Flexible clustering of substations for accurate and rapid hybrid simulation of district heating

Abstract

District Heating Networks (DHNs) are crucial to decarbonizing the heat supply sector, with the evolution toward 4th and 5th generation systems offering significant potential for efficiency. However, the increasing complexity of these modern systems makes high-fidelity dynamic thermo-hydraulic simulation computationally intensive, particularly for large-scale networks. These simulations are essential for key applications such as thermal loss prediction, supply temperature optimization, operational planning and during the sizing phase of the network. Recent research has utilized Machine Learning (ML)-based surrogate models to replace substation clusters, reducing spatial complexity and accelerating simulations. Yet, the efficacy of this spatial reduction is highly sensitive to the clusters definition. Poorly selected clusters degrade the surrogate models accuracy and undermine the simulation performance. This paper proposes a flexible, task-driven graph clustering methodology specifically designed for ML-based spatial reduction. We introduce physics-informed distance metrics that encode the primary drivers of ML surrogate model errors. These distance metrics are leveraged within a hierarchical agglomerative clustering framework. The methodology is evaluated across 16 DHNs with diverse topological and thermal characteristics. Our results reveal a clear, generalizable trade-off between simulation accuracy and computational time reduction, allowing the integration of user-preferences. On an independent validation DHN, a high physical accuracy preference yielded a deviation of 6.45 MWh in total thermal energy production estimation (3.76% of total thermal losses within the network), albeit with modest computational gains. Expressing the error relative to thermal losses, rather than total production, provides a more meaningful measure of the spatial reduction’s impact on the key operational objectives. Conversely, a high spatial reduction preference reduced the network from 123 to 5 remaining physical nodes and achieved a 91% decrease in computational time, at the cost of a 45.24 MWh deviation in total thermal energy production estimation, representing 26.37% error relative to thermal losses. These findings demonstrate that the proposed clustering framework provides a robust and flexible tool to calibrate the balance between physical fidelity of the simulation and computational speed across varying DHN generations.