title: Learning-based Hybrid Models for Operating 4th Generation District Heating Systems
Creators: name: Bott, Andreas
Publisher: name: UNSPECIFIED
Year: 2025

description: It is anticipated that district heating networks will undergo a substantial transformation in the forthcoming years. The conventional approach to district heating involves distributing heat from a single, high-temperature heating plant to dispersed consumers through a mostly tree-like network. Upcoming, so-called 4th generation district heating networks, on the other hand, are characterised by lower supply temperatures, distributed and flexibly operated heat sources, and loop-based grid layouts. This system transition necessitates novel approaches to address grid operation tasks. A particular challenge in this endeavour is the lack of real-time consumer demand measurements. The acquisition of real-time consumption data is costly, both financially and in terms of organisational resources. If these measurements are not available, the resulting thermal demand uncertainty has to be reflected in the operation algorithms. Moreover, since the physical equations describing heating grids are nonlinear, mapping the demand’s uncertainty onto the grid states can result in multimodal probability distributions, even if the initial demand uncertainty has a simple Gaussian form. It is, therefore, infeasible to find adequate parametric representations for the grid state’s uncertainty. Therefore, we propose to utilise learning-based hybrid models to model state uncertainties in state estimation and heating plant control tasks for 4th generation district heating systems. The idea of hybrid models is to integrate machine learning models with established stochastic algorithms. In particular, we employ surrogate models that approximate thermal power flow calculations, i.e., the mapping from the thermal powers and feed-in temperatures at producers and consumers onto the grid states. The possibility of rapid evaluation of these surrogate models then enables the usage of classic sampling-based stochastic algorithms, omitting the necessity for parametric uncertainty representations. The thesis first presents novel algorithms to facilitate the efficient construction of the required surrogate models. Then, it shows hybrid approaches for state estimation and heating plant control for 4th generation district heating grids. The training of a surrogate model requires a large number of training samples. These samples can be generated by solving the thermal power flow for randomly generated input values. However, this approach is impeded by its high computational costs, as the thermal power flow is defined implicitly and is consequently solved via iterative algorithms. Instead, we propose an importance-sampling-based approach, wherein we define a Proxy distribution over the mass flow rates at consumers and suppliers. By initially drawing samples from this proxy distribution, training samples can be obtained via an iterationfreealgorithm. In our numerical tests, our approach reduces the computation times for generating training samples by up to two orders of magnitude and achieves high effective sample rates of over 99.9% in all test settings. Our first application then is the state estimation task. Here, the objective is to approximate the posterior distribution over the grid states, given a prior distribution over the thermal powers and some measurements of selected grid states. We propose to employ a Markov Chain Monte Carlo algorithm to generate samples which represent the desired posterior distribution. As it is not possible to generate grid state samples directly, the Markov chains propose candidates consisting of thermal power values. For each candidate, the corresponding grid state is computed by solving the thermal power flow problem and the state is then compared against the measured values. By approximating the thermal power flow computations with a surrogate model, this procedure becomes computationally feasible to be used in real-time operation. Experiments on test heating grids demonstrate hat the approach is capable of approximating complex uncertainty distributions over grid state and achieves low computation times. Our second application for hybrid models is the control of heating grids, specifically ofthe powers and Feed-in temperatures of the heating plants. Depending on the uncertain thermal demand, these setpoints should be adjusted such that a grid state within predefined bounds is maintained. The resulting control task is formulated as a nonlinear stochastic optimal control problem. The uncertain thermal demands are, again, represented via samples. Whereas the decision variables of the optimal control problem are located in the space of thermal powers and feed-in temperatures, some boundary constraints, e.g., minimal supply temperatures at consumer sites, are defined in the space of grid states. These constraints can be efficiently verified, by passing the setpoints and thermal demands samples through a surrogate model, which approximates the thermal power flow. Tests on a grid with two heat suppliers demonstrate that our proposed hybrid approach clearly outperforms the linearisation-based baseline in terms of optimisation costs and risk of constraint violations while achieving low computation times. The two applications presented here demonstrate that hybrid approaches can adequately represent uncertainty distributions over grid states in district heating grids. They allow for estimating the probability of grid constraint violations as well as deducing optimal responses to minimise this probability. The approaches have low computation times, which allows them to be used in online operational settings. Overall, the proposed hybrid models allow the utilisation of the flexibility of 4th generation district heating networks without requiring a complete set of measurements first.