Stability conditions in a water hammer model involving two delays

Abstract

The linear model of a hydroelectric power plant under water hammer is considered. This model contains the hyperbolic Partial Differential Equations (hPDEs) of wave propagation along the distributed parameter tunnel and penstock, also a surge tank with throttling. The water hammer occurs following hydraulic turbine shut down. A system of Functional Differential Equations of neutral type (nFDEs) is associated to the basic Boundary Value Problem (BVP) and asymptotic stability is obtained using a quadratic Lyapunov functional suggested by the energy identity.