## 4 Discussion
### Behavior of the Optimal EMS  
The \"other behaviors\" are always very similar to behaviors 1 (following electricity demand) or 2 (following the greater of the electricity and heat demands) from the list of identified behaviors. This is inferred, on the one hand, from the analysis of the signals and the small values of \(\Phi\) that result when these behaviors are compared locally (see, for example, Figures 9 and 10, and the \(\Phi\) values indicated in the captions of those figures) and, on the other hand, from the small values of \(\Psi\). Furthermore, note that the \"other behaviors\" are not necessary to achieve near-optimal savings. Indeed, none of the rule-based EMSs operate according to these other behaviors, and yet they achieve savings very close to those of the optimal EMS (\(\Delta\leq 2\) pp). See, for example, the results in Figure 3.  
If, based on these observations, the \"other behaviors\" are disregarded, the results presented in Section 3.2 show that the behavior of the optimal EMS can be reduced to _four fundamental optimal operating patterns_: (1) follow electricity, (2) follow electricity and heat, (3) turn off the system, and (4) operate at maximum power. This result partially agrees with the findings of [PERSON] et al. (1977) for an SOFC-based micro-CHP system. In their study, patterns (3) and (4) were not identified. The reason for this is presumably that they included a minimum load constraint (relevant for SOFC) and a limit on the amount of heat that could be dumped. The optimal operating pattern strongly depends on the FiT. Compare, for example, scenarios 7 and 21 in Figure 3. This result exactly matches the findings of [PERSON] et al. (1977) (there, FiT is called electricity buyback rate). The optimal operating pattern also changes depending on the stack degradation level. Compare, for example, the following scenario changes due to changes in the degradation level, Figure 3: \(4\to 25,5\to 26,11\to 32,12\to 33,16\to 37,17\to 38,18\to 39\). This relationship between the optimal operating pattern and the level of degradation was not studied by [PERSON] et al. (1977). The optimal operating pattern is also sensitive to fuel prices (spark gap). This is clearly seen in Figure 3 (FiT25, BOL). This result contradicts what was reported by [PERSON] et al. [17], where it was concluded that prices (import energy prices) have little effect on the optimal operating pattern. The reason for this discrepancy likely lies in the difference in the range of spark gap considered: 3.15-4.53 (1.39) in [PERSON] et al. [17] versus 2.85-5.77 (2.92) in this study. The range is more than twice as large in the present study. Their smaller spark gap range is due to their study being limited to the United Kingdom, whereas ours considers the European market, where price variability is greater. In the studied framework (Europe) and under the assumed methodological assumptions, any of the four identified fundamental operating patterns can be optimal (or near-optimal), and only those four can be optimal (setting aside the \"other behaviors\"). This being the case, the problem of managing PEMFC-based micro-CHP systems comes down to this: choosing the most cost-effective of these four patterns for the given scenario. For this task, a key question is what time window to use in characterizing the scenario. From the preliminary study conducted to determine the prediction horizon of the optimal EMS (Section 2.2), as well as from the running phase of the simulations performed to obtain the savings of the optimal EMS in the 46 scenarios, it is inferred that 8 h (HP 480 samples) is an adequate time window for this purpose. Indeed, the fact that the EMS_O does not achieve greater savings with longer prediction horizons proves that the information beyond this time window is irrelevant for selecting the optimal operating pattern. An optimization horizon of 8 h is preferable to one day, which is the value chosen in the research conducted to date [17; 18; 19; 20; 21] (see Table 1, third block).