A transfer function method for thermal transient modeling in district heating networks: Optimizing accuracy and computational efficiency

District heating networks are essential for enabling multi-energy synergies in integrated energy systems (IES), yet their dynamic thermal behavior is often oversimplified in existing models, thereby constraining dispatch optimization. To address this limitation, this study introduces a novel frequency-domain transfer function (TF) methodology for efficient and high-fidelity thermal transient modeling. The approach begins with a one-dimensional advection–diffusion equation derived from turbulence theory, which is reformulated via Laplace transformation into a frequency-domain TF representation. From this formulation, analytical expressions for the thermal diffusion coefficient (α) and heat loss coefficient (γ) are obtained. These coefficients, calibrated through computational fluid dynamics simulations and numerical experiments to reflect actual pipeline conditions, support a validated single-pipe TF model that accurately captures key transient characteristics, including time delay, diffusion, and heat loss. The framework is then generalized to pipeline networks through a modular branch-based superposition strategy that avoids solving large coupled systems while preserving physical accuracy, thereby enhancing both computational efficiency and tractability. Case studies based on both a real single-pipe experiment and a practical district heating network with operational measurements benchmark the TF method against the nodal method and a third-order finite difference scheme, showing that it reduces the root-mean-square error (RMSE) by more than 86%, limits maximum deviation to within 2.3 °C, and achieves nearly three orders of magnitude in speed improvement. These findings highlight the method's strong potential for integration into large-scale IES optimization.