3. Armature reaction of synchronous machines

Assuming that the induced voltages and the fluxes through the turns are sinusoidal quantities of the same frequency, we can associate vectors to these machine quantities in Fresnel diagram (or in the complex plane).

For No-load operation, we use the generator convention (where the inductor flux Ф_J leads the e.m.f. by an angle of π/2 rad) and in the motor convention (where the flux Ф_J lags the e.m.f. by an angle of π/2 rad) . This is shown in Figure 13.

Figure 13: Position of the e.m.f. versus the inductor flux.

 

When the machine is operating under rated load, the currents circulating in the stator windings create an additional field rotating at the same speed as that generated by the rotor and superposed one on the other.

This has the effect of modifying the useful flux and therefore, the value of the induced useful e.m.f., which constitutes the magnetic armature reaction.

 

In the case of synchronous machines, the position of the stator field depends on the phase shift between currents and voltages. This causes significant variations in the resulting e.m.f. as the load changes.

- Case of a pure capacitive load (fig. 14.a), the armature reaction flux Ф_I is in the same direction as the inductor flux Ф_J.

- Case of a pure inductive load (fig. 14.b), the armature reaction flux Ф_I is on the same axis as the inductor flux Ф_J but in the opposite direction.

- Case of a pure resistive load (fig. 14.c), the armature reaction flux Ф_I is in front quadrature (leading of an angle of π/2 rad) with respect to the inductor flux Ф_J.

- Case of a random load (fig. 14.d), the armature reaction flux Ф_I is ahead by an angle of Ψ + π/2 with respect to the inductor flux Ф_J. In this case, the armature flux Ф_I is decomposed into two components: a longitudinal component Ф_{I ln} of the same axis as the inductor flux Ф_J and a transverse component Ф_{I tr} in front quadrature with respect to the inductor flux Ф_J.

The angle Ψ is negative when the load is capacitive and is positive when the load is inductive. The different armature reactions are given in Figure 14.

Figure 14: Position of the e.m.f. versus the armature flux for a random load.

 

In all cases, it is the resulting flux Ф_r (the vector sum of the inductor flux Ф_J and the armature reaction flux Ф_I) which induces a resulting e.m.f. called E_r different from the no-load e.m.f. noted E when the inductor flux acted alone. This new resulting e.m.f. is given by:

E_r = k . N . f . Ф_r

 

- Case of a salient pole machine

In the case of a synchronous machine with salient poles, the path of the armature reaction flux Ф_I depends on the position of the field poles.

Along the transverse axis, the effect of the armature reaction flux is less significant because the air gap is larger. Thus, the transverse reaction armature flux component named Ф_{I tr} no longer acts completely. Only a part of this component (multiplied by a reducing coefficient k') is added to the longitudinal component to form the resulting flux Ф_r. This modification of the armature reaction flux Ф_I in the case of a rotor with salient poles is given in figure 15.e.

The resulting flux Ф_r as well as the resulting e.m.f. "E_r" are given in Figure 15 with an angle of π/2 in advance of the resulting flux versus the resulting e.m.f. (using generator convention).

Figure 15: Position of the resulting e.m.f. versus the resulting flux.