Understanding the skin and proximity effects of power cables operating at 400-Hz
Although the use of 400-Hz power is certainly declining, especially in mainframe computer power systems, some existing systems may need upgrading because of additional equipment or retrofitting. As such, it's important that you understand the restrictions associated with this frequency. These restrictions are the result of skin effect and proximity effect.
Skin and proximity effects
Skin effect. In general, 3-phase, 400-Hz power systems are designed the same way as 60-Hz systems, except for one important aspect: size of conductor. The higher system frequency increases the skin effect on conductors.
Because of the magnetic linkages within a wire or cable's conductor (copper or aluminum) when it's carrying AC current, the current density on the conductor's outer surface becomes greater while at its center becomes less. In other words, the greater portion of current is concentrated near the outside of the conductor; thus the term "skin effect."
Because of this phenomenon the cross-sectional area of the conductor is effectively reduced and, as a result, its resistance is correspondingly increased.
There are several key relationships involving skin effect that you should remember.
- For a given conductor size and material, say 4/0 AWG copper or 500kcmil aluminum, the skin effect increases with frequency.
- For a given material and constant frequency, the skin effect increases with the size of conductor.
- For a given conductor size and constant frequency, the skin effect decreases as the resistivity of the conductor material increases. For example, the skin effect of a 4/0 AWG aluminum conductor is less than that of a same sized copper conductor.
Proximity effect. When two conductors carrying AC current are close together, their magnetic fields interact and force the current into the side of each adjacent conductor. This phenomenon is called proximity effect.
Like skin effect, this further reduces the effective cross-sectional area, with the AC resistance further within the conductor increased.
Proximity effect is the distortion of current distribution caused by the induction between the currents in conductors. This phenomenon causes a concentration of current in those parts of conductors nearest each other. As a result of this abnormal current concentration, the effective resistance of the conductors is increased accordingly.
In general, proximity effect is directly proportional to the magnitude of current and inversely proportional to the distance between conductors. In other words, as the current increases, proximity effect increases; and, as the distance between the conductors increases, proximity effect decreases.
As mentioned, increased frequency will increase the skin and proximity effects, thereby increasing the conductor material's effective resistance. The increased frequency will also increase reactance and this, combined with increased resistance, will increase voltage drop.
Higher frequency will also increase the effect of magnetic materials on cable reactance and heating. For this reason, you should not install cables on higher frequency systems in steel or magnetic conduits, or run them along magnetic structures in buildings.
AC/DC resistance ratio curves
The ratio of AC to DC resistance is called the skin effect ratio. The curves in the diagram show the AC/DC resistance ratio that would exist on a 400-Hz power system, along with the resulting reduction in current rating necessary from a heating standpoint to counteract the effect of this increased frequency.
In the discussion here, reactance can be taken as directly proportional to the frequency without introducing any appreciable errors. This method of determining reactance does not take into account the reduction due proximity effect; however, this change is not large and the error introduced by neglecting it is relatively small.
These curves are drawn up for single conductor 600V cables in nonmagnetic raceway or armor. The 400-Hz reactance curve should not be used for single conductor cables in air that are spaced apart from each other. By using these curves together with 60-Hz ampacity tables from the NEC, you will be able to properly size wire and cable for 400-Hz systems.