SKIN EFFECTSubject : FILED THEROY

Prepared By : Parth Patel - 140110109039 Jay Patel - 140110109034

G.H. Patel College Of Engineering And Technology

CONTENT

oThe skin effectoCauseoFormulaeoMaterial effect on skin depthoFactors affecting Skin depthoMitigation

The Skin effect• The phenomena arising due to unequal distribution

of current over the entire cross section of the conductor being used for long distance power transmission is referred as the skin effect in transmission lines. 

• With increase in the effective length of the conductors, skin effect increases considerably.

• The distribution of current over the entire cross section of the conductor is quite uniform in case of a DC system. But what we are using an alternating current system, where the current tends to flow with higher density through the surface of the conductors (i.e skin of the conductor), leaving the core deprived of necessary number of electrons.

• In fact there even arises a condition when absolutely no current flows through the core, and concentrating the entire amount on the surface region, thus resulting in an increase in the effective electrical resistance of the conductor.

• This particular trend of an AC transmission system to take the surface path for the flow of current depriving the core is referred to as the skin effect in transmission lines.

CAUSE• Let us initially consider the solid conductor to be split up into a number of

annular filaments spaced infinitely small distance apart, such that each filament carries an infinitely small fraction of the total current. Like if the total current = I Lets consider the conductor to be split up into n filament carrying current ‘i’ such that I = n i .

• During the flow of an alternating current, the current carrying filaments lying on the core has a flux linkage with the entire conductor cross section including the filaments of the surface as well as those in the core.

• Whereas the flux set up by the outer filaments is restricted only to the surface itself and is unable to link with the inner filaments.

• Thus the flux linkage of the conductor increases as we move closer towards the core and at the same rate increases the inductor as it has a direct proportionality relationship with flux linkage.

• This results in a larger inductive reactance being induced into the core as compared to the outer sections of the conductor.

• The high value of reactance in the inner section results in the current being distributed in an un-uniform manner and forcing the bulk of the current to flow through the outer surface or skin giving rise to the phenomena called skin effect in transmission lines.

FormulaeThe AC current density J in a conductor decreases exponentially from its

value at the surface JS according to the depth d from the surface, as follows:

where δ is called the skin depth. The skin depth is thus defined as the depth below the surface of the conductor at which the current density has fallen to 1/e (about 0.37) of JS. In normal cases it is well approximated as:

- where• ρ = resistivity of the conductor• ω = angular frequency of current = 2π × frequency• μ = absolute magnetic permeability of the conductor

Material effect on skin depth• In a good conductor, skin depth varies as the inverse square root of the

conductivity. This means that better conductors have a reduced skin depth.

• The overall resistance of the better conductor remains lower even with the reduced skin depth.

• Skin depth also varies as the inverse square root of the permeability of the conductor. In the case of iron, its conductivity is about 1/7 that of copper.

• In case of ferromagnetic its permeability is about 10,000 times greater. This reduces the skin depth for iron to about 1/38 that of copper, about 220 micrometres at 60 Hz.

• Iron wire is thus useless for A.C. power lines. The skin effect also reduces the effective thickness of laminations in power transformers, increasing their losses.

• Iron rods work well for (DC) welding but it is impossible to use them at frequencies much higher than 60 Hz.

Factors affecting Skin depth

o The skin effect in an ac system depends on a number of factors like:-

• Shape of conductor• Type of material• Diameter of the conductors• Operational frequency

Mitigation (Reduction)• Instead of normal conductors/wires A type of cable called litz wire (from

the German Litzendraht, braided wire) is used to mitigate the skin effect for frequencies of a few kilohertz to about one megahertz.

• It consists of a number of insulated wire strands woven together in a carefully designed pattern, so that the overall magnetic field acts equally on all the wires and causes the total current to be distributed equally among them.

• With the skin effect having little effect on each of the thin strands, the bundle does not suffer the same increase in AC resistance that a solid conductor of the same cross-sectional area would due to the skin effect.

Mitigation (Reduction)

ACSR : Aluminium conductor steel-reinforced cable