## 3 Results
### Investigation of the Behavior of the Optimal EMS  
The similarity of the savings achieved by the optimal EMS and the best rule-based EMS in each scenario could indicate a similarity in their behaviors. To investigate this hypothesis, the signal \(Pe_{SYS_{k}(bRE)}\) (the best rule-based EMS) was compared with the signal \(Pe_{SYS_{k}(O)}\) (the optimal EMS). Additionally, the indicator \(\Phi\) was calculated, which is the average absolute difference in percentage with respect to the stack nominal power (\(Pe_{SYS_{k}}\)), Equation (35). S is the number of samples taken to calculate the indicator; when considering a whole year, S = 365 days \(\times\) 1440 min/day (525,600 samples), and if the indicator is evaluated for one day, then S = 1440 samples. A value of \(\Phi=0\%\) would indicate that the signals are identical, while a value of \(\Phi=100\%\) would indicate a maximum difference between them within the possible range (0-0.75 kW). The values of \(\Phi\) are listed in Table 4.  
\[\Phi=\frac{\frac{1}{S}\sum_{k=1}^{S}\Bigl{|}Pe_{SYS_{k}(bRE)}-Pe_{SYS_{k}(O)} \Bigr{|}}{Pe_{SYS_{k}}}\times 100 \tag{35}\]  
Figure 5: Economic performance of the optimal EMS compared to those achieved by the rule-based EMSs, scenarios 45 and 46. Effect of a change in climate zone. Figure 6: Histogram of \(\Delta\). \(\Phi\) is in the range of 0.7-25.1%, with an average value of 8.5%. In 35 out of 46 scenarios (76%), \(\Phi\leq\) 10.5%. These numbers confirm the hypothesis posed at the beginning of this section; indeed, they show that the strategy followed by the optimal EMS in each of the scenarios is (globally, i.e., when considering the entire year) similar to the strategy of the best rule-based EMS. Now, the values of \(\Phi\) in Table 4 do not provide any information about how the optimal EMS behaves locally, that is when considering a time window of hours. To obtain a more precise view of the (local) behavior of the optimal EMS and its similarity to the behavior of the best rule-based EMS, the signals from the 46 simulations were graphically represented, compared, and analyzed. Figures 7-9 show three examples taken from this analysis. The signals in Figure 7 belong to the simulation of scenario 3. On the first day, the EMS_O does almost the same as the best rule-based EMS (EMS_ES), namely, it follows the electricity demand. On the second and third days, the behavior of EMS_O is different from that of EMS_ES, but it either follows the electricity demand or turns off the micro-CHP system. Figure 8 shows the signals from scenario 21. In this scenario, the best rule-based EMS is EMS_HE. Here, the behavior of EMS_O is different. It does not follow the electricity demand, nor the heat demand, nor the greater of the two: it sets the stack to maximum power. Finally, Figure 9 shows the signals corresponding to scenario 20. Here, too, the best rule-based EMS is EMS_HE. On the first day, the behavior of EMS_O is similar to that of EMS_HE, although not exactly the same. The same occurs on the third day: EMS_O does something similar to what EMS_HE does (following the electricity demand, since there is no heat demand), but not exactly the same. In this last case, the difference lies in the minimum value to which the stack is set. Although its behavior on these two days is different, it shows a strong similarity to that of the best rule-based EMS, with \(\Phi\) values of 5.9% and 6.9% for the first and third days, respectively. An additional example of similar but not identical behavior to that of the best rule-based EMS is shown in Figure 10.  
The complete analysis of the annual signals from the simulations in the 46 scenarios reveals that the optimal EMS does one of these five things (list of identified behaviors):  
1. Following the electricity demand. 2. Following the greater of the demands, electricity and heat. 3. Turning off the micro-CHP system. 4. Setting the micro-CHP system to maximum power. 5. Other behaviors that are similar but not identical to 1 or 2. Figure 10: Behavior of the optimal EMS. Additional example: Scenario 28.