## 4 Case Study Development and Results
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Case Study No.** & **Objectives** & **Considerations** \\ \hline \multirow{2}{*}{1} & Optimal station allocation & Predefined number of stations, different \\  & & initial stations positioning \\ \hline
2 & Optimal station allocation & Different station capacity constraints \\ \hline \multirow{2}{*}{3} & Optimal station number & \\  & and allocation & Different weighting coefficients w1 and w2 \\ \hline
4 & Optimal station allocation & Different station deployment cost zones \\ \hline
5 & Optimal station allocation & Varying EV charging demand levels \\ \hline
6 & Optimal station allocation & Varying service area shape \\ \hline
7 & Optimal station allocation & Large service area and number of stations \\ \hline
8 & Optimal station allocation & Different grid discretization levels \\ \hline
9 & Optimal station allocation & Two-phase station network deployment. \\ \hline
10 & Optimal station allocation & Varying EV range capacity, infeasible zones \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Case study objectives and considerations. Figure 3: Optimal charging station deployment for the case of 12 stations and different initial station distributions: center placement (brown color), symmetrical placement (red color), random placement (blue color), demand points (grey color). the algorithm requires on a typical laptop computer 90, 150, 350, and 1100 s for 10, 15, 20, and 25 station networks, respectively. Case Study 2: Station Allocation for EV Travel Distance (Cost) Minimization at Different Station Capacity Levels  
The proposed methodology focuses on charging station allocation based on the minimum travel distance of the participating EVs. In every case, the assignment of each EV is given to its closest station. In this way, however, there may be cases where some stations can be loaded with high charging demand while others may serve very few EVs. Both cases may present adverse financial consequences. For this reason, in the present case study, the algorithm is expanded with constraints about station capacity, i.e., the maximum number of EVs that can be served (a similar analysis can be done for the minimum number of EVs). The result of such a constraint is that some EVs may need to travel to another station but the closest one, if the capacity of the latter is exceeded. The objective of the optimization, in this case, is to assign the extra EV to the second-closest station, if the capacity level permits. Figure 4: Trade-off diagram between the number of charging stations and the average EV travel distance. Figure 5: Indicative charging station deployment optimization results: (**a**) 12-station network; (**b**) 20-station network (demand points in blue color, charging stations in orange color). In this analysis, the average number of EVs per charging station is considered (depending on the number of stations). Next, a station capacity tolerance (float) above the average value is assumed as a percentage increase. The results of the investigation are portrayed in Figure 6 for four indicative numbers of charging stations. As expected, the stricter the station capacity level, the longer the total (and average) distance traveled. The distance increases from the fully free EV allocation to a very restrictive station capacity of 10% above average, ranging between 7% and 21% without a specific pattern along the number of stations. Case Study 3: Optimization of Station Number and Allocation Based on Station Deployment Cost and EV Travel Cost  
Unlike most previous studies that solely focused on charging station allocation, the present algorithm can simultaneously handle the multi-objective problem of obtaining the optimal number of stations along with their optimal placement. This problem follows the classical trade-off between the cost of the charging station development, which relates to the number of stations and their construction cost, and the cost of EV total travel distance, which decreases with the number of charging stations.