The Skin Effect in Electrical Cables: A Simple Explanation


At DC, the current distribution over the cross-sectional area of the conductor is uniform and the entire cross-sectional area of the conductor is equally effective in carrying current. However, as frequency increases, the current tends to flow through a shallow layer just underneath the surface of the conductor. This phenomenon, known as the skin effect, reduces the effective cross-sectional area of the conductor and hence, leads to an increase in the conductor's AC resistance.



If we want to explain the skin effect simply: Imagine you have a garden hose. When you turn on the water, it flows through the whole hose evenly. But if the skin effect was happening, it would be like the water only flowing along the inside edges of the hose and not in the middle. In wires, this means that electricity prefers to flow on the outside parts of the wire and not so much in the center.


The general formula for skin depth, when there is no dielectric or magnetic loss, is:





At frequencies much below  1/ρε the quantity inside the large radical is close to unity and the formula is more usually given as:




However, in very poor conductors, at sufficiently high frequencies, the factor under the large radical increases. At frequencies much higher than 1/ρε it can be shown that skin depth, rather than continuing to decrease, approaches an asymptotic value.


Example for copper wire cable at 50 Hz:

μr = 1,256629*10^−6
μ0= 4π*10^-7
𝜇 = μr/μ0=0.9999935

𝜔 = 2πf = 2*50*3,14 =314,1593
ρ = 1.72x10^-8

𝛿 = ((2ρ)/(𝜔𝜇))^0,5 = 0,00934556 m =9,345 mm


Implications for Cable Design:

The skin effect influences cable design in several ways:
•    Increased resistance: As AC frequency increases, skin depth decreases, leading to higher resistance and power losses.
•    Heat generation: More resistance results in more heat, which can affect cable insulation and longevity.
•    Cable sizing: Engineers may need to use larger or differently designed cables to mitigate these effects.

Mitigation Strategies:

To reduce the impact of the skin effect, engineers can:
•    Use stranded conductors, which have more surface area for current flow.
•    Choose materials with higher conductivity and lower magnetic permeability.
•    Design cables with specific geometries that distribute current more evenly.

In summary, the skin effect can make power transmission less efficient and more costly, particularly in systems where alternating current is used at high frequencies.

Tacettin İKİZ - 18.06.2024

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