Synchronous Impedance

Author: E.E. Kimberly

The voltage E_z which forces the current I₁ through the impedance of the motor windings produces a voltage drop I₁Z_s. The impedance Z_s is called the synchronous impedance and is composed of two parts. One part is R_a+jX_a, which is the resistance and leakage reactance of the winding. The other part is X_r, which is not a reactance in the usual sense but is the result of the effect of the stator ampere-turns on the total flux of the motor. This effect is called armature reaction and its magnitude depends almost altogether on the angle by which the rotor poles lag the stator poles in space. It is apparent then that X_r depends on both the magnitude of the motor load and the motor power factor. If the mmf of the armature reaction tends to decrease the total flux, its effect is the same as additional reactance drop; and, therefore, X_r and X_a are commonly combined and the result is called X_s. The value of Z_s is composed of both parts. Thus,

Zs = Ra + jXa + jXr

[19-1]

To determine Z_s experimentally, the machine is driven at synchronous speed without excitation. The polyphase winding is short-circuited through three ammeters, one in each lead, to measure the current I_p per phase. A small direct current is then used to magnetize the field poles to the point where the three ammeters show full-load rated current. From the open-circuit saturation curve of the machine, the voltage E_p per phase is found corresponding to the direct current used. The synchronous impedance, in ohms, is then Z_s = E_p/I_p. With the polyphase winding short-circuited, all of E_p is used to force I_p through the total impedance Z_s of the machine. Refinements of this procedure are necessary if Z_s must be determined accurately for some particular condition of loading.