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The current energy transition promotes the convergence of operation betweenthe power and natural gas systems. In that direction, it becomes paramount toimprove the modeling of non-convex natural gas flow dynamics within thecoordinated power and gas dispatch. In this work, we propose aneural-network-constrained optimization method which includes a regressionmodel of the Weymouth equation, based on supervised machine learning. TheWeymouth equation links gas flow to inlet and outlet pressures for eachpipeline via a quadratic equality, which is captured by a neural network. Thelatter is encoded via a tractable mixed-integer linear program into the set ofconstraints. In addition, our proposed framework is capable of consideringbidirectionality without having recourse to complex and potentially inaccurateconvexification approaches. We further enhance our model by introducing areformulation of the activation function, which improves the computationalefficiency. An extensive numerical study based on the real-life Belgian powerand gas systems shows that the proposed methodology yields promising results interms of accuracy and tractability.

Machine Learning for Improved Gas Network Models in Coordinated Energy Systems