Geometric Mean Distance Formulae

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Figure 5 shows the analysis of three-phase power-distribution bars using FEM and PEEC methods. The

current density in three bars of one phase is drawn, showing proximity effects between conductors.
In alternating current and three-phase current systems, magnetic fields around the busbars are built up

when current flows. These magnetic fields lead to a higher current density in the peripheral regions of

the busbars.
In direct-current equipment, the number of busbars connected in parallel can be almost unlimited.

However, with alternating current and three-phase current the external rails carry a greater load on

account of the current displacement or skin effect. Therefore, as a rule, a maximum of four busbars are

connected in parallel and, in order to maintain a more uniform current distribution, the distance

between the two innermost busbars is increased, or in other words, the distance between the two

innermost busbars is greater than the distance between any one outermost busbar and its adjacent

innermost busbar.
The prior art includes busbars having a C-shaped cross section with walls of uniform thickness,

whereby the C-shaped profile was designed for the fastening of terminals to the busbar by means of

suitable terminal shoes or fastening devices.
In busbar systems in which the conductor busbars are installed in a common plane vertically or

horizontally parallel to one another, and the open distance between main conductors is less than 0.8

times the average center-to-center distance between main conductors, the negative influence of the skin

effect is more noticeable.
Proximity effect may be completely overcome by adopting a concentric arrangement of

conductors with one inside the other as is used for isolated phase busbar systems.
Both skin and proximity effects are due to circulating or 'eddy' currents caused by the

differences of inductance which exist between different 'elements' of current-carrying

Geometric Mean Distance Formulae
Rectangular bars
Three Phase conductors
Ref. Dwight ' Geometric Mean Distance for Rectangular Conductors' 1946
Geometric mean distance, short edges facing.
Geometric mean distance, long edges facing.
A. J. Sinclair – J. A. Ferreira: Analysis and design of transmission-line structures by means

of the geometric mean distance
1996 IEEE, page 1062
0-7803-3946-0/97/$10.00 1997


IEEE. WC2-3.1

Skin effect and proximity effect on current distribution
P. Silvester: Skin effect in multiple and polyphase conductors
IEEE Transactions on power apparatus and systems, Vol. PAS-88, No. 3, March

Three aluminium strips 1.65 x 82.6 mm
, spaced 82.6 mm apart. Frequency = 220 Hz.