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. C. Nicolet et al. / Cavitation and Dynamic Problems in Hydraulic Machinery and Systems 2006 2 INTRODUCTION Nowadays hydroelectric power plants are increasingly subject to off-design operation in order to follow the demand. In this context, Francis turbine power plants operating at part load may present instabilities in terms of pressure, discharge, rotational speed and torque. These phenomena are strongly linked to the flow structure at the runner outlet inducing a vortex core precession in the draft tube. This leads to hydrodynamic instabilities (Jacob, [5]). The decrease of the tailrace pressure level makes the vortex core visible as a gaseous vortex rope. The volume of the gaseous vortex rope is dependent of the cavitation number ! and affects the parameters characterizing the hydro-acoustic behavior of the entire power plant. As a result, natural frequencies of the hydraulic system decrease with the cavitation number (Tadel [16]). In addition, for a given cavitation number !, the volume of the vortex rope changes with the discharge rate (Jacob, [5]), thus the natural frequencies are also dependent on the turbine discharge, i.e. the operating point. Therefore, the risk of an interaction between the excitation sources such as vortex rope precession and the natural frequencies resulting in resonance effects, called draft tube surge, is dependant on the cavitation number, but also on the operating point. Such resonance may result in unacceptable pressure pulsation or electrical power swing, (Rheingans [13], Tadel [16]). In order to assess resonance risks on prototypes, pressure fluctuation measurements field are carried out during scale model tests to identify experimentally the pressure excitations sources and the vortex rope compliance [2]. Then, the pressure fluctuations due to non uniform pressure field at the runner outlet [9], [10], can be decomposed in two parts as proposed by Angelico [1]; (1) a rotating part, due to vortex rotation, and (2) a synchronous pulsating part resulting from the spatial perturbation of the rotating part. The pressure excitation source related to the synchronous pulsating part can be extracted using the procedure described by Dcrfler, [2]. It is then possible to deduce the resulting mechanical torque pulsation in the frequency domain, using an appropriate one dimensional model of the full hydraulic system based on impedance method, including the model of the vortex rope and the turbine itself, [3], [16], [4]. However, obtaining the induced electrical power pulsations, requires to include the linearized model of the synchronous machine, the voltage regulator, transformer, etc, which is very challenging. This paper presents a methodology using a time domain simulation for the determination of the part load resonance risk and its impact on the electrical power pulsations of a Francis turbine power plant. Therefore, the case of an hydroelectric power plant with 4x250MW Francis turbine is investigated, see Figure 1. First, the numerical model based on an electrical equivalent is presented. The model of the draft tube, taking into account the vortex rope volume and the pressure excitation source is described. Then a simplified model of the piping is derived for C. Nicolet et al. / Cavitation and Dynamic Problems in Hydraulic Machinery and Systems 2006 3 analyzing qualitatively the resonance risk of the power plant. Finally, a time domain simulation of the dynamic behavior of the whole hydroelectric power plant is performed with SIMSEN, in order to deduce the transfer function between the pressure excitation in the draft tube and the synchronous machine electrical active power. Influence of the draft tube wave speed, i.e. vortex rope volume, is presented. Figure 1 Hydraulic power plant layout. MODELING OF THE HYDROELECTRIC POWER PLANT Hydraulic system modeling By assuming uniform pressure and velocity distributions in the cross section and neglecting the convective terms, the one-dimensional momentum and continuity balances for an elementary pipe filled with water of length dx, cross section A and wave speed a, see Figure 2, yields to the following set of hyperbolic partial differential equations [18]: