A Milliken conductor is a specialized type of stranded electrical conductor used primarily in high-voltage (HV) and extra-high-voltage (EHV) power cables. It is designed to reduce the skin effect, proximity effect, and improve current distribution in large cross-sectional conductors, typically those exceeding 800 mm² (e.g., 1000, 1200, 1600, 2000, 2500, or even 3000 mm²).
Structure of Milliken Conductor
A Milliken conductor consists of multiple segments (usually 4, 5, 6, or 7) that are individually stranded and shaped like sectors or wedges. These segments are assembled into a circular conductor, with each segment lightly insulated from its neighbors using materials like insulating paper or semiconductive tape. This segmented design differentiates it from a conventional round, compacted conductor.
In large cross-sectional conductors due to skin effect, current concentrates to the outer strands of the conductor. It increases effective AC resistance of the conductor and hence reduces efficiency of the EHV cable. The Milliken design mitigates this by dividing the conductor into segments. Each segment acts like a smaller conductor, reducing the skin effect within that segment. Each segment is insulated by insulating paper or semiconductive tape. This minimizes current flow between segments, ensuring more uniform current distribution across the entire cross-section.
The strands within each segment are often twisted to further balance the current and reduce losses from the proximity effect.
The Milliken design, patented by Humphreys Milliken in 1933, is a smart fix for two basic physics problems in AC power transmission. Thse are skin effect and proximity effect. It is not just about making a conductor bigger. It is about making a large conductor act like assembly of smaller conductors. That’s why it is a key part of modern HV cable design.
Physics behind Milliken Design
The Skin Effect and Why It is a Problem
The skin effect occurs due to self-inductance within the conductor. When AC flows, it creates a changing magnetic field around the conductor, which in turn induces eddy currents. These eddy currents oppose the main current, especially in the center of the conductor, forcing the majority of the current toward the outer layers. As a result, the main current gets concentrated in a thin outer strand layer (the “skin”) rather than distributing evenly across all the strands of the conductor. Yes, it is obvious that stranding a solid conductor reduces the skin effect, but in very large cross-sectional stranded conductors, the skin effect can be further optimized. This is where the Milliken design comes into the picture.
The skin depth (δ) tells us how deep the current goes before dropping to about 37% of its surface value. The skin depth is calculated as follows,
\[\delta = \sqrt{\frac{2 \rho}{\omega \mu}}\]
Where, \(\rho\) = resistivity of the conductor (e.g., \(1.68 \times 10^{-8} \, \Omega – \text{m}\) for copper),
\(\omega = 2\pi f\) = angular frequency (e.g., \(2\pi \times 50 \, \text{rad/s}\) for 50 Hz),
\(\mu = \mu_0 \mu_r\) = magnetic permeability (\(\mu_0 = 4\pi \times 10^{-7} \, \text{H/m}\) for free space, \(\mu_r \approx 1\) for non-magnetic metals like copper or aluminum).
For copper at 50 Hz:
\[\delta = \sqrt{\frac{2 \times 1.68 \times 10^{-8}}{2\pi \times 50 \times 4\pi \times 10^{-7}}} \approx 9.3 \, \text{mm}\]
Practical Implications: The skin effect has tangible effects even on stranded conductors, especially in high-voltage AC applications like 220 kV cables.
Increased AC Resistance: Because, at 50 Hz, current uses only the cross-sectional area up to 9.3 mm depth from the outer surface of a copper conductor, the effective ac resistance exceeds the DC resistance. For example consider a large copper conductor with diameter of 45 mm. It can easily be calculated the AC resistance at 50 Hz will be 10–20% higher than its DC resistance.
Mitigating the Skin Effect using Milliken Design
Milliken Conductors: A standout solution for high-voltage cables is the Milliken design. Here, we divide the stranded conductor into few insulated segments. Say, the number of segment is 5 here. Since, the overall diameter of the conductor is 45 mm, the effective diameter of each segment may be around 20 mm. Now, due to previously calculated skin depth (\(\approx 9.3 \, \text{mm})\) nearly entire cross section of each segment will be utilized for current carrying. The insulation on each segment also prevents transverse eddy currents, ensuring uniform current flow. This lowers significantly the AC resistance of the overall conductor, making it ideal for 220 kV and above voltage systems.
Mitigating Proximity Effect
Segment Isolation: The insulation reduces magnetic coupling between segments, minimizing the proximity effect within the conductor itself. Each segment’s current distribution is less influenced by its neighbors.
Twisting: Within each segment, strands are often twisted or transposed (like a rope), averaging out the magnetic interactions over the length of a conductor and further balancing the current.