## 4 Discussion
### Economic Performance of the Optimal EMS  
For a given scenario, the savings achieved by the optimal EMS are small compared to the best rule-based EMS (\(\Delta\leq 2\) pp). This result is consistent with the data reported by [PERSON] et al. [18] (1 pp, scenario with a fixed tariff structure). The savings reported by [PERSON] et al. [17] (4 pp, case 2 kWe SOFC) is double that found here. This discrepancy could be due to our model taking into account certain physical phenomena that are neglected there, such as heat losses in the TES or the startup and shutdown costs (see Table 1, second block). Another possible explanation is that neither EMS_H nor EMS_E (with respect to which they calculate their figure) is the best of the rule-based EMS, but rather EMS_HE, which is not included in their comparison. [PERSON] et al. [20] report values significantly higher than those obtained in this study, namely, 15-22 pp for the electricity trading scenario, case FiT 100% (they do not provide their results in pp with respect to the operating cost of the reference system, the range provided is an estimate). The reason for this is most likely that their comparison did not include EMS_HE, which is indeed the best when FiT values are high, as demonstrated by the results in Figure 3. This highlights, as mentioned in the Introduction (Section 1), the great importance of including all four relevant rule-based EMS in the comparison. Only in this way can the economic performance of the optimal EMS be correctly evaluated in relation to the rule-based EMSs and a conclusive result be reached. The reason that the optimal EMS achieves such a small savings compared to the best rule-based EMS likely lies in the fact that the energy management of micro-CHP systems has few degrees of freedom, especially when compared to other systems like hybrid renewable energy systems (HRESs), which typically have multiple generators and energy storage units. This result, namely, the small benefit that the optimal EMS achieves compared to the best rule-based EMS in each scenario, might lead one to think that an optimal EMS is not worth it. This is indeed the opinion expressed in [12; 17; 18]. However, this conclusion would be hasty. The optimal EMS has a major advantage over the rule-based EMSs, namely, it is capable of adapting to changes of scenario. [PERSON] et al. [15] demonstrated that changes of scenario are frequent in micro-CHP (see Section 6.3, fourth paragraph) and that adapting the energy management strategy to the scenario can generate annual savings of up to 14.5 pp. In absolute terms, assuming an annual energy bill of EUR 2500 with the reference system, this translates to EUR 362. Over the lifetime of the system, therefore, this adaptability results in considerable economic savings. Thus, it is not generally the case, as stated in [PERSON] et al. (1977), that there is little economic benefit in operating the micro-CHP system with an optimal EMS, in comparison with rule-based EMSs. This is only true if a fixed scenario is assumed (as is done in that study), which is an unrealistic assumption for micro-CHP systems today. Similarly, [PERSON] et al. (1977), based on the results of [PERSON] et al. (1977), assumed in their study that the heat-and-electricity-led strategy produces economic savings close to those of an optimal EMS. Again, this is only true if a specific and fixed scenario is considered, not when there are scenario changes. For example, see the scenario change from \(16\to 2\) in Figure 3. [PERSON]'s assumption in (1977) holds true in scenario 16 but is false in scenario 2. In general, the importance of scenario changes has been overlooked in the studies conducted to date. Only when these are taken into account does the superiority of the optimal EMS over rule-based EMSs become evident. However, the optimal EMS also has significant drawbacks: it is complex, sensitive to errors in the predictions and the model, and has a high computational cost.