Electrical Machines
The synchronous reactance( Xs) is the

 combined reactance due to armature reaction and leakage flux
 reactance either due to armature reaction or leakage flux
 reactance due to armature reaction of the machine
 reactance due to leakage flux

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Electrical Machines
Compensating windings are used in DC generators

  to neutralize the cross magnetizing effect of the armature reaction.
None of these
  to provide path for the circulation of cooling air.
  mainly to reduce the eddy currents by providing local short circuit.

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