Effect of skin

The effect of skin or skin effect (or more rarely Kelvin effect) are an electromagnetic phenomenon which makes than, at raised frequency, the current tends to circulate only on the surface of the drivers. This phenomenon of electromagnetic origin exists for all the drivers traversed by alternative courses. It causes the decrease of the density of current as one moves away from the periphery of the driver. It results an increase from it from the resistance of the driver.
This effect can be used to reduce the weight of the lines of high frequency transmission by using tubular drivers, or even pipes, without loss of current. It is also useful in the electromagnetic shielding of coaxial wire by surrounding them of a thin metal case which keeps the currents induced by the ambient high frequencies on the outside of the cable.

Cause


Formation of loop of current induced by the variation of the magnetic field (H) in an alternative course.
Any current moving in a driver generates a magnetic field around this last. When a D.C. current crosses a driver, the potential difference is uniform and the loads move in the isotropic driver of manner what gives a constant magnetic field (H). On the other hand, when an alternative course circulates, the loads oscillate and the magnetic field varies what induces an opposite loop of electric current.
On the figure of right-hand side, one can see that the loop goes from the periphery of the driver towards the center. The direction of rotation is always opposite with that of the current fluctuation in the driver. Thus, the sum of the alternative course with that of the loop is increasingly weaker in the center of the driver whereas these two currents are added in periphery.
That means that the current does not circulate uniformly in all the section of the driver. All occurs as if the finished cross-section of the cable were smaller. Resistance thus increases, which leads to more important losses by Joule effect.

Description by Nikola Tesla

On its estrade, Nikola Tesla had windings, lamps incandescent, and especially, astonishing tubes of glass filled up of gas with very low pressure. Tesla seized with a hand a discussion thread coming from one of its reels, and where an alternative course with high voltage circulated. Other hand, it took a tube and this one was illuminated, with the amazement of the room. As Tesla employed a current with very high frequency, by effect of skin, this one did not penetrate in the driver which was its body but circulated with its periphery to reach the tube.

Thickness of skin in a metal

The thickness of skin determines, at first approximation, the width of the zone where the current in a driver concentrates. It makes it possible to calculate effective resistance to a given frequency. In this calculation, one neglects the real part in front of the imaginary part: the conductivity of metals being very high.
δ = √( 2 ⁄ ω * µ * σ ) = √( 2 * ρ ⁄ ω * µ)
δ : thickness of skin in meter [m]
ω : pulsation in radian a second [rad ⁄ s] (ω = 2.p.f)
f : frequency of the current in Hertz [Hz]
µ : magnetic permeability as a Henry per meter [H ⁄ m]
ρ : resistivity out of Ohmmeter [O.m] (ρ = 1 ⁄ s)
σ : electric conductivity in Siemens per meter [S ⁄ m]
For a driver of section significantly larger than D, one can calculate effective resistance to a frequency given by considering that only the part external thickness D contributes to conduction. For example for a cylindrical driver of ray R, one will have a finished cross-section of:
Su = π * ( R² - δ )²

Modeling in a cylindrical driver in harmonic mode


Function of distribution of the current in a cylindrical driver in harmonic mode. In X-coordinate: depth in p.u thickness of skin, by taking surface for origin. In ordinate: the report ⁄ ratio of the module of the current circulating between surface and a depth R given on the module of the total current crossing the section of the driver. The ray has cylinder was arbitrarily selected with 5 times the thickness of skin.
That is to say I (R) the current circulating in the thickness ranging between surface and the ray R of the cylinder, and I the total current.
The function of distribution of the current having for origin R = the 0 surface of the driver is given by the expression:
I (r) ⁄ I = { Ber (√2α ⁄ δ) - Ber (√2r ⁄ δ) + i [Bei (√2α ⁄ δ) - Bei (√2r ⁄ δ)] ⁄ Ber (√2α ⁄ δ) + i Bei (√2α ⁄ δ)
If one graphically represents the module of the function of distribution of the current in the cylindrical driver, that is to say I (R) ⁄ I, one notes that more than 80% of the current circulates in the thickness of skin, which justifies the approximation made during the calculation of the effective resistance of the driver. The going beyond of the value 1 which appears on the figure is due to the rotation of phase of the density of current which can be reversed with certain depth compared to the total current.

Attenuation

The effect of skin is generally a harmful effect, because it creates additional losses, attenuations at raised frequency, etc an effective manner to decrease the effect of it is to divide the driver, that is to say to replace it by several drivers in parallel isolated between them.
In the ideal, each bit of the driver thus formed should have a ray lower than D. the wire of Litz is a type of driver which pushes to the extreme this division.
Another technique consists in plating the driver with money. When the “skin” is entirely in the layer of money, it profits from what money with the lowest resistivity of all metals. This method can be a good compromise for a current made up of two components, one low frequency which will circulate in the totality of the section, the other with very high frequency which will circulate in the money.
One can finally consider geometries of drivers allowing to limit the effect of skin. In the electric stations high voltage, one frequently uses hollow tubular drivers out of aluminum or copper to transport strong currents. The thickness of the tube is in general about D, which allows an effective use of the whole of the driver. In low tension one uses sometimes more complex geometries and allowing a better thermal behavior, but the idea is always to have thicknesses of driver not exceeding D.

Between two drivers


Diagram showing a cross-section of two drivers which are in transmission. The green zone contains the carrying loads.
In a cable made up of two drivers (outward journey and return of the current), high frequency it can occur an effect of proximity between the two drivers, improperly confused with the effect of skin, which makes that the current tends to circulate only on the parts of the drivers in opposite.
This effect is added to the effect of skin itself. It is completely depend on the geometry of the unit: section of the drivers (circular, square, punt…), distance between drivers, asymmetry of the drivers (for example wire parallel with a plan of mass), etc the effect of proximity is practically negligible on drivers spaced of more than 20 cm.
In order to mitigate this effect, it is necessary to move away the drivers, but that has other disadvantages, like increasing inductance.

Corona effect around a reel high voltage

The corona effect, also called crown effect is an electric shock pulled by the ionization of the medium surrounding a driver, it occurs when the electric potential exceeds a breaking value but whose conditions do not allow the formation of an arc. This effect is used, inter alia, in the lamps with plasma.
At the macroscopic level
A discharge of corona in general occurs when a current, continuous or not, is created between two electrodes carried to a high potential and separated by a neutral fluid, the air, by ionization of this fluid. A plasma is then created and the electric charges are propagated while passing from the ions to the neutral gas molecules.
When the electric field in a point of the fluid is sufficiently large, the fluid ionizes around this point and becomes conducting. In particular, if an object charged has points or corners (ex: angle of 90 degrees), the electric field will be more important there than elsewhere (it is the capacity of the points), they is there in general, than will occur a discharge of corona: the phenomenon will tend to stabilize itself since the ionized area becoming conducting, the point will tend apparently to disappear. The particles charged are dissipated then under the effect of the electric force and are neutralized in contact with an opposite object of load. The discharges of corona thus occur in general between an electrode of weak radius of curvature (a defect of the driver forming a point for example) such as the electric field with its surroundings is sufficiently important to allow the formation of a plasma, and another of important radius of curvature (a metal plate or ground).
A discharge of corona can be positive or negative according to the polarity of the electrode of weak radius of curvature. If it is positive, one speaks about corona positive, if not, of corona negative. Because of difference in mass between the electrons (negative) and the ions (positive), the physics of these two types of corona is radically different. For example, a discharge of corona produces ozone (transforms the dioxygene O2 of the air into O3 ozone) whatever its polarity, but corona negative produces much more than one corona of it positive.
If the geometry of the driver and the value of the field are such as the ionized area extends instead of being stabilized, the current can end up finding a way to the opposite electrode, it is then formed sparks or an electric arc.
At the microscopic level
Discharges of corona, which they are positive or negative have of the joint mechanisms:
An atom or a neutral molecule of the fluid surrounding the electrode is ionized by an external event (for example by interaction with a photon), a positive ion and an electron are released.
These two particles being loads opposite, the electric field creates on each one of them an equal electric force normalizes some but opposite direction and separates them, preventing their recombination and bringing an important kinetic energy to them. This initiates the phenomenon of breakdown.
The electron being of mass much weaker than the ion, it is strongly accelerated, and enters in inelastic collision with neutral atoms, which tends to create new pairs electrons ⁄ positive ions, which will follow the same process. One speaks about effect of avalanche.
Ions thus created are attracted by the second electrode and thus allow the establishment of a current.
Electric properties
The tension necessary to start an effect crowns (in English: corona inception voltage, CIV) can be calculated with the law of Peek (1929), formulated starting from empirical data. Subsequent articles provide more precise formulas.
The current pulled by a discharge of corona can be determined by integrating the density of current into the surface of the driver. The dissipated power is the product of this current and the tension between the two electrodes.
Applications of the discharges of corona
The discharges of corona have many commercial and industrial applications.
Production of ozone
Filtering of the particles contained in the air (system of conditioned air)
Destruction of organic particles contained in the atmosphere: pesticide, solvent,
Surface treatment of certain polymers
Photocopier
Laser with nitrogen
Conducting and electrostatic non-conducting matter separation
Cooling of electronics components (the migration of the ionized particles generates a flow which expels the hot air)
Problems involved in the discharges of corona
The discharges of corona can produce audible noises and disturbances on the radio frequencies, in particular near the lines with high voltage. They also represent a loss of power. Lastly, the reactions which they cause in the atmosphere could have an impact on health. This is why the installations of electric drive are designed to minimize the formation of the discharges of corona.
The discharges of corona are particularly to avoid in:
installations of electric drive where they cause a loss of energy and noise
majority of electrical equipment: electric transformers, machines (as well generating as driving), etc where they damage insulators gradually bringing to a premature deterioration of the equipment
all situations requiring an important tension but where the production of ozone must be minimal.
Reduction of the corona effect on the electric lines
The reduction of the corona effect on the lines with high voltage by specific measures is in general necessary only when the level of tension of the line exceeds 345 Kv. Beyond the reduction of the harmful effects to the populations, the economic costs of on-line losses by corona effect can justify with him to only take corrective measures. These measurements are of 2 types:
use of drivers of large diameter, to limit the electric field to surface. This measurement often ineffective, and is seldom economically justified, because the effect of skin makes often ineffective the choice of drivers of large section.
use of beam of drivers (typically 2 drivers or more in 400 Kv, 3 drivers or more in 500 Kv) which in addition to their interest from a thermal point of view make it possible to decrease the surface field on the drivers.
The choice of the number of drivers of an electric line is thus made according to the current forward, of the climatic conditions, the effects of skin and corona, and of course of the economic aspects. A simple criterion making it possible to limit the corona effect on the electric lines consists in making sure that the surface field on the driver does not exceed a value of about 17 kV ⁄ cm.
Reduction of the corona effect in the electric stations
In the electric stations high voltage, the preceding considerations on the lines remain valid. There is however the possibility of using for the sets of bars of the tubular drivers of important ray external (80 to 220 mm) which have a weak surface field. The aspect of disturbances on the radio frequencies becomes critical, because of the possible presence of sensitive electronics components. Apparatuses HTB (disconnecting switch, circuit breaker with high-tension, lightning protector,) must be conceived and tested to limit these radio interferences related to the corona effect: one uses for that of the avoid-emanations with large radii of curvatures to limit this effect.

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