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Overhead Transmission Line Constants
Published in Amitava Sil, Saikat Maity, Industrial Power Systems, 2022
Skin Effect – The phenomena arising due to unequal distribution of alternating electric current over the entire cross section of the conductor is referred as the skin effect. Skin effect results in increased effective resistance but reduced effective internal reactance of the conductor. Skin depth is given by δ=(1/πfμσ), where f is the frequency, μ, the permeability and σ (=1/ρ), the conductivity of the conductor. Skin effect attenuates the higher frequency components of a signal more than the lower frequency components. The conductor resistance affects the attenuation of traveling waves due to lightning and switching operations, as well as radio-frequency energy generated by corona.
Electromagnetic Waves and Lasers
Published in Hitendra K. Malik, Laser-Matter Interaction for Radiation and Energy, 2021
The skin depth is small at the high frequencies. The skin effect causes the effective resistance of the conductor to increase at higher frequencies where the skin depth is smaller, thus reducing the effective cross-section of the conductor. For a typical metallic conductor such as copper, whose electrical conductivity at room temperature is about 6 × 107 (Ω-m)−1, the skin depth is given by δ≈6f(Hz)cm
Power Quality and Equipment Protection
Published in Ramesh Bansal, Power System Protection in Smart Grid Environment, 2019
Abhishek Chauhan, J. J. Justo, T. Adefarati, Ramesh Bansal
Skin effect is defined as the tendency of flowing alternating current on the outer surface of the conductor. This effect is prominent at high frequency supplies, and it is ignored at fundamental frequency. Above 350 Hz (seventh and above harmonics), this effect becomes significant and results in heating loss [2]. () δ=2ρωμ
Evaluation of residual stresses in additively produced thermoelastic cylinder. Part I. Thermal fields
Published in Mechanics of Advanced Materials and Structures, 2023
Sergei A. Lychev, Montaser Fekry
The solution of Eq. (14) with the conditions (13) is well-known and takes the form [33, 34]: where are the first kind of Bessel function of zero and first order [35] and R denotes the radius of cylindrical part of the assembly’s boundary. Note, that, since the electric current is alternating, it becomes distributed within the conductor such that the current density near the surface significantly increases with increasing the frequency This phenomenon is known as skin-effect [36]. If one suppose that then the relation for S transforms to the form, often seen in the technical literature: where δ denotes the skin depth, defined as the depth below the surface of the conductor at which the current density has fallen to (about 0.37) of the total current [37].
Modeling and Fabrication Aspects of Cu- and Carbon Nanotube-Based Through-Silicon Vias
Published in IETE Journal of Research, 2021
Tanu Goyal, Manoj Kumar Majumder, Brajesh Kumar Kaushik
It is noticed that the resistance of TSV increases with frequency due to skin effect. Skin effect arises when a high-frequency current flows close to the surface of conductor due to the formation of eddy currents. This results in the current penetration through the conductors when frequency is varied. When the frequency is high enough such that the skin depth is smaller than the radius of the circular via-holes, the current starts to distribute unevenly and becomes crowded at the surface of the conductor. Hence, the resistance and inductance effectively increase and reduce with frequency [10]. where RTSV0 and LTSV0 are resistance and inductance of vias at 500 MHz frequency [10]. The lossy characteristics Rsub can be modeled as The current induced in the substrate rises as a result of high frequency that consequently reduces substrate resistance Rsub(f). The primary issue with this model was that it measured the resistance and inductance of large TSV structures but did not correlate them with the physical dimensions and material characteristics. Moreover, the model incorrectly ignores the substrate and oxide parasitic.
Modelling of ferroalloy production processes in the SAF and converter
Published in Mineral Processing and Extractive Metallurgy, 2020
Haijuan Wang, Zhanbing Yang, Hurman Eric
Many of 2D models mentioned here assume the axial symmetry so the calculations can be projected to the 2D radial cross section of the electrode which will simplify the calculation. However, the axisymmetric models only captured the skin effect, yet the proximity effects between electrodes is also important (Herland et al. 2018). As studied by Lupi (2017), there are two effects in an AC furnace, which are the skin effect and the proximity effect. The skin effect causes the currents to accumulate near the surface of conductors while the proximity effect induces currents in the surrounding conductors. The induced eddy currents can have a high intensity and effectively modify the current distribution. Axisymmetric models will capture the skin effect, given that the AC formulation is used, but they will not capture proximity effects between electrodes. In this case, 3D single-electrode models have been investigated numerically.