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aligns with the voltage or not. Therefore the heat is always proportional to the

square of the current amplitude, irrespective of the phase angle (the shift

between voltage and current). So a transformer has to be rated (and selected) by

apparent power. It is often helpful to think of an extreme example: Imagine a use

case where the only and exclusive load is a static var compensator (and such cases

do exist). Would the load then be zero because the active power is zero? Most

certainly not. Caution: In this situation the voltage across the output terminalswill increase with load rather than drop!

Supplement:

Special care has to be taken if the load current of a transformer includes any

higher frequencies such as harmonics. Then the transformer may even overheatalthough the TRMS load current, measured correctly with a TRMS meter, does not

exceed the current rating!

Why is this? It is because the copper loss includes a share of about 5% to 10% of

so-called supplementary losses. These arise from eddy currents in mechanical,

electrically conductive parts made of ferromagnetic materials and especially in the

low voltage windings with their large cross sections. The magnetic stray fields

originating from a lack of magnetic coupling between the HV and LV windings

(main stray canal) induce something that could be called an eddy voltage inside

the conductors, which drives an eddy current flowing around in a circle across theconductor, perpendicular to the main load current. Now the amplitude of this eddyvoltage is proportional to the rate of change of the magnetic field strength. Therate of change of the magnetic field strength is proportional to both the amplitude

and the frequency of the current. So the eddy current increases proportionally to

the load current and proportionally to the operating frequency, for the limitation to

the eddy current is Ohms Law. The supplementary power loss caused by the eddycurrent is eddy current times eddy voltage.

Hence, the supplementary losses increase by the square of the load current, which

excites the magnetic stray field, and by the square of the frequency, while the

main copper loss increases only by the square of the load current amplitude.

Therefore the transformer runs hotter when the load current has the same

amplitude but is superimposed by higher frequency constituents above the rated

frequency. This additional heat loss is difficult to quantify, especially as the

transformers stray reactance limits the passage of higher frequency currents to

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some extent, but in an extreme case it may drive the supplementary loss up

from 10% to 80% of the copper loss. This means that the transformer may run

some 70% hotter (of temperature rise above ambient) than specified for rated

(sinusoidal) current. Since the ohmic heat loss, however, depends on the square of

the current, it is enough to limit the load current to some 65% of its rating to

avoid overheating.