Elastic water column model with dynamic elements: A case study

<p dir="ltr">This study extends the Elastic Water Column Model (EWCM) to incorporate dynamic components, specifically pressure reducing valves (PRVs) and pumps, for transient analysis and control of water distribution systems (WDSs). Using an electrical equivalent circuit (EEC) analogy, these elements are integrated into the model as lumped hydraulic components, resulting in a system of differential-algebraic equations (DAEs) built on an ODE-based formulation. The model adopts a graph-theoretical structure, with PRVs modeled as variable resistors and pumps as controlled energy sources. This formulation enables a structured state-space representation suitable for stability analysis, pressure regulation, and flow control tasks. Compared to traditional methods such as the Method of Characteristics (MOC), the EWCM supports flexible time-step selection and system discretization while preserving accuracy. A test case involving both a PRV and a pump illustrates the model’s ability to simulate network dynamics under feedback control. Although the controllers used are simple and do not fully achieve the intended targets, the results demonstrate that the EWCM captures both hydraulic transients and control interactions in a unified modeling framework.</p><p dir="ltr">This paper was presented at the 21st Computing and Control in the Water Industry Conference (CCWI 2025) at the University of Sheffield (1st - 3rd September 2025).</p>