## 2 Materials and Methods
### Data Collection
#### 2.3.2 Simulation Data  
The simulation data regarding the hourly power demand required from the grid are instead obtained using the _emobpy_ open-source tool [44]. Such tool employs a sampling approach to generate profiles BEVs by integrating customizable assumptions, vehicle physical properties, and empirical mobility data from German institutions. To create passenger car charging profiles, the tool requires the percentage distribution of the population among non-commuters, part-time commuters, and full-time commuters. After establishing Origin-Destination vehicle patterns, the tool needs the characteristics of the vehicle fleet to determine battery consumption for each trip. To evaluate the energy consumption for each time step t when the vehicle is in the \"driving\" state, the tool calculates a power balance across the battery as outlined in Equation (1). The positive power outputs considered are the auxiliary power (\(P_{t}^{\mathit{n}\mathit{t}\mathit{n}\mathit{t}}\)), the electrical power for heating/cooling device (\(P_{t}^{\mathit{device}}\)) and the power provided to the motor (\(P_{t}^{\mathit{m}\mathit{t}\mathit{n}\mathit{t}}\)), while the negative power input is provided by the generator in case of regenerative braking (\(P_{t}^{\mathit{G}\mathit{out}}\)):  
\[P_{t}^{\mathit{all}}=P_{t}^{\mathit{m}\mathit{t}\mathit{n}\mathit{t}}-P_{t}^{ \mathit{G}\mathit{out}}+P_{t}^{\mathit{aux}}+P_{t}^{\mathit{device}} \tag{1}\]  
As shown in Equation (2), if the sum of all the powers \(P_{t}^{\mathit{all}}\) is positive, the battery supplies energy to the vehicle and the discharging efficiency \(\eta_{\mathit{discharge}\mathit{BEV}}\) is used. If \(P_{t}^{\mathit{all}}\) is negative, then the battery is charged via regenerative braking. In that case, the battery load \(P_{t}^{\mathit{battery}}\) is negative, hence the charging efficiency \(\eta_{\mathit{charge}\mathit{BEV}}\) is utilized. \[P_{t}^{\mathit{battery}}=\left\{ \begin{aligned} &\frac{P_{t}^{\mathit{all}}}{\eta_{\mathit{discharge}\mathit{BEV}}},if\ P_{t}^{\mathit{all}}>0\\ & P_{t}^{\mathit{all}}\times\eta_{\mathit{charge}\mathit{BEV}}, \mathit{otherwise}\end{aligned} \right. \tag{2}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & \multicolumn{2}{c}{**Performance Feature**} & **Assumptions** \\ \hline Distribution & (a) & Recharging stations by brand and model \\ \cline{2-3} and expansion & (b) & Expansion of recharging points \\ \cline{2-3} of recharging points & (c) & Location and number of recharging points \\ \hline \multirow{5}{*}{Energy consumption and recharging sessions} & (d) & Monthly consumption and number of sessions \\ \cline{2-3}  & (e) & Monthly consumption (yearly comparison) \\ \cline{1-1} \cline{2-3} and recharging sessions & (f) & Consumption by municipality \\ \cline{1-1} \cline{2-3}  & (g) & Avg. consumption per recharging point by municipality \\ \hline \multirow{5}{*}{Profiles for energy consumption and session duration} & (h) & Consumption and duration distributions \\ \cline{1-1} \cline{2-3}  & (i) & Duration vs. energy consumption \\ \cline{1-1} \cline{2-3}  & (j) & Normalized profile of occupancy \\ \cline{1-1} \cline{2-3}  & (k) & Avg. consumption and duration by hour of session start \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of the performance features for the analyzed recharging points, based on data collected from January 2021 to December 2023. The total energy consumption per trip \(E^{BEV,total}\) is defined in Equation (3), where battery load is aggregated through the duration of the trip at every hourly time step \(t\). \[E^{BEV,total}=\sum_{t=1h}^{T}p_{t}^{battery} \tag{3}\]  
Once vehicle consumption is assessed, it is crucial to provide probability distributions for charging stations, outlining the likelihood of finding an available charging station with a specific power rating at each location. Using this information, _embryy_ determines whether a BEV is connected to the grid at any given timestep and at what power capacity.