Information and communication technology (ICT) and the technology of coupling points including power-to-gas (PtG), power-to-heat (PtH) and combined heat and power (CHP) reshape future energy systems fundamentally. To study the resulting multimodal smart energy system, a proposed method is to separate the behavior of the component layer from the control layer. The component layer includes pipelines, power-lines, generators, loads, coupling points and generally all components through which energy flows. In the work at hand, a model is presented to analyze the operational behavior of the component layer. The modeling problem is formulated as state and phase transition functions, which present the external commands and internal dynamics of system. Phase transition functions are approximated by ordinary differential equations, which are solved with integral methods. State transition functions are nonlinear algebraic functions, which are solved numerically and iteratively with a modified Newton-Raphson method. In a proof-of-concept case study, a scenario shows the expected multi-sector effects based on evaluated models.