What is transformer K-factor?
Transformers supplying power electronic equipment are exposed to non-sinusoidal load current. The harmonics cause additional losses in the transformer. One way to express the transformer design with respect to immunity against harmonic distortion is so called K-factor. Since transformer K-factor is a potential source of confusion, this post provides a short characteristic.
Introduction
Transformers supplying power electronic devices, such as variable frequency drives, STATCOM, static frequency converters, high power rectifiers etc shall be designed to withstand certain amount of harmonic distortion. It is because the non-linear load draws non-sinusoidal currents from the supply or injects non-sinusoidal current into the supply. The load current contains harmonics that cause additional losses in the transformer. The VFD manufacturers often provide a spectrum of harmonic currents (harmonic order and corresponding magnitude) as part of their design specifications. There are methods how to calculate harmonic losses in the transformers. One means is so called “K-factor”. This factor is used by the Underwriters Laboratories (UL), a global safety science company. Theoretical background to transformer K-factor is provided in the ANSI/IEEE standard [1].
Harmonics and losses
Non-sinusoidal load current produces higher losses than when the transformer is loaded with purely sinusoidal current waveform. These additional losses are characterized as harmonic losses [2]. However, the harmonic losses normally can’t be measured during factory testing (unless the test field would have special equipment able to inject that specific harmonic spectrum) and thus those losses may be indicated but they don’t constitute a guarantee value [3].
What is transformer K-factor?
K-factor is a way to quantify the harmonics. It is a weighted factor meaning that not only the magnitudes of individual harmonics are considered but also the harmonic order itself (harmonic of the same magnitude but higher frequency has higher weight).
Purpose of transformer K-factor
According to [4] the K-factor has dual purpose:
(a) address coil heating due to non-linear loading
(b) sizing of neutral conductor (bar) for 200% of rated secondary phase current (effect of triplen harmonics such as 3rd, 6th, 9th etc.)
K-factor rated transformers may also use electrostatic shield between primary (grid, line) and secondary (converter) windings.
K-factor expresses the ability of a transformer to withstand certain amount of harmonics without negative impact on transformer performance or lifetime.
Use of K-factor is recommended especially for dry-type transformers that are more sensitive to harmonics compared to liquid immersed transformers.
Note that K-factor addresses the thermal effect of harmonics producing additional losses. It does not cover other effects such as mechanical stress, increased acoustic noise etc.
Calculation
K-factor is calculated as a sum of the squares of harmonic currents (in pu) multiplied by the squares of the harmonic order:
- Σ Ih(pu)²⋅h²
- Σ (Ih/Irms)²⋅h²
Ih(pu) … harmonic current at harmonic order h (per unit value)
Ih … harmonic current at harmonic order h (in A)
Irms … RMS value of current (fundamental plus harmonics)
h … harmonic order
Range of K-factor
Transformer K-factor ranges from K-1 (complete absence of harmonics, i.e. pure sinusoidal current) up to K-50. UL recognizes K-factor values of 4, 9, 13, 20, 30, 40 and 50.
What transformer K-factor isn’t
Transformer K-factor is not a ratio between total losses of transformer including harmonics and load losses for sinusoidal current loading. For example, K-13 does not mean that load losses including harmonics are 13-times higher than load losses with sinusoidal supply. Imagine a 5 MVA transformer that has around 50 kW load losses (1% of rated power) and 5 kW no-load losses. These are the losses measured in the factory during routine testing with sinusoidal supply. If K-factor would be the ratio between total load losses incl. harmonics and load losses for pure sinusoidal current then the total load losses would increase to 650 kW. This would not be a transformer but rather an electric heater 😉
Author’s comment
The public material about transformer K-factor mostly provides the mathematical definition and the general purpose. However, it is extremely hard to find specific examples how the K-factor is applied in the transformer design, i.e. how much overdimensioning is required and how it is verified in the tests. In author’s view the K-factor was primarily introduced for distribution transformers feeding loads that may produce harmonics. The larger the portion of non-linear loads the higher the K-factor for such transformer. That makes perfectly sense. However, applying the K-factor to a VFD main input transformer may lead to dramatic overdimensioning of the transformer.
European practice is to use IEC 61378 as main standard for converter transformers. That standard addresses among others the harmonic loading. The practice is used since several decades and VFD transformers do not experience overheating due to excessive losses.
Conclusion
K-factor is a term defined in UL which shall express the increased losses of transformer when loaded with non-sinusoidal current. The definition does not come from the standard [1] directly but it uses the standard as a theoretical base. One shall be careful about the interpretation of K-factor.
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References
[1] ANSI/IEEE Std C57.110 IEEE Recommended Practice for Establishing Transformer Capability When Supplying Nonsinusoidal Load Currents (revision 2008)
[2] VFD transformers: Harmonics, https://mb-drive-services.com/vfd-transformers-harmonics/
[3] What are the transformer guaranteed values? https://mb-drive-services.com/what-are-the-transformer-guaranteed-values/
[4] What is K-factor? Answers to questions about K factor, K factor transformers, and non-linear loading, © General Electric Company, 1992
[5] J. M. Frank, Origin, Development and Design of K-Factor Transformers, Conference Record, IEEE Ind. Applications Society Annual Meeting, Denver, October 1994, pp. 2273-2274
