# Stateflow-Based Energy Management Strategy for Hybrid Energy System to Mitigate Load Shedding
## 5 Results and Discussions
### Resiliency in Summer  
The weather profile for a specific day (14 June 2020) during the peak summer season is shown in Figure 12. Since the surface solar irradiance is directly dependent upon the sky condition (clear, cloudy), the cloud opacity and the solar irradiance data are plotted to show the weather condition of the considered day. The constant availability of solar irradiance (of more than 1000 W/m\({}^{2}\)) during the daytime can be observed, indicating the normal weather conditions for the considered day. The HES operation for this day is depicted in Figure 13. The load shedding is imposed for five hours during 6-8, 13-15, and 17-18 h. The charging/discharging profile of the ESU is shown in plot a. The ESU charges from the grid during the off-peak hours (Grid_ch_ESU) and during the excess of PV power (PV_ch_ESU). It discharges during the load shedding intervals (negative ESU_disch value indicates discharging). The limits (on power exchange) for batteries and the grid are maintained using [42]. Consequently, the SOC variations can be noted with the charging and discharging trend of the ESU. At any instant, the energy delivered by the ESU is given as \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parent** & **Child State** & **CFT** & **Description of Event** \\ \hline Grid\_Connected\_Mode & PV\_Mode & P\_PV \textgreater{} 0 & \begin{tabular}{c} The availability of PV power is used to charge ESU and supply the load through PV\_to\_ESU\_Mode and PV\_to\_Load\_Mode \\ PV\_to\_Load\_Mode \\ SOCC \textless{} SOCU \\ \end{tabular} & \
\begin{tabular}{c} The availability of PV power is used to charge ESU and supply the load through PV\_to\_ESU\_Mode and PV\_to\_Load\_Mode \\ PV\_to\_Load\_Mode \\ Grid power is used to satisfy load requirement and charge ESU \\ \end{tabular} \\ \hline Islanded\_Mode & RES\_Mode & P\_PV + P\_ESU \textgreater{} P\_Load &
\begin{tabular}{c} Availability of PV and ESU power is used to supply the load through PV\_Mode or ESU\_Mode \\ Generator supplying the load through Gen1\_Mode \\ or/ and Gen2\_Mode \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The parent-child relationship and the condition for transition (CFT) for Grid_Connected_Mode and Islanded_Mode. \[P_{-}ESU(t)=P_{-}Load(t)-P_{-}PV(t) \tag{10}\]  
Note that Equation (10) may result in \(P_{-}ESU(t)<0\) due to the sporadic nature of PV. Such situation represents the PV surplus energy being absorbed by the ESU, i.e., within the bounds of Equations (5) and (6). Figure 12: The global tilted irradiance and the cloud opacity (on 14 June 2020). Figure 13: Resiliency of the HES during peak summer season (on 14 June 2020). (**a**) ESU charging and discharging operation with SOC variations. (**b**) Grid, PV, and ESU modes. (**c**) The resiliency of HES vs. variable load. The flow of power under different modes is shown in plot b. It can be observed that the grid supply is maintained by PV (PV_Mode) and/or ESU (ESU_Mode) during the shedding hours. The standby generator is not utilized at all. Since the utilization of PV is given the first priority, the ESU is only used if P_PV is not sufficient to satisfy the load. The combined operation of PV and ESU can be seen during the hours 6-8, 13-15, and 17-18. Furthermore, during hours 8-9 and 15-16, PV supporting grid operation can also be observed (refer to grey color shaded curve in plot b). Finally, the integrated power supplied by HES against the varying load demand is shown in plot c. The results demonstrate the stable and uninterrupted power supply operation for a 24-h period despite the heavy load shedding experienced by the grid. This proves that the HES is sufficiently resilient under the control of the proposed EMS in providing uninterrupted supply even without the need to start the standby generator during the summer season having normal weather conditions. For the case of abnormal weather (in the summer season), the irradiance and temperature profiles are based on the data obtained during a cloudy day (29 August 2019).