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Home / Technical Articles / Transformer Extra Losses Due To Harmonics

Harmonic voltages

Non-linear loads, such as power electronic devices, such as variable speed drives on motor systems, computers, UPS systems, TV sets and compact fluorescent lamps, cause harmonic currents on the network.

Transformer Extra Losses Due To Harmonics
Transformer Extra Losses Due To Harmonics (on photo PECO fin substation 2)

Harmonic voltages are generated in the impedance of the network by the harmonic load currents.

Harmonics increase both load and no-load losses due to increased skin effect, eddy current, stray and hysteresis losses. The most important of these losses is that due to eddy current losses in the winding; it can be very large and consequently most calculation models ignore the other harmonic induced losses. The precise impact of a harmonic current on load loss depends on the harmonic frequency and the way the transformer is designed.

In general, the eddy current loss increases by the square of the frequency and the square of the load current. So, if the load current contained 20% fifth harmonic, the eddy current loss due to the harmonic current component would be 5 x 5 x 0.2 x 0.2 multiplied by the eddy current loss at the fundamental frequency – meaning that the eddy current loss would have doubled.

In a transformer that is heavily loaded with harmonic currents, the excess loss can cause high temperature at some locations in the windings. This can seriously reduce the life span of the transformer and even cause immediate damage and sometimes fire. Reducing the maximum apparent power transferred by the transformer, often called de-rating.

To estimate the required de-rating of the transformer, the load’s de-rating factor may be calculated.

This method, used commonly in Europe, is to estimate by how much a standard transformer should be de-rated so that the total loss on harmonic load does not exceed the fundamental design loss. This de-rating parameter is known as “factor K”.

The factor K is given by:

Transformer de-rating factor formula

e – the eddy current loss at the fundamental fre-quency divided by the loss due to a DC current equal to the RMS value of the sinusoidal current, both at reference temperature.
n – the harmonic order
I – the RMS value of the sinusoidal current includ-ing all harmonics given by

RMS value of the sinusoidal current formula

In – the magnitude of the n-th harmonic
I1 – the magnitude of the fundamental current
q – exponential constant that is dependent on the type of winding and frequency.

Typical values are 1.7 for transformers with round rectangular cross-section conductors in both windings and 1.5 for those with foil low voltage windings.

Developing special transformer designs rated for non-sinusoidal load currents. This process requires analysis and minimising of the eddy loss in the windings, calculation of the hot spot temperature rise, individual insulation of laminations, and/or increasing the size of the core or windings. Each manufacturer will use any or all of these techniques according to labour rates, production volume and the capability of his plant and equipment. These products are sold as ‘K rated’ transformers.

During the transformer selection process, the designer should estimate the K factor of the load and select a transformer with the same or higher K factor.

K factor is defined as:

K factor formula

As an example IEC 61378-1 deals with the specification, design and testing of power transformers and reactors, which are intended for integration within semiconductor converter plants; it is not designed for industrial or public distribution of AC power in general.

The scope of this standard is limited to applications of power converters, of any power rating, for local
distribution, at moderate rated converter voltage, generally for industrial applications and typically with a highest voltage for equipment not exceeding 36 kV. The converter transformers covered by this standard may be of the oil immersed or dry-type design.

The oil-immersed transformers are required to comply with IEC 60076, and with IEC 60726 for dry-type transformers.

Resource: Selecting Energy Efficient Distribution Transformers by Intelligent Energy Europe

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More Information

Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry facilities. Professional in AutoCAD programming.


  1. Gunnar Hauge Jensen
    Oct 08, 2021

    “if the load current contained 20% fifth harmonic, the eddy current loss due to the harmonic current component would be 5 x 5 x 0.2 x 0.2 multiplied by the eddy current loss at the fundamental frequency – meaning that the eddy current loss would have doubled”.

    How can this come. 5x5x0,2×0,2 is 1, and eddy current loss multiplied with 1 doesn´t change anything?

    Mar 08, 2015

    During our college days, our Professors taught that the Magnitude of Harmonics is as follows.
    1. Even Harmonics – opposite in nature at 180 Degrees apart, hence annulled or cancelled.

    2 Odd Harmonics magnitude is 1/n^2 where n is the Harmonic of 3rd, 5th, 7th 11th, 13th 15th and so on. Hence 5th Harmonic is 1/5^2 = (1/25) x 100 = 4% and so on. But the present scenario – the above formulae is not correct.and what are the correct level.

    3. Does the Harmonic Magnitude and Harmonic Penetration mean the same.?


  3. Prabhjot Singh Kalsi
    Feb 12, 2015

    I want more automation and electrical knowledge . Therefore I like ur website.

  4. hulya
    Sep 11, 2014

    Thanks , this was helpful. However information about harmonic current testing on transformers would have been great. Maybe for your next article hopefully , yes?

    Mar 25, 2014



  6. govind nishad
    Dec 22, 2013

    Please can you tell me what is 7th, 5th,3rd harmonics in induction motor?
    And what is plugging in DC motor?

    • Steve Neunhoffer
      Apr 13, 2015

      I’m unsure what you mean about plugging a DC motor. About the only place I’m aware that you would plug a DC motor is on the long travel and trolley drives of DC cranes, and with these, currents are limited by resistors and step timing is done by flux decay timers. Usually, the motors are mill duty (= almost indestructable)
      I have not known plugging on motors using a DC drive package. Deceleration is controlled by reducing the terminal voltage to below the back EMF, and regulating that voltage using SCR’s.

      Uncontrolled plugging would leave to flashovers

  7. Norman Livhuwani Mapimele
    Jun 23, 2012

    Hi Edvard,

    this is the information that i am busy doing my research on, but i concentrated more on the effect of harmonics on power transformers.

    thanks Brother

    • Edvard
      Jun 25, 2012

      Busy or not, now you can use this technical article for your research! :)

      Glad you find it usefull!

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