## 2 Methods  
This section begins with a description of the micro-CHP system, the household, the energy demand profiles, the four rule-based EMSs against which the optimal EMS is compared, the scenario characterization, and the economic performance index. This description is brief since its content is addressed in detail in [PERSON] et al. [15]. The micro-CHP system is shown in Figure 1. Its main characteristics are listed in Table 2. A techno-economic model of that system was developed and presented in [PERSON] et al. [15], Section 2.2. The simulations in the current paper were performed with that model. Although the model does not incorporate low-level phenomena such as air and hydrogen pressures and flow rates, or fuel cell humidity, it does include all the physical phenomena considered relevant in the literature on PEMFC-based micro-CHP systems, such as fuel cell degradation, auxiliary energy losses, heat losses in the TES, and varying electrical efficiency as a function of operating point, among others. The complete list is shown in Table 1, second block. Among the modeled phenomena, the four mentioned are of particular importance. If these four phenomena are not taken into account, the validity of the results is uncertain. For a discussion of the importance of incorporating these four phenomena into the model, see [PERSON] et al. [15], Section 2.1. The characteristics of the house served by the micro-CHP system are shown in Table 3. The annual energy demand profiles of the house used in the simulations are of three types: (1) heat demand for heating, (2) heat demand for DHW (domestic hot water), and (3) electricity demand. The profiles were generated according to the VDI Guideline 4655 [28] standard. They are annual profiles and have a temporal resolution of one minute. For a detailed description, see [PERSON] et al. [15], Sections 3.2, 5.2, and 5.3. These profiles satisfy three requirements highlighted in the literature, namely, (1) they have a sufficiently high temporal resolution, (2) they are annual profiles, and (3) they are representative of the existing diversity in the case study (Europe). For a discussion of the importance of using profiles that satisfy these three requirements, see [PERSON] et al. [15], Section 3.1. The assumptions and the limitations of the energy demand profiles (heating, DHW, and  
Figure 1: Micro-CHP system [15]. electricity) used in the simulations are described in the VDI Guideline 4655 [28] and in [PERSON] et al. [15]. The characteristics of the demand profiles used in this study are compared with those of profiles used in other works in Table 1, fourth block. The simulation approach, in Table 1, fourth block, describes the way in which the simulations are performed. Sample day profiles means that a few days, representative of each season, are simulated and the annual results are calculated from the results obtained with those days, given an estimate of the number of days of each type. Complete annual profiles means that the simulations performed are annual. Methodologically, it is not the same to simulate with a few typical days and then estimate the annual economic savings as it is to simulate with annual demand profiles. No one has yet demonstrated that the former procedure provides the same results as the latter. For that reason, and because the second procedure is more realistic, it was preferred. Using demand profiles with a resolution of 1 min and simulating full years implied a high computational load. The 46 simulations took about 6 months, using 7 desktop computers. The four rule-based EMSs with respect to which the optimal EMS is compared are (1) heat-led strategy (EMS_H), (2) electricity-led strategy (EMS_E), (3) electricity-led-switch-off-in-summer strategy (EMS_ES), and (4) heat-and-electricity-led strategy (EMS_HE). For a detailed description, see [PERSON] et al. [15], Section 4. In the same study, it was shown that the four EMSs considered are relevant, because each of them proved to be the best in a considerable number of scenarios.