  Using hydraulic models in control design in district heating networks can
increase pumping efficiency and reduce sensitivity to hydraulic bottlenecks.
These models are usually white-box, as they are obtained based on full
knowledge of the district heating network and its parameters. This type of
model is time-consuming to obtain, and might differ from the actual behavior of
the system. In this paper, a method is proposed to obtain a grey-box hydraulic
model for tree-shaped district heating systems: hydraulic parameters are
estimated based on pressure measurements in only two locations. While previous
works only estimate parameters related to pressure losses in pipes, this work
also includes customers valves in the grey-box model structure, an important
inclusion for control-oriented applications. Finally, a numerical example
illustrates the proposed method on a small district heating network, showing
its ability to obtain an accurate model on the basis of noisy measurements.
