## 5 Results
### Cases C1 and C2: Sumny and Cloudy Days  
The results achieved during a sunny and a cloudy day (cases C1 and C2, respectively) are shown in Figures 13-17, while the corresponding FESS energy performance and efficiency are resumed in Table 6. In particular, Figures 13-15 refer only to the case of 720 V because all the evolutions are almost superimposed with those achieved at 360 V. On the other hand, Figures 16 and 17, and Table 6 highlight different losses and energy performance achieved at both 360 V and 720 V for comparison purposes. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Charging**} & \multicolumn{2}{c}{**Discharging**} & \multicolumn{2}{c}{**Round-Trip**} \\ \cline{2-7}
**Case** & \(\eta\) & \(\eta\) & \(\eta\) & \(\eta\) & \(\eta\) \\  & **@T\({}_{\mathbf{e}}\) = Const.** & **@P\({}_{\mathbf{m}}\) = Const.** & **@P\({}_{\mathbf{m}}\) = Const.** & **@T\({}_{\mathbf{e}}\) = Const.** & **@P\({}_{\mathbf{m}}\) = Const.** \\ \hline A1 & 92.6 & 96.2 & 96.2 & 92.6 & 91.8 & 92.6 \\ \hline A2 & 92.6 & 96.1 & 96.2 & 92.6 & 91.8 & 92.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: FESS energy efficiency achieved over round-trip tests (cases A1 and A2). Figure 11: The dq components of M/G-side and grid-side current space vectors (\(i_{m,dq}\) and \(i_{g,dq}\), respectively) achieved during round-trip tests (cases A1 and A2, quantities normalized to their corresponding rated values). Figure 12: FESS torque (\(T_{e}\)), power (\(P_{m}\)), state-of-energy (SOE), and speed (\(\omega_{m}\)) achieved during the self-discharge test (case B1, quantities normalized to their corresponding rated values). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Time@\(\omega_{\mathbf{m}}\) = 2 pu** & **Time@\(\omega_{\mathbf{m}}\) = 1.5 pu** & **Time@\(\omega_{\mathbf{m}}\) = 1 pu** & **Time@\(\omega_{\mathbf{m}}\) = 0 pu** \\ \hline B1 & 20 [h] & 35 [h] & 47 [h] & 81 [h] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: FESS self-discharge performance (case B1). Figure 14: Overall power exchanged with the main grid with and without FESS @720 V: cases C1 (a) and C2 (b). Figure 13: Load, PV, and FESS grid powers achieved over a real operating scenario @720 V: cases C1 (a) and C2 (b). Figure 15: SOE and speed evolutions achieved over a real operating scenario @720 V: cases C1 (a) and C2 (b). Considering case C1 at first (Figures 13a, 14a and 15a), it can be seen that FESS is started at 8:00, when PV production already overcomes the load demand, as detectable in Figure 13a; the FESS is then charged at reduced torque and power rating in order to achieve its rated speed not before 1 h (Figure 15a); in this regard, the _pre-charging_ stage, which could be accomplished in approximately 15 min (Figure 10), has been slowed down properly in order to avoid unsuitable peak power drawn from the grid. As soon as the rated speed is achieved, FESS enters into the _ready_ operating mode, by drawing the excess PV production in order to guarantee no energy exchange with the main grid, as shown in Figure 14a. As the speed approaches its maximum value, FESS absorbed power is reduced in accordance with Figure 5 until the FESS is almost fully charged at approximately 12:00 (Figure 15a). Afterwards, FESS becomes idle, namely it just absorbs the power needed to keep its speed constant. This operating condition persists approximately until 16:00, when PV production drops below the load demand (Figure 13a), enabling FESS to deliver the energy previously stored from PV. As a result, grid power exchange in nullified again (Figure 14a), while FESS speed decreases down to its rated value, which is reached at approximately 20:40 (Figure 15a). During this period of time, FESS also partially compensates for fast load power fluctuations occurring at 17:30-18:00, as shown in both Figures 13a and 14a.