Dynamical Analysis and Visualization of Tornadoes Time Series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.

Remuneration and tariffs in the context of virtual power players

Power systems have been through deep changes in recent years, namely with the operation of competitive electricity markets in the scope and the increasingly intensive use of renewable energy sources and distributed generation. This requires new business models able to cope with the new opportunities that have emerged. Virtual Power Players (VPPs) are a new player type which allows aggregating a diversity of players (Distributed Generation (DG), Storage Agents (SA), Electrical Vehicles, (V2G) and consumers), to facilitate their participation in the electricity markets and to provide a set of new services promoting generation and consumption efficiency, while improving players` benefits. A major task of VPPs is the remuneration of generation and services (maintenance, market operation costs and energy reserves), as well as charging energy consumption. This paper proposes a model to implement fair and strategic remuneration and tariff methodologies, able to allow efficient VPP operation and VPP goals accomplishment in the scope of electricity markets.

Analysis of temperature time-series: embedding dynamics into the MDS method

Global warming and the associated climate changes are being the subject of intensive research due to their major impact on social, economic and health aspects of the human life. Surface temperature time-series characterise Earth as a slow dynamics spatiotemporal system, evidencing long memory behaviour, typical of fractional order systems. Such phenomena are difficult to model and analyse, demanding for alternative approaches. This paper studies the complex correlations between global temperature time-series using the Multidimensional scaling (MDS) approach. MDS provides a graphical representation of the pattern of climatic similarities between regions around the globe. The similarities are quantified through two mathematical indices that correlate the monthly average temperatures observed in meteorological stations, over a given period of time. Furthermore, time dynamics is analysed by performing the MDS analysis over slices sampling the time series. MDS generates maps describing the stations’ locus in the perspective that, if they are perceived to be similar to each other, then they are placed on the map forming clusters. We show that MDS provides an intuitive and useful visual representation of the complex relationships that are present among temperature time-series, which are not perceived on traditional geographic maps. Moreover, MDS avoids sensitivity to the irregular distribution density of the meteorological stations.

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

Maximizing the Social Welfare of Virtual Power Players Operation in Case of Excessive Wind Power

The integration of growing amounts of distributed generation in power systems, namely at distribution networks level, has been fostered by energy policies in several countries around the world, including in Europe. This intensive integration of distributed, non-dispatchable, and natural sources based generation (including wind power) has caused several changes in the operation and planning of power systems and of electricity markets. Sometimes the available non-dispatchable generation is higher than the demand. This generation must be used; otherwise it is wasted if not stored or used to supply additional demand. New policies and market rules, as well as new players, are needed in order to competitively integrate all the resources. The methodology proposed in this paper aims at the maximization of the social welfare in a distribution network operated by a virtual power player that aggregates and manages the available energy resources. When facing a situation of excessive non-dispatchable generation, including wind power, real time pricing is applied in order to induce the increase of consumption so that wind curtailment is minimized. This method is especially useful when actual and day-ahead resources forecast differ significantly. The distribution network characteristics and concerns are addressed by including the network constraints in the optimization model. The proposed methodology has been implemented in GAMS optimization tool and its application is illustrated in this paper using a real 937-bus distribution network with 20.310 consumers and 548 distributed generators, some of them non-dispatchable and with must take contracts. The implemented scenario corresponds to a real day in Portuguese power system.

DC Fuzzy Multicriteria Approach to Increase the Probability of Delivering Power in Distribution Networks

This paper proposes a methodology to increase the probability of delivering power to any load point through the identification of new investments. The methodology uses a fuzzy set approach to model the uncertainty of outage parameters, load and generation. A DC fuzzy multicriteria optimization model considering the Pareto front and based on mixed integer non-linear optimization programming is developed in order to identify the adequate investments in distribution networks components which allow increasing the probability of delivering power to all customers in the distribution network at the minimum possible cost for the system operator, while minimizing the non supplied energy cost. To illustrate the application of the proposed methodology, the paper includes a case study which considers an 33 bus distribution network.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.