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

Abstract

a b s t r a c tThis 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 α, 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 τ , which exists between the signal and response in the hydraulic servo system, in the range from 0 s to 0.26 s is inserted on the right side of the model in increment of 0.04 s . Utilizing the principle of statistical physics, we respectively explored the effects of the fractional-order α and the time delay τ 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.

Stability of multi-hydro-turbine governing time-delay systems with sharing tailrace surge tank

“…is the intermediate variable, = − . In actual operation of hydropower station, considering the fact that the hydraulic servo system exists time lag, a discrete time-delay is introduced to the mathematical model of the hydraulic servo system and it can be expressed as [21]:…”

“…Nagode [17] assessed the relationship between random gate position and the hydro-turbine deviated power on random water disturbance and load variation, the deviated power can tracks deviated power target signal accurately. Xu and Wang [21,22] discussed the influence of fractional-order and time-delay on the hydro-turbine governing system with single unit, and their changing law was respectively identified. However, the influence of time-delay on the hydropower plant with sharing tailrace surge tank has not been discussed, considering the complexity of the above hydropower plant during the regulation process.…”

Design of a Finite-Time Terminal Sliding Mode Controller for a Nonlinear Hydro-Turbine Governing System

“…Some scholars introduced fractional calculus into the modeling of HGS and carried out dynamic analysis on it [16,17]. What is more, the linear hydro-turbine model and the first order fundamental power generator model [18][19][20] of an HGS have also been adopted for dynamical analysis and simulation.…”

Design of a Nonlinear Predictive Controller for a Fractional-Order Hydraulic Turbine Governing System with Mechanical Time Delay

“…There is a consensus that fractional calculus is superior to integer calculus in describing systems with memory, historical dependence, and viscoelasticity [18][19][20][21][22][23][24][25][26][27][28][29]. Considering the nonlinear, time-varying and nonminimum phase characteristics of hydraulic turbine governing systems, some scholars have introduced fractional calculus to establish mathematical models of HTGS which are more in line with engineering practice [30][31][32]. On the basis of accurate modeling, stability control of HTGS has attracted many scholars' attention.…”