Model order reduction of hyperbolic systems focusing on district heating networks

In this article a framework for the generation of a computationally fast surrogate model for district heating networks is presented. An appropriate model is given by in an index-1 hyperbolic, differential algebraic equation quadratic in state, exhibiting several hundred of outputs to be approximated. We show the existence of a global energy matrix which fulfills the Lyapunov inequality ensuring stability of the reduced model. By considering algebraic variables as parameters of the dynamical transport, a time varying (LTV) problem has to be reduced. We present a scheme to efficiently combine linear reductions to a global surrogate model using a greedy strategy in the frequency domain. The numerical effectiveness of the scheme is demonstrated at different, existing, large scale networks.