## 2 Methodology
### Key Performance Indicators  
To assess the seasonal efficiency and energy performance of hybrid configurations during a year, where the various heaters (biomass boilers and heat pumps) are powered by different energy sources (electric energy (EE) and biomass), the EU standards on energy efficiency for heating and cooling systems were first calculated. The system's seasonal efficiency for heating (\(\eta_{\text{s}}\)) is defined in Equation (1) as the ratio between the total thermal energy supplied by the heating system to the building (E\({}_{\text{th,tot}}\)) and the total primary energy consumption of the system (E\({}_{\text{p,tot}}\)):  
\[\eta_{\text{s}}=\frac{\text{E}_{\text{th,tot}}}{\text{E}_{\text{p,tot}}} \tag{1}\]  
To account for E\({}_{\text{p,tot}}\), the Primary Energy Factors (\(PEF_{\text{d}}\), \(PEF_{b}\)) for electricity and biomass for Spain have been taken [35]. Additional HP performance indicators can be  
Figure 4: Control algorithm implemented in TRNSYS for the AWHP (**a**) and the hybrid system configurations (**b**). associated for HHP systems. The SCOPnet is the net seasonal coefficient of performance of the HP operating in monovalent mode:  
\[\text{SCOPnet}=\frac{\text{E}_{\text{th,HP}}}{\text{E}_{\text{HP,ee}}} \tag{2}\]  
According to European standard EN 14825 [36], the adequate assessment of the efficiency in hybrid systems is the SCOPon for hybrid heating systems, which is closely related to \(\text{\ }\text{\eta}_{\text{s}}\) and can be calculated as follows:  
\[\text{SCOP}_{\text{on}}=\frac{\sum_{j=1}^{n}\text{h}_{j}\times\text{E}_{ \text{th,tot}}\left(\text{T}_{j}\right)}{\sum_{j=1}^{n}\text{h}_{j}\times \left[\frac{\text{E}_{\text{th,HP}}\left(\text{T}_{j}\right)-\text{E}_{\text{th, B}}\left(\text{T}_{j}\right)}{\text{COP}_{\text{HP}}\left(\text{T}_{j} \right)}+\frac{\text{E}_{\text{th, B}}\left(\text{T}_{j}\right)}{\text{\eta}_{ \text{B}}\times\text{CC}}\right]} \tag{3}\]  
where hj is every hourly period simulated in TRNSYS at temperature Tj; Eth,B is the heating supplied at temperature Tj by the boiler (kW); COPHP is the COP of the HP at every Tj; \(\text{\eta}_{\text{B}}\) is the seasonal heating efficiency of the boiler in active mode, in %; and CC is the conversion coefficient from primary to final energy, equal to 2.5 for EU. The Seasonal Energy Efficiency Ratio (SEER) for cooling is calculated by the following:  
\[\text{SEER}=\frac{\text{E}_{\text{HP,C}}}{\text{E}_{\text{HP,C,ee}}} \tag{4}\]  
where EHP,C,ee and EHP,C are the electric energy consumptions of the heat pump and the energy delivered by the heat pump, respectively. The Annual Performance Factor (APF), which describes the annual energy performance of the system by considering both heating and cooling behavior, is defined as follows:  
\[\text{APF}=\frac{\text{E}_{\text{th,HP}}\ +\ \text{E}_{\text{HP,C}}\ +\ \text{E}_{\text{th, B}}}{\text{E}_{\text{HP,th,ee}}\ +\ \text{E}_{\text{HP,ee}}\ +\ \text{E}_{\text{B,input}}} \tag{5}\]  
where EHP,th,ee and EHP,ce are the annual electricity consumptions for heating and cooling; and EB,input is the required boiler energy input. This accounts for the conversion from secondary to final energy, which is somewhat analogous to SCOPon. However, we do not apply a conversion factor for primary energy in the biomass boiler equivalent to electricity, and we also consider the cooling period. When the boiler is used extensively, the Annual Performance Factor (APF) is lower than SCOPon because its usage is penalized [11]. Regarding the CO2 emissions, we used as environmental KPI the Equivalent Warming Impact on the System (EWI), which evaluates the environmental impact of the various fuels used in the system throughout its life cycle [37]. For each fuel, the GWP or equivalent quantity of carbon dioxide per quantity of final energy (kgCO2/kWhFE) for a time frame of 100 years, coming from the Ecoinvent Data Base (2013) [38], widely used in LCA, was taken.