A data-based compact pipe model for district-heating-and-cooling networks with variable flow conditions

The present study develops a data-based compact model for the prediction of the fluid temperature evolution in district heating-and-cooling pipeline networks. This model is based on an existing "reduced-order model" by the authors obtained from reduction of the "full-order model" describing
the spatio-temporal energy balance for each pipe segment to a semi-analytical input-output relation between the pipe outlet temperature and the pipe inlet and ground temperatures. The proposed model (denoted XROM) expands on the original reduced-order model by incorporating variable mass flux as an additional input and thus greatly increases its practical relevance. The XROM represents variable mass flux by step-wise switching between mass-flux levels and thereby induces a prediction error relative to the true full-order model evolution after each switching. Theoretical analysis rigorously demonstrates that this error always decays and the XROM invariably converges on the full-order model evolution and, consequently, affords the same prediction
accuracy. Performance analyses reveal that prediction errors are restricted to short "convergence intervals" after each mass-flux switching and the XROM therefore can handle substantially faster operating schemes than the current ones based on hourly monitoring and control. Convergence intervals of O(minutes) are namely typically sufficient - and thus switching frequencies up to
O(minutes^-1) permissible during dynamic operation and control actions - for reliable predictions. Quantification of these convergence intervals by an easy-to-use empirical relation furthermore enables a priori determination of the conditions for reliable predictions. Moreover, the XROM can capture the full 3D system dynamics (provided incompressible flow and heat-transfer mechanisms
depending linearly on temperature) versus the essentially 1D approximation of current compact pipe models yet at similar computational cost. These attributes advance (parts of) district heating and cooling networks demanding prediction accuracies beyond 1D as its primary application area. This makes the XROM complementary to said pipe models and thereby expands the modelling
capabilities for handling the growing complexity of (next-generation) networks.