Water Hammer Stability for a Hydroelectric Plant with Local Nonlinear Hydraulic Losses

It is considered a typical configuration of hydroelectric power plant under water hammer for stability studies. It is shown that while (simple, non-asymptotic) Lyapunov stability can be easily obtained by using an energy-like Lyapunov functional, asymptotic stability is connected to the nature of the assumed hydraulic losses in the model. Three cases are discussed: the conservative case, "fragile" asymptotic stability and standard asymptotic stability as such; they are in direct connection with the asymptotic stability for the difference operator of an associated system of functional differential equations with deviated argument of neutral type.