A Graph Theoretical Approach to Modeling of District Energy Networks

Simulation of thermal dynamics in city-scale district energy grids often becomes computationally prohibitive for long simulation runs. Most current model order reduction methods offer limited interpretability with regards to the nonreduced system and are not in general applicable for varying flow rates, multiple producers, or changing flow directions. This article presents a graph perspective on modeling of district energy networks. Based on spectral graph theory, a novel method for model order reduction of district energy systems is proposed. The method approximates the solution of an optimization problem, minimizing the coefficients of the local truncation error for the advection equation. Furthermore, a method for calculating the intracluster temperature distribution is presented. It is shown that the method can be used to reduce the thermal dynamic model of a city-scale energy grid, resulting in a coarser temporal and spatial resolution, with a significant decrease in simulation time. The relative root-mean-square error (rRMSE) was 2.5% for the temperature in the evaluation scenario, comparing the reduced-order system with the nonreduced system at the instances of the coarser time step.