a function of the operating conditions (such as temperature, state of charge and C-rate) by means of a P2D-DFN model implemented with heat transfer. For each parameter, the relative variability range has been identified from the literature to explore its sensitivity over a range of meaningful values and according to its general knowledge. In this way, unconsolidated parameters, whose value spans entire orders of magnitude across the literature, have been studied in terms of their actual effect according to such uncertainty. The study enabled the identification and elimination from the calibration procedure of several unsensitive parameters. On the other side, among the other, sensitive, parameters, it permitted to highlight the combination of diagnostic techniques and operating conditions able to maximize their sensitivity on battery model response.
Applying the results, a multi-measurement diagnostic protocol (as reported in Attachment 2, combining partial discharges, voltage relaxation and EIS at two temperature and C-rate levels) has been combined with a stepwise algorithm, developing a methodology able to exploit the conditions of maximum sensitivity for each significative physical parameter, selectively calibrating their value at specific conditions of the protocol.
The results demonstrated the methodology to enable a wide and physically-sound simulation of battery performance and, potentially, state of health, with reasonable testing and computational time.

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Claudio Rabissi, Andrea Casalegno