Harmonics:
In addition to the operation of transformers on the sinusoidal supplies, the harmonic
behavior becomes important as the size and rating of the transformer increase. The effects
of the harmonic currents are:
- Additional copper losses due to harmonic currents
- Increased core losses
- Increased electromagnetic interference with communication circuits.
- Increased dielectric stress on insulation
- Electrostatic interference with communication circuits
- The resonance between winding reactance and feeder capacitance.
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| Harmonics Generated by Transformers |
Single Phase Transformer:
Modern transformers operate at increasing levels of saturation to reduce
the weight and cost of the core used in the same. Because of this and due to the hysteresis,
the transformer core behaves as a highly non-linear element and generates harmonic voltages
and currents. At any instant of the flux density wave, the ampere-turns required to establish the same are read out and plotted, traversing the
hysteresis loop once per cycle. The sinusoidal flux density curve represents the sinusoidal
applied voltage to some other scale. The plot of the magnetizing current which is peaky is
analyzed using Fourier analysis. The harmonic current components are obtained from this
analysis. These harmonic currents produce harmonic fields in the core and harmonic voltages
in the windings. A relatively small value of harmonic fields generates a considerable magnitude
of harmonic voltages.
These effects get even more pronounced for higher-order harmonics. As these harmonic voltages get short-circuited through the low impedance
of the supply they produce harmonic currents. These currents produce effects according to
Lenz’s law and tend to neutralize the harmonic flux and bring the flux wave to a sinusoid.
Normally the third harmonic is the largest in its magnitude. In the case of a single-phase transformer, the harmonics are confined mostly to the primary side as the source impedance is much
smaller compared to the load impedance. The understanding of the phenomenon becomes clearer if the transformer is supplied with a sinusoidal current source. In this case, the current
has to be sinusoidal and the harmonic currents cannot be supplied by the source hence
the induced emf will be peaky containing harmonic voltages. When the load is connected on
the secondary side the harmonic currents flow through the load and voltage tends to become
sinusoidal. The harmonic voltages induce electric stress on dielectrics and increased electrostatic interference. The harmonic currents produce losses and electromagnetic interference.
Three phase banks of Single Phase Transformers:
In the case of single-phase transformers connected to form a three-phase bank, each
transformer is magnetically decoupled from the other. The flow of harmonic currents is
decided by the type of electrical connection used on the primary and secondary sides.
Also, there are three fundamental voltages in the present case each displaced from the other
by 120 electrical degrees. Because of the symmetry of the a.c. wave about the time axis
only odd harmonics need to be considered. The harmonics which are triplen (multiples of
three) behave similarly as they are co-phasal or in phase in the three phases. The non-triplen harmonics behave similarly to the fundamental and have ±120◦ phase
displacement between them.
Three-Phase Transformer Units:
As against a bank of three single-phase transformers connected to three-phase
mains, a three-phase transformer generally has three magnetic circuits that are interacting.
The exception to this rule is a 3-phase shell-type transformer. In the shell type of
construction, even though the three cores are together, they are non-interacting. Three limb
core type 3-phase transformer is one in which the phases are magnetically also linked. The flux of each limb uses the other two limbs for its return path. This is true for fundamental
and non-triplen harmonics. The triplen harmonics being co-phrasal cannot use other limbs
for the return path (this holds good for zero sequences, unbalanced fundamental MMF also).
The flux path is completed through the air. So substantially large value of the MMF produces
a low value of third harmonic flux as the path of the flux is through the air and has a very high reluctance. Thus the flux in the core remains nearly sinusoidal, so also the induced emf.
This happens irrespective of the type of connection used. The triplen order flux sometimes
links the tank and produces losses in the same. Other harmonics can be suppressed by connecting tuned filters at the terminals.