STEADY STATE ARMATURE REACTION

The rotating field in the air gap of a synchronous machine is generally considered to be free of space harmonics, when the basic operation of the machine is being considered. In an actual machine there are space harmonics present in the air gap, more in salient pole machines than a cylindrical rotor machine. It is acceptable to ignore the effects of space harmonics when considering armature reaction and the associated reactance. Therefore the flux wave produced by the rotating field winding can be assumed to be distributed sinusoidally in space around the poles of the rotor and across the air gap.

If the stator winding, 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 X_sd . If the stator winding leakage reactance, X_a, is deducted from X_sd the resulting reactance is called the direct axis reactance X_d .

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 X_sq . Deducting X_a results in the quadrature axis reactance X_q .

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