SECTION 4: COMPOSITE, DOUBLE-CIRCUIT AND BUNDLED CONDUCTORS

Composite Conductors

2.1 What is a composite conductor?

A composite conductor consists of two or more strands or elements electrically connected in parallel. Stranded conductors are commonly used in overhead transmission lines because they provide flexibility and useful mechanical properties.

The chapter describes conductor types such as:

• Stranded copper conductors

• Hollow copper conductors

• Aluminium conductors

• Aluminium Conductor Steel Reinforced (ACSR)

Composite conductors containing different materials

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2.2 Aluminium Conductor Steel Reinforced (ACSR)

An ACSR conductor has a central steel core surrounded by aluminium strands. The steel core provides mechanical strength, while the aluminium strands carry most of the electrical current.

Advantages of ACSR:

1. Mechanical strength: The steel core allows the conductor to withstand greater tensile loads.

2. Longer spans: Stronger conductors can be used over longer distances between supports.

3. Reduced support requirements: Longer spans can reduce the number of towers or poles needed for a given route.

4. Lower conductor cost: ACSR can be more economical than an equivalent copper conductor.

5. Larger effective diameter: The conductor construction can provide a larger diameter, which helps reduce the electric-field intensity at its surface and can reduce corona effects.

6. Corrosion resistance: Aluminium strands provide useful resistance to atmospheric corrosion, though actual performance depends on the environment and construction.

The chapter notes that the steel core contributes relatively little to the current-carrying capacity compared with the aluminium portion.

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Inductance of Composite Conductors

A composite conductor may contain several strands, and each strand can have a different distance from the strands in the other conductor group. Therefore, its inductance is calculated using the equivalent self-geometric mean distance (GMR) and mutual geometric mean distance (GMD).

3.1 Mutual GMD between two conductor groups

Suppose conductor group A contains strands and group B contains strands. Let be the distance between strand in group A and strand in group B.

The mutual GMD between the two groups is:

 

This is the -th root of the product of all distances between the strands in the two groups.

3.2 Self-GMR of a conductor group

For a group containing strands, the self-GMR is obtained from the self and mutual distances among its strands. In the general composite-conductor calculation, the self-distance of each solid strand is represented by its own effective radius .

The group self-GMR can be expressed as:

 

Here, the diagonal terms represent the effective radius of each strand, and the off-diagonal terms represent distances between different strands.

3.3 Inductance of a composite conductor

Once the group GMD and self-GMR are known, the inductance per phase conductor is:

 

Similarly, for conductor group B:

 

For a single-phase line consisting of two conductor groups, the loop inductance is:

 

If both groups have the same self-GMR, then , and the loop inductance is twice the inductance of one conductor group.

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Inductance of Double-Circuit Transmission Lines

4.1 Construction

A double-circuit three-phase line has six phase conductors: two conductors for each phase. The two conductors belonging to the same phase are electrically connected in parallel, while the three phase groups form the three-phase system.

Double-circuit lines allow two three-phase circuits to be carried on a common tower or transmission structure.

4.2 Why transposition is considered

In a double-circuit line, the conductors may not be symmetrically positioned. The distances between the phase groups differ depending on their physical locations. The chapter therefore uses transposition to calculate the equivalent inductance.

The procedure is:

1. Determine the distances between conductors in each physical arrangement.

2. Calculate the mutual GMD for each transposition position.

3. Combine these values to obtain the equivalent GMD.

4. Calculate the self-GMR of each phase group.

5. Use the inductance equation to obtain the inductance per phase.

For three transposition positions, the equivalent mutual GMD is:

 

where , and are the mutual GMD values for the three positions.

If the equivalent self-GMR of the phase group is , then:

 

The exact and depend on the physical arrangement of the six conductors.

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Inductance of Double-Circuit Transmission Lines

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4.1 Construction

A double-circuit three-phase line has six phase conductors: two conductors for each phase. The two conductors belonging to the same phase are electrically connected in parallel, while the three phase groups form the three-phase system.

Double-circuit lines allow two three-phase circuits to be carried on a common tower or transmission structure.

4.2 Why transposition is considered

In a double-circuit line, the conductors may not be symmetrically positioned. The distances between the phase groups differ depending on their physical locations. The chapter therefore uses transposition to calculate the equivalent inductance.

The procedure is:

1. Determine the distances between conductors in each physical arrangement.

2. Calculate the mutual GMD for each transposition position.

3. Combine these values to obtain the equivalent GMD.

4. Calculate the self-GMR of each phase group.

5. Use the inductance equation to obtain the inductance per phase.

For three transposition positions, the equivalent mutual GMD is:

 

where , and are the mutual GMD values for the three positions.

If the equivalent self-GMR of the phase group is , then:

 

The exact and depend on the physical arrangement of the six conductors.

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Bundled Conductors

 

5.1 What is a bundled conductor?

A bundled conductor consists of two or more sub-conductors connected in parallel and used as one phase conductor. The sub-conductors are separated by spacers to maintain their arrangement.

Bundled conductors are used in high-voltage transmission lines, particularly at voltages above 230 kV, as discussed in the chapter.

5.2 Advantages of bundled conductors

• Reduced inductive reactance: Bundling increases the equivalent self-GMR of a phase.

• Reduced voltage gradient: The electric-field intensity at the conductor surface is reduced.

• Reduced corona loss: Lower surface electric stress can reduce corona discharge.

• Reduced radio interference: Lower corona activity can reduce radio interference.

• Reduced surge impedance: Bundling increases capacitance and reduces inductance, lowering surge impedance.

5.3 Equivalent GMR of a two-sub-conductor bundle

For two identical sub-conductors, let:

• = physical radius of each sub-conductor

• = effective radius of each sub-conductor

• = spacing between the two sub-conductors

The equivalent self-GMR of the bundle is:

 

This formula is used in the inductance calculation for a two-sub-conductor bundle.

5.4 Inductance of a bundled phase

If the equivalent GMD between phases is , then the inductance per phase is:

 

Since bundling increases the effective GMR, it reduces the inductance and inductive reactance, assuming the phase spacing remains unchanged.

5.5 Surge impedance

The surge impedance of a transmission line is:

 

where:

• = surge impedance in ohms ()

• = inductance per unit length (H/m)

• = capacitance per unit length (F/m)

Bundling generally increases capacitance and decreases inductance. Both changes reduce surge impedance.

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6. Skin Effect and Proximity Effect

6.1 Skin effect

When direct current flows through a conductor, the current is approximately uniformly distributed across its cross-section. With alternating current, the changing magnetic field causes the current distribution to become non-uniform. More current tends to flow near the conductor surface than near its centre.

This phenomenon is called skin effect.

 

Effects of skin effect:

• The effective AC resistance becomes greater than the DC resistance.

• The effect becomes more pronounced as frequency increases.

• It is also influenced by conductor size and material.

The chapter explains skin effect in terms of the unequal flux linkages of the inner and outer parts of the conductor.

6.2 Proximity effect

Proximity effect occurs when the alternating magnetic field produced by a nearby conductor causes circulating currents and a non-uniform current distribution in a conductor.

In a two-wire system, the current density becomes greater in some regions and smaller in others, depending on the relative positions of the conductors.

Effects of proximity effect:

• It increases the effective AC resistance.

• It is more significant when conductors are close together.

• It is generally less significant for overhead lines with widely spaced conductors than for closely spaced cables.

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6.3 Difference between skin effect and proximity effect

Skin effect

Proximity effect

Caused by the conductor's own alternating magnetic field.

Caused by the magnetic field of nearby conductors.

Current tends to concentrate near the conductor surface.

Current distribution changes due to nearby conductors.

More pronounced at higher frequencies and for larger conductors.

More pronounced when conductors are close together.

Increases effective AC resistance.

Also increases effective AC resistance.