Tensor-based modeling framework for district heating pipes

Abstract

District heating network simulation faces a fundamental computational challenge: traditional nonlinear models become intractable at large scales due to the curse of dimensionality, while linear models cannot accurately represent the nonlinear dynamics essential for district heating systems. Tensor-based methods have demonstrated effectiveness in modeling heating, ventilation, and air conditioning (HVAC) as well as local heating systems by providing a scalable compromise between accuracy and computational efficiency, yet their application to district heating networks is first described in this paper. This work applies multilinear time-invariant (MTI) modeling using a tensor-based framework for scalable representations of district heating networks.Tensor and multilinear functions efficiently represent the governing equations and their nonlinear relationships, especially the quadratic pressure-loss relationships defined by the Darcy-Weisbach equation and nonlinear friction factors across flow regimes without causing an exponential growth in model complexity. Binary variables model discontinuous transitions between laminar and turbulent flow, maintaining computational tractability while preserving physical accuracy. The tensor structure inherently avoids the curse of dimensionality that constrains conventional approaches by factorization. Benchmarking against established models on a small network shows minimal deviations alongside considerable memory reductions, demonstrating the potential of tensor-based methods for efficient simulation and optimization of large-scale district heating networks and supporting the integration of renewable energy sources and advanced control strategies essential for modern energy-efficient systems.