# Stateflow-Based Energy Management Strategy for Hybrid Energy System to Mitigate Load Shedding
## 5 Results and Discussions
### Resiliency in Winter  
For the winter season, two scenarios are considered: moderate and extreme weather conditions. The weather profile that represents a moderate winter day (7 November 2019) is shown in Figure 16. As observed, the intensity of solar radiation for this day is lower than the summer season. Furthermore, the delayed sunrise and the early sunset significantly reduce the interval of the total received irradiance during this day. The HES operation for this case study is shown in Figure 17. Here, the load demand for the winter season is used while the shedding follows the schedule set by the utility. The total load shedding for this day also consists of 4 h. Further, the same fleet size (\(\rm{N_{PV}},\rm{N_{ESU}}\), and \(\rm{N_{Gen}}\)) is used. As before, the goal is to observe the resiliency of HES when subjected to the operational constraints and variability of the weather. Due to the delayed sunrise, the PV production starts later (at hour six) in the morning, as shown in Figure 16. Thus, during the late evening and early morning, the alternative sources have to be utilized. As the PV is not producing sufficient power in the morning, the ESU discharges at 6-7 h and supports the power supply operation along with PV. At 7-8 h, the grid resumes the power \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Unit** & **Value (kW)** \\ \hline Number of PV modules & 67 & 21.7 \\ Number of batteries & 16 & 28.8 \\ Power of diesel generator & 2 & 10, 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Considered values of HES components. Figure 15: Resiliency of HES during cloudy weather (summer day on 29 August 2019). (**a**) ESU charging and discharging operation with SOC variations (**b**) Grid, PV, ESU and Gen1 modes. (**c**) The resiliency of HES vs. variable load. supply. During this time, the ESU starts to charge from the PV and surplus grid (referred to plot a). During the hours 8-10, when the load shedding is enforced, the PV starts supplying. Since the load demand increases, the ESU contributes until the grid resumes the power supply. The ESU discharging operation (negative dashed line) can be observed in plot a, while the coordinated operation of PV and ESU can be seen in plot b. At hour 10 when the load shedding ends, the PV starts charging the ESU with the grid. Since both sources are charging ESU, the \(SOC_{U}\) level is reached quickly. After the ESU is fully charged, the PV contributes to the load with the grid. The PV supplying load during grid_Connected_Mode can be observed from hours 11-16 in the grey color shaded area. This operation improves PV energy utilization. At hour 18-19 (late evening), the ESU discharges and maintains the power supply. This is because the PV is unavailable at this time. Please note that during this interval, the generator is not started as the ESU could solely satisfy the load requirement. At hour 19, the load shedding ends and the grid resumes the power supply. During this time, the SOC of ESU has reached the \(SOC_{L}\). Due to the peak time (hour 18-22), the grid is not able to charge the ESU. However, the charging process starts after hour two. The varying load and HES operation is shown in plot c. Clearly, the system resiliency can be observed throughout this day. Next, the HES performance during the extreme winter conditions is evaluated. The case study is presented for 2 January 2020. The temperature (at different time intervals of the day) falls below the freezing point and irradiance levels significantly decrease. The weather profile indicating the irradiance and cloud opacity is illustrated in Figure 18.  
The HES operation for this day is shown in Figure 19. The load shedding for this day happens for 7 h. At night, shedding happens for two consecutive hours, i.e., hours 2-4. Since the ESU can sustain the load for the first hour only, the remaining period of the shedding (3-4) has to be supported by Gen1. During hours 6-7, the demand is fulfilled again by Gen1 and ESU because the PV production has not started.