# The Proximity Effect in Transmission Lines

### Key Takeaways

• An increase in apparent resistance in a conductor causes a voltage drop and power loss. This phenomenon is called the proximity effect.

• A conductor's material, diameter, and structure all influence the intensity of the proximity effect.

• It is possible to reduce the proximity effect by reducing the size of the conductor and the frequency and by increasing the voltage and space between conductors.

The proximity effect is present in transmission lines when conductors are too close together

Delta-connected ac transmission lines transmit three-phase ac power between substations. When conductors are too close to each other in a delta arrangement, the proximity effect is present in transmission lines. The proximity effect could be avoided by keeping conductors spaced equally. However, extending the distance between transmission lines inflates the expense of the support structures, directly affecting the efficiency of the ac power transmission. In this article, we will discuss how to reduce the influence of the proximity effect in transmission lines.

## The Proximity Effect in Transmission Lines

Conductors carrying alternating current will produce alternating flux in adjacent conductors. This alternating flux will cause a circulating current to start flowing in the conductor, creating a non-uniform current distribution in the transmission line, increasing the conductor's apparent resistance. The increased resistance along the transmission line causes a voltage drop and power loss. This phenomenon is called the proximity effect.

### How Does the Proximity Effect Impact Transmission Lines?

The concentration of current through adjacent conductors varies with the alternating magnetic field and its associated eddy currents. When conductors carry current in the same direction, the currents flowing through them get concentrated at the conductors' farthest side. In contrast, when currents flowing through adjacent conductors flow in opposite directions, the currents get concentrated in the nearest side of both conductors.

As the alternating current frequency increases, the proximity effect becomes more intense. Conductors carrying 50Hz current endure less of the proximity effect than conductors carrying 60Hz current. The effective resistance and power loss is higher in 60Hz transmission lines than in 50Hz transmission lines. Most countries worldwide use 50Hz ac frequency, but the United States is not one of them. The 60Hz frequency in the transmission line causes more of the proximity effect than the 50Hz supply.

The proximity effect is due to varying magnetic fields, making it an impossible phenomenon in dc transmission. As dc frequency is zero, it fails to produce an alternating magnetic field in adjacent conductors. The current concentration remains uniform in dc transmission lines, apart from the influence of the skin effect.

## Factors Influencing the Proximity Effect

Both transmission lines and nearby conductors carrying alternating currents experience the proximity effect. In ac transformers and inductors, the windings are close enough that the proximity effect is more predominant than the skin effect. If the conductors are stranded, both the internal proximity effect and external proximity effect exist. Several factors influence the proximity effect in transmission lines, including:

1. The conductor’s material - High ferromagnetic materials experience more proximity effects than non-ferromagnetic materials.
2. The conductor’s diameter - As the conductor’s diameter increases, the proximity effect also increases. The conductor’s diameter is dependent on current, and when the system current is high, the proximity effect becomes stronger.
3. Frequency - As the frequency increases, the proximity effect becomes more intense.
4. The conductor’s structure - The proximity effect is higher in solid conductors than in stranded conductors. The decreased surface area of stranded conductors causes the proximity effect to be less than in solid conductors, which have more surface area. However, the internal proximity effect and external proximity effect exist in stranded conductors such as ACSR.

## How to Reduce the Proximity Effect

Knowing the factors that create the proximity effect in transmission lines, it is possible to implement some changes. Several fixes can reduce the influence of the proximity effect, which include:

1. Reducing the size of the conductor - The proximity effect is directly proportional to the surface area of the conductor. Therefore, as the surface area increases, the proximity effect becomes stronger. Replacing solid conductors with stranded conductors helps reduce the conductor's surface area, decreasing the proximity effect.
2. Increasing the space between conductors - Dummy conductors can help increase the space between conductors. However, this will come at an added cost in support structures.
3. Increasing voltage and reducing frequency - Transferring power constantly through transmission lines increases voltage and decreases current—the reduced size of conductors decreases the proximity effect. Although not as practical, reducing the transmission voltage and current frequency is another means of reducing the proximity effect.

The proximity effect in transmission lines is a limitation in electrical ac power transmission. The proximity effect is present not only in high voltage systems, but also in medium and low voltage systems. Cadence’s software can help reduce the proximity effect in microstrips or striplines in circuit boards.