• Title/Summary/Keyword: Newton's Approach

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Application of Newton's Approach for Transient Stability Improvement by Using Generation Rescheduling (발전력 재배분을 이용하여 과도안정도를 향상하기 위한 Newton's Approach 응용)

  • Kim, Kyu-Ho
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.27 no.1
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    • pp.68-75
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    • 2013
  • This paper presents a scheme to improve transient stability using Newton's Approach for generation rescheduling. For a given contingency, the energy margin and sensitivities are computed. The bigger energy margin sensitivity of generator is, the more the generation of the generator effects to the transient stability. According to energy margin sensitivity, the control variables of generation rescheduling are selected. The fuel cost function is used as objective function to reallocate power generation. The results are compared to the results of time simulation to show its the effectiveness.

ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HOLDERIAN INVERSES OF OPERATORS

  • Argyros, Ioannis K.
    • The Pure and Applied Mathematics
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    • v.16 no.1
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    • pp.13-18
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    • 2009
  • A semilocal convergence analysis is provided for Newton's method in a Banach space. The inverses of the operators involved are only locally $H{\ddot{o}}lderian$. We make use of a point-based approximation and center-$H{\ddot{o}}lderian$ hypotheses for the inverses of the operators involved. Such an approach can be used to approximate solutions of equations involving nonsmooth operators.

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ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY $H{\ddot{O}}LDERIAN$ OPERATORS

  • Argyros, Ioannis K.
    • The Pure and Applied Mathematics
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    • v.15 no.2
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    • pp.111-120
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    • 2008
  • A semi local convergence analysis is provided for Newton's method in a Banach space setting. The operators involved are only locally Holderian. We make use of a point-based approximation and center-Holderian hypotheses. This approach can be used to approximate solutions of equations involving nonsmooth operators.

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SOLVING MATRIX POLYNOMIALS BY NEWTON'S METHOD WITH EXACT LINE SEARCHES

  • Seo, Jong-Hyeon;Kim, Hyun-Min
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.12 no.2
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    • pp.55-68
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    • 2008
  • One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the form $P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m$, where $A_0$, $A_1$, ${\cdots}$, $A_m$ and X are $n{\times}n$ complex matrices. Newton's method was introduced a useful tool for solving the equation P(X)=0. Here, we suggest an improved approach to solve each Newton step and consider how to incorporate line searches into Newton's method for solving the matrix polynomial. Finally, we give some numerical experiment to show that line searches reduce the number of iterations for convergence.

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In Newton's proof of the inverse square law, geometric limit analysis and Educational discussion (Newton의 역제곱 법칙 증명에서 기하학적 극한 분석 및 교육적 시사점)

  • Kang, Jeong Gi
    • Journal of the Korean School Mathematics Society
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    • v.24 no.2
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    • pp.173-190
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    • 2021
  • This study analyzed the proof of the inverse square law, which is said to be the core of Newton's , in relation to the geometric limit. Newton, conscious of the debate over infinitely small, solved the dynamics problem with the traditional Euclid geometry. Newton reduced mechanics to a problem of geometry by expressing force, time, and the degree of inertia orbital deviation as a geometric line segment. Newton was able to take Euclid's geometry to a new level encompassing dynamics, especially by introducing geometric limits such as parabolic approximation, polygon approximation, and the limit of the ratio of the line segments. Based on this analysis, we proposed to use Newton's geometric limit as a tool to show the usefulness of mathematics, and to use it as a means to break the conventional notion that the area of the curve can only be obtained using the definite integral. In addition, to help the desirable use of geometric limits in school mathematics, we suggested the following efforts are required. It is necessary to emphasize the expansion of equivalence in the micro-world, use some questions that lead to use as heuristics, and help to recognize that the approach of ratio is useful for grasping the equivalence of line segments in the micro-world.

Generation Rescheduling Based on Energy Margin Sensitivity for Transient Stability Enhancement

  • Kim, Kyu-Ho;Rhee, Sang-Bong;Hwang, Kab-Ju;Song, Kyung-Bin;Lee, Kwang Y.
    • Journal of Electrical Engineering and Technology
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    • v.11 no.1
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    • pp.20-28
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    • 2016
  • This paper presents a generation rescheduling method for the enhancement of transient stability in power systems. The priority and the candidate generators for rescheduling are calculated by using the energy margin sensitivity. The generation rescheduling formulates the Lagrangian function with the fuel cost and emission such as NOx and SOx from power plants. The generation rescheduling searches for the solution that minimizes the Lagrangian function by using the Newton’s approach. While the Pareto optimum in the fuel cost and emission minimization has a drawback of finding a number of non-dominated solutions, the proposed approach can explore the non-inferior solutions of the multiobjective optimization problem more efficiently. The method proposed is applied to a 4-machine 6-bus system to demonstrate its effectiveness.

SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SINGULAR SYSTEMS WITH CONSTANT RANK DERIVATIVES

  • Argyros, Ioannis K.;Hilout, Said
    • The Pure and Applied Mathematics
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    • v.18 no.2
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    • pp.97-111
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    • 2011
  • We provide a semilocal convergence result for approximating a solution of a singular system with constant rank derivatives, using Newton's method in an Euclidean space setting. Our approach uses more precise estimates and a combination of two Lipschitz-type conditions leading to the following advantages over earlier works [13], [16], [17], [29]: tighter bounds on the distances involved, and a more precise information on the location of the solution. Numerical examples are also provided in this study.

Experimental approach for catalyst bed sizing of liquid propellant thruster (50 Newton 급 액체 추력기의 촉매베드 사이징)

  • An, Sung-Yong;Kwon, Se-Jin
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2008.05a
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    • pp.145-148
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    • 2008
  • A 50 Newton monopropellant thruster being developed for attitude control in a variety of aerospace application systems is described in this paper. A scaled down thruster with platinum on aluminum oxide in the reaction chamber was tested to determine the catalyst capacity. A scaled up thruster, was designed and fabricated using data obtained on small scale device, was evaluated by decomposition efficiency based on temperature, efficiency of characteristic velocity, and measurement of thrust. The performance of a scaled up thruster was 42 Newton in thrust, 98 % in efficiency of characteristic velocity, and 123 sec in specific impulse at sea level.

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