HARMONICS IN POWER TRANSFORMERS BASIC INFORMATION AND TUTORIALS

HARMONICS IN NO-LOAD EXCITING CURRENT
Because transformer cores are made of ferromagnetic materials, the exciting current of the transformer under no-load conditions is not sinusoidal even though the applied voltage and flux are sinusoidal due to the nonlinear nature of the B-H curve, and similarly the relationship between flux and magnetomotive force (MMF).

For anyvalue of flux, there are two values of MMF, depending on whether the flux is increasing or decreasing. From these MMFs, the magnetizing current can be computed and plotted corresponding to these values of flux, depending on whether the flux is rising or falling.

With three-limb transformers, as the triplen harmonics return through air (or rather through oil and tank), the higher reluctance of the path reduces the third harmonics to a lower value (about 10% of the value in independent core phases). The fifth and seventh harmonics may also be large enough, around 5–10%.

HARMONICS DUE TO INRUSH CURRENT
The transient current drawn by a transformer when it is first energized depends upon the instant of switching. If the transformer is energized when the applied sinusoidal voltage is at its peak, usually there is no transient.

If the transformer is energized when the applied voltage is zero and it has a residual flux fr with unfavorable polarity, then the total flux that would be required to counteract the applied voltage according to Lenz’s law would be 2 fm + fr.

To produce such a flux, the transformer may have to draw many times (say, 100 times) the normal exciting current of the transformer. In actual practice, the inrush current may be 8 to 10 times the full-load current of the transformer, depending upon the instant of switching and polarity of the applied voltage.

Depending upon the transformer, the inrush current phenomenon may persist for a few seconds, thus creating harmonics during this period.

DC MAGNETIZATION
Under unbalanced conditions, the transformer excitation current can contain odd and even harmonics. The transformers feeding half-wave rectifiers or supplying power to a three-phase converter with unbalanced firing fall into this category.

The magnitude of the harmonic components of the excitation current in the presence of the direct current on the secondary side of the transformer increase almost linearly with the dc content. The linearity is better for the lower-order harmonics.

As the harmonics generated by the transformer under dc magnetization are largely independent of the ac excitation, there appears to be no advantage in designing a transformer to run “underfluxed” in the presence of direct current.