Electrical Engineering ⇒ Topic : Synchronous Impedance
The synchronous impedance of an alternator can be determined using the open-circuit and short-circuit characteristics of the alternator shown in Figure (a). For a given field current, say OS1, the corresponding no-load voltage is Q1S1, and the corresponding armature current is R1S1. Then, the synchronous impedance per phase, Zs can be calculated as
FIGURE (a) Open-circuit characteristic, short-circuit characteristic and synchronous impedance (Zs) of an alternator
The value of Zs at different values of field current (If) can be determined using Eq. (1) and the data of the O.C. and S.C. characteristics shown in Fig. (a). The resultant data when plotted gives the Zs vs. If characteristic, also shown in Fig.(a). The values of Zs remain constant for the portion of the O.C. characteristic which is linear and decrease gradually thereafter, with increasing field currents. The decrease in the value of Zs in more rapid corresponding to the flat (saturation) portion of the O.C. characteristic.
Next, the value of Zs which is to be used for computing the regulation of the alternator has to be determined. To do this, an ordinate OP equal to the rated voltage of the alternator per phase is fixed. A horizontal drawn from the point P cuts the O.C. characteristic at Q. The field current (If) corresponding to the point Q is OS. This is the field current required to generate the voltage QS when the alternator is on open circuit and to circulate a current RS when it is short-circuited. The value of the synchronous impedance (Zs) corresponding to the alternator rated voltage of OP is
.........[using Eq. (1)]
An alternate method to determine the value of the alternator synchronous impedance (Zs) in a similar way is to determine it at a short circuit current equal to the full-load armature current.
The synchronous reactance Xs can be obtained as
Knowing the values of Rs and Xs, the regulation can be computed at different power factors, usually at unity power factor 0.80 lagging and 0.80 leading, using Eq. (a). To estimate E0, we use Eq. (b) which reads as
In this equation, plus sign is used when the power factor is lagging and minusmsign is used when the power factor is leading
It is given as follows
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