## 3 Results and Discussion
### Configuration Analysis  
Figure 6 illustrates the seasonal energy efficiency of the system (\(\rm{\eta_{S}}\)) and the total number of on-off cycles performed by the heat pump and the biomass boiler as functions of the building peak load ratio (\(\beta\)) across all configurations. Figure 6a shows that as \(\beta\) increases, the \(\rm{\eta_{S}}\) values for all configurations generally rise, albeit not uniformly [7]. Configurations 1 and 2 exhibit very similar trends, peaking at \(\beta=0.33\) and \(\beta=0.66\), with slight dips at \(\beta=0.5\). Configuration 3 has the lowest \(\rm{\eta_{S}}\) values for most of the range, while configuration 4 follows a pattern between configurations 1 and 3, with less pronounced peaks and valleys. Overall, the \(\rm{\eta_{S}}\) value for the serial configurations (1 and 2) is better than for the parallel configurations (3 and 4). Notably, the best performance is achieved with a 8 kW heat pump in the serial system, whereas in the parallel system, the 4 kW heat pump performs better. Figure 5: Thermal energy production delivered to the building for various hybrid heat pump–boiler configurations. The frequency of biomass boiler cycling is shown in Figure 6b. For configuration 4, the on-off cycles of the boiler increase as the heat pump capacity rises, while the other configurations exhibit a decreasing pattern. Although the highest values occur for the monovalent system (with only a boiler) compared to configurations 1, 2, and 3, configuration 4 reaches its peak at \(\beta=0.66\). Figure 6c likely depicts the frequency of heat pump cycling (on-off operations) for various value of \(\beta\). As \(\beta\) increases, the on-off cycles generally rise across all configurations. A dramatic increase is observed for the monovalent system, where the 12 kW heat pump  
Figure 6: Comparison of HHP characteristics for different configurations as functions of the building peak load ratio: (**a**) seasonal energy efficiency of the system, (**b**) boiler on-off cycles, and (**c**) heat pump on-off cycles. cycles on and off much more frequently to meet the demand. Additionally, configuration 1 exhibits the lowest on-off cycles for most of the range, especially diverging from the other configurations at \(\beta=0.66\). Moreover, the hybrid configuration reduces the number of on-off cycles performed by the heat pump. This reduction is due to the smaller size of the heat pump relative to the design heat load. Indeed, with undersized heat pumps, on-off cycling must be used to adapt the unit's heating capacity to the building's heat load only during the milder part of the heating season. When undersized devices are used in HHP systems, the energy losses associated with on-off cycles are reduced, thereby improving the energy performance of the heat pump. It is worth mentioning that the number of defrost cycles performed by the heat pump does not change, as the control strategy for activating the defrosting process depends on outdoor conditions and the HP operation. The parameters of this algorithm remain consistent for each case. The ratio of the greenhouse gas emissions to the useful energy output of the system (EWI) and the operation cost of heating and cooling of the building are indicated in Figure 7.  
The EWI considers the greenhouse gas emissions caused by the resource consumption of the different configurations when meeting the building's demand. As we expected, the lowest CO2 emission was related to using the biomass boiler as a heating system (EWI = 0.05) and the emissions increased more than four times when monovalent heating systems based on the heat pump were used. Generally, the EWI increases when the heat pump's power rises from 4 kW to 8 kW due to the reduced contribution of the biomass boiler to heating. Furthermore, the EWI remains almost constant across all configurations, with no meaningful differences observed. According to the operational cost data, the operational cost of the HHP system is always lower than that of the monovalent system when a boiler is used as the heating system.