Mutual Inductance To Blame?

I have an application where (10) 350mcm cables are arranged on 1" centers in an open wire tray.  All 10 cables carry  one phase of a three phase delta connected load.  The total phase current is 2200A.  When I measure the current on the individual conductors I get readings of 150A on the center cables and progressively higher readings towards the outside cables where I measure 350A.

Someone will be quick to first point out that the cable arrangement is not good, I know that.  My question is, could (or is) the mutual inductance between the cables in the center causing increased impedence and hence less current as compared to the cables on the outside?  

You are correct that the mutual inductance is causing the problem.  This is the same situation that causes skin effect.  More current will flow further from the center of a conductor.  Similarly, more current will flow further from the center of your group of cables.

Would rebundling of the cables into ten 3ø groups solve the imbalance problem?
  

busbar's recommendation is not only helpful to the situation, but the proper method of installation per the NEC(as far as grouping all the conductors in the circuit). Check the derating factors as far as the bundling part.

The mutual inductance effects are also infuenced by the open wire tray material, i.e., magnetic or non-magnetic.

Where are the other phases, now?  Are they also horizontally arranged as 10-single cores but located below the phase you described?

Busbar's suggestion is a good one.  As suggested arrange the three phases as one symmetric bundle.  This will eliminate variation of the self inductances, but only if the wire tray is non-magnetic or if the bundle is rolled or transposed along is length.  Then, adjacent bundles should be further transposed with respect to one another, to reduce mutual inductance effects.  It would also be helpful if the bundles can be arranged vertically, say three horizontally placed bundles, in three tray levels.

Please note, the above is academic if the actual distance is relatively short!

 

Gcudill- As you write the best way to to reduce the inductance is to rebundling the cable in ten groups,in every group three phase cable,this will reduce the electromagntic fild.

Jghrist-I think that the skin effect is dominant in the same cable core,i am not sure this is the case.

Thanks to everyone for their insightful responses.  In this particular application the load is configured such that the individual phases may not be routed as usual (it is neither a transformer or motor).  Each phase connects to different points of the load that are seperated by 15'-20'.  I will use measurements from this application to predict current variations in the future to ensure that cables and quantities are sized correctly.  

If the cables are serving single-phase loads, the neutrals from each load should be fully rated for the load and routed with the phase cables back to a point where they can be interconnected with the neutrals from the other phases.