Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

This work studies the stability and hidden dynamics of the nonlinear hydro-turbine governing system with an output limiting link,and propose a new six-dimensional system,which exhibits some hidden attractors.The parameter switching algorithm is used to numerically study the dynamic behaviors of the system.Moreover,it is investigated that for some parameters the system with a stable equilibrium point can generate strange hidden attractors.A self-excited attractor with the change of its parameters is also recognized.In addition,numerical simulations are carried out to analyze the dynamic behaviors of the proposed system by using the Lyapunov exponent spectra,Lyapunov dimensions,bifurcation diagrams,phase space orbits,and basins of attraction.Consequently,the findings in this work show that the basins of hidden attractors are tiny for which the standard computational procedure for localization is unavailable.These simulation results are conducive to better understanding of hidden chaotic attractors in higher-dimensional dynamical systems,and are also of great significance in revealing chaotic oscillations such as uncontrolled speed adjustment in the operation of hydropower station due to small changes of initial values.

Bursting oscillations in a hydro-turbine governing system with two time scales

A fast-slow coupled model of the hydro-turbine governing system （HTGS） is established by introducing frequency disturbance in this paper. Based on the proposed model, the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams, time waveforms and phase portraits. We find that stability and operational characteristics of the HTGS change with the value of system parameter kd. Furthermore, the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out. Meanwhile, we obtain that the relative deviation of the mechanical torque mt rises with the increase of a. These methods and results of the study, combined with the performance of two time scales and the fast-slow coupled engineering model, provide some theoretical bases for investigating interesting physical phenomena of the engineering system.

Fractional-Order Modeling and Dynamical Analysis of a Francis Hydro-Turbine Governing System with Complex Penstocks

This paper investigates the stability of the Francis hydro-turbine governing system with complex penstocks in the grid-connected mode. Firstly, a novel fractional-order nonlinear mathematical model of a Francis hydro-turbine governing system with complex penstocks is built from an engineering application perspective. This model is described by state-space equations and is composed of the Francis hydro-turbine model, the fractional-order complex penstocks model, the third-order generator model, and the hydraulic speed governing system model. Based on stability theory for a fractional-order nonlinear system, this study discovers a basic law of the bifurcation points of the above system with a change in the fractional-order a. Secondly, the stable region of the governing system is investigated in detail,and nonlinear dynamical behaviors of the system are identified and studied exhaustively via bifurcation diagrams, time waveforms, phase orbits, Poincare maps, power spectrums and spectrograms. Results of these numerical experiments provide a theoretical reference for further studies of the stability of hydropower stations.

Stability analysis of hydro-turbine governing system based on machine learning

Hydro-turbine governing system is a time-varying complex system with strong non-linearity,and its dynamic characteristics are jointly affected by hydraulic,mechanical,electrical,and other factors.Aiming at the stability of the hydroturbine governing system,this paper first builds a dynamic model of the hydro-turbine governing system through mechanism modeling,and introduces the transfer coefficient characteristics under different load conditions to obtain the stability category of the system.BP neural network is used to perform the machine study and the predictive analysis of the stability of the system under different working conditions is carried out by using the additional momentum method to optimize the algorithm.The test set results show that the method can accurately distinguish the stability category of the hydro-turbine governing system(HTGS),and the research results can provide a theoretical reference for the operation and management of smart hydropower stations in the future.

Technology Readiness of a Vertical-Axis Hydro-Kinetic Turbine

In this paper, the development of a vertical axis hydrokinetic twin turbine for harvesting energy from flowing water in man-made channels is described. The Technology Readiness Level (TRL) assessment procedure, developed by NASA and modified by the US Department of Energy, is followed and it is shown that the hydrokinetic turbine successfully reaches TRL 7, which is a full-scale, similar (prototypical) system demonstrated in a relevant environment. The concept of the twin turbine (TRL 1 - 3) is first validated and tested using a 1:10 scale laboratory model at Cardiff University and efficiencies of up to 75% are achieved (TRL 4 - 5). In order to justify system functionality and performance in a relevant environment as well as up-scalability, a 1:3 scale model of the twin turbine is implemented and tested in a discharge channel of a water treatment plant in Atlanta, thereby achieving TRL6. This paved the way for an application in the form of an array of ten full-scale twin turbine prototypes, including all relevant components such as housing, drive-train, gear-box and generator. Successful deployment and testing in the South Boulder Canal near Denver means that the hydrokinetic twin turbine system reached TRL7.

Design and Performance of a Novel Spillway Turbine

The high-speed supercritical flow in steeply sloped channels contains a significant amount of hydro-kinetic energy. A novel, horizontal axis, spillway turbine as presented in this paper attempts to convert that energy into electricity. We report on the turbine’s design and experimental testing. Its intended use is in low-head, low-flow, manmade, concrete-lined channels such as chutes, spillways and other similar steeply sloped open-channels. The design lends itself from an impulse turbine runner but without a pipe or a nozzle. The spillway turbine consists of 2 main components: 1) the runner and 2) an accelerator channel that directs the water towards the runner’s blades. The runner, once fitted with Pelton-inspired “cup inserts” shows performance improvements both in terms of efficiency and specific speeds. The specific speed and the speed factors calculated confirm that this novel spillway turbine runner can be categorized as an impulse turbine. The maximum efficiency obtained during laboratory testing is 43.4% and hence competes well with standard hydrokinetic turbines.