## 4 Result Analysis  
By considering all existing ToU rates by the Portuguese electricity retailer for the residential sector, the consumed energy cost of the AC unit can be calculated once the performance regarding the consumption of energy throughout the whole week is assessed.  
As stated throughout the paper, the performance of the ON/OFF, PID and MPC control methods of the air conditioning (AC) of the room is simulated and later compared. As expected, as these three control methods are rather different, the behavior of the temperature of the room will be somewhat different as well. The behavior of the room's temperature for all three control options during the entire week can be observed in Figures 9-11.  
By comparing Figures 12-14 for the remaining days, it can be seen that the costs appear to be similar. However, on 25 July, the PID control option turns out to be the most economical one.  
In Figure 15, the complete results of the entire simulation of ON/OFF, PID and MPC control methods can be observed, under all the six options of ToU rates. By cautiously analyzing Figure 15, it can be inferred that the MPC option has shown the best performance among the considered control methods. By analyzing this figure, it can also be concluded that tariff option that guarantees the lowest cost is Option E--a three tier ToU rate that gives lower prices during weekends. By continuing to examine the obtained results shown in Table 1, it can also be noticed that the ON/OFF happens to be the control method with the highest associated cost between the three control options. This observation can also be confirmed in Figure 15. This figure not only confirms that the MPC is the best option for the consumer but also confirms that the ONN/OF is by far the priciest one, with PID being close to the MPC. By quantifying exactly how much can be save by opting for the MPC, the results show with this control method it is possible to save 9.2% when compared to the conventional ON/OFF, while with the PID it is possible to save 7.4% when also compared with ON/OFF. Even though the PID control option shows better performance regarding the energy consumption during a few days of the week, as can be seen in Figure 16, the results show that the MPC performs better when compared to the PID by saving 1.8% in cost. This occurs because the MPC considers the price signal and during periods of the day when the cost is lower. Thus, in the cases, the MPC allows the consumption of more energy without compromising the overall cost.  
The results have shown that the option that allowed a price signal for the 24 h of the optimization horizon released by the retailer--Option F was still the second best tariff option and was surpassed only by tariff Option E since this option allowed much lower prices during the weekend. However, by selecting ToU Option F, the results show that the consumer spends just 5.2% more when compared with Option E--the optimal solution for the customer. By further analyzing Figure 15, it can be observed that the most expensive option happens to be Option B which is a two tier ToU rate that never changes throughout the whole summer, being a working day or not. To emphasize how much the consumer can save by selecting the best AC unit control option and ToU rate, the results show that up to 14.2% can be saved by electing ToUOption E rather than Option B, the costliest one.  
Figure 14: The consumed energy cost in cents by the MPC of the controlled AC unit by employing the 6 options of ToU rates.