This letter investigates how to identify the marginal bottleneck,which is defined as the constraint most likely to be violated with the increasing wind generation uncertainty of power system in real-time dispatch.The ...This letter investigates how to identify the marginal bottleneck,which is defined as the constraint most likely to be violated with the increasing wind generation uncertainty of power system in real-time dispatch.The presented method takes the correlation of wind power prediction error(WPPE)into account,leading to an ellipsoidal formulation of wind power generation region(WGR).Based on constructed WGR,the identification procedure is formulated as a max-max-min problem,which is solved by the algorithm based on iteration linear program with the proposed method to select appropriate initial points of WPPE.Finally,two cases are tested,demonstrating the efficacy and efficiency of the procedure to identify marginal bottleneck.展开更多
The sparse distribution characteristics of renewable energy resources can lead to there being tens of kilometers of transmission lines between a grid-connected inverter and the actual grid.Accurate analysis of the sta...The sparse distribution characteristics of renewable energy resources can lead to there being tens of kilometers of transmission lines between a grid-connected inverter and the actual grid.Accurate analysis of the stability of such gridconnected inverter systems currently involves using a complex hyperbolic function to shaped model of the transmission line circuit.This has proved to be problematic,so,drawing upon the distribution parameter characteristics of transmission lines,this paper looks at how to use impedance-based stability criteria to assess the stability of multi-paralleled grid-connected inverters.First,the topology of multi-paralleled inverters connected to the grid via transmission lines is established,using each transmission line terminal as a grid connection point.Each grid-connected system is taken to be equivalent to a small-signal circuit model of the“current source-grid”.Euler’s formula and the Nyquist stability criterion are combined to assess the stability of the associated grid-connected current transfer functions and evaluate the stability of the grid-connected current.Finally,a simulation analysis circuit is constructed to verify whether power line intervention will cause stability problems in the grid-connected system.Overall,it is found that long-distance transmission lines are more likely to cause unstable output of the grid-connected current.It is also found that the number of grid-connected inverters,the short-circuit ratio(SCR),the distorted grid and the inverter parameters can all have a significant impact on the stability of the grid-connected current.展开更多
We show how to combine in a natural way(i.e.,without any test nor switch)the conservative and non-conservative formulations of an hyperbolic system that has a conservative form.This is inspired from two different clas...We show how to combine in a natural way(i.e.,without any test nor switch)the conservative and non-conservative formulations of an hyperbolic system that has a conservative form.This is inspired from two different classes of schemes:the residual distribution one(Abgrall in Commun Appl Math Comput 2(3):341–368,2020),and the active flux formulations(Eyman and Roe in 49th AIAA Aerospace Science Meeting,2011;Eyman in active flux.PhD thesis,University of Michigan,2013;Helzel et al.in J Sci Comput 80(3):35–61,2019;Barsukow in J Sci Comput 86(1):paper No.3,34,2021;Roe in J Sci Comput 73:1094–1114,2017).The solution is globally continuous,and as in the active flux method,described by a combination of point values and average values.Unlike the“classical”active flux methods,the meaning of the point-wise and cell average degrees of freedom is different,and hence follow different forms of PDEs;it is a conservative version of the cell average,and a possibly non-conservative one for the points.This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem.We also develop a method to perform nonlinear stability.We illustrate the behaviour on several benchmarks,some quite challenging.展开更多
In this paper,we discuss the notion of discrete conservation for hyperbolic conservation laws.We introduce what we call fluctuation splitting schemes(or residual distribution,also RDS)and show through several examples...In this paper,we discuss the notion of discrete conservation for hyperbolic conservation laws.We introduce what we call fluctuation splitting schemes(or residual distribution,also RDS)and show through several examples how these schemes lead to new developments.In particular,we show that most,if not all,known schemes can be rephrased in flux form and also how to satisfy additional conservation laws.This review paper is built on Abgrall et al.(Computers and Fluids 169:10-22,2018),Abgrall and Tokareva(SIAM SISC 39(5):A2345-A2364,2017),Abgrall(J Sci Comput 73:461-494,2017),Abgrall(Methods Appl Math 18(3):327-351,2018a)and Abgrall(J Comput Phys 372,640--666,2018b).This paper is also a direct consequence of the work of Roe,in particular Deconinck et al.(Comput Fluids 22(2/3):215-222,1993)and Roe(J Comput Phys 43:357-372,1981)where the notion of conservation was first introduced.In[26],Roe mentioned the Hermes project and the role of Dassault Aviation.Bruno Stoufflet,Vice President R&D and advanced business of this company,proposed me to have a detailed look at Deconinck et al.(Comput Fluids 22(2/3):215-222,1993).To be honest,at the time,I did not understand anything,and this was the case for several years.I was lucky to work with Katherine Mer,who at the time was a postdoc,and is now research engineer at CEA.She helped me a lot in understanding the notion of conservation.The present contribution can be seen as the result of my understanding after many years of playing around with the notion of residual distribution schemes(or fluctuation-splitting schemes)introduced by Roe.展开更多
We describe and review non oscillatory residual distribution schemes that are rather natural extension of high order finite volume schemes when a special emphasis is put on the structure of the computational stencil.W...We describe and review non oscillatory residual distribution schemes that are rather natural extension of high order finite volume schemes when a special emphasis is put on the structure of the computational stencil.We provide their connections with standard stabilized finite element and discontinuous Galerkin schemes,show that their are really non oscillatory.We also discuss the extension to these methods to parabolic problems.We also draw some research perspectives.展开更多
文摘This letter investigates how to identify the marginal bottleneck,which is defined as the constraint most likely to be violated with the increasing wind generation uncertainty of power system in real-time dispatch.The presented method takes the correlation of wind power prediction error(WPPE)into account,leading to an ellipsoidal formulation of wind power generation region(WGR).Based on constructed WGR,the identification procedure is formulated as a max-max-min problem,which is solved by the algorithm based on iteration linear program with the proposed method to select appropriate initial points of WPPE.Finally,two cases are tested,demonstrating the efficacy and efficiency of the procedure to identify marginal bottleneck.
文摘The sparse distribution characteristics of renewable energy resources can lead to there being tens of kilometers of transmission lines between a grid-connected inverter and the actual grid.Accurate analysis of the stability of such gridconnected inverter systems currently involves using a complex hyperbolic function to shaped model of the transmission line circuit.This has proved to be problematic,so,drawing upon the distribution parameter characteristics of transmission lines,this paper looks at how to use impedance-based stability criteria to assess the stability of multi-paralleled grid-connected inverters.First,the topology of multi-paralleled inverters connected to the grid via transmission lines is established,using each transmission line terminal as a grid connection point.Each grid-connected system is taken to be equivalent to a small-signal circuit model of the“current source-grid”.Euler’s formula and the Nyquist stability criterion are combined to assess the stability of the associated grid-connected current transfer functions and evaluate the stability of the grid-connected current.Finally,a simulation analysis circuit is constructed to verify whether power line intervention will cause stability problems in the grid-connected system.Overall,it is found that long-distance transmission lines are more likely to cause unstable output of the grid-connected current.It is also found that the number of grid-connected inverters,the short-circuit ratio(SCR),the distorted grid and the inverter parameters can all have a significant impact on the stability of the grid-connected current.
基金the author was partially funded by the SNF project 200020_175784.
文摘We show how to combine in a natural way(i.e.,without any test nor switch)the conservative and non-conservative formulations of an hyperbolic system that has a conservative form.This is inspired from two different classes of schemes:the residual distribution one(Abgrall in Commun Appl Math Comput 2(3):341–368,2020),and the active flux formulations(Eyman and Roe in 49th AIAA Aerospace Science Meeting,2011;Eyman in active flux.PhD thesis,University of Michigan,2013;Helzel et al.in J Sci Comput 80(3):35–61,2019;Barsukow in J Sci Comput 86(1):paper No.3,34,2021;Roe in J Sci Comput 73:1094–1114,2017).The solution is globally continuous,and as in the active flux method,described by a combination of point values and average values.Unlike the“classical”active flux methods,the meaning of the point-wise and cell average degrees of freedom is different,and hence follow different forms of PDEs;it is a conservative version of the cell average,and a possibly non-conservative one for the points.This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem.We also develop a method to perform nonlinear stability.We illustrate the behaviour on several benchmarks,some quite challenging.
文摘In this paper,we discuss the notion of discrete conservation for hyperbolic conservation laws.We introduce what we call fluctuation splitting schemes(or residual distribution,also RDS)and show through several examples how these schemes lead to new developments.In particular,we show that most,if not all,known schemes can be rephrased in flux form and also how to satisfy additional conservation laws.This review paper is built on Abgrall et al.(Computers and Fluids 169:10-22,2018),Abgrall and Tokareva(SIAM SISC 39(5):A2345-A2364,2017),Abgrall(J Sci Comput 73:461-494,2017),Abgrall(Methods Appl Math 18(3):327-351,2018a)and Abgrall(J Comput Phys 372,640--666,2018b).This paper is also a direct consequence of the work of Roe,in particular Deconinck et al.(Comput Fluids 22(2/3):215-222,1993)and Roe(J Comput Phys 43:357-372,1981)where the notion of conservation was first introduced.In[26],Roe mentioned the Hermes project and the role of Dassault Aviation.Bruno Stoufflet,Vice President R&D and advanced business of this company,proposed me to have a detailed look at Deconinck et al.(Comput Fluids 22(2/3):215-222,1993).To be honest,at the time,I did not understand anything,and this was the case for several years.I was lucky to work with Katherine Mer,who at the time was a postdoc,and is now research engineer at CEA.She helped me a lot in understanding the notion of conservation.The present contribution can be seen as the result of my understanding after many years of playing around with the notion of residual distribution schemes(or fluctuation-splitting schemes)introduced by Roe.
基金The author has been supported by the FP7 Advanced Grant#226316“ADDECCO”.The help of Mario Richiuto(INRIA)and A.Larat(now CNRS researcher at Ecole Centrale de Paris,France)are warmly acknowledged.
文摘We describe and review non oscillatory residual distribution schemes that are rather natural extension of high order finite volume schemes when a special emphasis is put on the structure of the computational stencil.We provide their connections with standard stabilized finite element and discontinuous Galerkin schemes,show that their are really non oscillatory.We also discuss the extension to these methods to parabolic problems.We also draw some research perspectives.
