Nonlinear dynamics of a novel fractional-order Francis hydro-turbine governing system with time delay

摘要

This paper focuses on the stability of a hydropower station. First, we established a novel nonlinear mathematical model of a Francis hydro-turbine governing system considering both fractional-order derivative and time delay. The fractional-order a, which is introduced into the penstock system, in the range from 0.82 to 1.00 is on the left side of the model in a incommensurate manner in increment of 0.03 to provide an adjustable degree of system memory. The time delay tau, which exists between the signal and response in the hydraulic servo system, in the range from Os to 0.26s is inserted on the right side of the model in increment of 0.04s. Utilizing the principle of statistical physics, we respectively explored the effects of the fractional-order a and the time delay tau on the stable region of the system. Furthermore, we exhaustively investigated the nonlinear dynamic behaviors of the system with different governor parameters by using bifurcation diagrams, time waveforms and power spectrums, finding that only under the condition of reasonable collocation of governor parameters the system can maintain stable operation. Finally, all of the above numerical experiments supply new methods for studying the stability of a hydropower station. (C) 2016 Elsevier Ltd. All rights reserved.