The high faults current should not saturate the core of a reactor. Fault current is much higher than normal current. So, to keep the core of reactor unsaturated, a reactor needs a very large cross-section of its core. Air core may solve this issue of saturation. The utilities use mainly Dry-type Air Core Reactors and Oil Immersed Air Core Reactor.
Dry Type Reactors
Dry type reactors generally use natural or forced air cooling. The utilities use dry type reactor only up to 33 kV systems. They prefer, oil immersed designs of reactor for higher voltage system. Oil makes the size of the reactor more compact compared to a dry type reactor. A dry type reactor needs a large clearance from adjacent constructional work and iron works. Because of the absence of low reluctance or iron paths, the reactance of air-cored reactors becomes almost constant.

Air Core Oil Immersed Reactor
In an oil-immersed reactor uses an iron made oil tank. The reactor windings are placed inside this oil filled iron tank. When the current increases significantly, the magnetic flux increases. This flux may then link with the iron body of the tank. Hence, the flux induces eddy currents in it. These eddy currents can cause unnecessary heating and may create hot spots in the tank body.
To avoid this problem, the manufacturer provides laminated iron shields around the windings. These laminated iron shield provides a path for the magnetic flux. Therefore, it prevents a the flux to enter in the surrounding iron tank.
However, when the fault current increases abruptly, the iron shields may approach magnetic saturation. As a result, the overall reactance of the reactor may decrease up to 10% during the fault condition.
Iron Core Oil Immersed Reactor
Here, the winding contains an iron core inside it. However, the core contains air gaps. Because, the air gaps increase the magnetic reluctance of the core. Therefore, these air gaps prevent saturation due to high fault current.