## 4 Tests and Results
### Results, Indicators, and Discussion
The daily discharge-to-charge ratio \(\gamma_{j}\) indicates the performed EV discharge energy with respect to the total daily charge energy, as described in Equation (34), and is equal to 0 if the EV does not discharge. The average rate of discharge \(\beta_{j}\) relates the EV discharge with the maximum possible rate across the whole day, as reported in Equation (34). Due to the assumption of keeping the same SOC at the beginning and at the end of the day, \(\beta_{j}\) can reach at most 0.5 in the presence of continuous and full discharge, which is the most stressful condition for an EV battery. Finally, the number of cycles performed over the day by each EV, \(\varphi_{j}\), is drawn. \[\gamma_{j}=\frac{\sum\limits_{t=1}^{N_{t}}P_{j}^{d}(t)\cdot\Delta T}{\sum \limits_{t=1}^{N_{t}}P_{j}^{c}(t)\cdot\Delta T}, \tag{34}\]  
\[\beta_{j}=\frac{1}{N_{t}}\cdot\sum\limits_{t=1}^{N_{t}}\frac{P_{j}^{d}(t)}{ \overline{P}_{j}^{d}}\cdot 100. \tag{35}\]  
In Table 3, these values are reported for the five EVs and the two algorithms. It can be observed that the contribution of the EVs on the rainy day is lower than in the other two scenarios, since in the absence of excess renewable production, the procedure prefers to limit grid power withdrawal and to use the energy stored in the on-board batteries only for travel, reducing cost and battery wear. In all cases, EV utilization costs exceed relevant revenues, even though on the sunny day this difference is lower. An intense charging/discharging activity is observed on both sunny and cloudy days, where \(\gamma_{j}\) assumes average values between 0.3 and 0.5, with peaks of 0.9 for EV4 when it is not called to travel; however, the average discharge intensity \(\beta_{j}\) is usually below 10% of maximum. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Proposed Iterative MILP**} & \multicolumn{4}{c}{**Reference Non-Linear with GA**} \\ \hline  & & **EV 1** & **EV 2** & **EV 3** & **EV 4** & **EV 5** & **EV 1** & **EV 2** & **EV 3** & **EV 4** & **EV 5** \\ \hline \multirow{3}{*}{\(R_{j}^{d}\)} & **Sunny** & 4.14 & 4.14 & 3.93 & 4.14 & 4.85 & 4.15 & 4.15 & 3.84 & 4.2 & 4.48 \\  & **Cloudy** & 3.17 & 0.45 & 3.62 & 3.45 & 3.17 & 3.19 & 0.5 & 3.27 & 3.46 & 3.17 \\  & **Rainy** & 0 & 0.13 & 0 & 0 & 0.3 & 0 & 0.15 & 0.06 & 0.02 & 0.31 \\ \hline \multirow{3}{*}{\(C_{j}^{c}\)} & **Sunny** & 5.04 & 5.38 & 5 & 4.74 & 4.83 & 5.2 & 5.52 & 5.07 & 4.85 & 4.74 \\  & **Cloudy** & 4.56 & 3.27 & 4.54 & 2.01 & 4.58 & 4.66 & 3.36 & 4.43 & 2.07 & 4.69 \\  & **Rainy** & 3.19 & 0.1 & 1.78 & 3.52 & 0.22 & 3.3 & 0.11 & 1.82 & 3.55 & 0.22 \\ \hline \multirow{3}{*}{\(\gamma_{j}\)} & **Sunny** & 0.45 & 0.42 & 0.44 & 0.48 & 0.55 & 0.44 & 0.41 & 0.42 & 0.47 & 0.52 \\  & **Cloudy** & 0.37 & 0.07 & 0.43 & 0.92 & 0.37 & 0.37 & 0.08 & 0.4 & 0.9 & 0.36 \\  & **Rainy** & 0 & 0.74 & 0 & 0 & 0.82 & 0 & 0.77 & 0.02 & 0 & 0.83 \\ \hline \multirow{3}{*}{\(\beta_{j}\)} & **Sunny** & 9 & 9 & 8.57 & 9 & 10.57 & 9.03 & 9.03 & 8.35 & 9.13 & 9.76 \\  & **Cloudy** & 7.29 & 1.03 & 8.33 & 7.95 & 7.29 & 7.33 & 1.16 & 7.53 & 7.95 & 7.3 \\  & **Rainy** & 0 & 0.28 & 0 & 0 & 0.64 & 0 & 0.32 & 0.14 & 0.04 & 0.65 \\ \hline \multirow{3}{*}{\(\varphi_{j}\)} & **Sunny** & 0.64 & 0.64 & 0.60 & 0.64 & 0.76 & 0.64 & 0.64 & 0.59 & 0.65 & 0.70 \\  & **Cloudy** & 0.50 & 0.08 & 0.58 & 0.55 & 0.50 & 0.50 & 0.09 & 0.52 & 0.55 & 0.50 \\  & **Rainy** & 0.00 & 0.02 & 0.00 & 0.00 & 0.05 & 0.00 & 0.03 & 0.01 & 0.05 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Techno-economic performances of EVs for the three typical days. Occasional differences between the proposed procedure and the reference non-linear solution are observed, due to the ability of the stochastic solution process in the GA algorithm to inspect a wider range of the solution space. However, these differences seldom reach 10% on single quantities. It can be noted as well that no EV experiences more than 1 cycle per day.