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Magnetizing inrush conditions also occur at a much higher frequency than short circuits, so this phenomenon is worth exploring.

Consider what happens when you initially energize a single-phase transformer. The magnetic flux in the core is equal to the integral of the excitation voltage.

If the circuit is closed when the voltage passes through zero and the initial flux is zero, the sinusoidal flux will be completely offset from zero. The peak value of the full offset flux is twice the peak value of the symmetrical sine wave flux. In other words, the peak flux of the full offset wave can be nearly twice the normal peak flux, which is usually sufficient to drive the core into saturation.

At this point, the only thing limiting the magnetizing current is the air-core impedance of the winding, which is orders of magnitude smaller than the normal magnetizing impedance.

Therefore, during the half cycle of core saturation, the field current is much larger than the normal field current. During the opposite half cycle, the core is no longer saturated and the field current is approximately equal to the normal field current.


The situation is even more extreme when there is residual flux in the core and the direction of the residual flux is the same as the direction of the offset of the sinusoidal flux wave. As shown in Figure 2 below. Note that Figures 1 and 2 are plotted at different scales of current, so the peak current plotted in Figure 2 is actually much larger than the peak current plotted in Figure 1.


02 Excitation surge peak value


To find the peak surge current limited only by the air-core reactance, it is convenient to calculate the inductance of the winding using cgs units:

here:


N – number of coil turns


Amt – Area within the mean diameter of the coil, cm2


l – the axial length of the coil, cm


L – coil inductance, μH




The flux produced by the inductor φL is equal to the residual flux plus 2 times the normal flux change minus the saturation flux, since the saturation flux is in iron. But φL is related to inductance and current:


Therefore, the peak inrush current is expressed in the cgs unit system as follows:

here:


Ipeak in amps and


φr – residual flux


φn – normal magnetic flux change


φs – saturation flux




If there were no resistors in the circuit, each successive peak would have the same value, and the current inrush would continue indefinitely. However, in the presence of resistance in the circuit, the voltage drop across the resistance will be large and the rise in flux need not be as high as the previous cycle.




The integral of the voltage drop represents the net reduction in the magnetic flux required to support the applied voltage. Since the i×R voltage drop is always in the same direction, each cycle reduces the required magnetic flux. When the peak value of the magnetic flux falls below the saturation value of the core, the inrush current disappears. The decay rate is not exponential, although it is similar to an exponential decay current.




important! With large power transformers, the inrush current can last for a few seconds before eventually disappearing.




Line reactance has the effect of reducing peak inrush current by simply adding inductance to the air core inductance of the winding. There is a definite relationship between inrush current and short-circuit current, as both are related to the air-core inductance of the winding.




Remember that short circuits tend to push the flux out of the core.




Rule of thumb! Generally, the rule of thumb is that the peak magnetizing inrush current is slightly above 90% of the peak short circuit current. However, the magnetic force caused by the magnetizing inrush current is usually much smaller than the short-circuit force. Since each phase contains only one winding, there is no magnetic repulsion between the windings.




The whole problem of analyzing magnetizing inrush currents becomes more difficult when three-phase transformers are involved. This is because the phase angles of the excitation voltages are 120° apart, there is a current and voltage interaction between the phases, and the three poles of the switching device are not closed exactly at the same time.




However, it is safe to say that the peak inrush current of a three-phase transformer is close to the short-circuit current level.

One of the interesting features of magnetizing inrush currents is that there is a large proportion of even harmonics because the currents are completely canceled. Even harmonics are also rarely encountered in power circuits.




03 Empathy flow


There is also a phenomenon known as "sympathetic inrush", in which a previously energized transformer exhibits a sudden change in current when a nearby transformer turns on. The sympathetic surge is caused by the line voltage change caused by the inrush current of the second transformer.


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