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• Design of a novel SOFC-based CCHP system. • Incorporation of solar panels, heat pump, battery, EV charging and grid connection. • New MOPSO-GRA control algorithm provides objective multi-criteria optimization of system. • Simulation of UK residential conditions shows efficiency, emission & cost benefits. In the quest to achieve home comfort with the highest possible efficiency, there is an increasing interest in combined cooling, heating and power (CCHP) systems. These can be fuelled by natural gas and potentially by hydrogen enriched natural gas and ultimately by hydrogen. The optimised designs largely depend on the energy dispatch algorithms that take into account aspects of economic and environmental impacts as well as system efficiency. This paper details a new algorithm to optimise the operation of a novel hybrid solid oxide fuel cell (SOFC)-solar hybrid CCHP residential system. The proposed algorithm is based on the multi-objective particle swarm optimization (MOPSO) and the grey relationship analysis (GRA) (named as MOPSO-GRA) with the capability of resolving the objective energy dispatch issues within the system by effectively avoiding local optimum problem. More specifically, the grey incidences are first integrated into MOPSO to analyse the degree of closeness between non-ideal solutions and the ideal solution. Then, the relationship of degree is introduced to give objective energy dispatch in order to maximise the efficiency of energy utilization while minimising the system capital cost, operating costs, maintenance costs, fuel costs and emissions. Finally, the new algorithm is validated on the proposed new design of CCHP system. Ten cases are studied to evaluate the technical, economic and environmental performance of the MOPSO-GRA algorithm when being applied to an SOFC-based CCHP system under both the grid-connected and the island modes. A comparison is made with the conventional MOPSO method and system structure, and the impact of a plug-in EV is also evaluated. Based on a detailed cost and emissions analysis, the results indicate the environmental and economic advantages, in addition to the higher efficiency of the proposed methodology and system structure. The impact of these results and observations leads to the promotion of intelligent FC-based multi-energy system technologies for residential use. [ABSTRACT FROM AUTHOR]