In this article, we propose an economic nonlinear model predictive control (MPC) algorithm for district heating networks (DHNs). The proposed method features prosumers, multiple producers, and storage systems, which are essential components of 4th-generation DHNs. These networks are characterized by their ability to optimize their operations, aiming to reduce supply temperatures, accommodate distributed heat sources, and leverage the flexibility provided by thermal inertia and storage—each crucial for achieving a fossil-fuel-free energy supply. Developing a smart energy management system to accomplish these goals requires detailed models of highly complex nonlinear systems and computational algorithms able to handle large-scale optimization problems. To address this, we introduce a graph-based optimization-oriented model that efficiently integrates distributed producers, prosumers, storage buffers, and bidirectional pipe flows, such that it can be implemented in a real-time MPC setting. Furthermore, we conducted several numerical experiments to evaluate the performance of the proposed algorithms in closed loop. Our findings demonstrate that the MPC methods achieved up to 9% cost improvement over traditional rule-based controllers while better maintaining system constraints.

The inherently nonlinear, large-scale, and time-varying nature of district heating systems pose significant challenges from a control perspective. In this paper, we address these challenges by applying an economic MPC. Economic MPC is a dynamic real-time optimization method, enabling both optimal planning and stability of the closed-loop system. Our strategy constitutes several steps. First, we introduce a discrete-time modular framework for the district heating system, establishing its strict dissipativity with respect to a desired, potentially time-varying, equilibrium. We identify a set of meaningful objective functions for the district heating systems, preserving this property. Second, we show how strict dissipativity implies the turnpike property, which, in turn, guarantees approximate optimality, practical stability, and recursive feasibility for the EMPC closed-loop. Finally, we provide numerical simulations to demonstrate the effectiveness of our work.