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

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Data Mining - Concepts and Techniques.

Data Mining Practical Machine Learning Tools and Techniques

Power Oscillation Damping using VSC-based Multi-terminal HVDC Grids

Coordinated, sensitivity-based DSM for enhanced cross-border power transfers

This paper presents a risk-based framework to establish operational constraints for modern power systems. The methodology is established and subsequently applied to two areas of power system analysis - small-disturbance stability and sub-synchronous resonance (SSR). In the first case, probability density functions (pdfs) for critical oscillatory electromechanical modes are established based on the stochastic variation of system uncertainties such as generation and loading. These pdfs provide probabilities of unstable or poorly damped oscillations that are evaluated using risk-based approaches. For SSR analysis, frequency scans are completed to identify generators which are at risk of experiencing high mechanical torques. In both cases, evaluation using severity functions is used to ensure that acceptable levels of risk are not exceeded. The proposed methods are demonstrated using a meshed power system with capacitor series compensated AC tie lines.

Risk-based framework for assessment of operational constraints for power systems focusing on small-disturbance stability and sub-synchronous resonance

Frequency control of AC systems using Voltage Source Converter (VSC) HVDC links is of growing importance as interconnectors and links to offshore generation replace conventional synchronous generators in many countries. This paper investigates the use of local system feedback and advanced droop control to achieve frequency stabilization for a two-area test system.

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Frequency stabilisation using VSC-HVDC

Principal Component Analysis (PCA) has been recently introduced in the power system dynamics literature as a time domain coherency identification method. The method showed to be promising especially with the increased growth of Phasor Measurement Unit (PMU) installations in power networks. The method, how- ever, suffers from the inability of visualizing transformed information beyond three dimensions. In addition, visual inspection of three dimensional (3-D) results can be some- times misleading. In this paper, transformed data by the PCA method are further clustered by using the spatial distances between objects representing generators' re- sponses to a disturbance in the system. The objects are then linked together to build a multi-level hierarchical tree representing the dynamic behavior of network generators. The proposed technique enables adjustable (variable) clustering , thus adding more flexibility and applicability in different types of applications requiring network model order reduction and more efficient monitoring and control of power systems. The technique is illustrated on the New England test system. The results showed multi-level clus- tering of highly meshed network regardless of the number of principal components required to capture the original data variations.

Jovica V. Milanovic

Papers

Power Oscillation Damping using VSC-based Multi-terminal HVDC Grids

Coordinated, sensitivity-based DSM for enhanced cross-border power transfers

Risk-based framework for assessment of operational constraints for power systems focusing on small-disturbance stability and sub-synchronous resonance

Frequency stabilisation using VSC-HVDC

Identification of coherent generators using pca and cluster analysis