## 4 Conclusions  
This work investigated a lean methodology to estimate the optimal size of a minimum cost charging infrastructure for passenger vehicles, suitable for deployment in an urban area. An analytical model was therefore developed to simulate different scenarios, accounting separately for BEV and PHEV fleets, as well as for publicly accessible and private residential CS. 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. A discrete-time Markov chain (DTMC), applied to a countable, finite state-space was used to obtain the estimate of the average daily distribution of the charging events within the circulating fleet, and the corresponding energy requests. Due to the primary importance of the inputs related to the size of the circulating EV fleet and since substantial differences between the various forecasts emerged from the research, a novel method for data sorting and conditioning of EV fleets forecasts was developed, using circulating fleet turnover rate as a threshold indicator. The model was then applied to the two selected case studies of Florence Municipality for Italy and Bruxelles for Belgium, over the 2020-2030 period, with a 1-year timestep resolution; nine inputs scenarios and three outputs scenarios were defined for each area. The xEV fleet forecasts used as inputs for this work were presented with a broad range of variability: on 2030 they spanned between 2.3% and 17.8% of the total circulating fleet for the Florentine area, and between 4.6% and 16.5% for Bruxelles. In absolute terms, this translated to 194 to 2053 passenger cars for Florence and to 1210 to 5536 for Bruxelles. As a consequence of vehicle range and user behavior assumptions, only a share of xEV ranging from 34% to 89% of the theoretical total value was expected to use the charging infrastructure on an average day; this could lead to a smaller than expected infrastructure having the same average energy request thus, consequentially, a possibly higher power request. The optimal size for the publicly accessible charging infrastructure, to be reached on 2030, was estimated in about 194 to 2053 CS for Florence and 1210 to 5537 CS for Bruxelles; these numbers corresponded to about 0.75 to 8.3 MUR on deployment cost for Florence and to 4.5 to 21.4 MUR for Bruxelles. On average, it was estimated that 10 to 200 CS has to be installed every year in Florence to comply with the deployment trend, with the yearly cost of deployment spanning between 25 kUR and 1 MUR; these figures depended on the evaluated scenario and on the selected year of the time period. The same analysis, projected on Bruxelles, returned an estimate of 100 to 530 CS to be installed every year, for a cost ranging between 230 kUR and 2.6 MUR per year. The narrower range of values related to Bruxelles could be explained by the higher minimum level of xEV forecasted in comparison to Florence. Notably, the higher power CS results to be the smaller share of the total and this is clearly related to their worst charging events/cost ratio comparing to slow and medium CS. The private residential charging infrastructure size on 2030 was then estimated in 1700 to 13,400 CS and in 8600 to 31,400, respectively for Florence and Bruxelles, with deployment costs ranging from 1.3 MUR to 10.3 MUR and from 8.9 MUR and 24.4 MUR. These higher figures in terms of costs and number of CS are related to the lower EV/CS ratio of residential CS, that is assumed equal to be 1; moreover, these figures suggest the relevance of a possible implementation of support schemes for the installation of residential CS, since this could help to unlock the potential related to households with off-street private parking.