Increase of the delivered energy probability in DES using a fuzzy probabilistic modeling

The paper proposes a methodology to increase the probability of delivering power to any load point by identifying new investments in distribution energy systems. The proposed methodology is based on statistical failure and repair data of distribution components and it uses a fuzzy-probabilistic modeling for the components outage parameters. The fuzzy membership functions of the outage parameters of each component are based on statistical records. A mixed integer nonlinear programming optimization model is developed in order to identify the adequate investments in distribution energy system components which allow increasing the probability of delivering power to any customer in the distribution system at the minimum possible cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a 180 bus distribution network.

A probabilistic methodology for distributed generation location in isolated electrical service area

Distributed generation unlike centralized electrical generation aims to generate electrical energy on small scale as near as possible to load centers, interchanging electric power with the network. This work presents a probabilistic methodology conceived to assist the electric system planning engineers in the selection of the distributed generation location, taking into account the hourly load changes or the daily load cycle. The hourly load centers, for each of the different hourly load scenarios, are calculated deterministically. These location points, properly weighted according to their load magnitude, are used to calculate the best fit probability distribution. This distribution is used to determine the maximum likelihood perimeter of the area where each source distributed generation point should preferably be located by the planning engineers. This takes into account, for example, the availability and the cost of the land lots, which are factors of special relevance in urban areas, as well as several obstacles important for the final selection of the candidates of the distributed generation points. The proposed methodology has been applied to a real case, assuming three different bivariate probability distributions: the Gaussian distribution, a bivariate version of Freund’s exponential distribution and the Weibull probability distribution. The methodology algorithm has been programmed in MATLAB. Results are presented and discussed for the application of the methodology to a realistic case and demonstrate the ability of the proposed methodology for efficiently handling the determination of the best location of the distributed generation and their corresponding distribution networks.

Fractional calculus: a survey of useful formulas

This paper presents a survey of useful, established formulas in Fractional Calculus, systematically collected for reference purposes.

On development of fractional calculus during the last fifty years

Fractional calculus generalizes integer order derivatives and integrals. During the last half century a considerable progress took place in this scientific area. This paper addresses the evolution and establishes an assertive measure of the research development.

Science metrics on fractional calculus development since 1966

During the last fifty years the area of Fractional Calculus verified a considerable progress. This paper analyzes and measures the evolution that occurred since 1966.

Iterative refinement approach for QOS-Aware service configuration

In heterogeneous environments, diversity of resources among the devices may affect their ability to perform services with specific QoS constraints, and drive peers to group themselves in a coalition for cooperative service execution. The dynamic selection of peers should be influenced by user’s QoS requirements as well as local computation availability, tailoring provided service to user’s specific needs. However, complex dynamic real-time scenarios may prevent the possibility of computing optimal service configurations before execution. An iterative refinement approach with the ability to trade off deliberation time for the quality of the solution is proposed. We state the importance of quickly finding a good initial solution and propose heuristic evaluation functions that optimise the rate at which the quality of the current solution improves as the algorithms have more time to run.

Fractional order calculus: basic concepts and engineering applications

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

Recent history of fractional calculus

This survey intends to report some of the major documents and events in the area of fractional calculus that took place since 1974 up to the present date.

Particle swarm optimization: dynamical analysis through fractional calculus

This chapter considers the particle swarm optimization algorithm as a system, whose dynamics is studied from the point of view of fractional calculus. In this study some initial swarm particles are randomly changed, for the system stimulation, and its response is compared with a non-perturbed reference response. The perturbation effect in the PSO evolution is observed in the perspective of the fitness time behaviour of the best particle. The dynamics is represented through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence upon the global dynamics is also analyzed. Two main issues are reported: the PSO dynamics when the system is subjected to random perturbations, and its modelling with fractional order transfer functions.

Fractional calculus: application in modelling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.

Application of fractional calculus in engineering

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. It has been recognized the advantageous use of this mathematical tool in the modelling and control of many dynamical systems. Having these ideas in mind, this paper discusses a FC perspective in the study of the dynamics and control of several systems. The paper investigates the use of FC in the fields of controller tuning, legged robots, electrical systems and digital circuit synthesis.

Some applications of fractional calculus in engineering

Fractional Calculus FC goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

Electrical skin phenomena: a fractional calculus analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal.

A fractional calculus perspective in the evolutionary design of combinational circuits

This paper analyses the performance of a genetic algorithm (GA) in the synthesis of digital circuits using two novel approaches. The first concept consists in improving the static fitness function by including a discontinuity evaluation. The measure of variability in the error of the Boolean table has similarities with the function continuity issue in classical calculus. The second concept extends the static fitness by introducing a fractional-order dynamical evaluation.