Dynamic evolution characteristics of a fractional order hydropower station system

2018 ◽  
Vol 32 (02) ◽  
pp. 1750363 ◽  
Author(s):  
Xiang Gao ◽  
Diyi Chen ◽  
Donglin Yan ◽  
Beibei Xu ◽  
Xiangyu Wang
Keyword(s):  
Fractional Order ◽  
Careful Analysis ◽  
Hydropower Station ◽  
Dynamic Evolution ◽  
Engineering Practice ◽  
Shaft System ◽  
Dynamical Behaviors ◽  
Evolution Characteristics ◽  
Vertical Evolution ◽  
Hydropower Stations

This paper investigates the dynamic evolution characteristics of the hydropower station by introducing the fractional order damping forces. A careful analysis of the dynamic characteristics of the generator shaft system is carried out under different values of fractional order. It turns out the vibration state of the axis coordinates has a certain evolution law with the increase of the fractional order. Significantly, the obtained law exists in the horizontal evolution and vertical evolution of the dynamical behaviors. Meanwhile, some interesting dynamical phenomena were found in this process. The outcomes of this study enrich the nonlinear dynamic theory from the engineering practice of hydropower stations.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

scholarly journals Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xia Huang ◽  
Zhen Wang ◽  
Yuxia Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Hopfield Neural Network ◽  
Hopfield Neural Networks ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Motions ◽  
Dynamical Behaviors ◽  
Nonlinear Dynamics And Chaos

A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.

scholarly journals Finite Time Synchronization for Fractional Order Sprott C Systems with Hidden Attractors

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Cui Yan ◽  
He Hongjun ◽  
Lu Chenhui ◽  
Sun Guan
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Engineering Practice ◽  
Fractional Order Systems ◽  
Spectral Entropy ◽  
Hidden Attractors ◽  
Finite Time Stability ◽  
Peculiar Phenomenon

Fractional order systems have a wider range of applications. Hidden attractors are a peculiar phenomenon in nonlinear systems. In this paper, we construct a fractional-order chaotic system with hidden attractors based on the Sprott C system. According to the Adomain decomposition method, we numerically simulate from several algorithms and study the dynamic characteristics of the system through bifurcation diagram, phase diagram, spectral entropy, and C0 complexity. The results of spectral entropy and C0 complexity simulations show that the system is highly complex. In order to apply such research results to engineering practice, for such fractional-order chaotic systems with hidden attractors, we design a controller to synchronize according to the finite-time stability theory. The simulation results show that the synchronization time is short and the robustness is stable. This paper lays the foundation for the study of fractional order systems with hidden attractors.

Dynamical Behaviors of a Fractional-Order Predator–Prey Model with Holling Type IV Functional Response and Its Discretization

2019 ◽  
Vol 20 (2) ◽  
pp. 125-136
Author(s):  
A. M. Yousef ◽  
S. Z. Rida ◽  
Y. Gh. Gouda ◽  
A. S. Zaki
Keyword(s):  
Functional Response ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Theoretical Results

AbstractIn this paper, we investigate the dynamical behaviors of a fractional-order predator–prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark–Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results.

scholarly journals A Review of Critical Stable Sectional Areas for the Surge Tanks of Hydropower Stations

Energies ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 6466
Author(s):  
Wencheng Guo ◽  
Yang Liu ◽  
Fangle Qu ◽  
Xinyu Xu
Keyword(s):  
Electrical Coupling ◽  
Stable State ◽  
Future Research ◽  
Regulation System ◽  
Engineering Practice ◽  
Sectional Area ◽  
Surge Tank ◽  
Power Stations ◽  
Pumped Storage ◽  
Hydropower Stations

The critical stable sectional area (CSSA) for surge tanks corresponds to the critical stable state of hydropower stations and is an important index to evaluate the stability of the turbine regulation system. The research on CSSA for surge tanks is always one of the most important topics in the area of transient processes of hydropower stations. The CSSA for surge tanks provides the value basis for the sectional area of surge tanks. In engineering practice, the CSSA for surge tanks is widely used to guide their hydraulic design. This paper provides a systematic literature review about the CSSA for surge tank of hydropower stations. Firstly, the CSSA for surge tanks based on hydraulic transients is discussed. Secondly, the CSSA for surge tanks based on hydraulic-mechanical-electrical coupling transients is presented. Thirdly, the CSSA for air cushion surge tanks is illustrated. Finally, the CSSA for combined surge tanks, i.e., upstream and downstream double surge tanks and upstream series double surge tanks, is presented. In future research, the CSSA for surge tanks of pumped storage power stations should be explored. The CSSA for surge tanks considering multi-energy complement is worth studying.

scholarly journals Dynamic Safety Assessment in Nonlinear Hydropower Generation Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Shuang Li ◽  
Yong Yang ◽  
Qing Xia
Keyword(s):  
Transient Process ◽  
Safety Assessment ◽  
Hydropower Station ◽  
Generation System ◽  
Hydropower Generation ◽  
Safety Level ◽  
Fisher Discriminant ◽  
The Stability ◽  
Evolution Behavior ◽  
Hydropower Stations

This paper focuses on the stability problems in a hydropower station. To enable this study, we consider a nonlinear hydropower generation system for the load rejection transient process based on an existing hydropower station. Herein we identify four critical variables of the generation system. Then, we carry out the dynamic safety assessment based on the Fisher discriminant method. The dynamic safety level of the system is determined, and the evolution behavior in the transient process is also performed. The result demonstrates that the hydropower generation system in this study case can operate safely, which is in a good agreement with the corresponding theory and actual engineering. Thus, the framework of dynamic safety assessment aiming at transient processes will not only provide the guidance for safe operation, but also supply the design standard for hydropower stations.

scholarly journals Theoretical Analysis and Circuit Verification for Fractional-Order Chaotic Behavior in a New Hyperchaotic System

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ling Liu ◽  
Chongxin Liu
Keyword(s):  
Fractional Order ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Circuit Diagram ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Dynamical Behaviors ◽  
Mapping Parameter ◽  
New Hyperchaotic System ◽  
Observation Results

A novel nonlinear four-dimensional hyperchaotic system and its fractional-order form are presented. Some dynamical behaviors of this system are further investigated, including Poincaré mapping, parameter phase portraits, equilibrium points, bifurcations, and calculated Lyapunov exponents. A simple fourth-channel block circuit diagram is designed for generating strange attractors of this dynamical system. Specifically, a novel network module fractance is introduced to achieve fractional-order circuit diagram for hardware implementation of the fractional attractors of this nonlinear hyperchaotic system with order as low as 0.9. Observation results have been observed by using oscilloscope which demonstrate that the fractional-order nonlinear hyperchaotic attractors exist indeed in this new system.

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