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.

Terminal Sliding Mode Controllers for Hydraulic Turbine Governing System with Bifurcated Penstocks under Input Saturation

Terminal sliding mode controller method is introduced to enhance the regulation performance of the hydraulic turbine governing system(HTGS).For the purpose of describing the characteristics of controlled system and deducing the control rule,a nonlinear mathematic model of hydraulic turbine governing system with bifurcated penstocks(HTGSBF)under control input saturation is established,and the input/output state linearization feedback approach is used to obtain the relationship between turbine speed and controller output.To address the control input saturation problem,an adaptive assistant system is designed to compensate for controller truncation.Numerical simulations have been conducted under fixed point stabilization and periodic orbit tracking conditions to compare the dynamic performances of proposed terminal sliding mode controllers and conventional sliding mode controller.The results indicate that the proposed terminal sliding mode controllers not only have a faster response and accurate tracking results,but also own a stronger robustness to the system parameter variations.Moreover,the comparisons between the proposed terminal sliding mode controllers and current most often used proportional-integral-differential(PID)controller,as well its variant NPID controller,are discussed at the end of this paper,where the superiority of the terminal sliding mode controllers also have been verified.

Key Technologies of the Hydraulic Structures of the Three Gorges Project

To date,the Three Gorges Project is the largest hydro junction in the world.It is the key project for the integrated water resource management and development of the Changjiang River.The technology of the project,with its huge scale and comprehensive benefits,is extremely complicated,and the design difficulty is greater than that of any other hydro project in the world.A series of new design theories and methods have been proposed and applied in the design and research process.Many key technological problems regarding hydraulic structures have been overcome,such as a gravity dam with multi-layer large discharge orifices,a hydropower station of giant generating units,and a giant continual multi-step ship lock with a high water head.

Selection and Verification of the Structural Pattern of the Penstock and Spiral Case of the TGP Power Station

As a key backbone project in developing and harnessing the Yangtze, the Three Gorges Project (TGP) is a largest water conservancy and hydropower project in China and all the world as well. With a huge comprehensive benefit from flood control, power generation and navigation improvement, TGP, when completed, will exert a significant influence on the socio economic development across the Yangtze Basin and all China. Decisions on key technical issues concerning the construction of TGP were made on a huge number of scientific tests and verifications. The structural pattern selection of the penstock and the spiral case in the TGP power station is not only an important technical and economic issue, but also relating to the long term operation of the power station itself.