View source for Draft:K-factor (electrical engineering)

{{Short description|Measure of a transformer's ability to handle harmonic distortion}}
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In [[electrical engineering]], the '''K-factor''' of a [[Transformer|power transformer]] is a measure of how well it can handle [[harmonic distortion]]. Transformers which are designed to handle harmonic distortion are referred to as '''K-rated''' transformers.<ref name=CanadaTransformers >https://canadatransformers.com/k-factor</ref><ref name=ElectricalClassroom>https://www.electricalclassroom.com/k-factor-rated-transformers/</ref><ref name=RexPowerMagnetics>https://www.rexpowermagnetics.com/products/dry-type-low-voltage-transformers/k-rated-transformers</ref>

== Background ==

In an [[alternating current]] power system, electrical energy is ideally transmitted as a pure sine wave, typically at a fundamental frequency of 50 Hz or 60 Hz. However, [[electronic switch|switching]] can lead to distortion in the power system, resulting in a non-sinusoidal waveform. This deviation from a pure sinusoidal waveform is measured using [[harmonics]].<ref name=MaddoxTransformer>https://www.maddoxtransformer.com/resources/articles/guide-to-transformer-harmonics-and-k-factor</ref>

The {{math|n}}th harmonic is a waveform at an integer multiple of the fundamental frequency. For example, a wave transmitted with a fundamental frequency of 60 Hz would have its 2nd harmonic at 120 Hz, its 3rd harmonic at 180 Hz, its 4th harmonic at 240 Hz, and so on. The waveform is considered to be a sum of harmonic components.<ref name=MaddoxTransformer />

== Calculation ==

The following formula is used to calculate the K-factor of a transformer:<ref name=ABB>{{Cite web|first=Frank|last=Basciano|title=What is a transformer K-factor rating?|url=https://library.e.abb.com/public/53968e937e084cfea172fa33adb40ac2/20230429_ABB_1TQC194900E0001_K-factor%20ELSB%20LVDTT%20Tech%20Paper.pdf|publisher=[[ABB]]|date=2023-04-29}}</ref>

:<math>K = \sum_{h=1}^{\infin} I_h^2 h^2</math>

Where:
*{{math|K}} is the K-factor
*{{math|h}} is the harmonic order
*{{math|I<sub>h</sub>}} is the per-unit current at the {{math|h}}th harmonic order

== Typical Values ==

The following table lists typical K-factors used depending on the harmonics produced by the loads:<ref name=ABB/>

{| class="wikitable"
|+ Typical K-factors
|-
! K-factor !! Load description !! Harmonic activity
|-
| 1 || Standard, general-purpose transformer || <15% of loads generate harmonics
|-
| 4 || Induction heating, AC drives || Up to 35% of loads generate harmonics
|-
| 13 || Institutional electronically controlled lighting || 35-75% of loads generate harmonics
|-
| 20 || Data processing equipment, computer servers || 60-100% of loads generate harmonics
|-
| 30-50 || Loads consistently generate harmonics || 100% of loads generate harmonics
|}

Transformers with a larger K-factor are more expensive to produce.<ref name=ABB/>

== References ==
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