Optimal dynamic thermal plant control: A study and benchmark

TL;DR

This paper tackles the problem of improving energy efficiency in district heating networks (DHNs) by deploying a continuous optimization framework grounded in a thermodynamic model. It develops a solution-operator–based optimal control formulation that maps plant input temperatures to network states via a discretized convection–diffusion model and uses a loss function that can incorporate dynamic energy pricing. Key findings show that low-temperature operation can reduce energy use by about 8%, while incorporating dynamic pricing further reduces operating costs by roughly 12%, with simulations run on an openly available DHN benchmark (OpenDHN) in under 5 minutes on a standard desktop. The approach demonstrates real-time feasibility and offers a pathway for exploiting cheap energy periods as storage in DHNs, contributing to more flexible and economical district heating operations.

Abstract

District heating networks play a vital role in thermal energy supply in many countries. Thus, it comes to no surprise that these has been a central role in improving energy efficiency for private and public energy suppliers alike around the globe. Many studies have previously investigated the potential of energy saving by low temperature operation of the DHN and the integration of renewable energies. Many other studies consider this problem in terms of mixed integer lin-ear programming. Here, we instead investigate the utilization of well-established continuous optimization methods to improve DHN operation efficiency. We demonstrate that optimal control is able to model low temperature operation of a DHN for savings of around 8%, but can even further improve its operation when considering dynamic energy pricing, reducing the cost of operation by roughly 12%. We demonstrate the applicability of this method in a realistic, openly available network in Switzerland (OpenDHN), with a total runtime of less than 5 minutes on a standard desktop com-puter per experiment.

Figures (9)

• Figure 1: Illustration of a DHN graph, showing the duplicated graph structure and separation of nodes and edges. The nodes are separated into supply (black) and return nodes (blue), while the edges can either be considered supply (black), return (blue), consumer (purple) and producer (red) edges. Figure reproduced from krug_nonlinear_2021.
• Figure 2: OpenDHN Net created from data of Verbier in Switzerland boghetti_opendhn_2023. The pipes of the DHN are shown as lines, the blue dots represent consumer sites and the red stars visualize the thermal supply plants. The color of the lines represents the mass flow through the network (logarithmic scale).
• Figure 3: We show the average consumer model unfiltered in blue de_mulder_2021_2022 and its low-pass filtered version in orange (top), along with the created individual variations of the single substations as transparent black lines (bottom), over the chosen three day period.
• Figure 4: Histogram of the temperature mismatch ($x$-axis) of our solution operator $S$ against the PyDHN simulation on the OpenDHN benchmark.
• Figure 5: Optimal control result of the analyzed problem of Verbier over the chosen three day period. The top plot shows the input temperature of the network at the two thermal plants in different colors before (dashed) and after (solid) optimization. The middle plot shows the minimum input temperature over all consumer sites at the supply network. The bottom plot shows the minimum output temperature over all consumer sites at the return network. All constraints shown are denoted in the plot as black dashed lines. All values in ℃.