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Synchronous Impedance

Author: E.E. Kimberly

The voltage Ez which forces the current I1 through the impedance of the motor windings produces a voltage drop I1Zs. The impedance Zs is called the synchronous impedance and is composed of two parts. One part is Ra+jXa, which is the resistance and leakage reactance of the winding. The other part is Xr, 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 Xr 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, Xr and Xa are commonly combined and the result is called Xs. The value of Zs is composed of both parts. Thus,

 Zs = Ra + jXa + jXr [19-1]

To determine Zs 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 Ip 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 Ep per phase is found corresponding to the direct current used. The synchronous impedance, in ohms, is then Zs = Ep/Ip. With the polyphase winding short-circuited, all of Ep is used to force Ip through the total impedance Zs of the machine. Refinements of this procedure are necessary if Zs must be determined accurately for some particular condition of loading.

Last Update: 2011-01-18