Modeling and forecasting the dynamics of the natural gas transmission network in Germany with the demand and supply balance constraint

We develop a novel large-scale Network Autoregressive model with balance Constraint (NAC) to predict hourahead gas flows in the gas transmission network, where the total in- and out-flows of the network are balanced over time. By integrating recent advances in optimization and statistical modeling, the NAC model can provide an accurate hour-ahead forecast of the gas flow at all of the distribution points in the network. By detecting the influential nodes of the dynamic network, taking into account that demand and supply have to be balanced, the forecast can be used to compute an optimized schedule and resource allocation. We demonstrate an application of our model in forecasting hour-ahead gas in- and out-flows at 128 nodes in the German high-pressure natural gas transmission network over a time frame of 22 months. It dramatically improves the out-of-sample forecast accuracy with the average root mean squared error reduced from 1.116 to 0.725 (35% change) and the mean squared forecast error reduced from 36.389 to 11.914 (67% change). The NAC model successfully also improves the demand and supply balance, with the average deviation dropping from 7.590 to 2.391. Moreover, we identify three permanently influential nodes in the gas transmission network, and we also capture the dynamic changes in the network with 42 influential nodes on average and 17 influential nodes in summer months.