  This study concerns the development of a data-based compact model for the
prediction of the fluid temperature evolution in district heating (DH) pipeline
networks. This so-called "reduced-order model" (ROM) is obtained from reduction
of the conservation law for energy for each pipe segment to a semi-analytical
input-output relation between the pipe outlet temperature and the pipe inlet
and ground temperatures that can be identified from training data. The ROM
basically is valid for generic pipe configurations involving 3D unsteady heat
transfer and 3D steady flow as long as heat-transfer mechanisms are linearly
dependent on the temperature field. Moreover, the training data can be
generated by physics-based computational "full-order" models (FOMs) yet also by
(calibration) experiments or field measurements. Performance tests using
computational training data for a single 1D pipe configuration demonstrate that
the ROM (i) can be successfully identified and (ii) can accurately describe the
response of the outlet temperature to arbitrary input profiles for inlet and
ground temperatures. Application of the ROM to two case studies, i.e. fast
simulation of a small DH network and design of a controller for user-defined
temperature regulation of a DH system, demonstrate its predictive ability and
efficiency also for realistic systems. Dedicated cost analyses further reveal
that the ROM may significantly reduce the computational costs compared to FOMs
by (up to) orders of magnitude for higher-dimensional pipe configurations.
These findings advance the proposed ROM as a robust and efficient simulation
tool for practical DH systems with a far greater predictive ability than
existing compact models.
