K-Factor Transformers and Non-linear Loads

Published by

  • Kiran Deshpande & Prof. Rajesh Holmukhe, Dept. of Electrical Engineering, College of Engineering, Bharati Vidyapeeth University, Pune, E-mail: irkin85@hotmail.com
  • Prof. Yogesh Angal, Dept. of Instrumentation Engineering, Dr. D. Y.Patil Institute of Engineering and Technology, Pimpri, Pune: 411 018.

Abstract – Harmonic currents generated by non-linear loads can cause problems in the power systems and particularly the distribution transformers as they are vulnerable to overheating and premature failure. Normally designers recommend an oversized transformer to protect transformer from overheating. K-factor transformers are specifically designed to accommodate harmonic currents. K-transformers are preferred because they have additional thermal capacity of known limits, design features that minimize harmonic current losses, and neutral and terminal connections sized at 200% of normal. K-factor transformers allow operation up to nameplate capacity without derating.

Index Terms – Additional thermal capacity, Derating, Distribution transformers, Harmonic currents, K- Factor, Nameplate capacity, Neutral and Terminal connections, Non-linear loads, Overheating.


Today’s modem offices and plants are dominated by nonlinear loads, desktop computers, solid state ballasts, PID lighting, programmable controllers, and variable speed drives to name a few. Due to these electronic loads, significant harmonic loads have been added to the building’s distribution systems. The result is premature failure of the transformer due to overheating. Till recent times, the only solution to this problem was to derate the transformer. This solution is no longer acceptable.

II. A review of Nonlinear Loads

The effect of nonlinear loads on the electrical power systems has become matter of concern since past few years. Nonlinear loads draw currents which are not sinusoidal. They include equipment’s such as solid state motor drives, arc furnaces, battery chargers, UPS systems, and the increasing electronic power supplies. The increased use of these nonlinear loads is the cause of concern as larger percentage of power systems tend to become nonlinear. The nonlinear loads were thought to be matter of concern for industrial power systems where large static power converters were being used. But now larger application of electronics to practically every electrical load, nonlinear loads are present in commercial and even residential power system. Nonlinear loads produce harmonic currents which flow from the load towards the power source following the path of least impedances. Harmonic currents are the currents which have frequencies that are whole number multiples of fundamental frequency. The harmonic currents superimposed on the fundamental currents result in the non-sinusoidal waveform associated with the nonlinear loads. Fig.1 show the voltages and current waveforms for nonlinear loads. It can be seen that voltage waveform is sinusoidal but current waveform is not.

Fig. 1. Voltage and current waveform for nonlinear load.
III. Effects of Harmonic Currents on Power System

Harmonic currents adversely affect every component of the power system. These currents create additional dielectric, thermally, and/or mechanical stresses. Harmonic currents flowing through the power system impedances result in harmonic voltage drops which are observed as harmonic voltage distortion. The voltage distortions could become very severe when the power systems inductive and capacitive impedances become equal, a condition of parallel resonance. This condition could appear at one of the nonlinear load’s significant harmonic current frequencies (typically the 5th, 7th, 11th or 13th harmonic). Harmonic currents can cause losses in normal power components even when resonance conditions do not prevail. Due to skin and proximity effects, wiring experience additional heating. If normal wiring sizing methods are employed, then the derating for wiring for harmonics is minimal and can be ignored.

IV. Methods to Derate Transformer as suggested by ANSI / IEEE Standards.

Harmonic currents cause additional heating in the form of additional winding eddy current losses in transformers. ANSI / IEEE C 57.110 provides methods to derate a transformer for any given load profile. This standard considers the winding eddy current losses to be proportional to the harmonic number required. This relationship has been found to be accurate for lower power frequency harmonics, but result in an overestimation of losses for higher harmonics (generally greater than 11th). A typical derating curve is shown in fig.2. Transformers directly supplying single phase power supplies may require derating of 30% to 40% to avoid overheating. ‘Underwriters Laboratories’ (UL) recognize the potential safety hazards associated with nonlinear loads and developed a rating system to indicate the capability of transformer to handle harmonic loads. The ratings are described in UL-I56I and are known as K-Factors. K-Factors are a weighing of the harmonic load currents according to their effects on transformer heating, as derived from ANSI / IEEE C57.110. A K Factor of 1.0 indicates a linear load (no harmonics). The higher the K-Factor, the greater the effect of harmonic heating [1].

K – Factor = Σ(Ih)2 h2 (1)

Where Ih is the load current at the harmonic h, expressed in a per-unit basis such that the total RMS current equals one ampere, i.e.

Σ(Ih)2 = 1.0 (2)

The problem associated with calculating K- Factor is selecting the range of harmonic frequencies that should be included. Some use up to 15th harmonic, others up to 25th harmonic, and still others include up to 50th harmonic. For the same load, each of these calculations can yield significantly different K-Factors, because even very small current levels associated with higher harmonics, when multiplied by the harmonic number squared, can yield significantly to the K-Factor. Based on the underlying assumptions of C57.II0, it seems reasonable to limit the K-Factor calculation to harmonic currents less than 25th harmonic. Sample calculations are given in Table No.1. In establishing standard transformer K-Factor rating; UL chose ratings of 1, 4, 9, 13, 20, 30, 40 and 50. From a practical viewpoint individual loads with K-Factors greater than 20 are infrequent. At best office areas with some nonlinear loads and large computer rooms normally have observed K-Factors of 4 to 9. Areas with high concentrations of single phase computers and terminals have observed K- Factors of 13 to 17. When multiple nonlinear loads are powered from the same source, lower harmonic current levels may be expected due to phase shifts and cancellations. In one study of commercial buildings, single phase loads with current distortion of 104%, THD (Total Harmonic Distortion) resulted in only a 7% THD at the service entrance, when added with other loads in the building. Additional studies of typical loads are beginning to provide information which could aid in the development of additional rules of thumb to use when direct load measurements are not available. K – Factor transformers are designed to be operated fully loaded with any harmonic load having K-Factor equal to or less than its K-rating. For example, a K-13 transformer can be fully loaded with any harmonic load having a K-Factor up to K-13. If the load has a K-Factor greater than 13, then the transformer cannot be safely operated at full load and would require derating.

Fig. 2. Typical Transformer derating for
Nonlinear loads
V. How do K-Factor Transformers differ from Standard Transformers?

K-Factor transformers have additional thermal capacity to tolerate the heating effects of the harmonic currents. A well designed K-Transformer will also minimize the winding eddy current losses through the use of parallel conductors and other winding techniques. The K factor indicates the multiples of the 60 Hz winding eddy current losses that the transformer can safely dissipate. Transformer load losses consist of winding I2R losses plus stray losses. Using UL best methods, stray losses are assumed to be primarily winding eddy current losses for transformers 300 KVA and smaller.

For example, a transformer having winding I2R losses of2000 watts and 60 Hz stray losses of 1000 watts would, with a K-20 rating, is required to dissipate the 2000 watts of I2R losses plus 20 times the 60 Hz stray losses of 1000 watts for a total load loss of 4000 watts without exceeding the maximum winding temperature rise. The result is a larger, more expensive transformer.

For K-Factor transformers, UL also requires that the neutral terminal and connections to be sized to accommodate twice the rated phase conductor size (double the minimum neutral capacity) of standard transformers.

There are several areas where designs are changed to accommodate the effects of harmonics.

  1. Secondary Windings: The secondary windings, instead of working with a pure sine wave and producing normal values and stray losses have to cope up with non-sinusoidal waveforms containing multiple harmonics, which raise the stray losses significantly. To compensate for these increased losses, a multiple of small, individually insulated conductors are used. Transposition is used wherever necessary.
  2. Neutral: Since harmonic currents are additive in neutral, neutral currents in excess of two times phase currents can be measured. To compensate for this, double sized neutral lugs and lug pads is furnished.
  3. Primary winding: The primary winding has some lower order harmonics circulating within the delta, producing losses and additional heating. This is compensated for by using a heavier conductor.
  4. Core: The core is affected by voltage harmonic distortion. This voltage distortion increases the core flux density, creating higher core loss, higher magnetizing currents, higher audible noise and heating problems. To reduce flux density, alloy induction designed core is used.
VI. About Standard Transformers not marked with K-Factor ratings:

Standard transformers, i.e. transformers not marked with a K-Factor rating, may have some tolerance to nonlinear loading, but their capability is unknown to the user and is not certified by a third party such as UL. Currently marking transformer with a K-Factor rating is not required by UL. Due to conservative design application, some unmarked transformer may therefore have enough extra thermal capacity to tolerate additional harmonic load heating. This is particularly true for 80° C or 115°C rise transformers built with 220°C insulation material which can safely withstand a 150°C winding temperature rise.

VII. Consideration of additional Over Current Protection for Transformers supplying Nonlinear Loads.

Additional over current protection should be considered for all transformers supplying nonlinear loads. The National Electric Code allows primary-only over current protection at 125°C of the transformer’s primary full load amperes. With three-phase transformers, the triplen harmonics are cancelled in the delta winding and do not appear in the input current. The output currents and transformer loading greater than is apparent from the input current. Therefore a transformer can be overloaded without the primary over-current protection ever tripping. Adding secondary over-current protection helps, but it still does not protect the transformer from the heating effects of harmonic currents. The use of supplemental protection in the form of winding temperature sensors can be used to provide alarm and/or system shutdown in the event of overload, excessive harmonic current, high ambient temperature, or inadequate cooling.

Fig.3. Development of Triplen Harmonic current
VIII. More on Triplen Harmonic currents.

Triplen harmonic currents are phase currents which flow from each of the phases into the fourth wire neutral and have frequencies in integer multiples of three times the 60 Hz base frequency (180 Hz, 360 Hz, 540 Hz etc.). At each of these third multiple triplen frequencies, these triplen phase currents are in phase with each other and when flowing in the neutral as zero sequence currents are equal to three times their RMS phase values. The development of triplen harmonic current is shown in fig.3.

In a 3 phase, 4 wire system, single phase line to neutral currents flow in each phase conductor and return in common neutral. Since the three 60 Hz currents are separated by 120°, when balanced they cancel each other. The measured resultant current is equal to zero.

Theory also states that for even harmonics, starting with the second order, when balanced, the even harmonic will cancel in the common neutral. Other odd harmonics add in the common neutral, but their magnitude is considerably less than triplens. The RMS value of the total current is the square root of the RMS value of the individual currents squared.

ITotal = √ I260Hz + I2180Hz + I2300Hz + I2420Hz + … (3),

Where I = RMS value of current.

At any given instant, the 60 Hz currents on the three phase legs have a vector resultant of zero and cancel in the neutral. But, the third (and other odd triplen harmonics) on the phase legs are in phase and become additive in the neutral.

IX. The UL Approach to Transformers

A. A transformer intended for use with loads drawing non-sinusoidal currents shall be marked “Suitable for non-sinusoidal current load with K-Factor not to exceed x. (x= 4, 9, 13, 20, 30, 40 or 50).”

B. Formulas to determine eddy losses and total losses where the transformer load losses (PLL) are to be determined as follows:

PLL = PDC(1 + K(PEC)) (4)

Where, PDC = Total I2R losses

K = the K-Factor rating at the transformer (4, 9, 13, 20, 30, 40 or 50).

PEC = assumed eddy current losses calculated as follows:

For Transformers rated 300 KVA or less, and for transformers Rated 300 KVA and above, in which;

PAC = Impedance loss

C= 0.7 for transformers having a turn ratio greater than 4:1 and having one or more winding with a current rating greater than 1000 amperes., or C= 0.6 for all other transformers.

PDC-I = the I2R losses for the inner winding.

The impedance losses and the I2R losses shall be determined in accordance with the test code for Dry Type Distribution and Power Transformers, ANSI/IEEE C57.12.91-1979. [4]

As stated in ANSI/IEEE C57.1 10-1986, harmonic load currents may be accompanied by DC components in the load current which are frequently caused by the loss of a diode in a rectifier circuit. A DC component of load current will increase the transformer core loss slightly, and may increase the magnetizing current and audible sound level. [3].

Fig. 4. Shielded and unshielded Transformers.

Relatively small DC components (up to the RMS magnitude of the transformer excitation current at rated voltage) are expected to have no significant effects on the load carrying of the transformer excitation current at rated voltage) are expected to have no significant effect on the load carrying capability of a transformer determined by this recommended practice. Higher DC load components may adversely affect transformer capability and must be corrected by the user.

Harmonic currents flowing through transformer leakage Impedance and through system impedance may also produce some small harmonic distortion in the voltage waveform at the transformer terminals. Such voltage harmonics may cause extra harmonic losses in the transformer core. However, operating experience has indicated that core temperature rise usually will not be the limiting parameter for determination of safe magnitudes of non-sinusoidal load currents.

The Noise Isolation Transformer suppresses common mode noise by introducing a ground shield between its primary and secondary windings. The ground shield provides a low impedance path to ground by capacitive coupling which prevents unwanted high frequency signals contained in the source voltage from reaching the transformer secondary.

The grounded shield between primary and secondary windings is called an electrostatic shield. This shield does not perform any function with regard to harmonic current or voltage distortion wave forms. However this shield is extremely valuable in protecting sensitive equipment’s from common mode electrical noise and transients generated on the line side of the transformer. The shielded and unshielded transformers are shown in fig, 4.

The ratio of common mode noise attenuation (CMA) on the input to that of the output of the transformer is expressed in decibels as shown in equation shown here below:

CMA = 20 log10 [Vin/Vout] dB (5)

Table No.1.Calculations for a typical nonlinear load

Table No.2. K- Factors for various types of Loads

LoadK- FactorILK
Incandescent LightingK-10.00
Electric Resistance HeatingK-10.00
Motors (without solid state drives)K-10.00
Control TransformersK-10.00
Distribution TransformersK-10.00
Electric Discharge LightingK-425.82
Induction Heating EquipmentK-425.82
PLCs and solid state controlsK-425.82
Telecommunication Equipment (e.g. PBX)K-1357.74
UPS without input filteringK-1357.74
Multiwire receptable circuits in general care areas of health care facilitiesK-1357.74
Main frame computer loadsK-2080.94
Solid State Motor DrivesK-2080.94
Multiwire receptable circuits in Industrial, Medical and Educational LaboratoriesK-30123.54
Small Main Frames (Mini and Micro)K-30123.54
Other loads identified as producing very high amounts of harmonicsK-40208.17

Table No.3. Index of K-rating

K- FactorK-1K-4K-9K-13K-20K-30K-40

An isolation transformer with an electrostatic shield can have a ratio of input noise voltage (VIN) to output noise voltage (VOUT) within the range of 10:1 to 1000:1 or even higher. The calculations for K-Factor loads can be carried out with the help of information available in the Table No.2 and 3.

X. Disadvantage of using Derated Transformers instead of K-Factor Transformer

Transformers carries some disadvantage as under:

1.First is the issue of managing the derating when the transformer nameplate indicates greater capacity. Initially, the transformer may be operated at reduced loading. But in the future, the loading may be increased without considering the intended derating.

2.If smaller overcurrent protection is used intentionally to limit the overloading, nuisance tripping may occur due to the transformer inrush current. Larger overcurrent protection may be required for the oversized (derated) standard transformer resulting in larger conductor requirements with the associated higher feeder costs.

3.The transformers designed specifically for nonlinear loads minimize losses due to harmonic currents. They operate with the nonlinear loads more efficiently and generate less heat that need to be dissipated.

XI. Using a K-Factor Transformer

Once the harmonic current of the total load is known, and a K-Factor is specified (K4, K13 etc.), the appropriate type K-Factor transformer can be fully loaded up to 100% or nameplate KVA. All other optional feature that the industry is accustomed to can be specified.

  1. Copper or Aluminum
  2. 80° C, 115°C, 150°C.
  3. Electro-static shield.
XII. What should be remembered when using a K-Factor Transformer?

1) Harmonic loads do cause premature failure when standard transformers are used.
2) Average reading RMS meters do not measure harmonic currents. True reading RMS meters should be used.
3) Insist on a K-Factor transformer that has been 3rd party tested. Accept no verbal claims. The proof must be on the label.


Because transformers are the power system components most affected by nonlinear loads, they are the first to receive a harmonic rating system. K-Factor ratings are based on heating effects of harmonics and are not necessarily applicable to other power system components. If harmonic rating systems for other components are needed, they will have to be developed by other methods, e.g., THD, crest factor, or some new and component-specific weighing of harmonic currents.

What is the likelihood that additional rating systems will actually be developed? That’s hard to predict. The best solution to the problem caused by harmonic currents would be preventive, i.e. the use of components does not generate harmonics. Impending standards such as IEC 555 and IEEE 519 encourage the development of such devices.

Indeed, low harmonic current power supplies and electronic ballasts are already available. As such new designs are implemented, they should gradually displace existing electronic loads (and their greater harmonics), serving to reduce the prevalence of harmonic currents over the long term.

Short term, however, projection show harmonic levels in power systems increasing as more electronic loads are added. Whether this will provide sufficient impetus for new rating system for other power system components is problematical. One thing is sure, though, until the day that harmonic currents actually diminish, K-Factor Transformers will play an important role in coping with the problems harmonics create.


[I] The Institute of Electrical & Electronic Engineers, “Recommended Practice for establishing Transformer capabilities when supplying Non-sinusoidal Load Currents”, ANSIIIEEE C57.110-1986, New York, 1986.
[2] Gruzs, T.M. “A survey of Neutral Currents in Three phase Computer Power Systems”, IEEE Transactions on Industry Application, Vo1.26,No.4, July/August 1990.
[3] IEEE P-l100 Working Group. Recommended Practice for Powering and Grounding Sensitive Electronic Equipments. Draft 1992.
[4] Underwriters Laboratory. Proposed Requirements and Proposed Effective Dates for the First Edition of the Standard for Dry Type General Purpose and Power Transformers, UL 156. Santa Clara CA, 1991.
[5] Computer Business Equipment Association (CBEMA). Three Phase Power Source Overloading Caused by Small Computers and Electronic Office Equipment. ESC-3 Information Letter, 1987.
[6] McGranaghan et al. “Analysis of Harmonic Distortion Levels in Commercial Buildings.” PQA 91,Paris, France, October 1991.
[7] ANSI/IEEE Standard 519-1981. IEEE Guide to Harmonic Control and Reactive Compensation of Static Power Converters.
[8] McPartland Brian J.: “Use K-Factor Transformers? Definitely! But Which K-Factor?” EDI, June 1991, Vo.2 No.6.

Published by PQBlog

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