## 5 Case Study and Simulation Results
### Simulation Cases
#### 5.2.2 Case 2  
Case 2 investigates the characteristics of the energy router-based HEMS in response to rapid decrease of PV generation and transition from isolated mode to grid-connected mode. At the moment around t\({}_{2}\), the solar irradiance decreases rapidly. As shown in Figure 12a,b, the PV output drops from 3.75 kW to 3.0 kW at 1.0 s, and then drops to 2.0 kW at 2.0 s. Meanwhile, the active load power is 1.5 kW during 0.6-1.2 s, 3 kW during 1.8-2.4 s and 2.5 kW during rest of the time. The reactive load power remains 1 kVar all the time. The HEMS switches to grid-connected mode from isolated mode at 2.0 s due to insufficient PV generation for load demand.  
Figure 12c,d shows the operations of the self-energy storage system in case 2. As the energy buffer of the energy router, the self-energy storage system has played a critical role in suppressing the power fluctuations caused by operation mode switching and variations of PV generation and load consumptions, under the control of the fuzzy logic rules.  
It is observed from Figure 13a that the AC bus phase voltage is in dynamic balance under the V/f control before 2.0 s. After that, the AC bus voltage is synchronized with the power grid voltage. The situation of the AC bus frequency is same as the AC bus voltage; fluctuations in frequency occur during isolated mode.  
Similar to case 1, the DC bus voltage fluctuates at 0.6 s, 1.0 s, 1.2 s, 1.8 s, 2 s and 2.4 s due to transient imbalance caused by the instantaneous power fluctuations.  
Unlike case 1, phase congruency between the energy router and power grid should be taken into consideration when the energy router switches from isolated mode to grid-connected mode in case 2. Figure 13d shows the voltage phase difference between the power grid and AC bus of the energy  
Figure 12: Simulation results of energy router in case 2: (**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.  
router. The phase difference around 2.0 s is no more than \(\pm 2^{\circ}\), which means the energy router can transfer to grid-connected mode from isolated mode smoothly.  
In order to illustrate the dynamic mode switching course of the energy router, the situations of the switching process with and without the compensation strategy are demonstrated in Figure 14a,b, respectively. As shown for the case with compensation in Figure 14a, three-phase voltage waveforms are continuous and there is no distortion or abrupt change at the moment of mode switching. The smooth transition of three-phase voltage is realized under the control of reference voltage and current compensation strategy.  
Figure 14b shows the three-phase voltage waveforms without compensation strategy. During 2.00-2.04 s, the three-phase voltage waveforms are far from standard sinusoidal. Because both the reference currents and the inner loop PI regulator outputs have experienced an abrupt change during  
Figure 14: Mode switching results of the energy router: (**a**) Three-phase voltage waveforms of AC bus with compensation strategy; (**b**) Three-phase voltage waveforms of AC bus without compensation strategy.  
Figure 13: Parameter characteristics of the energy router in case 2: (**a**) AC bus phase voltage amplitude; (**b**) AC bus frequency; (**c**) DC bus voltage; (**d**) Voltage phase difference between energy router and power grid.  
mode switching, the output three-phase voltage waveforms are distorted obviously, which may cause severe fault or even failure of the mode switching.