Methodology for Risk Assessment of Part Load Resonance in Francis Turbine Power Plant

At low flow rate operation, Francis turbines feature a cavitating vortex rope in the draft tube resulting from the swirling flow of the runner outlet. The unsteady pressure field related to the precession of the vortex rope induces plane wave propagating in the entire hydraulic system. The frequency of the vortex rope precession being comprised between 0.2 and 0.4 times the turbine rotational speed, there is a risk of resonance between the hydraulic circuit, the synchronous machine and the turbine itself an acting as excitation source. This paper presents a systematic methodology for the assessment of the resonance risk for a given Francis turbine power plant. The test case investigated is a 1GW 4 Francis turbines power plant. The methodology is based on a transient simulation of the dynamic behavior of the whole power plant considering a 1D model of the hydraulic installation, comprising gallery, surge chamber, penstock, Francis turbine but also mechanical masses, synchronous machines, transformer, grid model, speed and voltage regulators. A stochastic excitation having energy uniformly distributed in the frequency range of interest is taken into account in the draft tube. As the vortex rope volume has a strong influence on the natural frequencies of the hydraulic system, the wave speed in the draft tube is considered as a parameter for the investigation. The transient simulation points out the key excitation frequencies and the draft tube wave speed producing resonance between the vortex rope excitation and the circuit and provide a good evaluation of the impact on power quality. The comparison with scale model tests results allows resonance risk assessment in the early stage of project pre-study.