Generalization and Analysis of Elastic Water Column Model for Hydraulic Transient Analysis of Water Distribution Systems

The elastic water column model (EWCM) has been enhanced through the integration of dynamic electromechanical elements, such as pressure-reducing valves (PRVs) and pumps, facilitating advanced transient analysis of water distribution systems in the time domain. The graph-theoretical framework has been employed to represent any arbitrary network configuration with different hydraulic components. Electric equivalent circuits (EECs) have been introduced for these dynamic components and integrated to the EWCM create a set of differential algebraic equations (DAEs). Verification against established models, such as the rigid water column model (RWCM) and the method of characteristics (MOC), confirms the enhanced EWCM’s accuracy, validity, and computational advantages. Specifically, in fast transient scenarios, the EWCM outperforms the RWCM by accounting for water compressibility. It also surpasses the MOC in computational efficiency due to its foundation on ordinary differential equations and independence from Courant–Friedrichs–Lewy condition constraints. The model’s accuracy is controllable by increasing the number of reaches, although this increases computational cost. The investigation into the model’s stiffness reveals a notable increase, with the EWCM being approximately 25 times stiffer than the RWCM. Although this allows for capturing a broader frequency range, it also increases numerical stiffness, making solver selection more critical. The study further emphasizes the computational advantages of employing sparse matrices within the EWCM. In large-scale networks, the graph representation of the EWCM predominantly features sparse matrices, which reduce computation time and memory usage.