Lumped and distributed-parameter pipe model framework for thermal transients: State-space and transfer function theory and application to multi-energy systems

The accurate prediction and simulation of thermal transients in district heating networks is essential for the meaningful analysis of combined heat and power systems. For this purpose, the focus of this paper lies on the development of a consistent and comprehensive modelling framework that links diverse pipe model categories to specific applications where flows are driven by forced convection. The framework considers pipe modelling based on lumped and distributed parameters. Related state-space and transfer function representations are formulated, and model performances are validated. The comparative analysis of the distributed-parameter versus the lumped-parameter categories is shown to be insightful. For the latter category, thermal transients in the form of changing temperature distributions may be observed along the spatial extension of the pipe. In the distributed-parameter pipe model, only the input and output temperatures are presented. On the other hand, the distributed-parameter pipe model offers higher computational efficiency. This is confirmed by the equivalent floating-point operation (eFLOP) count that is newly introduced to quantify the integer multiple of computation time needed for a mathematical operation with respect to the time needed for an elementary addition. The application of the models is illustrated for a combined heat and power network involving diverse transients.