*Article* **Determination of the Distribution of Relaxation Times by Means of Pulse Evaluation for Offline and Online Diagnosis of Lithium-Ion Batteries**

**Erik Goldammer \* and Julia Kowal**

Electrical Energy Storage Technology, Departement of Energy and Automation Technology, Faculty IV, Secr. EMH 2, Technische Universität Berlin, Einsteinufer 11, D-10587 Berlin, Germany; julia.kowal@tu-berlin.de **\*** Correspondence: goldammer@tu-berlin.de; Tel.: +49-30-314-73851

**Abstract:** The distribution of relaxation times (DRT) analysis of impedance spectra is a proven method to determine the number of occurring polarization processes in lithium-ion batteries (LIBs), their polarization contributions and characteristic time constants. Direct measurement of a spectrum by means of electrochemical impedance spectroscopy (EIS), however, suffers from a high expenditure of time for low-frequency impedances and a lack of general availability in most online applications. In this study, a method is presented to derive the DRT by evaluating the relaxation voltage after a current pulse. The method was experimentally validated using both EIS and the proposed pulse evaluation to determine the DRT of automotive pouch-cells and an aging study was carried out. The DRT derived from time domain data provided improved resolution of processes with large time constants and therefore enabled changes in low-frequency impedance and the correlated degradation mechanisms to be identified. One of the polarization contributions identified could be determined as an indicator for the potential risk of plating. The novel, general approach for batteries was tested with a sampling rate of 10 Hz and only requires relaxation periods. Therefore, the method is applicable in battery management systems and contributes to improving the reliability and safety of LIBs.

**Keywords:** lithium-ion battery; DRT by time domain data; pulse evaluation; relaxation voltage; online diagnosis; degradation mechanisms; EIS
