Flexible district heating grids form an important part of future, low-carbon energy systems. We examine probabilistic state estimation in such grids, i.e., we aim to estimate the posterior probability distribution over all grid state variables such as pressures, temperatures, and mass flows conditional on measurements of a subset of these states. Since the posterior state distribution does not belong to a standard class of probability distributions, we use Markov Chain Monte Carlo (MCMC) sampling in the space of network heat exchanges and evaluate the samples in the grid state space to estimate the posterior. Converting the heat exchange samples into grid states by solving the non-linear grid equations makes this approach computationally burdensome. However, we propose to speed it up by employing a deep neural network that is trained to approximate the solution of the exact but slow non-linear solver. This novel approach is shown to deliver highly accurate posterior distributions both for classic tree-shaped as well as meshed heating grids, at significantly reduced computational costs that are acceptable for online control. Our state estimation approach thus enables tightening the safety margins for temperature and pressure control and thereby a more efficient grid operation.

翻译：柔性区域供热管网是未来低碳能源系统的重要组成部分。我们研究了此类管网中的概率状态估计问题，即旨在基于部分状态变量的测量值，估计所有管网状态变量（如压力、温度和流量）的后验概率分布。由于后验状态分布不属于标准概率分布族，我们在网络热交换空间中使用马尔可夫链蒙特卡洛（MCMC）采样，并在网格状态空间中对样本进行评估以估计后验分布。通过求解非线性管网方程将热交换样本转换为网格状态，使得该方法计算负担沉重。然而，我们提出通过采用深度神经网络来加速这一过程，该网络经过训练可近似精确但缓慢的非线性求解器的解。这种新方法被证明能够为经典树状结构和网状供热管网提供高度精确的后验分布，同时显著降低计算成本，满足在线控制的实时性要求。因此，我们的状态估计方法能够缩小温度和压力控制的安全裕度，从而实现更高效的管网运行。