On the Solvability of the Pressure Driven Hydraulic Steady-State Equations Considering Feedback-Control Devices | Solvabilité des équations d'équilibrage hydraulique conduites par la pression considérant des stabilisateurs

Water supply networks (WSNs) represent an important part of urban technical infrastructure. Recently, the resilience of water distribution networks facing different physical and cyber threats has gained increasing attention. In order to improve the operation of complex water distribution systems under both, extreme and normal hydraulic conditions, mathematical simulation models are indispensable tools for engineers, network planners, network operators and decision makers. Especially, in the case of extremely disruptive events that might be caused by natural hazards or deliberate malevolent attacks by humans, the proper operation of the system for maintaining the supply of drinking water to at least parts of the population is a very challenging task. Resilient behaviour can be reached only by adaptive system operation including isolation of parts of the network and control of pressure and flows in the system. For that purpose, different kinds of control devices are used that may be remotely controlled or which are operated in the field. Existing hydraulic simulation software often fails to calculate reliable results for systems under control and pressure insufficiency. A mathematical framework for the simulation of the steady-state flow in reticulation water supply networks with special consideration of feedback control devices and pressure dependent demands is proposed in this paper. First, the importance of the steady-state calculation in the face of disruptive events is stressed and a brief review of synthetic and analytical methods for the hydraulic steady- state calculation is given. In this paper, the well-known content model is extended by the content of pressure dependent outflows. The nonlinear consumption functions in combination with linear inequality constraints (box constraints) replace the constant demands of demand driven analysis. It is also shown that the range of solvable problems in combination with flow control devices is enlarged by the relaxation of fixed demands.