Skin Effect
When the electricity is transmitted as high-frequency alternating current for the long distances, the skin effect occurs, which makes the effective resistance of the conductor higher, thus reducing the efficacy of the whole power line. The skin effect was first described in 1883, when the era of the radio began.
As the current flows in a conductor, which is often in the form of wires, it produces the magnetic field around the conductor. If the current in the wire is alternating, the magnetic field is also alternating that, in turn, originates the electric field, which opposes the electric field of the electrical energy source. The opposing electric field is called “back EMF” (counter-electromotive force) and is the strongest at the center of the wire. That forces the carriers of the current to the outside of the wire, which is shown on the picture on the right.
The skin effect causes a non-linear distribution of the current density J from the surface of the wire to its axis, which can be described by formula:
where JS – current density on the surface of the wire, d – the diameter of the wire, and δ – skin depth. According to the formula, the skin depth is defined as the distance from the surface of the wire to its axis at which the current density is 1/e times less, than the current density on the surface. It is calculated that over 98% of all current flows in the subsurface layer of 4δ.
The skin depth can be described by formula:
where ρ – resistivity of the conductor, ω - angular frequency of current, μr – relative magnetic permeability of the conductor, μ0 – the permeability of free space, μ = μrμ0, ϵr – relative permittivity of the material, ϵ0 – the permittivity of free space, ϵ = ϵrϵ0. The effective resistance of the wire with length L and diameter D (D >> δ) can be described by formula:
These formulas mean that the higher is the frequency of the alternating current and the longer is the wire, the less is the skin depth, and the more is the effective resistance of the wire. Thus, the effective resistance of the wire approximately equals the resistance of the hollow tube with the wall thickness δ carrying the direct current.
According to the formulas and conclusions above, the better conductors have less skin depth and the ratio between their AC and DC resistances is bigger, when compared with a conductor of higher resistivity.
But the bigger is the ratio, the less is the efficacy of the power line transmitting AC comparing to the same line transmitting DC. So it is very important to find the ways to mitigate the skin effect. One of the mitigation solutions is litz wire, which consists of a number of insulated wire strands that are woven together in a carefully designed pattern, so that the overall magnetic field acts equally on all the wires and causes the total …
