  We study the optimal control of district heating networks using a reduced
order model based on a system theoretic description close to the underlying
Euler equations. In the presented scenarios, the central task is to limit the
maximal feed-in power occurring as a product of control and state variables.
The underlying dynamics of heating networks acting as optimization constraints
pose the central computational complexity, prohibiting the determination of an
optimal control online. The advection of the injected energy density on the
network results in an index-1, quadratic in state differential algebraic
equation, challenging to reduce. The suggested reduced model decreases the
computation time of the optimization significantly. The effectiveness of the
presented approach is demonstrated for an existing, large-scale heating network
including changes of flux directions.
