What is quadrature axis reactance?

If the stator winding of a synchronized machine, which consists of many coils that are basically connected as a series

circuit, is not connected to a load then the resulting emf from all the coils is the open circuit emf of

the phase winding. Closing the circuit on to a load causes a steady state current to flow in the stator

coils. Each coil creates a flux and their total flux opposes the field flux from the rotor. The resulting

flux in the air gap is reduced. The emf corresponding to the air-gap flux drives the stator current

through the leakage reactance and conductor resistance of the stator coils. The voltage dropped across

this winding impedance is small in relation to the air-gap voltage. Deducting this voltage drop from

the air-gap voltage gives the terminal voltage of the loaded generator. In the circumstance described

thus far the reduction in air-gap flux is called armature reaction and the resulting flux is much smaller

than its value when the stator is open circuit. Restoring air gap and terminal voltage requires the

field current to be increased, which is the necessary function of the automatic voltage regulator and

the exciter.

When the rotor pole axis coincides with the axis of the stator coils the magnetic circuit

seen by the stator has minimum reluctance. The reactance corresponding to the armature reaction

in this rotor position is called the 'direct axis synchronous reactance Xsd '. If the stator winding

leakage reactance, Xa, is deducted from Xsd the resulting reactance is called the 'direct axis

reactance Xd '.

A similar situation occurs when the rotor pole axis is at right angles to the axis of the stator

coils. Here the magnetic reluctance is at its maximum value due to the widest part of the air gap facing

the stator coils. The complete reactance in this position is called the 'quadrature axis synchronous

reactance Xsq '. Deducting Xa results in the 'quadrature axis reactance Xq '.