## 4 Conclusions  
In this paper, a numerical study on the energy performance of hybrid heat pump systems has been conducted using a series of dynamic simulations with TRNSYS. The hybrid systems investigated are based on an air-to-water heat pump (AWHP), with a biomass boiler considered as a backup device. This type of hybrid installation is specifically designed for isolated homes, where it is highly likely that there is no connection to the grid and no access to the gas distribution networks. In such cases, electricity generation to power the efficient heat pump can be partially supported by photovoltaic (PV) systems, complemented by local biomass resources, which do not necessarily have to be pelletized. To investigate the configuration analysis, two operation systems (series and parallel) have been defined, represented by four different configurations. Firstly, these systems are compared to traditional monovalent configurations (heat pump only or the biomass boiler only) to determine if they improve the system's efficiency while minimizing operational costs and emissions. Secondly, the effect of layout and heat pump size is studied. Then, the effect of cut-off temperature on key parameters of the HHP system was investigated. Finally, defrosting was analyzed in terms of reduction in efficiency and additional cost. The optimum performance of the HHP system, in terms of energy efficiency, operational costs, and emissions, was depicted using a heat map diagram. The major results of the present study are highlighted as follows:  
* In the choice of selecting an HHP or a monovalent system, the adequate configuration is the key to select an HHP as the best choice. According to the integrated efficiency, HHP series operation is consistently the best solution, and even further when a thermostatic valve is used to regulate the water flow between the heat pump and the boiler (i.e., configuration 2). * Regarding the size of the HP in the HHP systems, the optimal performance depends on the configuration: in the serial HHP system, it is achieved with an 8 kW heat pump, while in the parallel system, the 4 kW heat pump outperforms the others. * In all HHP configurations, the on-off cycles for heat pumps increase with the size of the heat pump. In contrast, the on-off cycles for biomass boilers generally decrease, with the exception of configuration 3 whose operation is more affected by the buffer tank. * When examining environmental and economic KPIs, it is found that the HHP system is usually a better option than the monovalent system due to its combination of lower emissions and reduced costs. Among all configurations, configuration 2 is again identified as the optimal choice. * For each heat pump size, the seasonal energy performance improves with a higher cut-off temperature. As expected, this improvement comes from fewer defrost cycles and a shorter seasonal period during which the heat pump operates at a reduced COP because of the low temperatures. * Increasing the cut-off temperature reduces the equivalent warming impact but raises the operational cost. This effect is likely due to the enhanced role of the biomass boiler in the HHP system. * The defrosting effect is more pronounced in terms of efficiency, the number of on-off cycles, and additional costs with lower cut-off temperatures and a higher size of the HP in the HHP system. For future work, it would be valuable to investigate the optimum heat pump size, cut-off temperature, and storage tank capacity, as well as their impact on the performance of the HHP system. Additionally, exploring the use of Phase Change Materials (PCMs) in the storage tank to support heat recovery during defrosting cycles could be an interesting area of study. Conceptualization, methodology, formal analysis, data curation, supervision, project administration, funding acquisition, validation, J.U. ; formal analysis, software, investigation, writing--original draft preparation, M.T.J.