Model Reduction for Heat Grid State Estimation

Deep learning-enabled MCMC for probabilistic state estimation in district heating grids

“…However, the true posterior distributions often do not fall into any standard class of distributions but are often highly skewed to one side [22]. And, as our experiments show, these distributions may even be multimodal, especially for grids featuring loops.…”

“…The presented approach is demonstrated on both a traditional tree-like district heating grid and a grid topology featuring a loop structure. We show strongly superior approximation properties for the true posterior distributions compared to the linearisation approach [23,22]. At the same time, computation times are several orders of magnitude lower compared to solving the state equations via NR for each sample of a sample importance resampling Monte Carlo (SIR-MC) approach [26], which we use as a baseline since MCMC with NR is not computationally feasible.…”

“…Previous work has considered deterministic state estimation with complete load measurements [20] or with only partial information [21]. One route to probabilistic steady-state estimation in heating grids is linearising the grid equations around the best state estimate and using standard propagation rules for normal distributions to determine Gaussian posterior distributions [22,23]. For radial networks, non-linear approximation of the grid equations can be used as well to determine Gaussian posterior representations [24].…”

“…where c p denotes the specific heat capacity, l ij is the length of the pipe, T a the pipe ambient temperature, and k ij and λ ij are parameters that characterise the specific pressure or heat losses of the pipe. We assume these parameters to be constant within our temperature and mass flow range, an assumption validated in [22].…”

“…The first test case grid-tree, shown in Figure 3a, is a modified subsection of an existing district heating grid [22]. The grid contains 11 consumers with a total consumption of 1.7M W and features 57 edges and 47 nodes.…”