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An Algorithm for Short-Circuit Current Interval in Distribution Networks with Inverter Type Distributed Generation Based on affine arithmetic

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Energy Engineering 2024年第7期121卷 1903-1920页

作者： Yan Zhang Bowen Du Benren Pan GuannanWang Guoqiang Xie Tong Jiang Electric Power Research Institute State Grid Jiangxi Electric Power Co.Ltd.Nanchang330096China School of Electrical and Electronic Engineering North China Electric Power UniversityBeijing102206China

During faults in a distribution network,the output power of a distributed generation(DG)may be uncertain.Moreover,the output currents of distributed power sources are also affected by the output power,resulting in uncertainties in the calculation of the short-circuit current at the time of a fault.Additionally,the impacts of such uncertainties around short-circuit currents will increase with the increase of distributed power sources.Thus,it is very important to develop a method for calculating the short-circuit current while considering the uncertainties in a distribution network.In this study,an affine arithmetic algorithm for calculating short-circuit current intervals in distribution networks with distributed power sources while considering power fluctuations is presented.The proposed algorithm includes two stages.In the first stage,normal operations are considered to establish a conservative interval affine optimization model of injection currents in distributed power sources.Constrained by the fluctuation range of distributed generation power at the moment of fault occurrence,the model can then be used to solve for the fluctuation range of injected current amplitudes in distributed power sources.The second stage is implemented after a malfunction occurs.In this stage,an affine optimization model is first established.This model is developed to characterizes the short-circuit current interval of a transmission line,and is constrained by the fluctuation range of the injected current amplitude of DG during normal operations.Finally,the range of the short-circuit current amplitudes of distribution network lines after a short-circuit fault occurs is predicted.The algorithm proposed in this article obtains an interval range containing accurate results through interval operation.Compared with traditional point value calculation methods,interval calculation methods can provide more reliable analysis and calculation results.The range of short-circuit current amplitude obtained by this algorithm is slightly larger than

关键词： Short circuit calculation inverter type distributed power supplies affine arithmetic distribution network

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affine arithmetic in matrix form for polynomial evaluation and algebraic curve drawing

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Progress in Natural Science:Materials International 2002年第1期 79-82页

作者： Ralph MARTIN Irina VOICULESCU Adrian BOWYER Cardiff University Computing Laboratory Department of Computer Science Department of Mechanical Engineering Oxford University UK University of Bath

This paper shows how tight bounds for the range of a bivariate polynomial can be found using a matrix method based on affine arithmetic. Then, this method is applied to drawing an algebraic curve with a hierarchical algorithm, which demonstrates that more accurate answers can be obtained more rapidly than using conventional interval arithmetic.

关键词： affine arithmetic interval arithmetic algebraic curve drawing.

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Bi-level Multi-objective Joint Planning of Distribution Networks Considering Uncertainties

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Journal of Modern Power Systems and Clean Energy 2022年第6期10卷 1599-1613页

作者： Shouxiang Wang Yichao Dong Qianyu Zhao Xu Zhang Key Laboratory of Smart Grid of Ministry of Education Tianjin UniversityTianjin300072China State Grid Tianjin Electric Power Company Economic and Technological Research Institute Tianjin 300171China State Grid Tianjin Electric Power Company Tianjin300010China

With the increasing penetration of photovoltaics in distribution networks,the adaptability of distribution network under uncertainties needs to be considered in the planning of distribution systems.In this paper,the interval arithmetic and affine arithmetic are applied to deal with uncertainties,and an affine arithmetic based bi-level multi-objective joint planning model is built,which can obtain the planning schemes with low constraint-violation risk,high reliability and strong adaptability.On this basis,a bi-level multi-objective solution methodology using affine arithmetic based non-dominated sorting genetic algorithm II is proposed,and the planning schemes that simultaneously meet economy and adaptability goals under uncertainties can be obtained.To further eliminate bad solutions and improve the solution qualities,an affine arithmetic based dominance relation weakening criterion and a deviation distance based modification method are proposed.A 24-bus test system and a 10 kV distribution system of China are used for case studies.Different uncertainty levels are compared,and a sensitivity analysis of key parameters is conducted to explore their impacts on the final planning schemes.The simulation results verify the advantages of the proposed affine arithmetic based planning method.

关键词： affine arithmetic adaptability multi-objective joint planning Pareto optimal front uncertainty

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Solving Fully Fuzzy Nonlinear Eigenvalue Problems of Damped Spring-Mass Structural Systems Using Novel Fuzzy-affine Approach

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Computer Modeling in Engineering & Sciences 2019年第12期121卷 947-980页

作者： S.Rout S.Chakraverty Department of Mathematics National Institute of Technology RourkelaOdishaIndia

The dynamic analysis of damped structural system by using finite element method leads to nonlinear eigenvalue problem(NEP)(particularly,quadratic eigenvalue problem).In general,the parameters of NEP are considered as exact values.But in actual practice because of different errors and incomplete information,the parameters may have uncertain or vague values and such uncertain values may be considered in terms of fuzzy numbers.This article proposes an efficient fuzzy-affine approach to solve fully fuzzy nonlinear eigenvalue problems(FNEPs)where involved parameters are fuzzy numbers viz.triangular and trapezoidal.Based on the parametric form,fuzzy numbers have been transformed into family of standard intervals.Further due to the presence of interval overestimation problem in standard interval arithmetic,affine arithmetic based approach has been implemented.In the proposed method,the FNEP has been linearized into a generalized eigenvalue problem and further solved by using the fuzzy-affine approach.Several application problems of structures and also general NEPs with fuzzy parameters are investigated based on the proposed procedure.Lastly,fuzzy eigenvalue bounds are illustrated with fuzzy plots with respect to its membership function.Few comparisons are also demonstrated to show the reliability and efficacy of the present approach.

关键词： Fuzzy nonlinear eigenvalue problem fuzzy set theory affine arithmetic interval overestimation problem triangular fuzzy number trapezoidal fuzzy number fuzzy-affine approach

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