Water Hammer Stability in a Hydroelectric Plant with Surge Tank and Throttling

Abstract

There is considered the dynamics of a hydroelectric power plant with two conduits - the tunnel and the hydraulic turbine penstock - and a surge tank with throttling. The water hammer phenomenon is considered under the assumption that the hydraulic turbine is shut down. Under the standard assumptions of water hammer computations, both the dynamic head and the Darcy-Weisbach losses are neglected. The consequence of all aforementioned assumptions is a model described by linear hyperbolic partial differential equations with linear non-standard boundary conditions. Further, considering the Riemann invariants of the problem along the characteristics, a system of functional differential equations with deviated argument of neutral type is associated to the basic model. This system displays two rationally independent delays. Its stability is studied using the Lyapunov functional approach and taking into account the dissipativeness of the boundary conditions.