  The transformation of fossil fuel-based district heating grids (DHGs) to
CO$_2$-neutral DHGs requires the development of novel operating strategies.
Model predictive control (MPC) is a promising approach, as knowledge about
future heat demand and heat supply can be incorporated into the control,
operating constraints can be ensured and the stability of the closed-loop
system can be guaranteed. In this paper, we employ MPC for DHGs to control the
system mass flows and injected heat flows. Following common practice, we derive
terminal ingredients to stabilize given steady state temperatures and storage
masses in the DHG. To apply MPC with terminal ingredients, it is crucial that
the system under control is stabilizable. By exploiting the particular system
structure, we give a sufficient condition for the stabilizability in terms of
the grid topology and hence, for the applicability of the MPC scheme to DHGs.
Furthermore, we demonstrate the practicability of the application of MPC to an
exemplary DHG in a numerical case study.
