Unified Graph-Theoretic Modeling of Multi-Energy Flows in Distribution Systems

The 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, 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 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.