**6. Conclusions**

The requirement of accurate online estimation of LiB battery capacity and its remaining useful life (RUL) are important. In this work, we applied ECBE model and semi-empirical capacity fading (SECF) model to estimate SoH and its remaining useful life after a LiB is operated for different charge-discharge cycles. ECBE model is only used for initial SoH calculation twice to determine the parameters in the SECF model, which can then be used for the SoH and RUL estimation of cells for their subsequent charge-discharge cycles.

We demonstrate that SECF model for SoH estimation can provide accurate SoH estimation, using the ECBE model as reference, regardless of the discharge current and ambient temperature. The discharge rate considered is from 0.5 C to 5 C, and the ambient temperature is from 25 ◦C to 55 ◦C. As the model is in compact closed form, it can be used for the lifetime prediction of LiB, and this could provide a good method for LiB acceleration test so that the SECF model parameters can be determined for its lifetime estimation of LiB in other operating conditions in a short time. Also, with this closed form, this model is practical for on-line real time SoH estimation, as the estimation time after each discharge cycle is less than 5 s using a personal computer with capability of 8 GB RAM and Intel Core i5 processor.

**Author Contributions:** C.M.T. conceived and designed the research; P.S., C.C., and C.M.T. analyzed the testing data; P.S., C.C., and C.M.T. wrote the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Chang Gung University and Ming Chi University of Technology, Taiwan and The APC was funded by Chang Gung University, Taiwan.

**Acknowledgments:** The authors would like to acknowledge the support of Centre of Reliability Science and Technologies Lab, Chang Gung University and Center on Reliability Engineering, Ming Chi University of Technology for providing valuable equipment and support for smooth conduct of experiments.

**Conflicts of Interest:** The authors declare no conflict of interest.
