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Assumptions in Synchronous Impedance Method for Finding Voltage Regulation of Alternator
Following are the assumptions being made in the synchronous impedance method for finding the voltage regulation of the alternator or synchronous generator −
The synchronous impedance is constant.
For the synchronous generator, the synchronous impedance is determined from the open-circuit characteristics (O.C.C.) and short-circuit characteristics (S.C.C.). The synchronous impedance is the ratio of open-circuit voltage to short-circuit current i.e.
$$\mathrm{Synchronous\:impedance,\:𝑍_{𝑠}=\frac{open\: circuit\:voltage\:per\:phase}{short\:circuit \:armature\:current}}$$
When the O.C.C. and S.C.C. are linear, then the synchronous impedance is constant. Above the knee point of the O.C.C. when the saturation starts, the synchronous impedance decreases because in this condition, the O.C.C. and S.C.C. approach each other.
Therefore, the synchronous impedance obtained under test conditions below saturation is greater than that of the under normal operating conditions when the magnetic circuit of the machine becomes saturated.
Hence, in the case of synchronous impedance method, the effect of saturation is neglected and this is the greatest source of error in the measurement.
The flux under test conditions is the same as that under the normal operating conditions
It is considered that a given value of field current always produces the same flux in the machine. This assumption introduces considerable error in the measurement. When the armature of the alternator being short-circuited, the armature current lags the generated voltage by almost 90° and therefore, the armature reaction is completely demagnetised. This demagnetising effect of the armature reaction further reduces the degree of saturation. Thus, the actual resultant flux is very small and hence the generated voltage.
These test conditions may be different from those with normal operating conditions when the alternator is loaded and the field current is equal to that under short-circuit test. Hence, the open-circuit voltage found from the O.C.C. is larger than the current under short-circuit test and hence, the value of the synchronous impedance of the machine obtained by this method is very large.
The effect of the armature reaction flux can be replaced by a voltage drop proportional to the armature current and that armature reaction voltage drop is added to the armature reactance voltage drop.
Due to this substitution of voltage for the flux, the synchronous impedance method is also known as EMF method. These assumptions also cause error in the measurement, because the shift of the armature flux varies with the power factor of the machine and the load current and a distortion of the main field flux is produced. Therefore, the armature reaction voltage drop is not in phase with the armature reactance voltage drop.
The reluctance of the magnetic path to the armature flux is constant regardless of the power factor of the machine.
For a cylindrical rotor alternator, this assumption is true because of the uniform air gap. For the alternator having salient-pole type rotor, the position of the armature flux relative to the field poles varies with the power factor. This variation in the magnetic reluctance and the armature flux with the power factor causes considerable error in the salient pole type alternator.
The voltage regulation of the alternator obtained by using synchronous impedance method is greater than that is obtained by actual loading of the machine. Therefore, the synchronous impedance method is also known as pessimistic method.
The results obtained by this method are more likely on the safer side and the performance of the synchronous generator would be better than that is indicated by the calculations. At low excitation, the open-circuit characteristic coincides with the air-gap line, thus, the synchronous impedance of the alternator is constant and this value of the synchronous impedance is known as linear or unsaturated synchronous impedance.
Although, with the increasing excitation, the effect of the saturation decreases the value of synchronous impedance and hence the values of the synchronous impedance beyond the linear part of the O.C.C. are known as saturated synchronous impedances. The values of the saturated synchronous impedance are not constant but vary with the excitation and the power factor of the alternator on load. The value of the synchronous impedance to be used in a given situation is known as effective synchronous impedance of the machine.
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