Air Core Current Limiter Reactor Coils

When i constructed air-core current limiting inductors, i wound half of the coil in one direction and half in the other to reduce a lot of the external magnetic field.

If one coil is not reversed then you have an effective NORTH pole to NORTH pole magnetic field "fight" which reduces inductance. You get the same effect if you take the 3 phases of a generator and connect them in series to get a higher voltage single phase supply. You need to reverse one of the windings with respect to the other two.

Another example is the old lift variable voltage AC drive that used a 2 speed AC motor with the low speed winding connected in series to a DC supply to produce braking. Again, one winding of the low speed windings needs to be reversed in order to produce maximum braking torque and to prevent motor saturation.

Sorry , none of the answers are accurate. The main reason of the middle limb reversed wound is that to ensure total flux flow in each region are same. If they are all of same sense the bottom of red phase and top of yellow phase shield magnetic path will see three times the flux flow than the other region. Same for bottom of yellow phase and top of blue phase.

But if the middle phase is reversed wound the flow of flux will be the same in any region. Just draw a equivalent reluctance circuit with all mmf in same direction and with only middle mmf reversed direction you can realise what I am trying to say.

It is the very basic of air core reactor vertically stacked. For horizontal stacking the problem is no more so all phases are in same direction.