Efficient Training of Learning-Based Thermal Power Flow for 4th Generation District Heating Grids

TL;DR

This work proposes a novel, efficient scheme to generate a sufficiently large training data set covering relevant supply and demand values from a proxy distribution over generator and consumer mass flows, omitting the iterations needed for solving the heat grid equations.

Abstract

Thermal power flow (TPF) is an important task for various control purposes in 4 Th generation district heating grids with multiple decentral heat sources and meshed grid structures. Computing the TPF, i.e., determining the grid state consisting of temperatures, pressures, and mass flows for given supply and demand values, is classically done by solving the nonlinear heat grid equations, but can be sped up by orders of magnitude using learned models such as neural networks. We propose a novel, efficient scheme to generate a sufficiently large training data set covering relevant supply and demand values. Instead of sampling supply and demand values, our approach generates training examples from a proxy distribution over generator and consumer mass flows, omitting the iterations needed for solving the heat grid equations. The exact, but slightly different, training examples can be weighted to represent the original training distribution. We show with simulations for typical grid structures that the new approach can reduce training set generation times by two orders of magnitude compared to sampling supply and demand values directly, without loss of relevance for the training samples. Moreover, learning TPF with a training data set is shown to outperform sample-free, physics-aware training approaches significantly.

Figures (8)

• Figure 1: Learning-based approaches can be used to approximate computations (purple boxes). The training of such models requires a large number of training samples (blue box). A default way to generate such training samples is to define a distribution over the relevant input values and solve the for each sample (left green box). However, classic computation methods, such as the and algorithms, have an iterative structure, which leads to high computational costs. We propose a novel, importance-sampling-based algorithm to generate training samples (right green box). By defining a suitable proxy distribution over the space of mass flows at heat producers and consumers, we are able to generate each training data point non-iteratively in a single pass, thus drastically reducing computation times for the model-building process.
• Figure 2: A grid (top) is modeled as a directed graph (bottom). The edges' orientation is arbitrary for passive edges, i.e., pipes (blue). For active edges (green), i.e., consumers or generators, and the slack edge (red), i.e., one heat source, it is chosen such that $\dot{m}_{ij} \geq 0$ holds in all situations.
• Figure 3: The state variables in steady-state models of DH grids include node-bound variables such as fluid temperatures $T_{i}$ and pressures $p_{i}$. The sign of the edge-bound mass flows $\dot{m}_{ij}$ depends on the orientation with respect to the edge orientation (indicated by the thick arrow). The localization of the temperatures at the inlet $T_{}^{start}$ and outlet $T_{}^{end}$ of the pipe depends on the sign of $\dot{m}_{ij}$ (for positive mass flows see above the thick arrow, otherwise below).
• Figure 4: The default approach to generate training data is drawing $(\mathbf{\dot{q}}, \mathbf{T_{}}^{fi})$ samples from the input distribution and solving the , e.g. by using the classic decomposed algorithm. By defining a proxy distribution over $(\mathbf{\dot{m}^{a}}, \mathbf{T_{}}^{fi})$ and rearranging the computational steps of the algorithm, we omit the iterations and solve each training sample in a single pass.
• Figure 5: In the experiments, we consider two structurally different grid layouts with varying sizes and different numbers of heat supplies.