Nearly all types of energy systems (such as power systems, natural gas supply systems, fuel supply systems, and so forth) are going through a major transition from centralised, top-down structures to distributed, clean energy approaches in order to address the concerns regarding climate change, air quality, depletion of natural resources, and energy security, whilst also enabling the supply of energy to communities in line with the goals of sustainable development. Accordingly, the establishment of the concept of sustainable, decentralised, multi-carrier energy systems, together with the declining costs of renewable energy technologies, has proposed changes in the energy industry towards the development of integrated energy systems. Notwithstanding the potential benefits, the optimal capacity planning of these systems with multiple energy carriers (such as electricity, heat, hydrogen, and biogas) is exceedingly complex due to the concurrent goals and interrelated constraints that must be satisfied, as well as the heavily context-dependent nature of such schemes. This paper puts forward an innovative optimal capacity planning method for a cutting-edge, stand-alone multiple energy carrier micro-grid (MECM) serving the electricity, hot water, and transportation fuel demands of remote communities. The proposed MECM system is equipped with wind turbines, a hydrogen sub-system (including an electrolyser, a hydrogen reservoir, and a fuel cell), a hybrid super-capacitor/battery energy storage system, a hot water storage tank, a heat exchanger, an inline electric heater, a hydrogen refuelling station, and some power converters. A numerical case study for the optimal capacity planning of the suggested MECM configuration, to be realised on Stewart Island, New Zealand, is presented to evaluate the effectiveness of the proposed optimisation method.