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.

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 the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

FMFT electric schematic revision/update

The recent update of the R-Fieldbus testbed to the new Flexible Manufacturing Field Trial – FMFT – brought up the need for a complete revision of its electric schematic.This document comes as a sort of appendix to the Technical Report “Flexible Manufacturing Field Trial”, providing a reliable source of information about the FMFT electric schematic for further developments and/or maintenances.

Distributed Energy Resources Management using Plug-in Hybrid Electric Vehicles as a Fuel-Shifting Demand Response Resource

In the smart grids context, distributed energy resources management plays an important role in the power systems’ operation. Battery electric vehicles and plug-in hybrid electric vehicles should be important resources in the future distribution networks operation. Therefore, it is important to develop adequate methodologies to schedule the electric vehicles’ charge and discharge processes, avoiding network congestions and providing ancillary services. This paper proposes the participation of plug-in hybrid electric vehicles in fuel shifting demand response programs. Two services are proposed, namely the fuel shifting and the fuel discharging. The fuel shifting program consists in replacing the electric energy by fossil fuels in plug-in hybrid electric vehicles daily trips, and the fuel discharge program consists in use of their internal combustion engine to generate electricity injecting into the network. These programs are included in an energy resources management algorithm which integrates the management of other resources. The paper presents a case study considering a 37-bus distribution network with 25 distributed generators, 1908 consumers, and 2430 plug-in vehicles. Two scenarios are tested, namely a scenario with high photovoltaic generation, and a scenario without photovoltaic generation. A sensitivity analyses is performed in order to evaluate when each energy resource is required.