## 2 Model and Methodology  
### Model Definition  
In order to define the optimal size of the EV charging infrastructure, the model needs as inputs, for each timestep of the analysis, the number of daily charging events related to both BEV and PHEV fleets and the corresponding energy requests; moreover, it needs a full characterization of the CS in terms of expected performances and costs. An input pre-processing phase take place before the model's core steps execution, and a post-processing phase, delivering expected outputs is placed after them; this leads to a four-parts conceptual architecture, thoroughly described in the following sections and also briefly reported below and in Figure 1:  
* The first part is dedicated to data collection and pre-processing. * The second part performs a discrete-time Markov process to obtain as output the probability distribution of the charging events over the average range (in days) of BEVs and PHEVs; to do so it also considers users' behavior and preferences. Several control criteria are implemented, in order to assure coherence of the results. * In the third part the outputs are used to define a constrained space of solutions where all the possible charging infrastructures complying with EV fleet requests are defined; finally, CS costs are applied, and the optimal charging infrastructure size and composition is chosen. * In the fourth and last part the results are processed in order to obtain the desired outputs. The model structure has been conceived so to be flexible enough to capture the complexity of the evaluated scenarios, while maintaining a simple and lean structure. These initial requirements led to the following set of features:  
* Modular architecture and additivity of the model: Each timestep of the analysis is considered separately and the model is recursively operated. This approach is used as well within a single timestep: as an example, BEV and PHEV impacts on infrastructure are separately calculated using the same module. Partial outputs are collected at the end of each calculation step of and then post-processed in a final step, in order to obtain the total outputs. This feature allows us to model flexible and time-evolving scenarios, while remaining sufficiently simple. The downside of this choice is that it does not allow any change in the operating parameters of the already deployed infrastructure during the timespan of the analysis. * Complete battery charge at every charging event: This simplifying assumption derives from the fact that only few information is available on this specific charging behavior; moreover, it does not affect the average quantity of energy requested from the charging infrastructure, since it only depends on average EV fleet size and consumption. * All vehicles are used every day: This simplifying assumption set vehicles usage pattern as constant over time. This, together with the evaluation through the average daily travelled distance, allows us to define an average usage of the charging infrastructure. * Evaluation of both BEV and PHEV impacts on charging infrastructure: Given the difference in battery capacities, thus in energy requests during the charging phase, the model takes them into account separately. This choice allows us to better evaluate the impact on charging infrastructure, thus, to dimension it more precisely. * Implementation of publicly accessible and private residential charging infrastructure: Three different CS power levels are considered within the model to define publicly accessible charging infrastructure; the CS types used can also be changed through the evaluation time period. Moreover, it is of primary importance to investigate also the possible extension and impact of a residential charging infrastructure, since a high number of CS connected to residential distribution feeders could possibly lead to line congestions and voltage issues [21]. In fact, several studies state  
Figure 1: High-level visual description of the model structure.