Skin Effect and Factors Affecting Skin Effect in Power Lines

What is Skin Effect? Causes, Factors, Controlling & Disadvantages in Transmission Lines

What is Skin Effect?

When an alternating current “AC” flows through a conductor, it is distributed non-uniformly throughout the conductor and tends to stay more near the surface of the conductor. This phenomenon is called Skin Effect which is applicable to AC only as the flow of current is uniform in the X-section of conductors in case of DC.

Due to the said effect, the resistance of the wire increases, causing an increase in line losses (waste of power occurring due to resistance of the power lines I²R). The line losses occur in the form of heat which further increases the resistance of the conductor. It reduces the efficiency of the transmission line.

Skin effect occurs in power transmission lines over a long distance. For shorter distances, it does has no significance and pretty much doesn’t count. But power transmission over long distances has a much more significant skin effect.

Skin effect increases with an increase in frequency. If the frequency is very high, the charge distribution or the current density stays maximum at the very surface and forms a thin layer while the current density at the inner cross-sectional area or the core remains zero.

Skin effects maintain the current flow between the outer surface and a fixed depth from the surface called skin depth, δ. The skin depth varies inversely with frequency.

The skin depth can be calculated using the following formula.

Skin Depth = δ = 7.6 ÷ √ (f) … (cm)

As Direct Current DC has no frequency, the distribution of current flow is uniform throughout the conductor. It utilizes the whole cross-sectional area of the conductor reducing the line losses to a minimum. But modern power transmission uses alternating current having 50/60 Hz and also high-frequency application at the range of gigahertz are quite affected by it.

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Causes of Skin Effect

Let’s consider that a solid conductor is used to conduct alternating current. The cross-sectional area of the conductor is divided into very small concentric circles that can carry a very small current as shown below.

When the alternating current is passed through the conductor, each cylinder carries a fraction of the current and produces magnetic flux. Therefore there is a magnetic flux linkage between the individual cylinders throughout the conductor.

The magnetic flux linkage at the center cylinders is greater than those near the surface of the conductor. It is due to the fact that the cylinders at the core are surrounded by both internal and external magnetic flux while the surface cylinders are only affected by external magnetic flux. Therefore the magnetic flux linkage increases as we move near the core.

Inductance is directly proportional to the flux linkage therefore the inductance also increases toward the core. The cylinders near the core have high inductance as compared to the ones near the surface. Therefore, the core has higher inductive reactance as compared to the near the surface. The electrical current follows low reactance path.

Therefore, the alternating current tends towards the surface of the conductor due to low reactance. The current density is lower near the core while higher towards the surface of the conductor forming a non-uniform distribution of charge known as the skin effect.

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Factors Affecting Skin Effect

There are certain factor that affects the skin effect as follows.

Frequency

The current frequency is the main factor affecting skin effect and it is directly proportional to the skin effect. As we know that inductive reactance is given by

X_L = 2π f L

Inductance reactance is directly proportional to frequency. Increasing the frequency increases the reactance and decreases the skin depth of the conductor. Thus the current stays more to the surface or the skin effect increases.

Since DC has no frequency, its reactance is zero and the current is distributed uniformly throughout the conductor.

Shape of Conductor

The skin effect also depends on the shape of the conductor. Conductors are either solid or standard. The stranded conductor has a greater surface area as compared to a solid conductor of the same size. As the AC tends to stay at the surface, the stranded conductor has a less skin effect as compared to the solid conductor. It means AC is more efficient for transmission in stranded conductors than in solid conductors.

Diameter  of Conductor

The skin effect is directly proportional to the diameter of a conductor. It increases with an increase in diameter. It means it is minimum in conductors having a smaller diameter. As a matter of fact, if the radius of the conductor remains smaller than the skin depth, there will be no or minimum skin effect.

Material

The material is the conductor also affects the skin effect. It actually depends on the permeability of the material. It is the property of the material to support magnetic flux. A material having higher permeability is more affected by skin effect than the one having lower permeability. It allows higher magnetic flux linkage which increases the inductive reactance causing to force the alternating current to stay on the surface.

Temperature

The temperature of the conductor is also directly proportional to the skin effect in that conductor since temperature directly affects the resistance of the conductor.

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Disadvantages of Skin Effect

Skin effect has a negative impact on electrical power transmission. Here are some disadvantages explained below.

Resistance of Conductor: As we know skin effect reduces the effective area of the conductor because most of the current flow on the surface and the core of the conductor remains empty. The resistance is given by

R = ρl/A

Resistance R is inversely proportional to the area of the conductor. Since the effective area of the conductor is reduced, the effective resistance of the conductor increases.

Transmission losses: Also known as copper losses are the dissipation of energy in the conductor due to the resistance of the conductor. It is measured by I²R. The energy is wasted in the form of heat. As the resistance of the conductor increases due to the skin effect, the losses increases. Thus damaging the conductor.

Voltage Drop: there is a voltage drop across the transmission line due to the resistance of the conductor. As we know,  the resistance increases, and the voltage drop across the conductor also increases, causing a reduction in the transmission voltage.

Cost: The cost of the transmission line increases due to the skin effect. It is due to the fact that the resistance of the line increases and to compensate for the resistance, another conductor is installed in parallel to distribute the load. Thus increasing the cost.

Efficiency: skin effect reduces the efficiency of the transmission line as the voltage drop and power losses increases across the line.

Waste of material: the conductor is not utilized as most of our cross-sectional area has very low or no current density. The material in the non-effective area i.e. in the core of the conductor is wasted.

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How to Reduce Skin Effects?

There are certain methods to minimize the skin effects in a conductor during power transmission

Using Stranded Conductors: Stranded conductors have less diameter and increased surface area. Whereas a solid core conductor has less surface area. Thus using a stranded conductor reduces the skin effect.

Overhead power transmission lines use bundle conductor ACSR (Aluminum Conductor Steel Reinforced). Bundled Conductors are several conductors connected pretty phase in closed proximity.

Using Hollow Conductors: High-frequency RF applications use hollow conductors to eliminate the core and increase the surface area of the conductor. Thus reducing the skin effect

Reducing Frequency: Frequency of the alternating current increases the skin effect. Direct Current DC has zero frequency, hence it has no skin effect. Maintaining low frequency for transmission over long distance greatly reduce the skin effects.

Type of Material: A material having lower magnetic permeability has a lower skin effect as it has lower inductance reactance and reduced resistance.

Distance: Skin effect is more significant when transmitting power over a long distance. Therefore, a high-frequency circuit should be placed at short distances to reduce the skin effects and be more efficient.

High Voltage: transmitting power using high voltage reduces the current in the transmission line. And reducing the amount of current reduces the reactance of the line thus reducing the skin effect.

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