## 2 Methods
For this reason, it is important that the optimal EMS be compared with all four, otherwise the picture would be incomplete and the question of how much economic benefit an optimal EMS provides compared to rule-based EMSs could not be answered definitively. The comparison of the optimal EMS with the rule-based EMSs was performed in 46 different scenarios. A scenario is defined by five parameters: (1) spark gap, (2) FiT (feed-in tariff), (3) D (degradation), (4) CZ (climate zone), and (5) HPR (demand side heat to power \begin{table}
\begin{tabular}{l l} \hline
**Characteristic** & **Value** \\ \hline Nominal electrical power (BOL) & 0.75 kW \\ Minimum electrical power & 0.25 kW \\ Nominal thermal power (BOL) & 1.07 kW \\ Electrical efficiency (BOL) & 31.3\% (HHV) \\ Thermal efficiency (BOL) & 44.7\% (HHV) \\ Maximum ramp & 0.2 kW/min \\ Startup time & 45 min \\ Natural gas consumption at startup & 1.5 kW \\ Power consumption at startup & 75 W \\ Shutdown time & 5 min \\ Power consumption during shutdown & 50 W \\ Auxiliary boiler nominal thermal power & 26.5 kW \\ Auxiliary boiler efficiency & 93\% \\ Tank volume & 200 L \\ Tank temperature range & 50–70 \({}^{\circ}\)C \\ Tank capacity & 4.572 kWh \\ \hline \end{tabular}
\end{table} 
Table 2: Characteristics of the micro-CHP system [15]. \begin{table}
\begin{tabular}{l l} \hline
**Characteristic** & **Value** \\ \hline Type of building & Single-family house \\ Location & Oberhausen, Germany \\ N\({}^{\circ}\) of occupants & 3 \\ Annual heating demand & 11,000 kWh \\ Annual electricity demand & 5250 kWh \\ Annual DHW demand & 1500 kWh \\ \hline \end{tabular}
\end{table} 
Table 3: Characteristics of the house [15]. ratio). The spark gap is the ratio between the price of electricity and the price of natural gas. In [PERSON] et al. [15], it was shown that the percentage savings that the micro-CHP system achieves with respect to the reference system depends on the spark gap, not on prices. For this reason, the spark gap is used in the characterization of the scenario, instead of prices. The electricity and natural gas prices corresponding to the spark gap values used are those of seven European Union countries during the first half of 2021, namely, France (FR), Italy (IT), Denmark (DK), Austria (AT), Poland (PL), Germany (DE), and Belgium (BE). FiT is the price of the electricity fed into the grid, as a percentage of the electricity price. This parameter can take three values: 0%, 25%, and 50%. D is the stack degradation level. It takes three values: 0% (BOL), 10% (MOL), and 20% (EOL). CZ is the climate of the location of the house. It can take three values: warm (CZw), mild (CZm), and cold (CZc). The climate zone (CZ) determines the annual heating demand and the annual sequence of days. This is described in [PERSON] et al. [15], Sections 5.2 and 5.3. The annual demands corresponding to each CZ are 10,426 kWh (CZw), 13,752 kWh (CZm), and 16,917 kWh (CZc). A representation of the annual sequences of days corresponding to each CZ can be found in [PERSON] et al. [15], Figure 8. The annual heat demand for DHW and the annual electricity demand are 1500 kWh and 5250 kWh, respectively, the same for the three CZs. HPR is the ratio between the annual heat demand and the annual electricity demand. It can take three values: ED low (EDI), ED nominal (EDn), and ED high (EDh). EDn is 5250 kWh. EDI and EDh represent excursions of +20% and \(-\)20%, with respect to EDn. The values of the HPRs associated with each ED can be found in [PERSON] et al. [15], Table 6.  
For a justification of the five parameters chosen for the characterization of the scenario, as well as the values that each of them can take, see [PERSON] et al. [15], Section 5.1. In each of the 46 scenarios, the supply of the energy demand of the house, with the micro-CHP system operated by the optimal EMS, was simulated for one year.