The negative

**effects of harmonics on transformers**are commonly unnoticed and disregarded until an actual failure happens. Generally, transformers designed to operate at rated frequency have had their loads replaced with nonlinear types, which inject harmonic currents into the system. Consequently, transformers that have operated adequately for long periods have failed in a comparatively short time.Nowadays, it is well known that nonlinear loads like the Switched Mode Power Supply (SMPS), Variable Frequency Drives, electronic ballasts and arc furnaces generate harmonic currents and voltages. Combining these with the nonlinear nature of the transformer core, waveform distortions in currents and voltages are created leading to increase in power losses and winding temperature. In such cases, transformers supplying nonlinear devices should be derated based on the percentages of harmonic components in the rated winding eddy current loss and the load current. Another option is to use K-Factor Transformers. In other words, the need for looking into harmonic problems has become important.

**Eddy Current Loss**

Transformer losses are composed of copper and core losses - including the stray flux loss and eddy current. Eddy current loss is the power dissipated due to circulating currents in the core winding, as a result of electromotive forces induced by variation of magnetic flux, and it becomes considerable when harmonics exist. Harmonics tend to exponentially increase the transformer eddy current losses, causing higher operating temperature for the transformer. This is because eddy current loss is proportional to the square of the current in the conductor and the square of its frequency.

**K-Factor**

This is one way of establishing the capability of transformers to carry nonlinear loads. A K-factor of 1.0 means no harmonics. On the other hand, the presence of harmonic current gives a K-factor of more than 1.0. Basically, it is the sum of the product of the square of the harmonic currents and the square of corresponding harmonic frequency number.

In equation form:

K = [(I

_{1}/Irms)^{2 }(1)^{2}] + [(I_{2}/Irms)^{2 }(2)^{2}] + [(I_{3}/Irms)^{2 }(3)^{2}] +…..+ [(I_{n}/Irms)^{2 }(n)^{2}]where:

I

_{1 }= fundamental currentI

_{2 }= 2^{nd}harmonic currentI

_{3 }= 3^{rd}harmonic currentI

_{n}= nth harmonic currentIrms = RMS current

**Note:**Total RMS current is the square root of the sum of squares of the individual currents.

In addition, K-Factor Transformers are designed to tolerate K times the rated eddy current loss. In addition, these type of transformers have a larger neutral terminal – at least twice the size of the phase terminals, as protection against the so-called triplen harmonics (3

^{rd}, 9^{th}, 15^{th}, etc.) that flows through the neutral.**Summary**

To sum up, the effects of harmonic currents on transformers are:

· Increased eddy current losses

· Additional copper losses

· Electromagnetic interference with communication circuits

Meanwhile, harmonic voltages lead to the following:

· Increased dielectric stress on insulation (shortens insulation life)

· Resonance between winding reactance and feeder capacitance

· Electrostatic interference with communication circuits

Overall, the effect of harmonics is an increased heating in the transformer as compared to purely sinusoidal operation. Furthermore, harmonics will result to lower efficiency, lesser capacity, reduced power factor and decreased in productivity.

**References:**

IEEE 519. (1992). Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems

Sankaran, C. (1999). Effects of Harmonics on Power Systems 1

Sankaran, C. (1999). Effects of Harmonics on Power Systems 1

Elmoudi, A. (2005). Evaluation of Power System Harmonic Effects on Transformers

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