Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system

Xu, Beibei; Chen, Diyi; Zhang, Hao; Wang, Feifei

doi:10.1016/j.chaos.2015.01.025

Cited by 91 publications

(50 citation statements)

References 36 publications

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“…In addition, Ref. [47] indicated that water flowing in the penstock system possesses viscoelasticity. Thus, it is not hard to find that the penstock system has obvious viscoelastic properties which have a great effect on its dynamic behaviors.…”

Section: Fractional-order Mathematical Model Of the Penstock Systemmentioning

confidence: 99%

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

Wang

Chen

et al. 2016

Chaos, Solitons & Fractals

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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.

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Section: Fractional-order Mathematical Model Of the Penstock Systemmentioning

confidence: 99%

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

Wang

Chen

et al. 2016

Chaos, Solitons & Fractals

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“…thermal diffusion (Battaglia et al, 2001;Wang, 2010;Gabano and Poinot, 2011;Datsko, 2012;Battaglia et al, 2012;Victor et al, 2013;Maachou et al, 2014;Sierociuket et al, 2015); . viscoelastic materials (Moreau et al, 2002;Deng, 2004;Meral et al, 2010;Castaldo, 2013;Grzesikiewicz et al, 2013;Dai et al, 2015;Xu et al, 2015;Zerpa et al, 2015;Zopf, 2015); . hydrodynamics (Tarasov, 2005);…”

Section: Introductionmentioning

confidence: 97%

Stability and resonance conditions of second-order fractional systems

Иванова

Moreau

Malti

2016

Journal of Vibration and Control

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The interest of studying fractional systems of second order in electrical and mechanical engineering is first illustrated in this paper. Then, the stability and resonance conditions are established for such systems in terms of a pseudo-damping factor and a fractional differentiation order. It is shown that a second-order fractional system might have a resonance amplitude either greater or less than one. Moreover, three abaci are given allowing the pseudo-damping factor and the differentiation order to be determined for, respectively, a desired normalized gain at resonance, a desired phase at resonance, and a desired normalized resonant frequency. Furthermore, it is shown numerically that the system root locus presents a discontinuity when the fractional differentiation order is an integral number.

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“…The ranges of operation are however inseparably linked to the regulation of the hydro-turbine governing system. Several studies available in the literature focused on the definition of models for the study of ranges of operation and dynamics [4][5][6][7][8][9][10][11][12]. For example, Nagode et al [4] proposed a mathematical model of a Francis turbine with a surge tank and suggested a novel method for the control of a hydropower plant; Li et al [5] focused on the modeling of a dynamical hydraulic turbine governing systems with nonelastic water hammer effect.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag

Chen

Zhang

et al. 2017

Communications in Nonlinear Science and Numerical Simulation

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This paper focus on a Hamiltonian mathematical modeling for a hydro-turbine governing system including fractional item and time-lag. With regards to hydraulic pressure servo system, an universal dynamical model is proposed, taking into account the viscoelastic properties and low-temperature impact toughness of constitutive materials as well as the occurrence of time-lag in the signal transmissions. The Hamiltonian model of the hydro-turbine governing system is presented using the method of orthogonal decomposition. Furthermore, a novel Hamiltonian function that provides more detailed energy information is presented, since the choice of the Hamiltonian function is the key issue by putting the whole dynamical system to the theory framework of the generalized Hamiltonian system. From the numerical experiments based on a real large hydropower station, we prove that the Hamiltonian function can describe the energy variation of the hydro-turbine suitably during operation. Moreover, the effect of the fractional  and the time-lag  on the dynamic variables of the hydro-turbine governing system are explored and their change laws identified, respectively. The physical meaning between fractional calculus and time-lag are also discussed in nature. All of the above theories and numerical results are expected to provide a robust background for the safe operation and control of large hydropower stations.

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Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system

Cited by 91 publications

References 36 publications

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

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

Stability and resonance conditions of second-order fractional systems

Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag

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