## 4 Tests and Results
### Test Cases: Different Operation Days  
The proposed approach is tested for three typical days: a sunny day, a cloudy day, and a rainy day. These conditions are estimated according to historical data of a weather station close to the envisaged microgrid location [55]. Each day is affected by different availability of solar radiation, determined on the horizontal plane according to a proper forecast procedure, therefore power production level \(P_{PV}(t)\) is estimated according to the Liu-Jordan model of solar radiation [56] and PV panel efficiency. The resulting trends are reported in Figure 3.  
Parameters used in the study are further reported in Table 2, including nominal efficiencies of converters and loss coefficients of connections, depending on different cable lengths. For the sake of simplicity, step-wise approximations of non-linear characteristics for bidirectional DC/DC converter (in charge and discharge) and AC/DC converter efficiency with respect to flowing power, exploited in the iterative solution methodology sketched in Figure 1,  
Figure 3: Forecasted output of the photovoltaic system for the three different days.  
Moreover, starting from the data collection of current exploitation of fuel-based service cars within Bari Port Authority, the pattern of EV usage is derived for the specified model. In particular, the traveling intervals and the mobility needs for each journey are estimated through a stochastic procedure from the collected data for each vehicle, depending on seasonality, on the day of the week, and accounting for the possibility of different numbers of journeys during the day. This process leads to the EV usage patterns reported in Figure 5. It can be seen that the service use of EVs is usually concentrated between 10:00 and 19:00. In order to obtain EV power consumption for mobility, an average of 0.12 kWh/km is considered for a 24-kWh size EV battery.  
Finally, trends of cost coefficient over the considered days are reported in Figure 6. It can be observed that costs of power purchase from the grid \(c_{g}(t)\) vary in the range 0.12-0.2 \(\upxi\)/kWh. Additionally, \(r_{g}(t)\) is in the range 0.02-0.08 \(\upxi\)/kWh. As for EV utilization, the charge cost \(c_{j}(t)\) is between 0.18 and 0.25 \(\upxi\)/kWh and the premium for discharge \(r_{j}(t)\) is higher, in the range of 0.32-0.4 \(\upxi\)/kWh. In any case, the cost coefficients are higher on rainy days and lower on cloudy days, and they follow analogous trends, with peaks in the morning (10:00-12:00) and evening (19:00-22:00).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Nominal Value** \\ \hline EV charge efficiency & \(\eta_{j}^{c}\) & 0.95 \\ EV discharge efficiency & \(\eta_{j}^{d}\) & 0.95 \\ Grid converter efficiency & \(h_{g}\) & 0.93 \\ DC/DC converter efficiency & \(h_{i}\,,\ h_{j}\,,\ h_{PV}\) & 0.965 \\ Storage charge efficiency & \(\eta_{i}^{c}\) & 0.9 \\ Storage discharge efficiency & \(\eta_{i}^{d}\) & 0.9 \\ Connection losses coefficient & \(\alpha\) & 0.035\(\pm\)0.055 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Test system. Nominal Parameters.  
Figure 4: Converter efficiency curves.