**3. Results**

As mentioned in Section 2, the power flow model receives three variables: battery capacity, C rate, and time step. For each load profile in our dataset, we carried out multiple simulations by varying only the battery capacity, whereas both the time step and the C rate were set at constant values. The peak threshold was calculated using the dichotomy method after defining the battery capacity.

The time step was set at 15 min which is the time resolution of the dataset. The C rate was set at 1 C; higher values are not recommended for the chosen battery technology because this would negatively impact its lifetime. Furthermore, based on our experience, for most applications, 1 C is su fficiently high to meet a given peak threshold. In general, the extent to which we can reduce the peak power depends on the battery's energy capacity rather than its power capacity. Nevertheless, we do sugges<sup>t</sup> for future research to investigate the impact of the C rate as well, but in this study, it will not be addressed. Regarding the battery capacity, since we deal with several users, in order to maintain a common reference of comparison between the users, we normalized the battery capacity by dividing it by the mean power of the user. Finally, the ratio battery capacity-to-mean power was varied within 0.1–10.
