## 4 Simulation Results and Discussion
### Simulation Results  
In order to verify the effectiveness of the proposed method, the simulation results obtained in four different cases are compared and discussed in this sub-section. Case 1 is that the optimization is executed using the data only in the previous day for forecasting PV output in next day in which re-forecast, re-plan and uncertainties are not considered. Case 2 is that the optimization considering  
Figure 7: Power consumption and PV output power. uncertainties of PV output is executed but re-forecast and re-plan are not considered in the case. Case 3 is that the optimization considering re-forecast and re-plan is executed but uncertainties for PV output are not considered in the case. Case 4 is that all (uncertainties, re-forecast and re-plan) in former ones are considered in the optimization. The simulation result in the case 1 is depicted in Figure 8. This figure shows that result which the scheduling obtained by the optimization without considering re-forecast and re-plan, was operated for the real PV output as shown in Figure 7b. The temperature in a storage tank in case is depicted in Figure 8a. It can be seen from these figures, the temperature in the storage tank does not fall 40 \({}^{\circ}\)C at 8:00 and 22:00 by heat supply from SC and the HP. The power consumption of the HP is depicted in Figure 8b. It is confirmed that the HP operates before at 6:00, since the temperature in the storage tank falls to 40 \({}^{\circ}\)C at 7:00 without heating from the HP. As respects the use of heat water at night time, the temperature in the storage tank does not fall 40 \({}^{\circ}\)C without heating from the HP after at 22:00 because much insolation in the daytime in fair day was obtained and SC could supply the storage tank with collected heat. It can be seen that the operation time of the HP is minimized with the maximized utilization of solar energy. Next, the power flow of interconnected point in the smart home in case 1 is indicated in Figure 8c. It can be observed that the power flow deviates from bandwidth given by a power company due to the forecasted error in which re-forecast, re-plan and uncertainties are not considered. Furthermore, the state of charge for the battery and EV in case 1 is shown in Figure 8d, the charge/discharge power of the batteries is performed within the allowed constraints conditions. The simulation result in the case 2 is depicted in Figure 9. This figure shows that result which the scheduling obtained by the optimization with considering uncertainties except for consideration of re-forecast and re-plan, was operated for the real PV output. The temperature in the storage tank does not fall 40 \({}^{\circ}\)C at 8:00 and 22:00 by heat supply from SC and the HP as can be seen from Figure 9a,b. It can be seen from Figure 9c, the deviation from bandwidth of power flow is improved in comparison with case 1 however, it can be observed that the deviation from bandwidth of power flow exist at around 17:00 a little. Additionally, the power flow exist in the vicinity of the bandwidth limit in the daytime. Figure 8: Simulation results without considering re-forecast, re-plan and uncertainties on a fair day (Case 1). The simulation result in the case 3 is depicted in Figure 10. This figure shows that result which the scheduling obtained by the optimization with considering re-forecast and re-plan except for uncertainties, was operated for the real PV output. It can be seen that the heat demand is satisfied as shown in Figure 10a,b as well as case 1 and case 2. It can be seen from Figure 10c, the deviation from bandwidth of power flow is improved in comparison with case 1 however, in this case, it can be observed that the deviation from bandwidth of power flow partially still exist at around 8:00\(\sim\)10:00 a little. The simulation result in the case 4 is shown in Figure 11. This figure shows that result which the scheduling obtained by the optimization with considering uncertainties, re-forecast and re-plan, was operated for the real PV output.