There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

Power system restoration is a highly complex task that must be performed in a timely manner following a blackout. It is crucial to have the capability of developing a reliable restoration plan that can be adjusted quickly to different system conditions. This paper introduces a framework of an automated process that creates a restoration plan for a given power system. The required input includes the original system data under normal operating conditions and the status of the resources in the system that can be used for restoration. With a set of criteria to select as an option, the presented process can produce a restoration sequence in terms of which generator, load, branches, and breakers to close until a stopping criterion is met. The algorithm of the restoration process is described, and its application to a synthetic 200-bus case provides a restoration sequence from blackstart generating units to critical loads first and then to the rest of the system without violating any limits for frequency, voltage and branch loading.

Considerations in the Automatic Development of Electric Grid Restoration Plans

As power systems become more heavily loaded, system operation will be increasingly constrained by contingent cases where the power flow equations have no real solutions. Since such cases often represent the most severe threat to viable operation of the transmission system infrastructure, it is critical that a computationally efficient method be developed to provide practical control recommendations to mitigate these cases. Such an algorithm is developed in this paper. The degree of unsolvability is quantified using the distance in parameter space between the desired operating point and the closest solvable operating point. The sensitivity of this measure to different system controls, including FACTS devices, is then calculated. These sensitivities are then used to determine the optimal way to mitigate the contingency. Additionally, the dynamic consequences of loss of solution are also discussed. The method is demonstrated on systems of up to 118 buses.

Improvement of power system transfer capability for contingency constrained cases

Bigdata analytic applications using phasor measurements help improve the situation awareness of grid operators to better operate and control the system. Phasor measurement unit (PMU) data from actual grids is viewed as highly confidential and is not publicly available to researchers and educators. This paper develops a methodology to synthesize PMU data that can be accessed and shared freely, with a focus on input data preparation. Time series of demand- and generation-side input data are generated using public data from different utilities and statistical analysis methods. Detailed load dynamics modeling is also performed in this paper to extend the synthetic electric network models.

Synthesize Phasor Measurement Unit Data Using Large-Scale Electric Network Models

Market power potential is a major concern in design, planning, operations and control of electricity markets. This paper uses a perturbation analysis in the linear programming (LP) OPF context to examine market power potentials of generation companies (GenCos) gained by small-scale output withholdings. Based on the definition for market power, we use a two-step scheme. With small-scale withholdings simulated by bid perturbations, the GenCos' profitability from bid perturbations is first examined, and then the effects on locational marginal prices (LMPs) of the identified profitable bid perturbations are investigated. With the LP OPF, LMPs and generators' dispatched output might be differentiable or discontinuous as bidding parameters perturb. For the differentiable case, profit and LMP sensitivities are calculated to analyze profitability and market power potentials. For the discontinuous cases, we explicitly calculate the jumps in LMPs or dispatches, and examine the incentive of GenCos to cause these jumps as well as the effects of these jumps on market outcomes. The proposed perturbation analysis provides valuable insights for both the GenCos and the independent system operator (ISO). For the GenCos, the profitability analysis provides guidance in how to perturb their bids and with which other GenCos they should merge or collude to reap more profit. For the ISO, the market power potential results are insightful in examining the vulnerability of the market in face of generation bidding manipulations and predicting GenCos' bidding behaviors.

/pdf/market-power-potential-examination-for-electricity-markets-18grhpanfo.pdf

Market Power Potential Examination for Electricity Markets Using Perturbation Analysis in Linear Programming OPF Context

Phase Shifting Transformers (PST) are used to control or block certain flows of real power through phase angle regulation across the device. Its functionality is crucial to special situations such as eliminating loop flow through an area and balancing real power flow between parallel paths. Impedance correction tables are used to model that the impedance of phase shifting transformers often vary as a function of their phase angle shift. The focus of this paper is to consider the modeling errors if the impact of this changing impedance is ignored. The simulations are tested through different scenarios using a 37-bus test case and a 10,000-bus synthetic power grid. The results verify the important role of impedance correction factor to get more accurate and optimal power solutions.

Thomas J. Overbye

Papers

Considerations in the Automatic Development of Electric Grid Restoration Plans

Improvement of power system transfer capability for contingency constrained cases

Synthesize Phasor Measurement Unit Data Using Large-Scale Electric Network Models

Market Power Potential Examination for Electricity Markets Using Perturbation Analysis in Linear Programming OPF Context

Application of Transformer Impedance Correction Tables in Power Flow Studies