## 2 Model and Methodology
### Model Structure
#### 2.2.1 Data Collection
* At 2050, \(\left(\frac{xEV_{output}}{\overline{xEV_{input}}}\right)_{2050}\) was assumed equal to \(\left(\frac{TOT_{output}}{TOT_{input}}\right)_{2050}\), which expresses the ratio between the total circulating car fleets forecast in the two considered areas. * Finally, \(\left(\frac{xEV_{output}}{\overline{xEV_{input}}}\right)_{\gamma}\) was related to the Y-th year of the considered time period and was calculated under the assumption of a linear behavior, as described in Figure 2.  
Once the forecasts for the xEV fleets size were scaled down to the municipality level, the resulting values were compared, for every year of the period, with a threshold value \(Th_{y}\), calculated as following:  
\[Th_{y}=\sum_{i=1}^{y}[To*(share_{xEV})_{i}*TOT_{i}], \tag{1}\]  
where \(To\) is the average EU-28 car fleet yearly turnover, with a value of 5.4% [25; 26] and \(\left(share_{xEV}\right)_{i}\) is defined as the xEV share of the EU-28 yearly car turnover, variable over 2020-2030 the period and assuming the values shown in Table 1. Currently, the share of xEV in the annual turnover equals 0.24% for Italy (2017 data) and stays below 4% for most of the European countries [13]; however, it has to be considered the impact that incentives and policies may have on the development of the EV market and the high probability of being activated in the period considered by this study, as highlighted by [13]. Finally, \(TOT_{y}\) defines the forecast total circulating fleet (ICEV, BEV and PHEV) on the y-th year of period. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **2020** & **2025** & **2030** \\ \hline xEV share of EU-28 & & & \\ yearly car turnover & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Assumed xEV share of EU-28 yearly car turnover for the various years of the analyzed timeframe. Figure 2: Scaling down process for the collected xEV fleet size forecast values. A specific forecast was used in the following steps only if all its values were below the threshold, otherwise it was discarded. The equation used for evaluation is described below:  
\[xEV_{y}\leq Th_{y}\forall y\in(time\ period). \tag{2}\]  
Finally, the remaining municipality level forecasts were used to define three scenarios for each municipality considered, using the following criteria:  
* Low Scenario: it uses the lowest value of all the selected forecasts for every year of the time period. * Medium Scenario: it uses an average value calculated from the values of all the selected forecasts for every year of the time period. * High Scenario: it uses the highest value of all the selected forecasts for every year of the time period. Average BEV and PHEV energy consumption and batteries capacity:  
Average xEV consumption (expressed in kWh km\({}^{-1}\)) and battery capacity (expressed in kWh) has been considered as a variable, to reflect the inevitable technological advances that will take place over the analyzed period. The values attributed for the year 2020 were obtained from the analysis of the current BEV and PHEV fleet [27] average consumption--measured using WLTP cycle estimations [28]--and capacity of the battery pack. More specifically, the capacity of the battery pack assigned for the first year of analysis timeframe has been defined as the average of the capacities of the 15 best-seller M1-class BEV (and PHEV), weighted by sales volumes [29]. In order to consider the actual battery discharging capacity the obtained values have been reduced by 30% [28], then assigned to variables \((batt_{PHEV})_{2020}\) and \((batt_{BEV})_{2020}\). The same approach was also used to define the average mean BEV consumption \((avc_{BEV})_{2020}\), while to obtain the average mean PHEV consumption \((avc_{PHEV})_{2020}\) a further step was required, since their typical use involves the simultaneous operation of both thermal and electric motor.