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Alternating current tends to flow on the outer surface of a conductor. This is known as skin effect and is more pronounced at high frequencies. This document describe this effect and provide users some useful tools to evaluate skin effect for various metals.
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Angelo Baggini – University of Bergamo, Italy – [email protected]
David Chapman – CDA UK, UK - [email protected]
Francesco Buratti – ECD, Italy – [email protected]
SKIN EFFECT
Alternating current tends to flow on the outer surface of a conductor. This is known as skin effect and is more pronounced at high frequencies. Skin effect is normally ignored because it has very little effect at power supply frequencies but above about 350 Hz, i.e. the seventh harmonic and above, skin effect will become significant, causing additional loss and heating. . As frequency is increased the depth to which the flow can
penetrate, δ, is reduced.
where:
• ρ is the conductor resistivity (ohm m)
• µr is the relative permeability
• f is the frequency (Hz). 50Hz 1kHz 100kHz 1MHz 10MHz Copper 9.36E-03 2.09E-03 2.09E-04 6.62E-05 2.09E-05 Aluminium 1.16E-02 2.59E-03 2.59E-04 8.19E-05 2.59E-05 Iron (3% Si) µr=300 2.82E-03 6.30E-04 6.30E-05 1.99E-05 6.30E-06 Graphite 2.64E-01 5.90E-02 5.90E-03 1.87E-03 5.90E-04
Table 1 - Skin depths for some metals (m)
Skin effect occurs because current flow moves away from those regions of the conductor having the strongest magnetic field. Skin effect causes the apparent resistance of a conductor to increase above that suggested by the DC value, thus lowering the Q-factor in resonant circuits and reducing the efficiency in switching supplies, but most of all increasing losses in conductors. This will cause cable derating because current capacity must be reduced. Of course this problem becomes much more important as cable size increases, because losses increase proportionally. Multiple cable cores or laminated bus-bars can be used to help overcome this problem.
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Angelo Baggini – University of Bergamo, Italy – [email protected]
David Chapman – CDA UK, UK - [email protected]
Francesco Buratti – ECD, Italy – [email protected]
Figure 1 – Skin depths for some metals
Generally in case of conductors where an AC current flows, the AC Resistance (Rac) to DC resistance (Rdc) ratio depends on conductor shape and on frequency square root value with a complicated formula. The following figure shows the ratio Rac/Rdc of a cable (rounded conductor) against the
ratio r/δ, where: r is the conductor radium
δ =
2ρ/ωµ is the skin effect penetration factor
ρ is the electrical resistivity of the conductor material
µ is the magnetic permeability of the conductor material
ω is the pulsation of the current
Rca/Rcc
0
1
2
3
4
5
6
0 1 2 3 4 5 6 7 8 9 10
Figure 2 - Rac/Rdc of a cable (rounded conductor) against the ratio r/δ
Rac/Rdc
r/δ
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Angelo Baggini – University of Bergamo, Italy – [email protected]
David Chapman – CDA UK, UK - [email protected]
Francesco Buratti – ECD, Italy – [email protected]
For example a copper made cylindrical conductor with a diameter of 20 mm, at frequency of 350 Hz i.e. 7
th harmonics, the ratio Rac/Rdc is equal to 1,6.
The growth of resistance, but most of all of inductance of a cable, due to the higher frequency value also causes an increase of voltage drop on cables. In case of harmonics, where components with different frequency values are simultaneously present, voltage drop must then be calculated taking into account all frequency components.
REFERENCES
[1] A. Baggini - Handbook of Power Quality, Wiley 2008. [2] D. Chapman – Harmonics, causes and effects, LPQI Application Guide [3] Department of Electronic Engineering – University of Surrey, UK [4] Wikipedia - www.wikipedia.org
