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Day-ahead Optimal Dispatch Model for coupled system Considering Ladder-type Ramping Rate and Flexible Spinning Reserve of Thermal Power Units

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Journal of Modern Power systems and Clean Energy 2022年第6期10卷 1482-1493页

作者： Longjie Yang Niancheng Zhou Guiping Zhou Yuan Chi Ning Chen Lei Wang Qianggang Wang Dongfeng Chang State Key Laboratory of Power Transmission Equipment and system Security and New Technology Chongqing UniversityChongqing 400044China State Grid Liaoning Electric Power Company Limited Shenyang 110006China State Key Laboratory of Operation and Control of Renewable Energy&Storage systems(China Electric Power Research Institute) Nanjing 210003China Xi’an Thermal Power Research Institute Company Limited Xi’an 710054China IEEE

In northern China,thermal power units(TPUs)are important in improving the penetration level of renewable *** such areas,the potentials of coordinated dispatch of renewable energy sources(RESs)and TPUs can be better realized,if RESs and TPUs connected to the power grid at the same point of common coupling(PCC)are dispatched as a coupled ***,the definition of the coupled system is introduced,followed by an analysis on its ***,based on the operation characteristics of deep peak regulation(DPR)of TPUs in the coupled system,the constraint of the ladder-type ramping rate applicable for day-ahead dispatch is proposed,and the corresponding flexible spinning reserve constraint is further ***,considering these constraints and peak regulation ancillary services,a day-ahead optimal dispatch model of the coupled system is ***,the operational characteristics and advantages of the coupled system are analyzed in several case studies based on a real-world power grid in Liaoning province,*** numerical results show that the coupled system can further improve the economic benefits of RESs and TPUs under the existing policies.

关键词： coupled system ladder-type ramping rate flexible spinning reserve day-ahead optimal dispatch deep peak regulation peak regulation ancillary services

RATIONAL SPECTRAL COLLOCATION METHOD FOR A coupled system OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS

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Journal of Computational Mathematics 2011年第4期29卷 458-473页

作者： Suqin Chen Yingwei Wang Xionghua Wu Department of Mathematics Tongji University Shanghai 200092 China

A, novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.

关键词： Singular perturbation coupled system Rational spectral collocation method,Boundary layer Reaction-diffusion Convection-diffusion.

A coupled system OF INTEGRAL EQUATIONS IN REFLEXIVE BANACH SPACES

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Acta Mathematica Scientia 2012年第5期32卷 2021-2028页

作者： A.M.A.El-Sayed H.H.G.Hashem Faculty of Science Alexandria UniversityAlexandriaEgypt Collage of Science & Arts Qassim UniversityBuraidahSaudi Arabia

We present an existence theorem for at least one weak solution for a coupled system of integral equations of Volterra type in a reflexive Banach spaces relative to the weak topology.

关键词： weak solution Volterra integral equation coupled system

LOCAL CLASSICAL SOLUTION OF FREE BOUNDARY PROBLEM FOR A coupled system

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Acta Mathematica Scientia 2005年第2期25卷 259-273页

作者：王晓华易法槐杨舟 School of Mathematical Sciences South China University of Technology Guangzhou 510640China Infomation & Electron Technological InstituteSouth China Normal UniversityGuangzhou 510631China Department of Mathematics South China Normal University Guangzhou 510631China

This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary (?) y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.

关键词： Local existence free boundary coupled system

Nonlinear parabolic predator-prey coupled system with convection

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International Journal of Biomathematics 2021年第2期14卷 83-118页

作者： Jose Luis Diaz Palencia Mariano Fernandez Lopez University Foundation San Pablo CEU Spain

The aim of this work is to provide a formulation of two related nonlinear diffusive convective models in the form of coupled reaction-absorption ***,the postulated models are studied with an analytical *** on,numerical evidences are considered to account for a precise *** problem(P)analyzed is of the form:ut=δΔu+c⋅∇u+v^(n),vt=ϵΔv+c⋅∇v−um,n,m∈(0,1),u_(0)(x),v_(0)(x)>0∈L^(1)_(loc)(RN)∩L^(∞)(R^(N)).(0.1)Afterwards,a related problem P_(T)is studied:ut=δΔu+c⋅∇u−v^(n)(u−d),vt=ϵΔv+c⋅∇v−u^(m)v,n,m∈(0,1),u_(0)(x),v_(0)(x)>0∈L^(1)_(loc)(R^(N))∩L^(∞)(R^(N)).(0.2)The principal aspects for analysis are related to the existence and the derivation of particular solutions to reproduce the dynamic of the interacting *** the problem PT,we make use of the TW approach to study existence of solutions and precise evolution of *** that the term predator is used to refer to an invasive behavior,while the term prey is used for the invaded species.

关键词： Nonlinearity reaction absorption coupled system diffusion,traveling waves

THE UPWIND FINITE DIFFERENCE FRACTIONAL STEPS METHOD FOR NONLINEAR coupled system OF DYNAMICS OF FLUIDS IN POROUS MEDIA

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Journal of systems Science & Complexity 2006年第4期19卷 498-516页

作者： Yirang YUAN Institute of Mathematics Shandong University Jinan 250100 China.

For nonlinear coupled system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward, trod two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources.

关键词： Convergence coupled system multilayer dynamics of fluids in porous media nonlinear equations upwind finite difference fractional steps method.

A Parameter-Uniform Finite Difference Method for a coupled system of Convection-Diffusion Two-Point Boundary Value Problems

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Numerical Mathematics(Theory,Methods and Applications) 2008年第2期1卷 176-197页

作者： Eugene O'Riordan Jeanne Stynes Martin Stynes School of Mathematical Sciences Dublin City University Glasnevin Department of Computing Cork Institute of Technology Department of Mathematics National University of Ireland

A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their convective and reactive terms via matrices B and A *** system is in general singularly perturbed. Unlike the case of a single equation,it does not satisfy a conventional maximum princi- *** hypotheses are placed on the coupling matrices B and A that ensure exis- tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain;these hypotheses can be regarded as a strong form of diagonal dominance of *** solution is decomposed into a sum of regular and layer *** are established on these compo- nents and their derivatives to show explicitly their dependence on the small parameterε.Finally,numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver- gent,uniformly inε,to the true solution in the discrete maximum *** results on Shishkin meshes are presented to support these theoretical bounds.

关键词： Singularly perturbed convection-diffusion coupled system piecewise-uniform mesh

Positive Solutions of Boundary Value Problem for a coupled system of Nonlinear Third-order Differential Equations

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Chinese Quarterly Journal of Mathematics 2013年第4期28卷 522-531页

作者： ZHANG Yu-chuan ZHOU Zong-fu XU Xin School of Mathematical Sciences Anhui University Hefei 230039 China

By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results.

关键词： boundary value problem coupled system positive solution cone expansion-compression theorem

Existence of Solution for a coupled system of Fractional Integro-Differential Equations on an Unbounded Domain

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Analysis in Theory and Applications 2013年第1期29卷 47-61页

作者： Azizollah Babakhani Department of Mathematics Faculty of Basic Science Babol University of Technology

We present the existence of solution for a coupled system of fractional integro-differential equations. The differential operator is taken in the Caputo fractional sense. We combine the diagonalization method with Arz... 详细信息

关键词： Fractional derivative/integral coupled system Volterra integral equation diagonalization method.