Scalable Predictive Control for District Heating Networks: A Physics-Guided Koopman Operator Approach

Abstract

This article addresses the control of large-scale district heating networks (DHNs). Traditional nonlinear model predictive control (MPC) suffers from computational intractability due to the nonconvex optimization of complex thermal-hydraulic dynamics. We present scalable predictive control strategies based on the Koopman operator framework, developing a physics-guided methodology to construct meaningful Koopman observables by integrating the network’s graph topology and thermodynamic conservation laws. This ensures that critical nonlinear interactions and energy transport phenomena are accurately captured in physically interpretable lifted representations. The resulting linear model enables a Koopman-based receding horizon formulation in which each iteration reduces to a convex quadratic program (QP), guaranteeing global optimality of the QP surrogate at each step. Extensive numerical validation on benchmark DHNs demonstrates computational speedups exceeding one order of magnitude over state-of-the-art nonlinear MPC while maintaining comparable control performance. We further extend the methodology to DHNs with bidirectional-flow pipes, providing a tractable optimization framework with superior performance compared to nonlinear MPC.