ansi std c57.120-1991(ieee loss evaluation guide for

8/13/2019 ANSI Std C57.120-1991(IEEE Loss Evaluation Guide For

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Recognized as anAmerican National Standard(ANSI) IEEEStdC57.120-1991-

IEEE L o s s Evaluat ion Guide forPower Trans formers andR e a c t o r s

IEEE Power Engineering SocietySponsored by theTransformers Committee

Published by the Institute of Electricaiand Electronics Engineers Inc. 345East 47th Street New York, NY 1001Z USAAugust 12. 1992 s i 1 5 51


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Recognized as anA m e r i c a n National Standard(ANSI)

I mStd C57.120-1991

IEEE Loss Evaluation Guide forPower Transformers and ReactorsSponsor

Transformers Com mitteeof theIEEE Power En gineerin g SocietyApproved September 16,1991IEEE Standards BoardApproved February 28,1992

American National Standards Institute

Abstract: A method for establishing the dollar value of the electric power needed t o supplythe losses of a transformer or reactor is provided. Users can use this loss evaluation t odetermine the relative economic benefit of a high-first-cost, low-loss unit versus one with alower first cost and higher losses, and t o compare the offerings of two o r moremanufacturers t o aid in making the best purchase choice. Manufacturers can use theevaluation t o optimize the design and provide the most economical unit t o bid andmanufacture. The various types of losses are reviewed.Keywords: economic, loss evaluation, reactors, transformers

The Institute of Electrical and Electronics Engineers, Inc.345 East 47th Street,New York, NY 10017-2394,USACopyright0 1992 byThe Institute of Electrical and Electronics Engineers, Inc.All rights reserved. Published 1992Printed in the United States of AmericaISBN 1-55937-245-1

N o par t of this publication may be reproduced in any form ,in an electronic retrieval system or otherwise,without the prior written permission of the publisher.


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IEEE Standards documents are developed within the TechnicalCommittees of the IEEE Societies and the Standards CoordinatingCommittees of the IEEE Standards Board. Members of the committeesserve voluntarily and without compensation. They are not necessar-ily members of the Institute. The standards developed within IEEErepresent a consensus of the broad expertise on the subject within theInstitute as well as those activities outside of IEEE th at have expressedan interest in participating in the development of the standard.Use of an IEEE Standard is wholly voluntary. he existence of anIEEE Standard does not imply tha t there are no other ways to produce,test, measure, purchase, market, o r provide other goods and servicesrelated to the scope of the IEEE Standard. Furthermore, the viewpointexpressed a t the time a standard is approved and issued is subject tochange brought about through developments in the s tate of the ar t andcomments received from users of the standard. Every IEEE Standardis subjected to review at least every five years for revision or r e a f bmation. When a document is more than five years old and has notbeen reaffirmed, it is reasonable t o conclude that its contents, al-though still of some value, do not wholly reflect the present s tate of theart. Users are cautioned to check to determine tha t they have the latestedition of any IEEE Standard.Comments for revision of IEEE Standards are welcome from anyinterested party, regardless of membership affiliation with IEEE.Suggestions for changes in documents should be in the form of a pro-posed change of text, together with appropriate supporting comments.Interpretations: Occasionally questions may arise regarding themeaning of portions of standards as they relate to specific applica-tions. When the need for interpretations is brought t o the attention ofIEEE, the Institute will initiate action t o prepare appropriate re-sponses. Since IEEE Standards represent a consensus of all con-cerned interests, i t is important to ensure that any interpretation hasalso received the concurrence of a balance of interests. For thisreason IEEE and the members of its technical committees are not ablet o provide an instant response t o interpretation requests except inthose cases where the matter has previously received formalconsideration.

Comments on standards and reques ts for interpretat ions should beaddressed to: Secretary, IEEE Standards Board445Hoes LaneP.O. ox 1331Piscataway,N J 08855-1331USAIEEE Standards documents are adopted by the Ins titute of Electricaland Electronics Engineers without regard t o whether their adoptionmay involve patents on articles, materials, o r processes. Such adop-tion does not assume any liability t o any patent owner, nor does itassume any obligation whatever t o parties adopting the standards

documents.


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ForewordThis oreword is not a par t of IEEE S td C67.120-1991, IEE E LossEvaluation Guide for Power Transformers an dReactors.)

The users of power transformers and reactors have become more concerned about thevalue of losses as the cost of energy and of insta lling generat ing capacity ha s increased.The evaluation of losses has become a very significant part of the purchase decision forsome users.This guide has been written to provide a method of establishing loss evaluation factorsfor transformers or reactors. With loss evaluation factors, the economic benefit of a high-first-cost, low-loss unit can be compared with a unit with a lower first cost and higherlosses. This enables a user to compare the offerings of two o r more manufacturers to aid inmaking the best purchase choice among competing transformers or reactors. Loss evalua-tion also provides information to establish the optimum time to retire or replace existingunits with modern low-loss transformers o r reactors.This guide was prepared by the Transformer Loss Evaluation Working Group of theIEEE West Coast Transformer Subcommittee. The following Working Group membersparticipated in the development of the guide:Roger Jacobsen, Chair

Ray Allust iart iI. Stephen BenkoFred ElliotDennis GerlachJ i m Gi ll iesThomas HawkinsChar l es Hendr i cksonJess J. H e r r e r a

Charles HoeselWil l iam IsbergHerbert JohnsonRobert KimballGary Lindl andRon LittleGeorge McCraeLarr y M errifield

Dan NixRobert NortonSamuel OkluDenise RothPete SorensenLou TauberL.Kay ThompsonCharles Todd


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The following persons were on the balloting committee th at approved this document f o rsubmission to the IEEE Standards Board:L.C. AicherD. J. AllanB. F. AllenR. Allust iart iR. J. AltonS J. Antal isE. H. ArjeskiJ. C. ArnoldR. BancmftP. L. BellaschiS.BennonJ. J. BergemnJ. V. B O M U C ~ ~J. D. orstG. H. BowersD. J. CashE. Chitwood0. R. ComptonF. W. Cook, Sr.J. CorkranD. W. CroftsM. G. DanielsD. H. DouglasJ. D.DouglassJ. C. DuttonJ. K. EasleyJ. A. EbertR. L. EnsignC. G. EvansP. P. FalkowskiH . G. FischerS. L. FosterM. FrydmanH. E. Gabel, Jr.D. A. GilliesR. L. GrubbG Gunnels, Jr.G. Hal l

J. H. HarlowT. K. HawkinsF. W. HeinrichsW. HenningK. R. HightonP. J. HoeflerC. R. HoeselR. H. HollisterC. C. HoneyF. Huber, Jr.C. H u r t yG. W. IliffR. G. JacobsenD. . JohnsonA. J. Jonnat t iC. P. KappelerR. B. KaufmanE. J. KellyJ. J. KellyW.H. KennedyA. D. KlineE. KoenigJ. G. LackeyH . F. LightT. G. LipscombR. LittleL. W. LongR. I. LuweM. L. ManningH. B. MargolisJ. W. Mat thewsL. S.McCormickJ. W. McGillC. J. McMillenW. J. McNuttS. . MehtaC. K. Miller

C. Mill ianR. E. MinkwitzH . R. MooreR. J. MusilW. H. MutschlerE. T. NortonB. K. PatelH. A. PearceD. erCOC. A. RobbinsL. J. SavioW. E. SaxonV. ShenoyB. E. SmithW.W. SteinL. R. StenslandR. B. StetsonE. G. StrangasL. SwensonA. L. TantonV. ThenappanR. C. ThomasF. W. ThomasonJ. A. ThompsonJ. P. T r a u bD. E. TruaxR. E. UptegraffG. VaillancourtR. A. VeitchF. VogelL. B. WagenaarJ. W. WaltonR. J. Whear tyA. WilksW. E. WrennA. C. WurdackD.A. YamucciE. J. Yasuda


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ContentsSECTION PAGE1.2.

Purpose an d Scope ............................................................................... 7List of Terms Applicable to Transformer Loss Evaluation Equa tions ..................

3. Definitions ....................................................................................... 94 . Basic Concept 11

Description of Transformer and Reactor Power Losses .................................. 115.1 Transformers ............................................................................ 115.2.1 Shu nt Reactors .................................................................. 125.2.2 Series Reactors .................................................................. l2No-Load (Excitation) Losses (NLL)................................................... 12Load Losses (LL)......................................................................... 12Auxiliary Power Losses (APL) ........................................................ 12Total Power Losses ...................................................................... 13

Cost Evaluation Methodology ................................................................. E3Explanation of Factors .................................................................. E3

....................................................................................5.

5.2 Reactors ................................................................................... 125.35.45.55.6

6. 6.1 6.1.16.1.26.1.36.1.46.1.56.1.66.1.76.1.86.1.96.1.106.1.116.1.126.1.13

Efficiency of Transmission (ET) ........................................... l3Availabi l i ty Factor (AF)....................................................... 13Peak Responsibility Factor (PRF) ........................................... 14Peak er. ni t Lo ad PUL).................................................... 14Tranf ormer Loading Factor (TLF) ......................................... 14FCRS for Transmission Systems, an d FCRT for Transform ers) .....14Capital Recovery Factor (CRF)............................................... 14Increase Factor (IF)............................................................ l5Levelized Total System Inve stment Cost (LIC) ............................ 15Levelized Auxiliary Energy Cost for Stage One (LAEC1)................16

Fixed Charge Ra te or C arrying Charge Rate (FCRG for Generators,

Levelized Energy Cost (LECN for No-Load Loss Evaluation,an d LECL for Load Loss Evalua tion) ....................................... 16Levelized Auxiliary Energy Cost for Sta ge Two (LAEC2) ............... 16FOA. FOW Cooling Methods ................................................. 17

6.2 Loss Cost Rate Formulas ................................................................ 17No-Load Power Loss Cost Rate (NLLCR) ................................... 17Load Power Loss Cost Rate (LLCR).......................................... 17Auxiliary Power Loss Cost Rat es............................................. 18Use of Power Loss Cost Ra tes .......................................................... 187 . Bibliography..................................................................................... l9

6.2.16.2.26.2.36.3

APPENDIXESAppendix A-Levelized Energy Costs ............................................................ 21Appendix B-Example Calculation of Transformer Loss Cost Rat es ....................... 25


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IEEE Loss Evaluation Guide forPower Transformers and Reactors

1 Purpose and ScopeThe purpose of this guide is to provide a method of establishing the dollar value of theelectric power needed t o supply the losses of a transformer or reactor. Users can use thisloss evaluation to determine the relative economic benefit of a high-first-cost, low-loss unitversus one with a lower first cost and higher losses. Manufacturers can use the evaluationt o optimize the design and provide the most economical unit t o bid and manufacture. Theevaluated cos t of losses also enables a user t o compare the offerings of two o r moremanufacturers to aid in making the best purchase choice among competing transformerso r reactors. Loss evaluation also provides information t o a user for establishing theoptimum time t o retire o r replace existing units with modern low-loss transformers o rreactors.The user should determine, on a dollars-per-kilowatt basis, the sum of the present worthof each kilowatt of losses of a transformer throughout its life, o r some other selected periodof time. This figure represents the maximum amount tha t can be spent to save a kilowatt ofloss. A portion of this evaluated cost can be paid t o the manufacturer t o reduce losses.However, this evaluated cost includes other costs associated with owning a more expensivepiece of equipment, such as financing costs, taxes, etc.This guide provides formulas by which the costs of energy, power, and money, and theloading pattern of a transformer can be converted t o dollars-per-kilowatt values of thetransformer losses.These dollars-per-kilowatt figures should be furnished to the manufacturer when bidsare requested. If the final tested values of losses vary from the manufacturers guaranteed

values, economic adjustments may be made.Nothing in this guide is mandatory. It should not be inferred from this paper t ha t themethodology described in the following pages is the only valid methodology for computingthe cost of transformer losses. Many users have developed their own transformer lossevaluation techniques that are suitable for the intended purpose. The list of terms inSection 2 uses symbols selected for mnemonic effectiveness and might be different fromsymbols used in other references.

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IEEEStd C57.120-1991 IEEE LOSS EVALUATION GUIDE FOR2. List of Terms Applicable to TransformerLoss Evaluation Equations

TextUnit Sym bol ReferenceermAuxiliary loss cost rate ofstage one cooling equipment $/kW ALCRl 6.2.3.1Auxiliary loss cost rate ofstage two cooling equipment $/k W ALCRZ 6.2.3.2

Auxiliary power lost in kWstage one cooling equipment APLl 5.5

Auxiliary power lost in kWstage two cooling equipment APLZ 5.5

Auxiliary power loss kW APLA FAHPY1

5.56.1.25.5

Availability factorAverage hours per year forstage one cooling alone hours 01)

Average hours per year forstage two cooling equipment hours h) AHPY2 5.5

Booklife ye ar s BLCRF

Section 46.1.7apital recovery factor

Carrying charge (see fixed charge rate)Current year energy cost $/kWh CYEC

E TEIRFCRGFCRTFCRSGICIFm c 1

APP. B6.1.1Al .6.1.66.1.66.1.66.1.96.1.86.1.11

Efficiency of transmissionEnergy cost inflation rate per yearFixed charge rat e (generator) $/$/yrFixed charge rate (transformer)Fixed charge rate (transmission systems) $/$/yrGeneration installation cost $/ kWIncrease factorLevelized auxiliary energy cost $/kW-yrfor stage one


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POWER TRANSFORMERS AND REACTORS m mStdC67.120-1991

_ -

Term Unit Symbol ReferenceLevelized auxiliary energy costfor stage twoLevelized energy and operating cost

Levelized generation investment costLevelized total system investment costLevelized transmission systeminvestment costLoad Loss (copper o r conductor loss)Load loss cost ra teNo-load loss (iron o r core loss)No-load loss cost rateNumber of yearsPeak-per-unit loadPeak responsibility factorPresent worth energy and operating costRate of return

/kW yr

$/kW-yr

$/kW-yr$/kW-yr$/kW-yr

kW$/kWkW$/kWyears

$/kWhper year

Sum of present worthenergy and operating cost or$/kwh booklife

$/kW-yr booklifeTransformer loading factorTransmission system $/ kWinstallation cost

LAEc2

LECNLECLLGICLICLSICLLLLCRNLLNLLCRNPULPRFPWECRORSPWECHSPWECYT L FSIC

6.1.12

6.1.106.1.106.1.96.1.96.1.9

5.46.2.25.36.2.16.1.76.1.46.1.36.1.106.1.76.1.106.1.106.1.56.1.9

3. DefinitionsFor further explanation of the following terms, see Sections 5 and 6. For definitions notfound in thi s guide, consult IEEE Std 100-1988 rB31.1

auxiliary power losses (APL). he power required for cooling fans, oil pumps, andother ancillary equipment.

The numbers n brackets correspond to those of the Bibliography in Section 7.

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lEEEStdC57.120-1991 IEEE LOSS EVALUATION GUIDE FORavailability factor (AF). he proportion of time that a transformer is predicted to beenergized.capital recovery factor (CRF). The factor used t o determine total levelized annualcosts.core loss. The power dissipated in a magnetic core subjected t o a time-varying magnetiz-ing force.efficiency of transmission (ET). The energy received at the input terminals of thetransformer divided by the energy transmitted from he source.fixed charge rate or carrying charge rate (FCRG for generators, FCRS fortransmission systems, and FCRT for transformers). The levelized annual costdivided by the cost of investment.increase factor (IF).The factor representing the total th at the user must pay to acquire thetransformer, including the purchase price, overhead, fee, tax, etc., based on its value.levelized auxiliary energy cost for stage one (LAEC1).The sum of the present worthof energy an d operating costs in do llars-per-kilowatthour booklife (SPWECH) ismultiplied by the total number of hours per year that stage one cooling is expected to beoperating, t o get the sum of the present worth of energy and operating cost in dollars-per-kilowatt-year booklife (SPWECYl).levelized auxiliary energy cost for stage two (LAEC2). The sum of the presentworth of energy and opera ting cost in dollars-per-kilowatthour booklife (SPWECH) ismultiplied by the total number of hours per year t ha t stage two cooling is expected to beoperating, t o get the sum of the present worth of energy and operating cost in dollars-per-kilowatt-year booklife (SPWECYB).levelized energy cost (LECN for no-load loss evaluation, and LECL for loadloss evaluation).The cost of energy and operation is expressed in dollars per kilowatt-year.levelized total system investment cost (LIC). The annual cos t , in dollars perkilowatt-year, of the additional generation and transmission system capacity needed t osupply the power used by the losses, including the cost of financing th at investment.load losses (LL). Those losses that are incident t o the carrying of a specified load.no-load (excitation) losses (NLL).Those losses that a re incident to the excitation of thetransformer.peak-per-unit load (PULL he average of yearly peaks over the lifetime of the trans-former, o r some other load growth cycle,2 divided by the ra ting a t which the load losses areguaranteed and tested.peak responsibility factor (PRF).The power transformers load at the time of thesystem peak divided by the power transformers peak load.total power losses. The sum of the no-load losses and the load losses, not includingauxiliary losses.transformer loading factor ULF). The root-mean-square value of the predicted loadsof the power transformer over a representative yearly period is an equivalent load.

A load growth cycle may be, for instance, the time between the initial loading and when the planned loadinglimit of the transformer is reached.

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POWER TRANSFORMERS AND REACTORS EEEStd C57.120-19914. Basic Concept

The basic concept of this guide is that the evaluation for each type of loss (no-load, load,(1) The demand portion is the cost of installing system capacity in dollars per kilowatt,

and(2) The energy portion is the present value of the energy tha t will be used by one kilowattof loss during the booklife of the transformer, converted to dollars per kilowatt.For convenience in adding like terms, the values are levelized, that is, converted t oyearly values, and then the sum is divided by the fixed charge rate for transformers andany other appropriate factors, to give equivalent values that can be used directly by themanufacturer in designing and pricing the transformer, and later by the user incomparing bids. Fixed charge ra tes are the cost of ownership, and have the dimensionsof dollars-per-dollar-per-year,o r simply per-year. The units are satisfied in the followingbasic equation:

and auxiliary) is the sum of (1) he demand portion, and 2) the energy portion.

Yearly Cost of Yearly Cost ofDemand Portion Energv Portioncost of fixed ] I hours perinstalling charge cost of a year thata kilowatt rate of kilowatthour transformerX1 ofplant plant J 1 is energized

(fixed charge rate)he loss cost rate =(for transformers)

The numerator of the above formula shows how much it will cost per year t o provide acontinuous kilowatt. The denominator is the fixed charge rate for transformers. Thenumerator divided by the denominator determines how much a user can afford t o pay for amore efficient transformer t o save th at kilowatt.

xyr = -+-=-kWyr kWyr kW kW kWNOTE: Dimensionless factors, such as transmission efficiency, tax rate, transformer loading factor, peak-per-unit load, and peak responsibility fador, may also be involved.

5. Description of Transformer and Reactor Power Losses5.1 Transformers.The losses in a transformer are basically of two types: no-load losses,which occur simply because the transformer is energized; and load losses, which vary withthe transformers loading. In addition, auxiliary power is required by fans, pumps,heaters, and other ancillary equipment. This auxiliary power is not necessarily

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IEEEStdC57.120-1991 IEEE LOSS EVALUATION GUIDE FORdependent upon the load. All losses and auxiliary power requirements, a s discussed in thisguide, are expressed in kilowatts.5.2 Reactors52.1 Shunt Reactors. A shunt reactor acts as a constant load at a given voltage. Its total

loss cost evaluation (even though consisting mainly of I losses) is calculated using onlythe no load loss formula in 6.2.1 (Eq 7). Its losses increase as the impressed voltageincreases.5.2.2 Series Reactors. A series reactor experiences a varying load. Because it does nothave a no-load loss, its total power loss cost evaluation is calculated using only the loudloss formula in 6.2.2 (Eq 8).

5.3 No-Load (Excitation) Losses (NLL). Those losses tha t ar e incident to the excitationof the transformer. No-load (excitation) losses include dielectric loss, conductor loss in thewinding due t o exciting current, conductor loss due t o circulating current in parallelwindings, and core loss. Core loss is the power dissipated in a magnetic core subjected t o atime-varying magnetizing force. Core loss includes hysteresis and eddy curr ent losses ofthe core. These losses change with the excitation voltage, and may increase sharply if therated voltage of the transformer is exceeded. The no-load losses also increase as thetemperature of the core decreases.When transformer no-load losses are compared, thesame reference temperature should be used.

5.4 Load Losses (LL). Those losses that are incident t o the carrying of a specified load.Load losses include PR loss in the winding due to load and eddy currents, stray loss due t oleakage fluxes in the windings, core clamps, and other part s, and the loss due to circulat-ing currents (if any) in parallel windings o r in parallel winding strands. These lossesare often referred t o as copper losses, although the actual winding may be of some othermaterial, such as aluminum. These losses vary with the square of the load. The losses alsovary with the absolute temperature of the windings. For comparative purposes, load lossvalues a re given at a reference load and at reference winding temperature. I t is importanttha t these reference values be stated whenever loss values ar e given.NOTE: The rating upon which the load losses are based usually refers to the self-cooled rating of the transformer(for those transformers that have a self-cooled rating), based on cooling class and temperature rise, and not to theextended ratings available with auxiliary cooling. For example, 12/16/20 MVA transformers having a self-cooled rating of 12 MVA usually have load losses tested at 12 MVA. When carrying 20 MVA, the load losses wouldbe approximately 2.78, i.e. , (20/12)'times the tested losses. In addition, the extended loading would call for fansand pumps to be running, which require additional power as listed in 5.5.For an FOA or FOW ransformer, the losses are measured at the FOA or FOW rating, or other agreed uponratings.Any rating may be used to evaluate load losses (even one that may not be shown on the nameplate), so long asthe manufacturer knows in advance, for optimizing the design and the test results are appropriately shownon thetest report.5.5 Auxil iary Power Losses (APL). The power required for cooling fans, oil pumps,and other ancillary equipment. All of these power requirements are expressed inkilowatts. If two o r more separate stages of cooling ar e used, these should be expressed inseparate parts, APL1, APL2, etc., because the individual stages will be used for differentamounts of time. The number of hour per year for each s tage of cooling, AHPY1, AHPY2,etc., will need t o be estimated in order t o calculate a value for the energy for each stage. Itshould be kept in mind that generally stage one cooling is also running whenever stagetwo is on.


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POWER TRANSFORMERS AND REACTORS IEEEStd C57.120-1991NOTES:(1)The above three loss values: NLL, LL, and APL, are normal ly stated by the manufac turer wi th his bid, andlater determined by actual tests.2) For power transf orm ers used in HVDC converter stations, additional considera tions are necessary for lossesincurred by harmonic currents. These harmonic losses are not discussed in this guide.5.6Total Power Losses. Defined by IEEE C57.12.00-1987 [B41, subsection 5.9, these lossesare the sum of the no-load losses and the load losses, and do not include auxiliary losses.For purposes of economic evaluation, however, the user should consider no-load, load, andauxiliary power losses. Care should be taken not to use the term total load loss as the readerwill not know whether load loss or total loss is meant.In addition to kilowatt losses, there also exists a kilovar consumption. However, the costof providing the kilovar consumption is typically not evaluated. Only real power losses areconsidered in th is guide. However, if the kilovar consumption were to be evaluated, the costper kvar of installing capacitors might be used as a basis of evaluation.NOTE: The losses in load tapchanging (LTC) transformers vary with the LTC position. In addition, at any givenposition, the losses may vary with different configurations of LTC equipment, such as t ap winding location, thepresence of series t ransformers, prevent ive autot ransformers, etc. The user should consider these variat ionswhen comparing t wo or more offerings.

6. C o s t E v a l u a t i o n M e t h o d o lo g y6.1 Explanat ion of FactorsNOTE: In this guide, base and peak costs are used a s i f they were the same. If they are not th e same, the usershould determine the relative cost and the complex interrelationship of each, for no-load and load losses.

The determination of the cost of transformer losses involves many loss cost factors,some of which must be estimated. The user is advised t o pay particular attention t o thenumber of significant figures in the d at a and the assumed economic values, and to beconsistent in the application of these significant digits in the calculations. There is littlejustification in using assumed values with two-place accuracy to calculate the cost of lossesto four or more places. The factors that are used to develop the power loss cost ra tes for no-load losses, load losses, and auxiliary losses are defined in the following subsections:6.1.1 Efficiency of Transmission (ET). he energy received at the input terminals ofthe transformer divided by the energy transmitted from the source. The efficiency willvary seasonally, o r by loading, location, o r voltage level, but unless this variation isunusually large for a particular instance, a general overall system efficiency willprobably be adequate for this factor. Also, the capacity and the energy portions of the lossequations may have differing efficiency values applied to them, but here again, in mostcases, one overall system efficiency factor will probably be adequate.(If different values were to be used, then Eq 7 (6.2.1), or instance, might become thefollowing:

LIC LECN(ET,)(FCRT)(IF) (ET,)(FCRT)(IF)NLLCR =

where ETc = efficiency for capacity, and ETE = efficiency for energy.)6.1.2 Availability Factor AF).he proportion of time tha t a transformer is predictedto be energized. This factor is significant in connection with the energy cost of the losses.


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lEEEStdC57.120-1991 IEEE LOSS EVALUATION GUIDE FOR

6.1.3 Peak Responsibility Factor (PRF).The power transformers load at the time ofthe system peak divided by the power transformers peak load. The portion of the systemscapability allocated t o meet this transformers losses varies a s the square of this ratio.6.1.4 Peak-Per-Unit Load (PULI.The average of the yearly peaks over the lifetime of

the transformer, o r some other load growth cycle: divided by the rating at which the loadlosses are guaranteed and tested. The demand portion of load loss cost rate will vary as thesquare of this ratio.NOTE: The above definition gives an approximation that is consistent with the accuracy of most est imated,future peak loading values. If the transformer is planned to be oaded to a compound or a linear load growth rate,then PUL can be determinedby using other methods. One such method is given on pp. 790-91 in Nickel andBraunstein [B71.

6.1.5 Transformer Loading Factor (TLF).The root-mean-square value of the pre-dicted loads of the power transformer over a representative yearly period is an equivalentload. This equivalent load, in MVA, divided by the rating at which the load losses areguaranteed and tested, yields an equivalent load in per unit, which is referred t o in thisguide as the transformer loading factor (TLF).The energy cost of the load losses will vary as the square of this factor. The equivalentload, if applied uniformly 8760 hours of one year, would produce the same amount of loadlosses as th at produced in the transformer by the actual load current during a given year.Equivalent load is discussed in IEEE C57.92-1981 B61,where it is defined as the constantload that generates losses at the same rate as the average rate caused by the fluctuatingload.If the representative yearly loss factor is known, a generally easier way t o find (TLFI2 sby the following formula (keeping in mind th at the loss factor must be based on 8760 hoursof a representat ive yearly period, the same as the basis for TLF):

(TLF)~ loss factor x PUL)~ Es 4)6.1.6 Fixed Charge Rate or Carrying Charge Rate (FCRG for Generators, FCRSfor Transmission Systems, and FCRT for Transformers). The levelized annual costdivided by the cost of investment. The fixed charge rate represents the cost of ownership.:The costs are fixed inasmuch as they do not depend on system kilowatthours sold. The use

of this rate shows the income (savings) per year necessary t o support a capital investment.Some of the components of cos t in the fixed charge rate, expressed as a proportion ofinvestment, are as follows:(1)Minimum acceptable rate of return;(2)Annual cost of depreciation;(3) Levelized federal and state income tax; and(4) Annual cost of property taxes and insurance.

NOTE: The fured charge rate for transformers is used in the denominator of the loss cost rate formulas (see 6.2.1,6.2.2, 6.2.3). A high fmed charge rate will result in a low dollars-per-kilowatt valuation, and a low fured chargerate will result in a high evaluation. The formulas are only meaningful for realistic values of fmed charge rate.Users who buy transformers with some form of financing that does not include interest, depreciation, taxes,insurance, etc., cannot use the formulas given in this guide.6.1.7 Capital Recovery Factor (CRF). The factor used t o determine total levelizedannual costs. The sum of the present worth of the costs is levelized by multiplying by the

capital recovery factor.

SeeFootnote2.

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POWER TRANSFORMERS AND REACTORS IEEEStdC57.120-1991ROR (1+RORINCRF= (I+ O R I ~ 1 (Eq 5 )

whereCRF = the capital recovery factor, expressed in unitsROR = the rate of returnN = the number of years the costs are to be levelized6.1.8 Increase Factor (IF).The factor representing the total ha he user must pay t oacquire the transformer, including the purchase price, overhead, fee, tax, etc., based on itsv a l u e .The loss evaluation figures supplied t o the manufacturers at the time of soliciting bidsshould be reduced appropriately, below the ac tual value of a kilowatt of power. Internallyimposed, in-house overheads may not apply here, depending upon user practices.Examples of applicable cost increase factor a re the following:Sales taxArchitect-Engineer's feeConstruction supervision feeContractor's fee

Inter est during constructionJob order fee (imposed by outside organization)Extended warranty and transportation insurance, if these can be uniformly appliedto all biddersExamples of possible applicable cost increase factor are the following:General overheadStores chargesAll of the applicable rates in per unit are added t o 1.0, nd the resulting value is used inExample:Sales tax 8%Architect-Engineer's fee 10%Transportation insurance 1%

Interest during constructionIncrease fador = 1.00 0.08 +0.10 0.01 0.02= 1.21

the denominator of the loss cost rate formulas in 6.2.1, .2.2, nd 6.2.3.

2% (2months @ 12% per annum)

6.1.9 Levelized Total System Investment Cost (LICL4The annual cost, in dollarsper kilowatt-year, of the additional generation and transmission system capacity neededto supply the power used by the losses, including the cost of financing that investment.

The discussion in this paragraph is applicable to users who own t he i r genera t i on and/or t ransmiss ionfaci l i t ies. Many users who do not own those faci l i t ies pay a demand charge. This demand charge can beconverted to LIC by m ultiplying by a suitable factor. For example, if the demand c harge is levied in dollars perkilowatt per month, it can be multiplied by 12 to give the value of LIC in do llars per kilowatt-year.


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IEEEStd C57.120-1991 IEEE LOSS EVALUATION GUIDE FORNOTE: The concept of levelization is described in Appendix A. The levelized total system investment cost (LIC)is computed as follows:

LIC = (GICXFCRG) (SIC)(FCRS) (Eq6)where GIC = the cost of installing generation, expressed in dollars per kilowattSIC = cost of installing transmission systems, expressed in dollars per kilowattFCRG = the fixed charge rate for generation

FCRS = the fixed charge rate for the transmission system(GICXFCRG) = LGIC, the levelized generation investment cost(SIC)(FCRS) = LSIC, the levelized transmission system investment cost6.1.10 Levelized Energy Cost (LECN for No-Load Loss Evaluation, and LECLfor Load Loss Evaluation). The cost of energy and operation is expressed in dollars perkilowatt-year. This cost is computed by using the following method t o obtain a presentworth value:(1) List the projected cost of energy in dollars per kilowatthour for each year beingconsidered.2) Discount these annual inflated energy costs by the appropriate present worth factor,at the user's rate of return, for each year being considered (see Appendix A), t o get thepresent worth value of each year's energy and operating cost in dollars per kilowatt-year (PWEC).(3) Add each of the present worth values, for all of the years being considered, to get the

sum of the present worth of energy and operating cost in dollars-per-kilowatthourbooklife (SPWECH).(4) Multiply SPWECH, the sum of the present worth of energy and operating cost indollars per kilowatthour by 8760 hours per year ( o r the number of hours thetransformer is expected to be energized per year or 8760 imes the availability factor),to get SPWECY, the sum of the present worth of energy and operating cost in dollars-per-kilowatt-year booklife for the operation of the transformer.

Determine the capital recovery factor (CRF) by Eq 5 (6.1.7).Multiply SPWECY by CRF to get LECN, the levelized annual energy and operatingco s t of no-load losses in dollars per kilowatt-year for the operation of thetransformer.NOTE: The calculation covered here by (4) yields the levelized annual energy and operating cost of no-lo d losses. When finding the levelized annual energy and operating cost of load losses, SPWECH in (4)shouldbe multiplied by 8760 Wyr to get SPWECY.

In calculating LECL, it is not appropriate t o use a reduced number of hours per year,See Appendix B for example calculations.because the transformer loading factor takes this into account.

6.1.11 Levelized Auxiliary Energy Cost for Stage One (LAEC1).The sum of thepresent worth of energy and operating costs in dolla rs-per-kilowatthour booklife(SPWECH) is multiplied by the total number of hours per year that stage one cooling isexpected to be operating, to get the sum of the present worth of energy and operating cost indollars-per-kilowatt-year booklife (SPWECY1). (Note that stage one cooling is alsooperating whenever stage two cooling is operating.) SPWECYl is then multiplied by thecapital recovery factor (CRF) t o get the levelized annual energy and operating costs forstage one cooling (LAECl), in dollars per kilowatt-year.6.1.12 Levelized Auxiliary Energy Cost for Stage Two (LAEC2).The sum of the

present worth of energy and operating cost in dollars-pe r-kilowatthour booklife(SPWECH) is multiplied by the total number of hours per year th at stage two cooling isexpected to be operating, to get the sum of the present worth of energy and operating cost indollars -per -kilowatt-year booklife (SPWECYB).

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POWER I'RANSFORMERS AND REACTORS B E EStdC57.120-1991SPWECY2 is then multiplied by the capital recovery factor (CRF) t o get the levelizedannual present worth of energy and operating cost for stage two cooling (LAECB), in dol-lars per kilowatt-year.6.1.13 FOA, FOW Cooling Methods. The discussions in 6.1.11 and 6.1.12 are basedon a triple-rated transformer. A similar evaluation can be made for FOA and FOW trans-

formers using the number of hours per year that each fan or pump is expected to run. Equip-ment t ha t runs continuously will be evaluated the same as the no-load losses.6.2 Loss Cost Rate Formulas. Loss cost ra te formulas are developed for no-load losses,load losses, and auxiliary losses. The resul ts of these formulas-loss cost rates-aresupplied to the manufacturer at the time of requesting bids. The cost rates in dollars perkilowatt, multiplied by their respective guaranteed losses in kilowatts, can be addeddirectly t o the bid price in the evaluation of purchase alternatives.The loss cost rate formulas represent the cost of insta lling generation and transmissiont o supply the demand represented by one kilowatt of transformer loss, and the cost ofproducing the energy consumed by that loss.The loss cost rate formulas are computed in the following manner:

6.2.1 No-LoadPower Loss Cost Rate (NLLCR)yearly cost of demand portion+ yearly cost of energy portionNLLCR = fixed charge rate for t ransformersx efficiency and tax, etc., factors

LIC+LECN(ET)(FCRT)(IF)NLLCR = (Eq 7)

whereNLLCR =

LIC =LECN =

E T =FCRT =I F =

the equivalent no-load loss cost rate in dollars per kilowatt. This is the valueof no-load power losses that the user should furnish t o the manufacturers atthe time of soliciting bids.the levelized annual total system investment cost in dollars per kilowatt-yearthe levelized annual energy and operating cost of no-load losses, expressedin dollars per kilowatt-yearthe efficiency of transmissionthe fixed charge rate for transformersthe increase factor

6.2.2 Load Power Loss Cost Rate (LLCR)yearly cost of demand portion yearly cost of energy portionLLCR = fixed charge rate for transformersx efficiency and tax, tc., factors,-and as modified by the loading factors squared

LIC) PRF)~PUL)~ LECLXTLF)~(ET)(FCRT)(IF)LLCR =

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IEEEStdC57.120-1991 IEEE LOSS EVALUATION GUIDE FORwhereLLCR = the equivalent load loss cost rate, in dollars per kilowatt. This is the value ofload power losses tha t the user should furnish to the manufacturers at the time ofsoliciting bids.LIC = the levelized annual total system investment cost in dollars per kilowatt-yearPRF = the peak responsibility factor

PUL = the peak-per-unit loadTLF = the transformer loading factorLECL = the levelized annual energy and operating cost of load losses, expressed indollars per kilowatt-yearET = the efficiency of transmissionFCRT = the fixed charge rate for transformersIF = the increase factor6.2.3 Auxiliary Power Loss Cost Rates

6.2.3.1 Auxiliary Loss Cost Rate for Stage One (ALCR1)LIC+LAECl

(ET)(FCRT)(IF)ALCRl= Eq 9)whereALCRl = the rat e of the auxiliary power costs related to stage one cooling, expressed in

LIC = the levelized annual total system investment cost expressed in dollars perLAECl = the levelized annual energy and operating cost for stage one, expressed in

dollars per kilowattkilowatt-yeardollars per kilowatt-yearET = the effkiency of transmissionFCRT = the fixed charge rate for transformers

6.2.3.2 Auxiliary Loss Cost Rate for Stage Two ALCR.2)LIC+LAEc2

(ET)(FCRT)(IF)ALCR2=whereALCFU = the rate of the auxiliary power costs related to stage two cooling, expressed in

LIC = the levelized annual total system investment cost, expressed in dollars perLAEC2 = the levelized annual energy and operating cost for stage two, expressed in

dollars per kilowattkilowatt-yeardollars per kilowatt-yearET = the efficiency of transmissionFCRT = the fixed charge rate for transformersIF = the increase factor

6.3 Use of Power Loss Cost Rates. Following are some of the ways in which trans-former loss cost rates can be used:(1) By manufacturers, to design and build efficient, cost-effective transformers.(2) By users, to choose between two or more offerings.(3) By owners, to decide whether o r not to replace existing units with new, more efficientequipment, o r to build new systems to eliminate double transformations, etc.


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POWER TRANSFORMERS AND REACTORS IEEEStd C57.120-1991The loss cost rates, in dollars per kilowatt, for no-load, load, and auxiliary losses, asfound in 6.2.1, 6.2.2 and 6.2.3, respectively, are the figures th at should be furnished t o themanufacturers at the time of soliciting bids.The manufacturer may utilize the cost rate values t o build a transformer that hasamounts of conductor and iron that are economically dictated by the dollar evaluation.That is, the manufacturer may reduce losses, by adding conductor and iron up t o anamount where the incremental construction costs of adding conductor and iron equal theincremental value of the transformer.The rates should be preferably furnished to the manufacturers in the dollars-per-kilo-watt form as discussed above. They may also be given in the levelized annual form ofdollars-per-kilowatt-yeary ut if they are so given, it will be necessary also t o supply themanufacturer with information as to the purchasers fixed charge rate, sales tax rate,overheads, etc., and to rely on the manufacturer t o make the proper calculations. Use of thedollars-per-kilowatt form will ensure t ha t each manufacturer is using the same basis foroptimizing the design.In order to compare two o r more bids, add the following products to the bid price (for eachseparate bid):(1) The manufacturers guaranteed no-load losses in kilowatts, times the dollars-per-

(2) The manufacturers guaranteed load losses in kilowatts, times the dollars-per-(3) The manufacturers guaranteed losses for each type of auxiliary loss, times theWhen all of these a re added to the bid price, the lowest resulting figure indicates the bestbuy, provided, of course, that the offered transformers are comparable in other respects.If loss evaluation figures are furnished t o the manufacturers at the time of solicitingbids, the steps outlined above should be used to select the best offering. A selection basedonly on bid price will not necessarily represent the true value of the offered equipment.

kilowatt figure for NLLCR.kilowatt figure for LLCR.appropriate dollars-per-kilowatt figures for ALCR1, ALCR2, etc.

7. Bibliography[B11 Electrical Power Research Institute, Technical Assessment Guide, PS-1201-SR,Special Report, July 1979.[B21 Grant, Eugene L., Principles of Engineering Economy, 6th ed., Ronald PressCompany, 1976.[B31 IEEE Std 100-1988, IEEE Standard Dictionary of Electrical and Electronics Terms(ANSI).[B41 IEEE C57.12.00-1987, IEEE Standard General Requirements for Liquid-ImmersedDistribution, Power, and Regulating Transformers (ANSI).[B51 IEEE C57.12.80-1978 (Reaff 1986), IEEE Standard Terminology for Power andDistribution Transformers (ANSI).[BSI IEEE (37.92-1981 (Re& 1991), IEEE Guide for Loading Mineral-Oil-Immersed PowerTransformers up to and Including 100 MVA with 55 C or 65 C Winding Rise (ANSI).[B71 Nickel, D. L. and H. R. Braunstein, Distribution Transformer Loss Evaluation-Part 1: Proposed Techniques, pp. 788-97, and Dist ribut ion Transformer LossEvaluation-Part 2: Load Characteristics and System Cost Parameters, pp. 798-811, IEEETransact ions on Power Apparatus and Systems, Vol. PAS-100, o. 2.


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IEEEStd C57.120-1991

(These appendixes are not part of IEEE Std C57.120-1991,ut are ncluded for information only.)

The energy costs utilized in the no-load loss, load loss, and auxiliary loss power costformulas represent present worth values th at have been levelized (see 6.1.10, 6.1.11, and6.1.12). This appendix describes the concept of a present worth value and the concept oflevelization.

Al. Present Worth ValueAn understanding of the procedure of inflating, discounting, and summing may begained by development of the following ten-year present worth value table. The procedureinvolves the escalation of energy costs by year at a constant rate over a selected period oftime-ten years in thi s example. In actuality, the time frame may be selected t o beconsistent with the booklife of the transformer and variable inflation rates may bee mp1oyed.To introduce the concept of present worth value, Table A1uses a constant 5 energy costinflation rate. Each years inflated energy cost is discounted by the appropriate presentworth factor and then summed to a total present worth energy cost for the entire time period.The discount factor is defined as the users required rate of return.Present worth value calculations are described as follows:A l . l Es ca la te d Value. The escalated value equation, F =P(1 i>N, may be utilized inorder to escalate a present value (P), o a future value F , n a future year NI, for a givenescalation rate i). For a 5 escalation, the following years average escalated energyvalue is as follows:

F=P 1 .05)Example:Using a 5 escalation rate, the energy value five years from a current years energyvalue of .051 $/kwh is computed a s follows:F = .051(1.05)5= .065 $/kwh

A1.2 Present Worth Value. The present worth calculation utilizes the inverse of theescalation formula. The present worth equation, P =F(l r ) -N ,may be utilized in order tocalculate the present worth (P),rom a future value F), from a future year N), for a givendiscount rate r).Example:Using a 16% discount rate o r rate of return, the current present worth value of the cost ofenergy of .068 $/kwh six years in the future is computed as follows:P=.068(1+ 16)4 = .0279 kwh

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IEEEStd C57.120-1991 I E E E LQSS EVALUATION GUIDE FOR

present worth table may be computed utilizing (1 + r k N . Table A1 results fromapplying a 16% rate of return t o obtain the present worth factor per year over a ten-yearperiod ((1 .16)FN).Table A1Ten-Year Present Worth Value Table

Year I II Iv V VI w VI11 M xPresen tWorth .862 .743 .641 5 5 2 A76 .410 .354 3 0 5 263 .227An example of energy cost of $0.05lAtWh escalated at a 5 rate over a ten-year period and brought back to apresent worth value is as follows:

At EndRow ofYear I II III Iv V V I W V I I I K XA CostofB Presen tEnergy .054 O S .059 .062 .065 .068 .072 .075 .079 .083Worth B62 .743 .641 552 A76 ,410 .354 305 263 227C Presen tWor th .047 .042 .038 .034 .031 .027 .025 .023 .021 .019ValueThe Sum of Present Worth Values = 0.307 /kWhNOTE: T he levelized energy cost in dollars per kilowatthour equals 0.307 imes th e capital -very fado r.

levelized energy cost = $0.307 x CRF' = $0.307 x 0.207 = 0.064(See explanation of this step in the following paragraphs.)Row A of Table A1shows the escalated cost of energy in dollars per kilowatthour over aten-year period. The cost of energy is assumed to grow at a 5 annual rate from year one t oyear ten. The cost of energy is multiplied by the present worth factor (Row B) in order t oarrive a t the present value of energy costs on a yearly basis (Row C).The present worth

values per year are summed over the entire ten-year period in order to arrive at the sum ofpresent worth values of the escalated energy costs for the selected time frame. The sum ofpresent worth values = 0.307 (Row D).The capital recovery factor is calculated by using Eq 5 (6.1.7) as follows:

The sum of the present worth energy and operating cost is multiplied by the capitalrecovery factor (CRF) in order to compute the levelized energy cost (Row E).$0.064/kWh is then multiplied by the number of hours per year tha t the transformer willbe energized, to yield the levelized annual cost of energy in dollars per kilowatt-year.

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POWER TRANSFORMERS AND REACTORSA2. Levelization

The concept of levelization is illustrated in Fig A l .

IEEZStdC57.120-1991

/NCREASlNGANNUALCOSTSANNUALLEVELIZEDCOSTS

EQUIPMENT TIME IN YEARS BOOKLIFEPURCHASE DATE DATE

Fig A1Illustration of Levelization

The solid line in the graph above represents increasing annual costs from time ofequipment purchase to the last year of the equipment booklife. he procedure of levelizationtakes the present worth value of thi s increasing stream of energy costs and spreads thislump sum present worth value equally over the years of the equipment's booklife.The dotted line in the graph represents the levelized energy costs. In this guide, energycosts are levelized on an annual basis. Levelization is accomplished by multiplying thesum of the present worth values by the capital recovery factor. The levelized energy cost isan i npu t variable in the equations for the cost rate s of no-load, load, and auxiliary powerlosses a s described in 6.2.1, .2.2, nd 6.2.3.

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IEEEStdC57.120-1991 IEEE LOSS EVALUATION GUIDE FOR

A3. Variable Inflation Rate FormulaWhen annual energy inflation rates are not constant over the evaluation time period,each year's present worth factor may be calculated and summed. The example calculation

below shows the calculation of the present worth of energy cost for a three-year time period.Given that the energy cost inflation rate is 6% in year one, 4% in year two, and 2% inyear three, the rate of return is 16%, and the current-year energy cost is .03 /kWh, thepresent worth energy calculation is as follows:(1+.06)' 106-.914(1+.16)' 116YearL

(1+.06)( +.04) .819Year 2: (l+. 6)2(1+.06)( +.04)(1+.02).720Year 3: l+.1613

SPWECH= .030(.914 .819 .720 each succeeding year's value)SPWECH = .0736 /kwhwhereSPWECH = the sum of the present worth of energy and operation costs, in dollars perkilowatthour


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P O m R TRANSFORMERS AND REACTORS EmStd CS7.120-19914-BExampleCalculationofTransformerLoss CostRates

Assuming the following data, calculate the cost rates for the following:A. No-Load Losses NLLCRB. Load Losses LLCRC. Auxiliary Losses ALCRl and ALCR2

Availability factor AF 97%Average hours per yea r for stage one cooling, running alone AHPY1 2000 hAverage hours per year for stage two cooling AHPY2 l000hBooklife BL 35YrCurrent year energy costEfficiency of transmissionEnergy cost inflation rateFixed charge rate-generationFixed charge rate-transformerFixed charge rate-transmission systemGeneration installation costPeak-per-unit loadPeak responsibility factorRate of returnIncrease factorTransformer loading factorTransmission system installation costCapital recovery factor

CYEC $0.05l/kWhET 95%EIR 5%FCRG 17%FCRT 19%FCRS 18%GIC $800/kWPUL 1.67PRF 0.96ROR 16%IF 1.07TLF 0.5SIC $2OO/kWCRF 17%

A. No-Load Loss Cost Rate:LIC+LECN

(ET)(FCRT)(IF)NLLCR=To determine LIC:

LIC = (800)(0.17) + (200)(0.18)= 136+ 36= $172/kW-vTo determine LECN:Transformer users have many different ways of predicting their fu ture energy costs.In th e interest of continuing this example, the following is presented a s one way t o

determine LECN (steps (1) hrough (4), below, are illustrated in Table A1of Appendix A):(1) Determine each years energy cost in dollars per kilowatthour for the period of timebeing considered, (e.g., the booklife of the transformer).


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POWER TRANSFORMERS AND REACTORS IEmStdC57.120-1991C. Auxiliary Loss Cost Rate:

LIC LAEC1(ET)(FCRT)(IF)ALCRl=

LECN, found in A. above, can be converted to LAEC1 by multiplying LECN by the ratio ofthe total number of hours per year that stage 1 cooling will be running, t o the number ofhours per year used for finding LECN. (In the present example,

LAEC1 =LECN-=000 (500)(3000)= $176.5 k w yr.)8497 8497LIC+LAECl 172+176.5 348.5

(ET)(FCRT)(IF) 0.95)(0.19)(107) 0.95)(0. 19)(107)ALCRl=

$1804/ kW

LECN, found in A. above, can be converted to LAEC2 by multiplying LECN by the ratio ofthe total number of hours per year that stage 2 cooling will be running, t o the number ofhours per year used for finding LECN. (In the present example,

172+59 231IC+LAEC2ALCR2= (ET)(FCRT)(IF) 0.95)(0.19)(107) (0.95)(0.19)(107)$1196/ kW

When bids are solicited, the values found above should be stated to the manufacturers asfollows:Losses will be evaluated at th e following values:

No-load loss at 100%of rated voltage $3479/kWStage one cooling equipment power $1804kWLoad loss at self-cooled ra ting $2958/kWStage t w o cooling equipment power $1196kW

In the bid evaluation procedure, each loss evaluation figure listed abovewill be multiplied by it s respective guaranteed loss value in kilowatts, andthe resulting figures will be added to the bid price to give a total evaluatedprice for bid comparison.*If the following bids were received, they would be compared as shown below (assume thatall four bids represent acceptable transformers with comparable features):


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ansi std c57.120-1991(ieee loss evaluation guide for

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