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, Z_s can be calculated as

        FIGURE (a) Open-circuit characteristic, short-circuit characteristic and synchronous impedance (Z_s) of an alternator

                                                                           ................. (1)

The value of Z_s at different values of field current (I_f) 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 Z_s vs. I_f characteristic, also shown in Fig.(a). The values of Z_s 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 Z_s in more rapid corresponding to the flat (saturation) portion of the O.C. characteristic.

   Next, the value of Z_s 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 (I_f) 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 (Z_s) corresponding to the alternator rated voltage of OP is

                                                                       .........[using Eq. (1)]

An alternate method to determine the value of the alternator synchronous impedance (Z_s) in a similar way is to determine it at a short circuit current equal to the full-load armature current.

The synchronous reactance X_s 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

                                                                     .................. (a)

                               ..................  (b)

                                 ..............  (2)

In this equation, plus sign is used when the power factor is lagging and minusmsign is used when the power factor is leading

SYNCHRONOUS IMPEDANCE

It is given as follows