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Fault Analysis and Application Based on Improved Phase-Coordinates fixed-point iterative method in Three-Phase Power Systems

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JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY 2019年第4期14卷 1429-1440页

作者： Mo, Mingrui Hang, Naishan Guangxi Univ Sch Elect Engn Nanning 530004 Peoples R China

This paper proposes an improved version of the fixed-point iterative method to solve the fault problems in three-phase power systems by phase-coordinates. The proposed method has non-expansive characteristic using for fault analysis and calculation, when the injected currents of the loads are with non-increasing functions about voltages. Based on the decoupling method, the network topologies enable to obtain the connections models for the system's equipment and faults by adjusting the values of connected admittances, which makes the fault power systems easy to integrate into the proposed method rather than the multi-port Thevenin's theory or the compensation method. And the matched version of the fixed-point iterative method is designed and developed that can be used directly to calculate and analyze all kinds of simple faults and complicated faults both in the power systems and in the power system of multiple parallel lines. The validity and effectiveness of the proposed method can be demonstrated by the numerical test systems.

关键词： Decoupled method Phase-coordinate Network topology Fault analysis fixed-point iterative method

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Existence-uniqueness and fixed-point iterative method for general nonlinear fourth-order boundary value problems

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2021年第1-2期67卷 221-231页

作者： Chang, Shih-Hsiang Far East Univ Dept Mech Engn Tainan 74448 Taiwan

Existence and uniqueness results are established for the general nonlinear fourth-order two-point boundary value problem with general linear homogeneous boundary conditions. The proofs are based on the Banach fixed-point theorem under the conditions that the nonlinear term is bounded and Lipschitz in a specific region. A fixed-point iterative method for finding the solution of the problem is also proposed with error estimates. The resulting iterative solutions automatically satisfy the boundary conditions provided that the initial iterate does so. Two examples are given to illustrate the applicability of the proposed approach and the efficiency of the iterative method.

关键词： Fourth-order boundary value problem Existence and uniqueness fixed-point iterative method

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An inertial extrapolation method for convex simple bilevel optimization

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OPTIMIZATION methodS & SOFTWARE 2021年第1期36卷 1-19页

作者： Shehu, Yekini Phan Tu Vuong Zemkoho, Alain Univ Nigeria Dept Math Nsukka Nigeria Univ Vienna Fac Math Vienna Austria Univ Southampton Sch Math Southampton Hants England Univ Wurzburg Inst Math Emil Fischer Str 30 D-97074 Wurzburg Germany

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as a simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner problem consists of minimizing the sum of smooth and non-smooth functions while the outer one is the minimization of a smooth convex function. We first formulate and give strong convergence analysis of an inertial algorithm for fixed-point problem of a non-expansive operator in an infinite dimensional Hilbert space. Then we convert the simple bilevel optimization problem to a fixed-point problem of a non-expansive operator in finite dimensional space and design the corresponding algorithm and establish its convergence. Our numerical experiments show that the proposed method in this paper outperforms the currently known best algorithm to solve the class of bilevel optimization problem considered.

关键词： Simple bilevel optimization fixed-point iterative method inertial extrapolation

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Kinematically Exact Inverse-Simulation Techniques with Applications to Rotorcraft Aggressive-Maneuver Analyses

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INTERNATIONAL JOURNAL OF AERONAUTICAL AND SPACE SCIENCES 2020年第3期21卷 790-805页

作者： Kim, Chang-Joo Lee, Seong Han Hur, Sung Wook Konkuk Univ Dept Aerosp Informat Syst Engn Seoul 05029 South Korea

An inverse-simulation problem is reformulated to exactly satisfy the kinematic constraints imposed by the prescribed trajectory. Thereby, the problem can be transformed into an index 1 differential-algebraic equation that is much more easily solvable than the higher index system of the conventional formulation. Various numerical methods which have been successfully used in the pseudo-spectral inverse-simulation techniques are adopted with some modifications to efficiently solve the resultant system. The paper proposes a formal algorithm to describe the detailed solution process. The algorithm is applied to the analyses of the vertical, slalom, and helical-turn maneuvers of Bo-105. The simulation results with both the conventional and present formulations are compared to show the numerical features of the present methods. Effects of the solution-control parameters, the aggressiveness level of a maneuver, the quality of the prescribed trajectory, and the fidelity level of the math model are thoroughly investigated. The results of applications show that the proposed algorithm is extremely robust in that solution convergence is less sensitive to the maneuver aggressiveness, the quality of the generated trajectory, and the solution-control parameters. Therefore, it can be concluded that the kinematically exact inverse-simulation techniques deserve to be a one of the promising inverse-simulation methods like the pseudo-spectral inverse-simulation techniques.

关键词： Inverse simulation Aggressive maneuver Pseudo-spectral method Quasi-Newton method fixed-point iterative method

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Fault section location for distribution network based on linear integer programming

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2023年第2期54卷 391-404页

作者： Yu, Haocheng Wu, Zhengtian Jiang, Baoping Karimi, Hamid Reza Suzhou Univ Sci & Technol Sch Elect & Informat Engn Suzhou 215009 Peoples R China Politecn Milan Dept Mech Engn I-20156 Milan Italy

In the power society, the fault location of the distribution network has always been the focus of scholars. When a fault occurs, it needs to be located quickly and accurately to avoid more significant losses. Due to the wide application of distributed generation in the distribution network, many traditional methods are no longer applicable. Thus, a fast and high fault tolerance method is urgently needed to solve the complex fault location problem of the distribution network. According to the logical and algebraic relationship of fault location, a linear integer programming model for fault section location of the distribution network is established. This paper adopts a new method for solving integer programming, called the fixed-point iterative method. This method has unique advantages in dealing with such large-scale problems and is easily realised through distributed computing, thereby saving time. Finally, through MATLAB experimental simulation, results show that the integer programming method can quickly locate the fault and has high fault tolerance.

关键词： Distribution network distributed generation fault section location linear integer programming fixed-point iterative method

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Efficient and Robust Inverse Simulation Techniques Using Pseudo-Spectral Integrator with Applications to Rotorcraft Aggressive Maneuver Analyses

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INTERNATIONAL JOURNAL OF AERONAUTICAL AND SPACE SCIENCES 2019年第3期20卷 768-780页

作者： Kim, Chang-Joo Lee, Do Hyeon Hur, Sung Wook Konkuk Univ Dept Aerosp Informat Syst Engn Seoul 05029 South Korea

This paper intends to propose new inverse simulation techniques to cope with the numerical stability and accuracy problems frequently encountered with the integration inverse simulation methods widely used today. To achieve this, the pseudo-spectral method is adopted as a time integrator of the aircraft motion equations. In addition, the quasi-Newton and fixed-point iterative methods are applied to solve the resultant nonlinear algebraic equations in an efficient manner. These algorithms are integrated into a moving horizon framework to guarantee fast numerical convergence. The proposed methods are applied to the analyses of rotorcraft aggressive maneuvers such as popup, pirouette, and depart/abort mission-task-elements defined in the rotorcraft handling qualities requirements, ADS-33E-PRF. Numerical properties of the proposed methods are thoroughly investigated to clarify the effect of the numbers of quadrature nodes and time-horizon segments, and the level of maneuver aggressiveness on the robustness and efficiency of the analyses. Numerical efficiency and robustness of the present method are identified using specially designed performance measures such as the number of iterations to obtain a converged solution, functional residuals at the final solutions, and the variation of the adaptive relaxation factor. The results show that the present approach can provide extremely fast solutions of the inverse simulation problems and presents strong robustness to the level of maneuver aggressiveness, long-term simulation, and solution control parameters. Therefore, it is worthwhile to use the present techniques as one of the inverse simulation methods.

关键词： Inverse simulation Aggressive maneuver Pseudo-spectral method Quasi-Newton method fixed-point iterative method

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Solving the Market Split Problem Using a Distributed Computation Approach

Solving the Market Split Problem Using a Distributed Computa...

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IEEE International Conference on Information and Automation (ICIA)

作者： Wu, Zhengtian Dang, Chuangyin Zhu, Changan Univ Sci & Technol China Dept Precis Machinery & Precis Instrumentat Hefei 230026 Peoples R China City Univ Hong Kong Kowloon Dept Syst Engn & Engn Management Hong Kong Peoples R China

ISBN: (纸本)9781479913343

A distributed implementation of Dang's fixed-point iterative method is proposed to solve the market split problem which has been considered as a benchmark and a challenge to the algorithms solving linear systems with 0/1 variables. There are two steps to solve the market split problem in this paper. The first step is converting the problem to a reformulated polytope judgement problem based on lattice basis reduction. In the next step, the distributed Dang's method is used to judge whether there exits an integer point in the polytope. This is the first distributed implementation to solve the market split problem to our knowledge. Numerical results show that the approach is effective and it is more powerful than CPLEX to solve the market split problem.

关键词： Market Split Problem fixed-point iterative method Basis Reduction Distributed Implementation

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正规型纳什均衡点的整数规划计算方法及不动点算法的分布式实现

正规型纳什均衡点的整数规划计算方法及不动点算法的分布式实现

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作者：吴征天中国科学技术大学

学位级别：博士

纳什均衡的正式定义第一次出现在文章[1]中,但对它的研究已经具有了很长的历史,并且它在博弈论及其相关应用(比如经济学,计算机科学,管理科学,生物学,社会学等等)中发挥着基石作用。纳什均衡的概念是用来分析多决策者同时做决策时的决... 详细信息

纳什均衡的正式定义第一次出现在文章[1]中,但对它的研究已经具有了很长的历史,并且它在博弈论及其相关应用(比如经济学,计算机科学,管理科学,生物学,社会学等等)中发挥着基石作用。纳什均衡的概念是用来分析多决策者同时做决策时的决策结果,换句话说,它提供了当所有人的决策结果相互依赖时,对决策组的一种提前预测。纳什均衡是以John Forbes Nash命名的,他和博弈论理论学家Reinhard Selten, John Harsanyi在1994共享了诺贝尔经济学奖。在Antoine Augustin Cournot的垄断理论书[2]中,第一次出现了纳什均衡的概念,在Cournot的理论中所有公司都可以选择提高产品数量来提高公司利润,然而,对某一个公司来说,它最佳的生产产品数量依赖于别的公司,如果给定了其他的公司的生产数量,每个公司生产数量都可以使本公司利润最大化,就是一个Cournot均衡点,这是最早的关于纯策略纳什均衡点的研究。在Cournot分析均衡稳定性的时候,最佳动态响应的概念也被用到。当提出混合策略的纳什均衡的概念后,现在博弈论中关于纳什均衡的概念就完全被改变了。在这样的混合策略纳什均衡中,每一个参与者对可能的行动可以以一种概率的方式来选择决策。这种纳什均衡问题在书[3]中第一次被提及,但是书中仅仅考虑了一种零和的特殊类型。文章[1]第一次给出了纳什均衡的正式定义,并证明了任何有限策略博弈中至少存在一个混合策略的纳什均衡。随着纳什均衡概念的发展,一些博弈论研究者发现在一些情况下所做的预测总是有误差,这主要是因为一个博弈中经常存在着多个纳什均衡点,而这些均衡点通常和我的直观概念不同。为了得到更精确的预测,一些被称为改良版纳什均衡的概念在文章[4-7]中被提出来。自从纳什均衡的概念被提出来,纳什均衡已经被应用到了各行各业。书[3]使用纳什均衡的概念扩展了经济学的范围；文章[8]第一次使用纳什均衡的概念来分析敌对情况,比如军备竞赛和战争[10]；纳什均衡可以用来分析不同人之间合作的可能性,分析他们是否会冒险来得到一个合作结果[11]；文章[12]使用纳什均衡的概念来分析货币危机和银行倒闭的概率；其他方面的应用包括交通流[13],如何组织拍卖[14-16],立法管理[17],足球比赛里的点球[18]以及教育过程中多社团竞争效果的分析[19]。在这些纳什均衡的应用中,一个重要的研究课题是如何有效的选择一个纳什均衡点,特别是如何选择一个多人有限策略博弈的均衡点。为了解决这个问题,接下来的文献中做了很多贡献。从计算复杂度方面来说,文章[20,21]证明了仅仅寻找一个纳什均衡点的问题就是PAD-complete问题,所以很难寻找到一个纳什均衡点,寻找所有纳什均衡点就更加困难了。Lemke-Howson算法[26]是计算双矩阵博弈均衡点的第一个方法,这个算法是在用代数方法证明双矩阵博弈至少存在一个均衡点时得到的,在实际应用中,这个算法效率很高,被称为至今计算纳什均衡点最好的方法[27],但是在最坏的情况下,旋转操作的数量会随纯策略数量指数增长[28].后来,文章[29]证明了用Lemke-Howson算法寻找任何一个纳什均衡点都是一个PSPACE-complete问题。文章[30,31]把Lemke-Howson算法扩展为可以求解多人博弈问题。为了估计一个连续映射的不动点,单纯型法第一次在文章[32]提出,并在[33-39]中得到了进一步的发展,这个单纯型法后来被用来计算纳什均衡点[40]。文章[41]很好的处理了非线性互补问题,这篇文章提出来一种很好的求解非合作多人博弈的纳什均衡点的方法。关于单纯型法的进一步研究可以在文章[42,43]中找到,计算结果显示这种方法的迭代次数很少。通过开发文章[44]中的线性追踪过程,一种旋转过程的方法在文章[45,46]中被提出用来计算双人博弈的纳什均衡点,这种旋转过程的方法可以表述如下：所有人开始任选一个策略组,通过考虑初始策略组而对现有策略进行改变,从而达到一个均衡点。更精确的说,初始最优化策略组被选到的概率越来越大,别的策略组被选到的概率越来越小。初始策略组在整个调整过程中发挥了很重要的作用,因为所有的调整都是基于初始策略组,这种方法很容易被计算机实现,同时,这个过程已经被扩展为寻找多人博弈的纳什均衡点[47]。1996年前关于计算纳什均衡点的文献可以在文章[48]中找到,计算两人博弈的纳什均衡点的文献可以在文章[49]中找到。通过研究问题的可微性,一些关于计算纳什均衡的方法已经在以下文献中提出。通过两个系数,一种平滑的对数跟踪过程在文章[50,6]中被开发出来,对每个博弈,这个对数跟踪过程首先在这个博弈的策略组规定一个优先的概率分布,给定优先概率分布,这个过程会在所有纳什均

关键词： Nash Equilibrium Mixed Integer Programming NP-hard Problem Mul-tilinear Term fixed-point iterative method Distributed Implementation

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