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K-Factor Transformers and Non-linear Loads

Kiran Deshpande*, Prof.Rajesh Holmukhe*, Prof.Yogesh Angal**

Abstract-Harmonic currents generated by non-linear loads can cause problems in the power systems and particularly thedistribution transformers as they are vulnerable to overheating and premature failure. Normally designers recommend an oversizedtransformer to protect transformer from overheating. K-factor transformers are specifically designed to accommodate harmoniccurrents. K-transformers are preferred because they have additional thermal capacity of known limits, design features that minimizeharmonic current losses, and neutral and terminal connections sized at 200% of normal. K-factor transformers allow operation up tonameplate 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.

I. INTRODUCTION

Today's modem offices and plants are dominated by nonlinearloads, desktop computers, solid state ballasts, PID lighting,programmable controllers, and variable speed drives to name afew. Due to these electronic loads, significant harmonic loadshave been added to the building's distribution systems. Theresult is premature failure ofthe transformer due tooverheating. Till recent times, the only solution to this problemwas to derate the transformer. This solution is no longeracceptable.

II. A review of Nonlinear Loads

The effect of nonlinear loads on the electrical power systemshas become matter of concern since past few years. Nonlinearloads draw currents which are not sinusoidal. They includeequipments such as solid state motor drives, arc furnaces,battery chargers, UPS systems, and the increasing electronicpower supplies. The increased use of these nonlinear loads isthe cause of concern as larger percentage of power systemstend to become nonlinear. The nonlinear loads were thought tobe matter of concern for industrial power systems where largestatic power converters were being used. But now largerapplication of electronics to practically every electrical load,nonlinear loads are present in commercial and even residentialpower system. Nonlinear loads produce harmonic currentswhich flow from the load towards the power source followingthe path of least impedances. Harmonic currents are thecurrents which have frequencies that are whole numbermultiples of fundamental frequency. The harmonic currentssuperimposed on the fundamental currents result in the non-sinusoidal waveform associated with the nonlinear loads.Fig.lshow the voltages and current waveforms for nonlinear loads.It can be seen that voltage waveform is sinusoidal but currentwaveform is not.

• Dept.of Electrical Engineering, College of Engineering, Bharati VidyapeethUniversity, Pune,E-mail: irkin85@hotmail.com

•• Dept.of Instrumentation Engineering, Dr.D. Y.Patil Institute of Engineeringand Technology, Pimpri, Pune: 411 018.

Fig. 1. Voltage and current waveform for nonlinear load.

III. Effects of Harmonic Currents on Power System

Harmonic currents adversely affect every component of thepower system. These currents create additional dielectric,thermally, and/or mechanical stresses. Harmonic currentsflowing through the power system impedances result inharmonic voltage drops which are observed as harmonicvoltage distortion. The voltage distortions could become verysevere when the power systems inductive and capacitiveimpedances become equal, a condition of parallel resonance.This condition could appear at one of the nonlinear load'ssignificant harmonic current frequencies (typically the 5th

, r.II th or 13th harmonic). Harmonic currents can cause losses innormal power components even when resonance conditions donot prevail. Due to skin and proximity effects, wiringexperience additional heating. If normal wiring sizing methodsare employed, then the derating for wiring for harmonics isminimal 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 forany given load profile. This standard considers the windingeddy current losses to be proportional to the harmonic numberrequired. This relationship has been found to be accurate forlower power frequency harmonics, but result in anoverestimation of losses for higher harmonics (generallygreater than II th). A typical derating curve is shown in fig.2.Transformers directly supplying single phase power suppliesmay require derating of 30% to 40% to avoid overheating.'Underwriters Laboratories' (UL) recognize the potentialsafety hazards associated with nonlinear loads and developeda rating system to indicate the capability of transformer tohandle harmonic loads. The ratings are described in UL-I56Iand are known as K-Factors. K-Factors are a weighing of theharmonic load currents according to their effects ontransformer heating, as derived from ANSIIIEEE C57.II O.AK-Factor of 1.0 indicates a linear load (no harmonics).Thehigher the K-Factor, the greater the effect of harmonicheating (I].

Where Ih is the load current at the harmonic h, expressed in aper-unit basis such that the total RMS current equals oneampere, i.e.

The problem associated with calculating K- Factor is selectingthe range of harmonic frequencies that should be included.Some use up to 15th harmonic, others up to 25 th harmonic, andstill others include up to 50th harmonic. For the same load,each of these calculations can yield significantly differentK-Factors, because even very small current levels associatedwith higher harmonics, when multiplied by the harmonicnumber squared, can yield significantly to the K-Factor. Basedon the underlying assumptions of C57.II0, it seemsreasonable to limit the K-Factor calculation to harmoniccurrents less than 25 th harmonic. Sample calculations aregiven in Table No.l.ln establishing standard transformer K-Factor rating; UL chose ratings of 1, 4, 9, 13, 20, 30, 40 and50. From a practical viewpoint individual loads with K-Factors greater than 20 are infrequent. At best office areaswith some nonlinear loads and large computer rooms normallyhave observed K-Factors of 4 to 9. Areas with highconcentrations of single phase computers and terminals haveobserved K- Factors of 13 to 17. When multiple nonlinearloads are powered from the same source, lower harmoniccurrent levels may be expected due to phase shifts andcancellations. In one study of commercial buildings, singlephase loads with current distortion of 104%, THD (TotalHarmonic Distortion) resulted in only a 7% THD at theservice entrance, when added with other loads in the building.Additional studies of typical loads are beginning to provideinformation which could aid in the development ofadditional rules of thumb to use when direct load

Typical tr.m fo mer dtrall

(1) U) 1! ~

Load K~acto'

Fig. 2.Typical Transformer derating forNonlinear loads

(2) measurements are not available. K-Factor transformers aredesigned to be operated fully loaded with any harmonic loadhaving K-Factor equal to or less than its K-rating. Forexample, a K-13 transformer can be fully loaded with anyharmonic load having a K-Factor up to K-13. If the load has aK-Factor greater than 13, then the transformer cannot besafely operated at full load and would require derating.

v. How do K-Factor Transformers differ fromStandard Transformers?

K-Factor transformers have additional thermal capacity totolerate the heating effects of the harmonic currents. A welldesigned K-Transformer will also minimize the winding eddy-current losses through the use of parallel conductors and otherwinding techniques. The K-factor indicates the multiples ofthe 60 Hz winding eddy current losses that the transformer cansafely dissipate. Transformer load losses consist of winding12R losses plus stray losses. Using UL best methods, straylosses are assumed to be primarily winding eddy currentlosses for transformers 300 KVA and smaller.

For example, a transformer having winding 12Rlosses of2000watts and 60 Hz stray losses of 1000 watts would, with a K-20rating, is required to dissipate the 2000 watts ofeR losses plus20 times the 60Hz stray losses of 1000 watts for a total loadloss of 4000 watts without exceeding the maximum windingtemperature rise. The result is a larger, more expensivetransformer.

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

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

1. Secondary Windings: The secondary windings,instead of working with a pure sine wave andproducing normal values and stray losses have tocope up with non-sinusoidal waveforms containingmultiple harmonics, which raise the stray lossessignificantly. To compensate for these increasedlosses, a multiple of small, individually insulatedconductors are used. Transposition is used wherevernecessary.

2. Neutral: Since harmonic currents are additive inneutral, neutral currents in excess of two times phasecurrents can be measured. To compensate for this,double sized neutral lugs and lug pads is furnished.

3. Primary winding: The primary winding has somelower order harmonics circulating within the delta,producing losses and additional heating. This iscompensated for by using a heavier conductor.

4. Core: The core is affected by voltage harmonicdistortion. This voltage distortion increases the coreflux density, creating higher core loss, highermagnetizing currents, higher audible noise andheating problems. To reduce flux density, alloyinduction designed core is used.

VI. About Standard Transformers not marked withK-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 certifiedby a third party such as UL. Currently marking transformerwith a K-Factor rating is not required by UL. Due toconservative design application, some unmarked transformermay therefore have enough extra thermal capacity to tolerateadditional harmonic load heating. This is particularly true for80° C or 115°C rise transformers built with 220°C insulationmaterial which can safely withstand a 150°C windingtemperature rise.

VII. Consideration of additional Over CurrentProtection for Transformers supplyingNonlinear Loads.

Additional over current protection should be considered for alltransformers supplying nonlinear loads. The National ElectricCode allows primary-only over current protection at 125°C ofthe transformer's primary full load amperes. With three-phasetransformers, the triplen harmonics are cancelled in the deltawinding and do not appear in the input current. The outputcurrents and transformer loading greater than is apparent from

Development ofTriplen Harmonic CurrentInstantaneous 3.phase 60 Hz currents = 0 at any instant

AmPSC

Instantaneous triplen 3rd harmonic currents (180Hz )where neutral current = 3 x phase currents

Fig.3. Development of Triplen Harmonic current.

the input current. Therefore a transformer can be overloadedwithout the primary over-current protection ever tripping.Adding secondary over-current protection helps, but itstill does not protect the transformer from the heating effectsof harmonic currents. The use of supplemental protection inthe form of winding temperature sensors can be used toprovide alarm and/or system shutdown in the event ofoverload, excessive harmonic current, high ambienttemperature, or inadequate cooling

VIII. More on Triplen Harmonic currents.

Triplen harmonic currents are phase currents which flow fromeach of the phases into the fourth wire neutral and havefrequencies in integer multiples of three times the 60 Hz basefrequency (180 Hz, 360Hz, 540Hz etc). At each of these thirdmultiple triplen frequencies, these triplen phase currents are inphase with each other and when flowing in the neutral as zerosequence currents are equal to three times their RMS phasevalues. The development of triplen harmonic current is shownin fig.3.

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

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

I - IJoHz + liaoHz + liooHz + IJzoHz + ... (3)Total -

Where I = RMS value of current.

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

IX. The UL Approach to Transformers

A. A transformer intended for use with loads drawingnon-sinusoidal currents shall be marked "Suitable fornon-sinusoidal current load with K-Factor not toexceed x. (x= 4, 9, 13, 20, 30, 40 or 50).

B. Formulas to determine eddy losses and total losseswhere the transformer load losses (PLL) are to bedetermined as follows:

PLL = PDC(l + K(PEC))

Where, PDC = Total 12Rlosses

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 transformersRated 300 KVA and above, in which;

PAC = Impedance loss

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

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

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

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

Shielde~Transformer UnshieldedTransformersn~l~

&~1t~~t- ~l ~~l1t-~I J I ~ T ~I'" ',.r. :..·.1.~ I I i! ~.~ ~ \ '-----''j

Fig. 4. Shielded and unshielded Transformers.

Relatively small DC components (up to the RMS magnitudeof the transformer excitation current at rated voltage) areexpected to have no significant effects on the load carryingof the transformer excitation current at rated voltage) areexpected to have no significant effect on the load carryingcapability of a transformer determined by this recommendedpractice. Higher DC load components may adversely affecttransformer capability and must be corrected by the user.

(4)Harmonic currents flowing through transformer leakageImpedance and through system impedance may also producesome small harmonic distortion in the voltage waveform at thetransformer terminals. Such voltage harmonics may causeextra harmonic losses in the transformer core. However,operating experience has indicated that core temperature riseusually will not be the limiting parameter for determination ofsafe magnitudes of non-sinusoidal load currents.

The Noise Isolation Transformer suppresses common modenoise by introducing a ground shield between its primary andsecondary windings. The ground shield provides a lowimpedance path to ground by capacitive coupling whichprevents unwanted high frequency signals contained in thesource voltage from reaching the transformer secondary.

The grounded shield between primary and secondary windingsis called an electrostatic shield. This shield does not performany function with regard to harmonic current or voltagedistortion wave forms. However this shield is extremelyvaluable in protecting sensitive equipments from commonmode electrical noise and transients generated on the line sideof the transformer. The shielded and unshielded transformersare shown in fig, 4.

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

CMA = 20 10glo [Vin] dBVout

(5)

Table No.1.Calculations for a typical nonlinear load

h In (In)2 InlL (In)2) (In)2(harmonic (nonlinear

h2number) Load

Current)

I 100.0% 1.000 0.792 0.626 0.626

3 65.7 0.432 0.520 0.270 2.434

5 37.7 0.142 0.296 0.089 2.226

7 12.7 0.016 0.101 0.010 0.495

9 4.4 0.002 0.035 0.001 0.098

II 5.3 0.003 0.042 0.002 0.213

13 2.5 0.001 0.020 0.000 0.066

15 1.9 0.000 0.015 0.000 0.051

17 1.8 0.000 0.014 0.000 0.059

19 1.1 0.000 0.009 0.000 0.027

21 0.6 0.000 0.005 0.000 0.010

23 0.8 0.000 0.006 0.000 0.021

25 0.4 0.000 0.003 0.000 0.006

Total 1.596 1.00 6.33

An isolation transformer with an electrostatic shield can havea 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 thehelp of information available in the Table No.2 and 3.

X. Disadvantage of using Derated Transformersinstead ofK-Factor Transformer

The use of derated standard transformers instead of K-FactorTransformers carries some disadvantage as under:

I. First is the issue of managing the derating when thetransformer nameplate indicates greater capacity.Initially, the transformer may be operated at reducedloading. But in the future, the loading may beincreased without considering the intended derating.

2. If smaller overcurrent protection is used intentionallyto limit the overloading, nuisance tripping may occurdue to the transformer inrush current. Larger over-current protection may be required for the oversized(derated) standard transformer resulting in largerconductor requirements with the associated higher

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

Load K- Factor ILKIncandescent K-I 0.00LightingElectric Resistance K-I 0.00HeatingMotors (without K-I 0.00solid state drives)Control K-I 0.00TransformersMotor-Generators K-I 0.00Distribution K-I 0.00TransformersElectric Discharge K-4 25.82LightingUPS K-4 25.82Welders K-4 25.82Induction Heating K-4 25.82EquipmentPLCs and solid K-4 25.82state controlsTelecommunicationEquipment (e.g. K-13 57.74PBX)UPS without input K-13 57.74filteringMultiwirereceptable circuitsin general care K-13 57.74areas of health carefacilitiesMain frame K-20 80.94computer loadsSolid State Motor K-20 80.94DrivesMultiwirereceptable circuitsin Industrial, K-30 123.54Medical andEducationalLaboratoriesSmall Main Frames K-30 123.54(Mini and Micro)Other loadsidentified asproducing very high K-40 208.17amounts ofharmonics

Table No.3. Index of K-rating

K- K-I K-4 K-9 K-13 K-20 K-30 K-40FactorILK 0.0 25.82 44.72 57.74 80.94 123.54 208.17

.:

feeder costs.3. The transformers designed specifically for nonlinear

loads minimize losses due to harmonic currents. Theyoperate with the nonlinear loads more efficiently andgenerate less heat that need to be dissipated.

Xl. 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% ornameplate KVA. All other optional feature that the industry isaccustomed to can be specified.

I. Copper or Aluminum.2. 80° C, 115°C, 150°C.3. Electro-static shield.

XII. What should be remembered when using aK-Factor Transformer?

I). Harmonic loads do cause premature failure whenstandard transformers are used.

2) Average reading RMS meters do not measureharmonic currents. True reading RMS meters shouldbe used.

3) Insist on a K-Factor transformer that has been 3rd

party tested. Accept no verbal claims. The proof mustbe on the label.

Conclusions:

Because transformers are the power system components mostaffected by nonlinear loads, they are the first to receive aharmonic rating system. K-Factor ratings are based on heatingeffects of harmonics and are not necessarily applicable toother power system components. If harmonic rating systemsfor other components are needed, they will have to bedeveloped by other methods, e.g., THD, crest factor, or somenew and component-specific weighing of harmonic currents.

What is the likelihood that additional rating systems willactually be developed? That's hard to predict. The bestsolution to the problem caused by harmonic currents would bepreventive, i.e. the use of components does not generateharmonics. Impending standards such as lEC 555 and IEEE519 encourage the development of such devices.

Indeed, low harmonic current power supplies and electronicballasts are already available. As such new designs areimplemented, they should gradually displace existingelectronic loads (and their greater harmonics), serving toreduce 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 ratingsystem for other power system components is problematical.One thing is sure, though, until the day that harmonic currentsactually diminish, K-Factor Transformers will play animportant role in coping with the problems harmonics create.

References

[I] The Institute of Electrical & Electronic Engineers,"Recommended Practice for establishing Transformercapabilities when supplying Non-sinusoidal LoadCurrents", ANSIIIEEE C57.110-1986, New York, 1986.

[2] Gruzs, T.M. "A survey of Neutral Currents in Three-phase Computer Power Systems", IEEE Transactions onIndustry Application, Vo1.26,No.4, July/August 1990.

[3] IEEE P-l100 Working Group. Recommended Practicefor Powering and Grounding Sensitive ElectronicEquipments. Draft 1992.

[4] Underwriters Laboratory. Proposed Requirements andProposed Effective Dates for the First Edition of theStandard for Dry Type General Purpose and PowerTransformers, UL 156. Santa Clara CA, 1991.

[5] Computer Business Equipment Association (CBEMA).Three Phase Power Source Overloading Caused by SmallComputers and Electronic Office Equipment. ESC-3Information Letter, 1987.

[6] McGranaghan et al. "Analysis of Harmonic DistortionLevels in Commercial Buildings." PQA 91,Paris, France,October 1991.

[7] ANSI/IEEE Standard 519-1981. IEEE Guide to HarmonicControl and Reactive Compensation of Static PowerConverters.

[8] McPartland Brian J.: "Use K-Factor Transformers?Definitely! But Which K-Factor?" EDI, June 1991, Vo\.2No.6.