Various researches are being conducted on how to incorporate multi-energy systems into society, which is one of the efforts to transform what energy systems are. In optimizing a multi-energy system, it is important not only to pursue efficiency through a complicated configuration but also to design the simplest possible configuration with an awareness of cost, and it is also important to design various configuration candidates systematically rather than heuristically. Therefore, we aim to exhaustively search for cycle candidates by mathematically defining the cycle expression format for deriving the optimum cycle configuration according to the heat source conditions. However, at present, the required representation format is organized insufficiently or is not defined, and these are the reasons why heuristic consideration, examination, and codification are still required for the derivation of configuration candidates and the configuration of simulations. In this paper, we newly proposed and modified the representation forms, and we distinguished the configuration candidates, which have not been distinguished in previous studies, from the viewpoint of complexity for the first time.
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