## 7 Conclusions  
This research has shown that there are differences in battery life under different frequency regulation. The following can be observed for each type of frequency regulation:  
For systems under dReg0.5, those with a lower SOC level target had a longer battery life and, thus, a higher net profit.  
Then, comparing the systems in dReg0.5 and dReg0.25 modes, although the battery life of the system with a lower C-rate was longer, when considering the construction cost, it did not mean that the net profit would be more than that of the system with a higher C-rate.  
Finally, for the sReg, since most of the aging comes from calendar aging, the SOC level maintained for a long time seriously affected its battery life. Furthermore, the lower the SOC level, the longer the life. In addition, the effect of a low-C-rate battery on increasing the lifetime was not significant, and the cost was relatively high, so the high C-rate scenario had higher net profit. For a BESS with the same rated power and the same total energy capacity, due to sReg usually being used in response to possible emergencies which needs BESS to maintain a higher SOC level than that in the other two services, it results in a shorter battery life and a lower net income for the batteries operating with sReg.  
The limitation of the proposed method is that even for batteries of the same chemical material, batteries manufactured by different battery manufacturers will still have different aging properties, and the parameters of the model need to be adjusted according to different batteries.  
Future research will focus on evaluating the optimal capacity configuration of BESS in various ancillary services. Because the BESS of more than hundreds of MW will be composed of dozens of PCS with batteries of a specific capacity, the overall C-rate can be very fine; any number between 0.25-1C is possible, and it is not limited to a specific C-rate. It depends on how many PCS and how many batteries are used. The method proposed in this study can iterate the most suitable configuration according to various regions and various auxiliary services.  
Conceptualization, C-C.K.; Data curation, C-H.K.; Funding acquisition, C-C.K.; Investigation, C-H.W. and J.-Z.J.; Project administration, C-H.W. and C-C.K.; Resources, C-H.W.; Software, C-H.K.; Supervision, C-C.K.; Validation, J.-Z.J.; Visualization, C-H.K.; Writing--original draft, C-H.K.; Writing--review & editing, J.-Z.J. All authors have read and agreed to the published version of the manuscript.  
The support of this research by the Ministry of Science and Technology of the Republic of China under Grant No. MOST 111-2622-8-011-006-TE1 is gratefully acknowledged.  
Not applicable.  
All data are provided in this manuscript.  
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.
Figure A1: Example of extracting a single cycle using the rainflow counting algorithm. (**a**) It shows a line graph of the original sequence [4, 7, 2, 10, 5, 9, 4, 6] (**b**) Using rainflow counting method extract cycle: 5-9, the depth of this cycle is 4, the average is 7. (**c**) It shows the sequence after the extraction (**d**) Concatenate the original sequence with other sequences.  
Figure A6: SOC curve and aging features of Scenario 2.