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

In high voltage electric grids, phase shifting transformers (PSTs) are devices in which the phase shift across the device can be varied to control the flow of real power. A consequence of this phase variation is that PST’s series impedance often varies with the phase shift, sometimes substantially. In power system analysis applications this variation is often modeled using a piecewise-linear impedance correction table. This paper analyzes the influence of incorporating impedance correction tables on a power flow solution. The presented method is implemented in two different test systems. A two-bus test system shows various transformer correction tables can make different power flow solutions. A 37-bus test system demonstrates the influence of the impedance correction table on both normal operating condition and contingency scenarios. The results reveal that impedance correction tables have impacts on power flow solutions and may help alleviate the overloaded lines following a contingency.

Power Flow Consideration of Impedance Correction for Phase Shifting Transformers

Geomagnetic disturbances (GMDs) threaten the secure and reliable operation of the electric power grid. During a GMD, geomagnetically induced currents (GICs) cause additional reactive power losses and a lowered voltage profile. Preventing and mitigating a widespread system collapse in such an occurrence requires accurate knowledge of the current system state. This is provided by power system state estimation, but as traditional methods do not account for GIC-related monitoring and modeling, they may fail to provide accurate results during a GMD. Therefore, in this work excess reactive power losses are explicitly modeled in the state estimation method and GIC-related values are included among the states and measurements. The modeling scheme is thoroughly discussed and estimation results on a 20 bus and 150 bus case validate the estimation accuracy improvement provided by a GIC-inclusive modified state estimator during a GMD.

https://ieeexplore.ieee.org/ielam/59/9460709/9271869-aam.pdf

GIC-Inclusive State Estimator for Power System Awareness During Geomagnetic Disturbance Events

Newer dynamic load models are being developed in industry through field-tests, to better represent the actual system response. Some of these models are quite complex, and include feeders, distribution transformers and various types of static and dynamic loads, thus resulting in more than a hundred parameters per model. This paper presents a methodology on how such complex dynamic load models in commercial software packages can be tested for errors such as software bugs, or implementation differences across the packages. The key lies in testing individual components of such models, through comparisons of simulation results from different packages. This method could be particularly useful where actual PMU data is not available for validating parts of load models. Case studies show that implementation differences exist due to incomplete documentation or bugs, and the techniques in this paper can be useful in finding and addressing the discrepancies in these evolving load models.

Assessment of discrepancies in load models across transient stability software packages

Electromechanical disturbances are caused by an imbalance between power supply and demand at any location of an electric grid. However, the associated propagation delay phenomenon is generally observed in large-scale interconnected power systems, and the transient effect of large changes in load or in generation can be felt over a wide geographic area. In the first part of this paper, background material will be covered to motivate the research ideas being pursued. In particular, focusing on the reason why the same amount of power imbalance, in a system with higher renewable penetration, can cause larger and more widespread frequency excursions. In the second part, a 9-bus system is introduced, and the transient response is studied with non-linear differential-algebraic equations, and then with a linearized approximation. Frequency-domain analysis of the transient response is also presented. Lastly, some relevant work in progress is touched upon, followed by concluding remarks.

Analysis of electromechanical disturbance propagation in power systems

Power systems are changing with the integration of substantial amounts of renewable energy, lightweight turbine generators and electronic devices. This trend results in less resource inertia and may consequently worsen system primary frequency response. This paper develops several metrics to effectively quantify the impacts of resource inertia on power system dynamic performances. Governor and inertial responses are the two primary contributors to alleviate frequency deviations during the first few seconds after the system experiences some contingency events that result in imbalance between the demand and the generation. Burdens on governors caused by inertia reduction are also evaluated. To provide insightful, realistic simulation results, synthetic electric grid models are used to investigate inertia's impacts and their locational dependence.

Thomas J. Overbye

Papers

Power Flow Consideration of Impedance Correction for Phase Shifting Transformers

GIC-Inclusive State Estimator for Power System Awareness During Geomagnetic Disturbance Events

Assessment of discrepancies in load models across transient stability software packages

Analysis of electromechanical disturbance propagation in power systems

Metric development for evaluating inertia's locational impacts on system primary frequency response