## 5 Case Study and Simulation Results
### Simulation Cases
#### 5.2.1 Case 1  
Case 1 investigates the characteristics of the energy router-based HEMS in response to rapid increase of PV generation and transition from grid-connected mode to isolated mode. The variations of the PV output and load consumptions are shown in Figure 10a,b. As shown in Figure 9, solar irradiance varies rapidly around the moments of t1 and t2. As a consequence, PV output rises from 1.5 kW to 2.5 kW at 1.0 s, and then to 4 kW at 2.0 s. Meanwhile, the active load power changes from 2.25 kW to 3 kW at 0.6 s, to 2.5 kW at 1.2 s, to 3.5 kW at 1.8 s and 3 kW at 2.4 s, respectively. The reactive load power remains 0.5 kVar all the time. The HEMS switches from grid-connected mode to isolated mode at 2.0 s.  
Figure 10c,d shows the operations of the self-energy storage system in case 1. According to the fuzzy logic rules, the charging or discharging power of the self-energy storage system is related to the difference between PV generation power and load consumption. Since PV generation power is lower than load consumption during 0-2.0 s, the self-energy storage system is discharging. However, as the discharging power cannot satisfy all the load demand, the power deficit is filled by energy input from the power grid. After that, the HEMS is in isolated mode and the self-energy storage system absorbs the excess power completely. According to the working characteristics of the battery and supercapacitor, the charging or discharging power of battery accounts for the majority of the energy surplus or deficit, while the supercapacitor mainly compensates for the drastic power fluctuations caused by abrupt changes of PV generation and load consumptions, since the battery cannot follow the quick variations of current supply.  
Figure 9: PV generation power and load power curves of energy router in a day.  
Figure 11a shows that the phase voltage amplitude of the AC bus remains constant before 2.0 s because the energy router is in connection with the power grid. When the energy router is in isolated mode during 2.0-3.0 s, there is slight fluctuation in the AC bus voltage, but is within dynamic balance under the V/f control. Similar to the AC bus voltage, there is little fluctuation in AC bus frequency, but is no more than \(\pm\)0.1 Hz as shown in Figure 11b.  
Figure 11c shows that DC bus voltage fluctuates at the moment of 0.6 s, 1.0 s, 1.2 s, 1.8 s, 2.0 s and 2.4 s when the energy router encounters instantaneous power imbalance caused by abrupt changes in  
Figure 11: Parameter characteristics of energy router in case 1: (**a**) AC bus phase voltage amplitude; (**b**) AC bus frequency; (**c**) DC bus voltage; (**d**) Three-phase voltage waveforms of AC bus around the moment of mode switching.  
Figure 10: Simulation results of energy router in case 1: (**a**) PV generation; (**b**) Load consumptions; (**c**) Total charging or discharging power of the self-energy storage system; (**d**) Charging or discharging power of the battery and supercapacitor.  
PV output and load consumption, but restores stability in short time and remains constant during the rest of the time. As DC bus is the \"energy pool\" of the HEMS, these fluctuations are totally acceptable.  
Figure 11d shows the three-phase voltage waveforms of the AC bus during the course of mode switching. The reference voltage and current compensation strategy ensures smooth transition at 2.0 s and there is no distortion on voltage waveforms. After 2.0 s, voltage amplitude isn't 311 V seriously, which corresponds to the situation in Figure 11a.