Modal Analysis of Water Distribution Systems With the Elastic Water Column Model

Abstract This paper presents a modal and participation factor (PF) analysis of water distribution systems (WDSs) using the elastic water column model (EWCM). Modal analysis, widely used in other engineering fields, is adapted here to characterize the dynamic behavior of WDSs under transient conditions. By linearizing the EWCM around an operating point, a state‐space representation is developed, enabling the extraction of natural modes via eigenvalue analysis. These modes, defined by their frequencies and damping ratios, are validated through comparison with the admittance matrix method in the frequency domain. The study introduces PF analysis to quantify how each state variable (nodal head or flow rate) contributes to each mode. This spatial information identifies critical locations that are more sensitive to excitations and capable of amplifying transient responses. To verify the effectiveness of PF analysis, time‐domain simulations are conducted for three test cases, including a real‐world network (the New York tunnel system). The results confirm that exciting the system at high‐PF locations can generate significant transients, while low‐PF locations produce minimal responses. The analysis also reveals how resonance behavior in WDSs is spatially distributed, enabling the identification of vulnerable areas where transients are amplified. This work provides a unified time‐domain framework for modal and PF analysis, contributing to improved system monitoring, management, and fault detection in WDSs.