## 2 Model and Methodology
### Model Structure
#### 2.2.1 Data Collection
A literature study shown that on average PHEVs cover about 32%-55% of their mileage using electric energy taken from the grid [30]; another approach, presented in [31], suggests an electric load reduction of about 50% compared to BEV vehicles. With a view to make the model easier to implement, the approach of [31] was chosen to define the \((avc_{PHEV})_{2020}\) value, thus defined as the half of \((avc_{BEV})_{2020}\). On the upper end of the timeframe, namely 2030, these variables were estimated through literature research ([32; 33] for consumption and [31; 34] for battery capacities). The figures for the remaining years of the period were obtained as linear interpolation of the two extremes. Public and private stalls availability:  
The objective was to assess the availability of adequate space for the installation of private and publicly accessible CS, with a view to define upper limits to the planned charging infrastructure and to allow the evaluation of its impact on stalls occupation. The following input variables were defined: public parking stalls available on Florence and Bruxelles areas \(PP_{FI}\), \(PP_{BXL}\) and private residential parking available on Florence and Bruxelles areas \(PR_{FI}\), \(PR_{BXL}\). Data has been collected through research on an existing database; all these variables are defined as constant during the evaluated period. CS characteristics definition:  
The proper functioning of the model requires the characterization of the charging infrastructure in terms of:  
* Charging power levels \((P_{k})_{y}\): the number of power levels and the related power outputs are defined after literature research; private residential and publicly accessible CS are accounted separately. * Capital costs of the various types of CS \((C_{k})_{y}\): they take into account CS cost, installation and grid connection costs; operation and maintenance costs are not considered. * Estimated utilization rate of the various types of CS \(\left(r_{k,j}\right)_{y}\): it is expressed in terms of the maximum number of charging events manageable by the CS on an average daily basis. They depend on the assumed daily usage timeframe \(h_{k}\), on the charging power level \(\left(P_{k}\right)_{y}\) and on the energy request of the charging event \(E_{j}\); subscript \(k\) relates to the power level, while subscript \(j\) relates to the charging energy request class. They are calculated by comparing the hours of assumed daily availability with the time needed for a charge:  
\[\left(r_{k,j}\right)=\frac{h_{k}}{\left(\frac{E_{j}}{\left(P_{k}\right)_{y}} \right)}. \tag{3}\]  
The values assumed by these three variables can be updated during the analyzed period; within this study the same values were used for each analyzed municipality. Driving and charging behavior of users:  
The driving and parking habits of users, together with the way they are expected to use the EV charging infrastructure, have a great impact on its characterization, and thus on model outputs. A set of three variables was implemented in order to describe this scenario:  
* Average daily driven distance: A literature research focused on urban areas did not return appropriate results, so national level values were used. Anyway, given the fact that urban travels are shorter than the average, the data used was more conservative in terms of energy request to the infrastructure. The values were considered as constant over the timeframe, but differentiated within the two considered areas: \(avd_{FI}\) and \(avd_{BXL}\). * Use of publicly accessible or private residential CS: It is crucial to estimate the share of BEV and PHEV that will weigh on average on the public charging infrastructure; therefore, a literature research has been carried out in order to estimate the percentage of BEV and PHEV that will use the public charging infrastructure over the y-th year of the period: \(\left(\%BEV_{P}\right)_{y}\) and \(\left(\%PHEV_{P}\right)_{y}\).