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An innovative modelling approach for the design of biomass-based, solar-assisted combined cooling, heating, and power (CCHP) and heat pump (HP) systems for various climate scenarios is proposed in this work. The modelling approach is comprised of three sub-models (a demand sub-model, a supply sub-model, an economic sub-model) allowing for cost-optimal sizing of the system components based on net present cost (NPC). Subsequently a transient optimization model has been developed, which computes the technical and economic performance for each component size and for each ambient temperature of the different climate scenarios. Additionally, the model provides data on energy efficiency, exergy efficiency, and CO2-emissions of a given CCHP/HP system. The model has then been employed in a case study in order to analyse the performance of a CCHP/HP system for a tourist, museum, and guest accommodation structure located at the Montjuic castle in Barcelona, Spain. The results show that the smallest simulated biomass-based CCHP system using a 25 kWe syngas-fuelled engine would reduce lifetime costs by 7% compared to an only-HP system while operating with a high total energy efficiency of over 60%. The combined CCHP/HP system would operate with an exergy efficiency of 18%. However, larger CCHP systems cannot offset the much higher capital costs despite increasing electricity sales. The findings also reveal that for the high climate change scenario the overall project costs drop by up to 2.5%, however the effects have little impact on the optimal CCHP/HP system sizing. Even the smallest CCHP system would reduce emissions already by 75% with an increasing trend for larger systems. Although CCHP/HP systems would lead to lower NPC and emissions, the high investment costs and the complexity of the combined system remain considerable obstacles.