## 4 Simulation Results and Analyses
### Simulation Case  
The simulation case is based on an operational period of 24 h separated into five time periods, 0:00-6:00, 6:00-8:00, 8:00-17:00, 17:00-22:00, and 22:00-24:00. The simulation is based on the PV generator, the public grid, the BS, the SC, the DG, the DC load, and DC bus modeling. The PV generator is composed of 14 PV panels (SF 130/2-125, Solar-Fabrik, Germany) in series, whose maximum power is 1750 W under standard test conditions (STC). The weather data were recorded on the 20 June 2018 in Compiegne, France. The public grid was considered as a single-phase voltage power source. The BS is composed of five lead-acid batteries in series, whose characteristics are 12 V/6.6 Ah for each one. The DG used in this simulation was SDMO Technic 6500 E AVR. Regarding the SC, its capacity \(C_{SC}\) is 94 F and the \(\overline{v}_{SC\_Ratel}\) is 75 V. The load power curve is scaled according to a real daily consumption profile of our university building during the weekdays, which consists of 49 appliances, as stated in [23]. It should be noted that the proposed power management system allows BS charging with public grid energy during the night when the public grid is less stressed. Regarding energy resale, the microgrid can only sell energy from the PV generator. The simulation parameters are given in Table 1.  
To allow DG start-up during daytime operation, the public grid power was limited to 200 W or 600 W in this simulation. The BS power was limited to 1000 W. The state of charge, SOC, limitations of BS was from 20% to 80%, and the initial value of BS was 50%. The DG power was limited to 1500 W to be at the same level of the PV and the load demand power; the DG duty cycle was set to 1 h. The maximal power of the SC was limited to 1500 W, the as same as the DG; the SC working period, \(T_{SC\_MIN}\), was constrained to be more than 3 min. The SOC of the SC was from 35% to 85%, and the two recharging SOC values of the SC were 45% and 75% in two different conditions as described in Section 2.5. The coefficient \(k_{L\_CRIT}\) was set to be 80% or 100%. The common DC bus voltage reference was 400 V by considering the power conversion efficiency between the microgrid and the public grid. Table 2 presents the simulation scenarios and parameters following the different periods, the choice of sub-flowchart a and sub-flowchart b, the set of the coefficient \(k_{L\_CRIT}\), and public grid power limitation. These configurations, shown in Table 2, were set according to the energy demand of the university building during the week. In Table 2 the five time periods can be seen. During 0:00-6:00 and 22:00-24:00, it is assumed that the load demand power is low, respecting sub-flowchart b. The coefficient \(k_{L\_CRIT}\) is set at 100% because all the load demand is the critical load that cannot be shedding, and the public grid power is limited to 600 W. During 6:00-8:00, the PV energy production is different according to the seasons and it is assumed that sub-flowchart a is used. The coefficient \(k_{L\_CRIT}\) is set at 80%, and the public grid power is limited to 200 W. During 8:00-17:00, the load demand varies according to the energy demand of the university building, and it is assumed that the power management uses sub-flowchart a. The coefficient \(k_{L\_CRIT}\) is set at 80%, and the public grid power is limited to 200 W. During 17:00-22:00, the load demand for tertiary buildings is low but for residential buildings it is very high so that the