Mostafa, MarwanMarwanMostafaWenser, DanielDanielWenserTeimourzadeh Baboli, PayamPayamTeimourzadeh BaboliBecker, ChristianChristianBecker2026-01-052026-01-052025-10-20IEEE PES Innovative Smart Grid Technologies Conference Europe, ISGT Europe 2025https://hdl.handle.net/11420/60498The increasing complexity of energy systems due to sector coupling and decarbonization calls for unified modeling frameworks that capture the physical and structural interactions between electricity, gas, and heat networks. This paper presents a graph-based modeling approach for multi-energy systems (MES), where each domain is represented as a layer in a multi-layer graph, and coupling technologies are modeled as inter-layer edges via a dedicated coupling layer. A steady-state solver based on a block-structured Newton-Raphson (NR) method is developed to jointly compute flows and state variables across all carriers. The proposed model is tested and validated on a realistic case study based on data from a German distribution network. The results demonstrate convergence, numerical accuracy, and consistent domain interaction, and demonstrate the method’s applicability for system-wide analysis and its potential as a foundation for future optimizations in integrated energy systems.enDistribution SystemUnified ModelEnergy SystemPower GridDistribution NetworkNumerical AccuracyNewton-Raphson MethodGas NetworkMass FlowJacobian MatrixHeating SystemModular StructureMass Flow RateElectric HeatingBlock StructureFlow ProblemIntegral OperatorEnergy CarrierSteady-state ModelSteady-state EquationDistrict Heating Combined Heat And PowerEstablished ToolElectrical LoadSteady-state FlowPower Flow EquationsEnergy Balance EquationSupply TemperatureTechnology::600: TechnologyConference Paper10.1109/isgteurope64741.2025.11305330Conference Paper