**5. Conclusions**

In this paper we proposed a BMS algorithm that considers battery efficiency. The algorithm was applied to an ESS to improve the battery safety and performance. The algorithm proposed in this paper was divided into three parts.

First, the efficiency of the battery was used to estimate the state of the battery. The internal resistance of the battery was estimated based on the difference between the charging and discharging power to obtain the value of the variable internal resistance. The variation in the internal resistance was confirmed by the experimental results, which showed the increase in the charging-discharging power difference during the battery's operation.

Second, the SoC and SoH estimation methods were proposed. For SoC estimation, the method of combining OCV and CCM with the estimated battery states was proposed to compensate for both low initial estimation accuracies of CCM and incorrect estimation of OCV. An SoH estimation algorithm based on the charging time was also proposed. This proposal was based on the fact that an increase in the temperature of a battery results in an increase in its internal resistance and a decrease in the CC charging time. This charging time decrement according to the internal resistance variation was confirmed in the experiment. Based on the estimated SoH, the battery lifespan estimation method, which observes the charging-discharging SoH difference for a long period of time, was proposed. Additionally, the proposed method is more flexible than conventional methods, since it does not require any additional analysis of different kinds of battery cells for SoH estimation.

Third, this paper proposed a battery fault diagnosis algorithm that aims to improve battery safety. Using this method, faults are diagnosed through efficiency and SoH, and this fault diagnosis algorithm was validated through experiments.

In conclusion, accurate SoC and SoH estimations were proposed by applying battery efficiency to the estimation process. The estimated SoC and SoH were used to improve not only the performance of BMS but also the battery safety via a fault diagnosis algorithm with accurate SoH estimation.

**Author Contributions:** Conceptualization, J.L.; software, J.L. and J.-M.K.; formal analysis, J.L.; investigation, J.L. and J.-M.K.; writing—original draft preparation, J.L.; writing—review and editing, J.Y. and C.-Y.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry, and Energy (MOTIE) of the Republic of Korea (No. 2019381010001B).

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