## 5 Results
### Cases C1 and C2: Sumny and Cloudy Days
As PV production does not occur further, and FESS has already reached its minimum energy content, its operating mode is switched to _shut down_; similar to the _pre-charging_ stage, this operating mode has been slowed down to 1 h in order to prevent unsuitable power peak. Consequently, FESS speed decreases, while FESS delivers reduced and decreasing power until it is fully discharged. Figure 16: Losses evolutions achieved over a real operating scenario: (**a**) @360 V and (**b**) @720 V (case C1). Figure 17: Losses evolutions achieved over a real operating scenario @360 V and @720 V (case C2). Considerations similar to those provided for case C1 still apply to case C2 (Figures 12(b), 13(b) and 14(b)), although some differences occur. In particular, the cloudy day determines a high-fluctuating PV production profile (Figure 12(b)), with less energy content than case C1. Consequently, FESS is able to compensate for PV production over the overall day (Figure 13(b)) because FESS never reaches its maximum and minimum energy content (Figure 14(b)). As a result, almost no power exchange occurs with the main grid when FESS is at the _ready_ operating mode, apart from some fast power fluctuations that could not be completely compensated. Considering now the losses evolutions achieved in both cases C1 and C2 (Figures 15 and 16, respectively), it can be seen that iron losses are reduced significantly in case C1 by flux-weakening operation (Figure 15(a), @360 V), with just a marginal increase of Joule losses compared to the case at 720 V. This results in lower overall losses and it is particularly relevant because maximum speed is kept for several hours (from 12:00 to 16:00). Much less benefit is achieved by flux-weaking in case C2 (Figure 16) due to relatively low speed range swept by FESS during the cloudy day. Power and energy performance achieved by FESS over the overall two days are resumed in Table 6. In particular, peak, average, and ripple powers have been computed in accordance with the following relationships, respectively:  
\[\hat{P}_{g}=\max_{t}\{\big{|}P_{g}(t)\big{|}\}\,\ \overline{P}_{g}=\frac{1}{T} \int\limits_{0}^{T}P_{g}(t)dt\,\ \widetilde{P}_{g}=\sqrt{\frac{1}{T}\int\limits_{0}^{T} \big{(}P_{g}(t)-\overline{P}_{g}\big{)}^{2}dt}. \tag{14}\]  
The power data reported in Table 6 reveals that FESS is able to reduce peak grid power, especially over the cloudy day (case C2). This comes at the cost of increased energy drawn from the grid due to FESS losses, as highlighted by the lower average powers achieved compared to the case without FESS. In addition, a significant power ripple reduction is achieved by FESS, meaning that FESS reduces grid power fluctuations during both cases C1 and C2. Considering now energy performance, Table 6 reveals daily energy efficiency lower than those reported in Table 4, as expected. This is because of some idle periods, during which FESS draws energy for keeping its speed constant at maximum or minimum values, thus operating at zero efficiency. Such undesirable operating conditions more often occur during the sunny day (case C1), thus justifying lower daily efficiencies than case C2. Furthermore, when operating at maximum speed for approximately 4 h (case C1), higher losses occur at 720 V compared to 360 V, as already highlighted in Figure 15, thus justifying the slightly lower efficiency achieved with no flux-weakening operation. This difference does not almost occur during the cloudy day (case C2) because FESS operating speed range is generally below 1.8 pu (Figure 14(b)), thus flux-weakening is rarely required.