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Transient Stability Analysis of Grid-connected Converters in Wind Turbine systems Based on Linear Lyapunov Function and Reverse-time Trajectory

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Journal of Modern Power systems and Clean Energy 2024年第3期12卷 782-790页

作者： Mohammad Kazem Bakhshizadeh Sujay Ghosh Guangya Yang ?ukasz Kocewiak ?rsted Wind Power A/S the Technical University of Denmark

As the proportion of converter-interfaced renewable energy resources in the power system is increasing, the strength of the power grid at the connection point of wind turbine generators(WTGs) is gradually weakening. Existing research has shown that when connected with the weak grid, the stability of the traditional grid-following controlled converters will deteriorate, and they are prone to unstable phenomena such as oscillation. Due to the limitations of linear analysis that cannot sufficiently capture the stability phenomena, transient stability must be investigated. So far, standalone time-domain simulations or analytical Lyapunov stability criteria have been used to investigate transient stability. However, the time-domain simulations have proven to be computationally too heavy, while analytical methods are difficult to formulate for larger systems, require many modelling assumptions, and are often conservative in estimating the stability boundary. This paper proposes and demonstrates an innovative approach to estimating the transient stability boundary via combining the linear Lyapunov function and the reverse-time trajectory technique. The proposed methodology eliminates the need of time-consuming simulations and the conservative nature of Lyapunov functions. This study brings out the clear distinction between the stability boundaries with different post-fault active current ramp rate controls. At the same time, it provides a new perspective on critical clearing time for wind turbine systems. The stability boundary is verified using time-domain simulation studies.

关键词： Power system stability Trajectory Stability criteria Transient analysis dynamical systems Time-domain analysis Wind turbines

The global stability and optimal control of the COVID-19 epidemic model

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International Journal of Biomathematics 2024年第1期17卷 1-28页

作者： Fengsheng Chien Hassan Saberi Nik Mohammad Shiraziant J.F.Gomez-Aguilar School of Finance and Accounting Fuzhou University of International Studies and Trade Fuzhou 352020 P.R.China Faculty of Business City university of Macao Macao 999078P.R.China Department of Mathematics and Statistics University of Neyshabur NeyshaburIran CONACyT-Tecnologico Nacional de Mécico/CENIDET Interior Internado Palmira S/N Col.Palmira C.P.62490CuernavacaMorelosMérico

This paper considers stability analysis of a Susceptible-Exposed-Infected-Recovered-Virus(SEIRV)model with nonlinear incidence rates and indicates the severity and weakness of control factors for disease transmission.The Lyapunov function using Volterra-Lyapunov matrices makes it possible to study the global stability of the endemic equilibrium point.An optimal control strategy is proposed to prevent the spread of coronavirus,in addition to governmental intervention.The objective is to minimize together with the quantity of infected and exposed individuals while minimizing the total costs of treatment.A numerical study of the model is also carried out to investigate the analytical results.

关键词： Global stability SEIRV epidemic model dynamical systems Volterra-Lyapunov stability optimal control

Dissipativity of Multistep Methods for Delay dynamical systems

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 72-75页

作者： Chengming HUANG (Graduate School of China Academy of Engineering Physics, Beijing 100088, China) E-mail: chengming_huang@*** Graduate School of China Academy of Engineering Physics Beijing 100088 China

This paper is concerned with the numerical solution of dissipative initial value problems with delays by one-leg methods. We focus on the dissipativity of numerical methods. Some general results are given. Specially, an irreducible one-leg method is dissipative for finite-dimensional dynamical systems with delays if and only if it is Astable, and it is dissipative for infinite-dimensional systems if and only if it is strongly A-stable.

关键词： dynamical systems delays one-leg methods dissipativity

A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in dynamical systems

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Communications in Computational Physics 2015年第6期18卷 203-229页

作者： Guoqiao You Shingyu Leung The School of Science Nanjing Audit UniversityNanjingJiangsu ProvinceChina Department of Mathematics The Hong Kong University of Science and TechnologyClear Water BayHong Kong

We propose a new semi-implicit level set approach to a class of curvature dependent flows.The method generalizes a recent algorithm proposed for the motion by mean curvature where the interface is updated by solving the Rudin-Osher-Fatemi(ROF)model for image regularization.Our proposal is general enough so that one can easily extend and apply the method to other curvature dependent motions.Since the derivation is based on a semi-implicit time discretization,this suggests that the numerical scheme is stable even using a time-step significantly larger than that of the corresponding explicit method.As an interesting application of the numerical approach,we propose a new variational approach for extracting limit cycles in dynamical systems.The resulting algorithm can automatically detect multiple limit cycles staying inside the initial guess with no condition imposed on the number nor the location of the limit cycles.Further,we also propose in this work an Eulerian approach based on the level set method to test if the limit cycles are stable or unstable.

关键词： Numerical methods for PDEs level set method dynamical systems flow visualization

Dynamics of Plate Equations with Memory Driven by Multiplicative Noise on Bounded Domains

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Journal of Applied Mathematics and Physics 2024年第4期12卷 1492-1521页

作者： Mohamed Y. A. Bakhet Abdelmajid Ali Dafallah Jing Wang Qiaozhen Ma Fadlallah Mustafa Mosa Ahmed Eshag Mohamed Paride O. Lolika Makur Mukuac Chinor School of Mathematics University of Juba Juba South Sudan Department of Mathematics Faculty of Petroleum and Hydrology Engineering Alsalam University Almugled Sudan College of Mathematics and Statistics Northwest Normal University Lanzhou China Department of Mathematics and Physics Faculty of Education University of Kassala Kassala Sudan Department of Mathematics School of Education University of Juba Juba South Sudan

This article examines the dynamics for stochastic plate equations with linear memory in the case of bounded domain. We investigate the existence of solutions and bounded absorbing set by using the uniform pullback attractors on the tails estimates, and the asymptotic compactness of the random dynamical system is proved by decomposition method, and then we obtain the existence of a random attractor.

关键词： Plate Equations Random Attractors Memory Term dynamical systems

A dynamical inequality for the output of uncertain nonlinear systems

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Science China(Information Sciences) 2013年第1期56卷 112-120页

作者： LI ChanYing GUO Lei National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Key Laboratory of systems and Control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

An important task in control theory is to study the limitations of feedback principle in dealing with uncertainties.Although some progresses have been achieved in this area,they are all focused on some special classes of linearly parameterized nonlinear uncertain systems.In this paper,we will present a dynamic inequality for the output process of a quite general class of nonlinear dynamical control systems with nonlinearly parameterized uncertain parameters.This inequality will be established using a stochastic imbedding approach based on a Cramér-Rao inequality for dynamical systems,and will be shown to play a crucial role in investigating the fundamental limitations of the feedback mechanism.

关键词： dynamical systems uncertain parameters feedback control Cramer-Rao bound

Gedanken Experiment for Looking at δg_tt for Initial Expansion of the Universe and Influence on HUP via dynamical systems, with Positive Pre-Planckian Acceleration

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Journal of High Energy Physics, Gravitation and Cosmology 2016年第4期2卷 531-545页

作者： Andrew Walcott Beckwith Physics Department College of Physics Chongqing University Huxi Campus Chongqing China

We examine through the lens of dynamical systems a “one dimensional” time mapping of emergent VEV from Pre-Planckian space time conditions. As it is, we will from first principles examine what adding acceleration does as to the HUP previously derived. In doing so, we will be trying it in our discussion with the earlier work done on the HUP. not equal to zero, constant, but large would frequently imply which would have three dissimilar real valued roots. And the situation with not equal to zero yields more tractable result for which will have implications for the HUP inequality in Pre-Planckian space-time, and buttresses an analysis of a 1 dimensional “time” mapping for emergent VEV (vacuum expectation values).

关键词： HUP dynamical systems

Dedicated to Professor Chi-Wang Shu on the occasion of his 60th birthday A Proposal on Machine Learning via dynamical systems

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Communications in Mathematics and Statistics 2017年第1期5卷 1-11页

作者： Weinan E Beijing Institute of Big Data Research(BIBDR) BeijingChina Department of Mathematics and PACM Princeton UniversityPrincetonNJUSA Center for Data Science and BICMR Peking UniversityBeijingChina

Wediscuss the idea of using continuous dynamicalsystemstomodel generalhigh-dimensional nonlinear functions used in machine learning.We also discuss theconnection with deep learning.

关键词： Deep learning Machine learning dynamical systems

Analysis of the Caratheodory's Theorem on dynamical System Trajectories Under Numerical Uncertainty

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IEEE/CAA Journal of Automatica Sinica 2018年第4期5卷 787-793页

作者： Pavel Osinenko Grigory Devadze Stefan Streif Automatic Control and System Dynamics Laboratory Technische Universitat Chemnitz09107 ChemnitzGermany IEEE

The current work proposes a new and constructive proof for the Caratheodory's theorem on existence and uniqueness of trajectories of dynamical systems. The key concern is the numerical uncertainty, i.e., the discrepancy between mathematical proofs, algorithms, and their implementations, which may affect the correct functioning of a control system. Due to growing demands on security and compliance with specifications,correctness of the control system functioning is becoming ever more important. Since in both dynamical systems and many control design approaches, one of the central notions is the system trajectory, it is important to address existence and uniqueness of system trajectories in a way which incorporates numerical uncertainty. Constructive analysis is a particular approach to formalizing numerical uncertainty and is used as the basis of the current work. The major difficulties of guaranteeing existence and uniqueness of system trajectories arise in the case of systems and controllers which possess discontinuities in time,since classical solutions to initial value problems do not exist.This issue is addressed in Caratheodory's theorem. A particular constructive variant of the theorem is proven which covers a large class of problems found in practice.

关键词： Constructive analysis Caratheodory’s theorem dynamical systems

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