Calculation of screen current

["Winfried Graupner" <winfried.graupner@xxxxxx>]

Dear All,

First of all many thanks to David Meeker for this great program.
I use this tool for EMC related issues.
I would like to address a problem in conjunction to calculation of 
currents in screened cables.
The arrangement (see file: Screen current.zip in FEMM file directory) 
consists of three single screened cables of a three-phase system.
The cables are laid in parallel at a certain distance. All screens 
are connected to each other but they are isolated from the domain 
boundary. 
The magnitude of the screen current depends on the mutual coupling, 
the frequency and the impedance of the representative screen loop 
(see file: Screen current.zip in FEMM file directory).
For low frequencies the resistor in this loop cannot be neglected 
against the reactance of this loop. This disruptive factor is the 
cause, why a cable with e.g. copper-braid screen is not suited at low 
frequencies.
For frequencies, approx. four times higher than the corner frequency 
of the cable the magnitude of the current in the screen reaches the 
excitation current and becomes independent on frequency. 
In principle the calculation with FEMM confirms this mechanism as 
shown in the diagram (see pdf-file).
For frequencies in this intermediate section below 10 kHz the current 
in the centre screen is lower than in the right and left screen due 
to its lower self inductance (higher corner frequency). 
However, I have no explanation for the current distribution in the 
right screen. The magnitude versus frequency of this current must be 
the same as for the current in the left screen due to quasi-
symmetrical conditions. But the trace does not follow this rule.
I could establish the following details:
- increasing of solver precision or refinement of the mesh has no 
noticeable influence on this phenomenon
- the current density in all three screens is not only composed of 
eddy currents but also of a certain share of source current in spite 
of their isolation from the domain boundary
- the phenomenon changes from the right to the left screen if the 
complex space vector rotates in the opposite direction (e.g. exchange 
of phase currents in two conductors)
- this phenomenon completely disappears if all three cables are 
arranged in a triangle with perfect symmetry, in this case all three 
screen currents have the same amount versus frequency.

What is wrong? Do I violate the scope of FEMM?
I would be pleased for any help! 

Best regards
Winfried