Instability of the Tank-Level Control System of Water Mains in Mountainous Environments

The stability of the tank-level controller of hydraulic infrastructures is a complex issue. Past studies have focused on run-of-river hydropower plants with a short penstock, and where the upstream tank level is regulated by a variable-speed turbine. The short penstock entails that the flow regulation performed by the turbine can be considered instantaneously effective in the upstream tank. This is not true in water supply systems in mountain areas, where the length of the water main easily exceeds 10 km. This work is devoted to assessing the stability of the water-level controller of hydraulic systems made up of very long conduits. To do this, we numerically studied the stability of a large number of ideal case studies representative of real hydraulic infrastructures. The key results are (1) the understanding of the causes of the water-level controller instability; and (2) a set of charts that predicts whether the control system is unstable. These charts should be used during the design stage of this type of systems to select values of the tank area that avoid tank-level-controller instabilities.