Introducing the Loewner Method as a Data-Driven and Regularization-Free Approach for the Distribution of Relaxation Times Analysis of Lithium-Ion Batteries

For the identification of processes in lithium-ion batteries (LIB) by electrochemical impedance spectroscopy, frequency data is often transferred into the time domain using the method of distribution of relaxation times (DRT). As this requires regularization due to the ill-conditioned optimization problem, the investigation of data-driven methods becomes of interest. One promising approach is the Loewner method (LM), which has already had a number of applications in different fields of science but has not been applied to batteries yet. In this work, it is first deployed on synthetic data with predefined time constants and gains. The results are analyzed concerning the choice of model order, the type of processes , i.e., distributed and discrete, and the signal-to-noise ratio. Afterwards, the LM is used to identify and analyze the processes of a cylindrical LIB. To verify the results of this assessment a comparison is made with the generalized DRT at two different states of health of the LIB. It is shown that both methods lead to the same qualitative results. For the assignment of processes as well as for the interpretation of minor gains, the LM shows advantageous behavior, whereas the generalized DRT shows better results for the determination of lumped elements and resistive-inductive processes.