Hydraulic Parameter Estimation for District Heating Based on Laboratory Experiments

TL;DR

This work tackles hydraulic parameter estimation for district heating under real-world challenges such as unknown valve characteristics and hysteresis. It introduces a grey-box, data-driven framework on a tree-structured network, leveraging two open laboratory datasets, and models valve behavior as a linear combination of multiple basis characteristics while compensating for hysteresis with a filtered valve position signal. The approach, solved via a convex $\ell_1$ objective with nonnegativity constraints, demonstrates that accounting for valve nonlinearities and hysteresis significantly improves predictive accuracy within the training range, though extrapolation to unobserved valve operating regions remains difficult in realistic data. The study highlights practical implications for calibrating hydraulic models in district heating and provides a path toward more robust, data-driven calibration in smart energy systems, complemented by open data for further research.

Abstract

In this paper we consider calibration of hydraulic models for district heating systems based on operational data. We extend previous theoretical work on the topic to handle real-world complications, namely unknown valve characteristics and hysteresis. We generate two datasets in the Smart Water Infrastructure laboratory in Aalborg, Denmark, on which we evaluate the proposed procedure. In the first data set the system is controlled in such a way to excite all operational modes in terms of combinations of valve set-points. Here the best performing model predicted volume flow rates within roughly 5 and 10 \% deviation from the mean volume flow rate for the consumer with the highest and lowest mean volume flow rates respectively. This performance was met in the majority of the operational region. In the second data set, the system was controlled in order to mimic real load curves. The model trained on this data set performed similarly well when evaluated on data in the operational range represented in the training data. However, the model performance deteriorated when evaluated on data which was not represented in the training data.

Figures (16)

• Figure 1: A schematic example of a tree-structured district heating system. The nodes $\mathcal{N} = \{\alpha, 1, \dots, 7 \}$ are connected by edges $\mathcal{E} = \{1,\dots,7 \}$. The supply-and-return-networks are symmetrical except for their edges having opposite direction. Valves $\mathcal{V} = \{ 1, \dots, 4\}$ connect the supply and return lines. Root nodes $\alpha$ and $\beta$ in the supply-and-return networks respectively connect the branch either to a production facility, or a greater part of the grid. The path $\mathcal{L}_2 = \{2, 5, 6 \}$ highlighted in green contains the edges leading from $\alpha$ to $\beta$ via valve 2.
• Figure 2: Examples of valve characteristics $k_i(v_i)$.
• Figure 3: Scatter-plot of flow rates $q_1(t)$ against valve set-points $v_1(t)$ for valve 1 in the experiment setup to be described in the subsequent section.
• Figure 4: Diagram of the experimental setup used to recreate \ref{['fig:graph-example']}. PT and FT denote respectively flow and pressure transmitters, while the two blocks in each consumer unit are water-to-air heat exchangers.
• Figure 5: Images from the laboratory setup.