**4. Conclusions**

In this work we presented a sensorless method for predicting the temperatures of lithium ion cells that uses ANNs which take electrochemical impedance spectra as input data. Investigation were performed on Samsung INR18650-15L1, Sony US18650VTC6 and Panasonic NCA 103450 cells. To simulate real applications, the SoC was varied; a superimposed DC current during the EIS measurement was applied; and for every cell type at least nine cells were investigated to include the cell to cell variance. In addition, Samsung 15L cells with different SoHCs were investigated. The RMSE for all temperature estimations were around 1 K, which makes the presented method attractive for practical applications. SoC estimation was also investigated likewise. For the Sony VTC6 and the Panasonic NCA 103450 cells, the RMSE was about 3%. Different cell temperatures during

the EIS measurement were taken into account. The SoC estimation for the Samsung 15L cells was not successful, with an RMSE of above 8%. In this case the influence of the SoC on the impedance spectrum was of the same order of magnitude as the influence of the cell to cell variance. Therefore, for the SoC estimation, it is necessary to investigate each cell system individually for its applicability. At last, the ANN was applied to estimate the SoHCs of Samsung 15L cells. Since the estimation errors for all cells were below 2%, this seams to be a feasible use of the method as well. However further investigations on cells with different aging profiles are necessary to give a definitive evaluation of the suitability. Its advantages compared to other temperature estimation methods are that there is no need to fit a battery model to the data, and no differential equation needs to be solved. Furthermore, the ANN needs only a single EIS spectrum to estimate the cell temperature. There is no need for handling time series data. The presented prediction method seems to be a promising way to estimate the inner cell temperature with high accuracy in a short time period, as little effort regarding measurements and calculations is required. Further work is suggested to investigate the ability of the neural network to estimating the temperatures of cells within electrical circuits. Furthermore, a reduction in the number of input parameters will be investigated to improve this method by reducing and simplifying the computational effort and the measurement time.

**Author Contributions:** Conceptualization, M.S., J.P.-B., M.K. and K.P.B.; methodology, M.S., J.P.-B., M.K. and K.P.B.; investigation, M.S., J.P.-B.; writing—original draft preparation, M.S. and J.P.-B.; writing—review and editing, M.K. and K.P.B.; visualization, M.S.; supervision, K.P.B.; project administration, M.S.; funding acquisition, K.P.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Robert Bosch GmbH due to the Bosch Promotionskolleg.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

## **References**

