Effect of harmonics on 3 Phase Transformer

Transformer is one of the most essential equipment in a power system. It transfers the electrical energy between two circuits linked magnetically through electromagnetic induction and hence the name transformer.

Transformer require an AC supply for its functioning. Alternating current flowing through the primary winding creates an alternating flux which links the secondary through a magnetic core. Due to changing flux, emf is induced in the secondary winding. The ratio of voltage appearing across the primary and secondary depends upon their turn ratio, being more specific on the transformation ratio.

This was something too basic which I needed to discuss before I take up the more important topic – Harmonics in transformer.

The first question what comes in mind is why will harmonics be produced after all. When we are supply of constant frequency f how can we hope to get multiple frequency? The reason is the B-H curve of the magnetic core through which the flux flows which leads to the production of harmonics.


Let us consider the B-H curve without hysteresis loss. Flux is directly proportional to the magnetic field (B). Current will correspond to the Magnetic field intensity (H). Let us consider a sinusoidal flux and plot the corresponding current on the same axis. What we observe is that the current is peaky when the flux is sinusoidal. Now if we consider the Fourier analysis of the current wave form then we could represent it as a combination of fundamental and third harmonics as shown in the diagram. Other odd harmonics are also present but there effect at this instance can be neglected.



This is how the harmonics come into existence. Since the voltage is in quadrature with both the fundamental and 3^rd harmonic current the power loss due to both of them is zero. Taking hysteresis loss into consideration, one more current waveform (Ih) adds to it which is 90 degree leading to the flux wave form or we can say it is in phase with voltage (V).  It corresponds to the hysteresis loss as VI_h


Proceeding the same way, we would get the flux to be flat topped when the current is sinusoidal.



Induced voltage due to changing flux in the coil can be found by calculating its derivative with respect to time. A completely sinusoidal flux include only the fundamental period so the induced voltage is also sinusoidal. A flat toped flux and its time derivative can be represented as:

Which corresponds to a peaky voltage. In a similar fashion we would get that a peaky flux produces flat toped emf

.



These harmonics do not have visible effect on single phase transformers since the exciting current is 2 to 6% of the full load current but they do affect 3 phase transformers badly.

All the phases of 3 phase transformer are 120 degree phase shifted. The 3^rd harmonic will have this difference multiplied by 3 which brings us to the conclusion that all the 3 phases will be in phase. Major impact of this is the shifting of the neutral point which would increase the voltage across any two phase and decrease it in one. The 5^th harmonic produces opposite sequence and 7^th harmonic produces positive sequence.



In a star connection the 3^rd harmonic current is either towards the neutral point or away from it. If there is a neutral connection available then there is a path for the flow of 3^rd harmonic current. If 3^rd harmonic current flows then the current is peaky. If the current is peaky then flux is sinusoidal which implies voltage is sinusoidal. Third harmonic current will flow through the line.

If we don’t have a neutral connection then there is no flow of 3^rd harmonic current which implies the current is sinusoidal which implies the flux will be flat topped and voltage will be peaky. It would% increase the peak voltage by 160 % . So voltage harmonics are more undesirable than current harmonics. Thus neutral connection is must on high voltage side if we are using a star connection.

A delta connection also allows the flow of 3^rd harmonic current thus providing a sinusoidal flux and voltage.

The induced voltage on the secondary is will depend on nature of the flux linking primary and secondary. The nature of the emf developed, the current and the voltage can easily



be deduced thereafter. For eg. Consider Yd connection with neutral point given. Since we have neutral connection on primary, the current will be peaky and the flux and voltage will be sinusoidal. Sinusoidal flux will produce sinusoidal emf in the secondary. For a Dd transformer the flux and voltage in both are sinusoidal. Like this we can find the nature of the voltage current in all the groups of transformer.