Short Circuit Calculation Procedures

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS,VOL. 29, NO. 3, MAYIJUNE 1993 625

Comparison of ANSI and IEC 909Short-circuit Current Calculation Procedures

Gene Knigh t , Member, IEEE nd a r r y Siel ing, Member, IEEE

Abstruct- Although ANSI fault calculation methods are de-signed to determine a value to compare with the equipmentratings, the IEC 909 Standard presents a method that inherentlymore accurately models the fault currents that flow. The IEmethod requires significantly more complex modeling of thepower system fault contr ibutions than AN SI requires. By under-standing the calcu lation differences, the differen ce in equipmentratings becomes more insightful.I. INTRODUCTION

N THE EMERG ING world marketplace, engineers shouldI e familiar with the basic differences between the Amer-ican National Standards Institute ANS I) and InternationalElectrotechnical Commission-909 IEC909) sh ort-circuit cal-culation procedures. With the removal of trade barriers in theEuropean Community in 1992, the globalization of electricalmanufacturers, and the expansion of the engineering market-place to new countries around the world, engineering firmsable to cross international borders will gain a co mpetitive edge.Both the IEC and the ANSI standards for short-circuitcurrent calculation procedures were developed to provideconservative results for determination of the capacity or ratingof electrical equipment. Additionally, the IEC 909 Standardprovides procedures for determining minimum short-circuitcurrents to be used as the basis for selecting fuses, settingprotective devices, and checking the run-up of motors.The IEC 909 procedure requires significantly more detailedmodeling of the power system short-circuit contributions thandoes the ANSI. It should be mentioned that even thoughboth standards provide detailed procedures for the calculationof short-circuit currents, they do not exclude the possibilityof alternate methods if the alternate methods give at leastthe same precision. However, neither standard specificallyidentifies these alternate methods, thus laying the burden ofproof on the engineer.The A NSI standards that currently apply to equipment ratingvalues include C37.010 for systems lo00 V and above andC37.13 for systems below lo00 V. The ANSI/IEEE Stan-dard 141-1986 the IEEE Red Book) provides supplementalguidelines and interpretation of these ANSI standards.The first edition of the IEC 909 Standar d 1988) is derivativework taken from the German Verband Deutscher Electrotech-

Paper PID 92-19, approved by the Petroleum and Chemical Industry Com-mittee of the IEEE Industry Applications Society for Presentation at the 1991Petroleum and Chemical Industry Committee Technical Conference, Toronto,Canada, September 9-1 1. Manuscript released for publication September 3,1992.The authors are with SKh4 Systems Analysis, Inc., Manhattan Beach, CA90266.IEEE Log Number 9208800.

niker VD E) Standard. This standard applies to all voltagesup to 230 kV op erating at nominal frequency 50 or 60 Hz).This standard is supplemented by the proposed draft StandardIEC/TC 73 that provides supplementary documentation forexplanation and derivation of the factors used in the IEC 909publication.The follow ing sections present a generalization of the meth-ods used by both standards. The philosophical differences incalculation procedures are discussed. No attemp t is made hereto present the complete method of either standard or to m akejudgements on the correctness of either standard.11. ANSI IMPEDANCE-BASEDALCULATIONS

The method of short-circuit calculations provided by theANSI standards is best described as impedance based. Strictinterpretation of the ANSI stand ards requires separate networksolutions for 1) the low-voltage impedance network, 2) themedium- and high-voltage momentary impedance network,and 3) the medium- and high-voltage interrupting impedancenetwork. Each of these three networks is different. The fol-lowing paragraphs outline the differences of the impedancenetworks.The low-voltage standard requires that all machines, in-cluding all sizes of induction motors, be included as partof the impedance network. For this standard, the machinesubtransient impedances are used for all machines. For thelow-voltage network, symmetrical currents are calculated forcomparison with equipment ratings. If the X R atio at theshort-circuit location exceeds a value of 6.6, then multiplyingfactors are applied to the symmetrical rating to arrive at anumber that can be compa red with the tested value of the low-voltage breakers. There are additional factors that may enterinto the direct comparison of the calculated numbers beforethey are compared with the equipment.For the closing and latching momentary) network, theANSI C37.010 Standard requires the use of various multi-plying factors for the sub transient reactance. A factor of 1.2 isused for induction motors from 50 to lo00 hp at 1800 r/min orless and for induction motors from 50 to 250 hp at 3600 r/min.The standard also permits neglecting all motors below 5 0 hpas well as all single-phase motors. Using these impedances torepresent the machines, this momentary network is used forcalculating the closing and latching duty for all high-voltagecircuit breakers rated on a symmetrical current basis. Thisclose-and-latch value is equivalent to the half-cycle current.The value is calculated s an rms value of an asymmetricalcurrent and depends on an X R atio at the short-circuit

0162-8828/93 03.00 1993 IEEE

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626 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29 NO. 3, MAYIJUNE 1993

Utility Contribution100 MVA, WR=30Fig. 1 Simplified power system.

location, which must be determined by separately reducedR and X networks. The Red Book permits the momentarynetwork to be used for the low -voltage network, thus reducingthe calculation complexities.The interrupting network for the ANS I C37.010 Standard re-quires the use of various multiplying factors for the resistanceand reactance networks. A factor of 1.5 is used fo r inductionmotors above lo00 hp at 1800 r/min or less and for inductionmotors from 50 to 250 hp at 3600 r/min. A factor of 3.0 isused for all other induction motors. A factor of 1.5 is also usedfor all synchronous motors. Using a network with machinesrepresented by these impedances, rms currents are calculated.The rms currents calculated, along with the separately reducedX / R values, and various curves contained within the standardare used to arrive at interrupting currents.The C37.010 Standard recommends the use of separateresistance and reactance networks for d etermination of X/Rratios used for the momentary and interrupting current cal-culations. This standard also provides some empirical rulesfor determination of local and remote generation. The ac/dcdecrements or dc decrements only are determined from thelocalhemote status of generators; the X/R atio is calculatedby the separate network reduction techniques. For all pointsin time, the impedance multipliers for the induction andsynchronous machines remain fixed for the interrupting dutycalculations. This equipment is assumed to have the sameimpedance calculation for breakers opening at two cycles orat some other delayed value.Having modified the contribution impedance values to sim-ulate the momentary and interrupting equivalent networks,ANSI calculates an rms current. This value of current is thenused to calculate the momentary and interrupting equipmentratings.ANSI interrupting ratings deserve closer examination. Theactual interrupting rating for equipment is determined byapplying multiplying factors which are taken from graphspresented in the standard) to the calculated interrupting rmscurrent. It is interesting to note that as the opening time ofbreakers is increased, the ANSI standards require a higherinterrupting rating for the breaker.Fig. 1 illustrates a simplified power system with a remoteutility source. In this circuit, it is assumed there is only a dcdecay current factor.Fig. 2illustrates the ANSI interrupting ratings for the circuitin Fin. 1 at a constant XIR = 30. The m ultiplying factors are

1.6

1.5

1.4

1.3

1.2

1.1

1 o I I I I I0 .5 1 1.5 2 3 4 5

Time In Cyclesig. 2. ANSI nd E C nterrupting ratings.

A M f R

1 0H.1 I2 1 1 I 4MULTIPLYING FACTORS FOR E l X

LO 1 1.2 1.1AMPERES

1 0 11 11 1.3

Fig. 3. ANSI decrement curves.

The graphs shown in Fig. 3are taken from p. 36 ofANSVIEEE Standard C37.010-1979. They are replicated hereto dem onstrate the interrupting factors illustrated in Fig. 2.We can generalize about the solution methodology byobserving that three different impedance networks are used:1) the low-voltage, 2) the closing and latching, and 3) theinterrupting. In addition, it is important to note that theseimpedance networks are used to obtain total currents at theshort-circuit location; these total currents are then modified ona global basis to obtain the short-circuit currents flowing atvarious times. This standard does not attempt to model thepreloading of the generators or to model in detail the varyingdecay rates of each individual motor and generator.

LII. IEC CURR ENT-B ASEDALCULATIONS-1.097, 1.150, 1.135, and 1.185 for two, three, five, and eightcycle breakers taken from Fig. 10 on p. 36 of ANSI C37.010-1979 and Fig. 104 on p. 307 of E E E Standard 141-1986.The figure also illustrates dc decay calculated using classicaltechniques.

For each short-circuit location in the network, the IEC 909Standard calculates a total initial symmetrical short-circuitrms current (I:) as well as the initial symmetrical short-circuit rms current at a synchronous machine ICG) in eachcontributing source, as illustrated in Fig. 4. The network



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KNIGHT AND SIELING: COMPARISON OF ANSI AND IEC PROCEDURES 627

Vokagesource

total contributions (NACD ratio) should be used to interpolatebetween the dc-only decrem ent curves and the ac/dc decreme ntcurves to determine a more accurate factor.IEC 909 examines the magnitude of the ILG currents thatflow from each individual contributing source to the short-circuit location. For calculating breaking currents, motors areall considered near if the sum of all motors I G currents ex-

I kG.np...?re ....2...n3 _,zu .... zar

Fault3 zwl

m u h

includes all contributing sources. These I currents areimportant because they form the basis of determining 1) theinstantaneous peak short-circuit current i 2) the decayingdc aperiodic) comp onent of short-circuit current i ~ c )the symmetrical short-circuit breaking rms current 16 4) theasymmetrical short-circuit breaking rms current la asym., and5) the sym metrical steady-state short-circuit rms curren t I k foreach contributing source. Fig. 2illustrates breaking currentsfor the circuit in Fig. 1.The IEC 909 procedure requires calculating the contributingsources component of short-circuit current for each of thecurrents described above and then using these componentsto derive the short-circuit locations totals. To apply theequipment, it is necessary to know how these currents aredistributed throughout the network. Therefore, it is necessaryto track each contributing sources currents throughout thenetwork to the short-circuit location, as illustrated in Fig.4. These individual contributing source currents are each afunction of the machine characteristics, the R / X ratio thateach contributing source sees to the short-circuit location, theminimum clearing time for breaker operation, the initial sym-metrical short-circuit current, the type of excitation, and thedetermination as to whether the contributions flow through ameshed or nonmeshed network and whether the contribution isnear or far from the short-circuit location. IEC 909 procedurestreat each of the above factors differently for each contributingsource.

ceeds 5 of the total I: without motors. Otherw ise, all motors

IV. ANSI LOCAU REMOTE VERSUS IEC 909 NEAWFARANSI makes no attempt to account for the remoteness ofinduction and synchronous motors during the calculation ofinterrupting currents. Motors are represented by fixed imped-ances as previously described. For generators, ANSI statesthat if the short-circuit location is more than two transform ersaway or if the transfer reactance between the generator andshort-circuit location is greater than 1.5 times the subtransientreactance of the generator, the generation is considered to beremote. Otherwise, the generation is considered to be local.

are considered far.Each motor or generator is treated individually for theapplication of decay factors. For synchron ous machines, thesefactors are a function of the minimum breaker clearing timesand the ratio of the m achines contribution short-circuit currentcontribution I: to the machines rated current. To address thefaster decay rates of asynchronous machines, an additionaldecay factor that is a function of the machines rated activepower per pole pair is used.

V. CONTRIBUTIONATAFrom the above discussion, it is apparent that calculationprocedures of each standard require the typing of sourcecontributions into different categories. These categories in-clude induction or asynchronous motors, synchronous motors,generators or synchronous generators, and utility or networkfeeders. Data required fo r representing these contribution typesvaries slightly between the ANSI and the IEC 909 Standards.Some of these differences are briefly noted below.For asynchronous motors, ANSI requires information onr/min and hp rating for determining the subtransient reactancemultiplying factors. IEC 909 requires inform ation on rated real

power per pole pair for determining decay rates.For synchronous machines, IEC 909 requires additionalinformation on rated power factor in order to calculate thecorrection factor for synchronous machines I C G factor) usedto account for m achine initial loading conditions. The IEC 909also requires additional information on the type of excitationand Xdsat reciprocal of the short-circuit ratio) in order tocalculate the steady-state current IkG The IEC 909 Standarddefines an additional contribution type that is not directlyfound in the ANSI Standard. The power station unit (PSU)consists of a generator and a transformer treated as a singleentity. The IEC 909 Standard contains separate proceduresfor short-circuit calculations, depending on whether the short-circuit location is between the generator and the transformeror whether the short-circuit location is on the load side of thetransformer.

The standard provides ac/dc decrement curves and dc-onlydecrement curves for determining multiplying factors that reapplied on a globa l basis to the total short-circuit current. Thechoice of using the ac/dc decrement factor or dc decrementfactor only is determined by whether the source contributions

VI. TRANSFORMERODELSThe IEC 909 Standard contains procedures for modelingtransformers whose primary and secondary rated voltagesmay not be the same as the systems voltage levels. These



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628 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29 NO. 3, MAYNUNE 1993

procedures are addressed with regard to the modeling of powerstation units and are further expanded on by the examplescontained in Appendix A p. 109 of IEC 909 Standard). Everytransformer (18 total) in these examples contains rated voltagesthat are different from the system voltage levels, that is, thetransformer nominal turns ratio is different from the ratio ofsystem voltage levels. The intent of the IEC 909 Standardto model this condition is obvious, but it fails to address thegeneral problem of finding transformers of unequal turns ratiosanywhere in the system and not just at radial fed locations.This problem is further complicated by the current-basedprocedures of the IEC 909 Standard, regardless of whetherthe solution is performed using ohmic or per-unit quantities.The ANSI Standard does not specifically discuss solution ofthe network, thus leaving the engineer to solve these problems.VII. REF F ULT VOLTAGES

Normally, ANSI Standard fault calculations are performedat a nominal 1.0 per unit voltage. If actual operating voltagesare less than or greater than a breakers rated maximum volt-age, the breakers rated short-circuit current may be adjustedwithin the range of the correction factor for impedances Kfactor).The IEC 909 Standard requires the use of a voltage factorc table see Table I on p. 27 of IEC 909 Standard). Thistable specifies two sets of v oltage factors that vary by voltagelevels. One set of factors is used to determine maximum short-circuit currents, and the other set of voltage factors is usedto determine minimum short-circuit currents. The use of thesefactors accounts for worst-case prefault voltage conditions, theeffects of off nominal transformer taps, and the effects of allline capacitances and parallel adm ittances of nonrotating loadsexcept for those of the zero sequence system. These voltagefactors are used for determining an equivalent voltage sourceat the short-circuit location so that the initial symmetricalshort-circuit current can be calculated. A default set of voltagefactors appears in Table I on p. 113 of the IEC 909 Standardand can be used for countries that have not yet standardizedon a set of voltage factors.

VIII. NETWORK ONFIGURATIONSANSI makes no direct reference on differences in calcula-tion between radial and loop sy stems. This standard does statethat the use of separate R and X networks used to calculatethe X / R ratio tends to correct for multiple time constantsand associated decay rates due to short-circuit currents passingthrough multiple paths to the short-circuit location.The IEC standards make a major effort to distinguish be-tween short-circuit currents that flow through both meshed an dnonmeshed networks. W hen contributions are supplied through

a nonmeshed network only, the contributions are simply addedscalar or vectorially) to determine the total short-circuitcurrent. For contributions flowing through meshed networks,the standards allow three different correctional methods ofcalculation.Method A: If there is a uniform R / X ratio, then use thefactor taken from a standard figure see Fig. 8 on p. 47 of

Current

Top EnvelopeDCecaying aperiodic) compon ent i

Bottom EnvelopeIIL = initial symmetrical short-circuit currentip = peak short-circuit currentlk = steady-state short circuit currenti ~ cA = initial value of the aperio dic component iDCdecaying aperiodic) component of short-circuit current

Fig. 5 . Short-circuit current of a near-to-generator short-circuit (schem aticdiagram .

IEC 909) using the smallest ratio of R / X of all branches ofthe network. Here, it is only necessary to choo se the branchesthat together carry 80 of the current at the nominal voltagecorresponding to the short-circuit location. Any branch maybe a series combination of several elements.

Method B: Determine a multiplying factor from Fig. 8 usedin Method A based on the R / X at the short-circuit location,and then multiply this value by 1.15 for safety reasons.Method C: Calculate an equivalent frequency network todetermine the mu ltiplying factor. For a 60-Hz system, solve acomplete new impedan ce network at a frequency of 24 cycles,and then, a number of complex ratios must be taken.These correctional methods are used to determine the peakshort-circuit current as well as the dc aperiodic current. Thepeak current multiplying factor may be determined from theIEC graph or from the following equation:

peak current factor = 1.02+ 0 . 98e - 3R/ Xwhere R / X is the resistance/reactance ratio.

I x . CALCULATED DATAANSI C37.010 calculates an rms symmetrical current forthe momentary network and states that if this current is belowthe rms rating of the breaker and the X / R ratio is lessthan 15, then no additional calculations are required. If the

X / R ratio is greater than 15, then it is required to calculatethe rms momentary close and latch) current by using theANSI simplified rule of 1.6 times the rms symmetrical currentbased on the momentary impedance network. Optionally, thestandard permits a more accurate calculation based on thecalculated X / R value at the short-circuit location.

ANS I calculates a value of rms asym metrical current for theinterrupting network and uses this value with a multiplyingfactor to arrive at an interrupting duty, which is a function ofthe opening time of the breaker. Multiplying factors for theinterrupting duty are determined from charts in the standard.The chart of choice is dependent on the localhemo te status ofthe contributions to the short-circuit location.



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KNIGHT AND SIELING: COMPARISON OF ANSI AND IEC PROCEDURES 629

-E

l

0.0064j0.420

20 BUS POSITIVE SEQUENCEONE-LINE IMPEDANCE DIAGRAMOMPUTER BUS NUMBERPER UNIT VALUESSHOWN ON 100 MVA BASE

13.8 kV UTILITY0.01 4+j0.034.017+j0.032

13.8 kVLINE 1 LINE 2

3.8kV BUS 1 BUS 2 13.8kV

BUSNo.1234567891011121314151617181920

1.01 +jO.O14 0.002+j0.003 0.002+j0.003T

3.8 kV0.650+j5.750

O.W6+jO.620

3.8kV

4.300+j38.200

Fig. 6. One-line diagram for short-circuit calculations.TABLE ICOMPARINGALCULATEDESULTS

0.008 j0.820

7 1 3 . 8 V

3.8kV0.@34+io.380 8.699+j63.000

IEC IECkV

138.00138.00138.0013.8013.8013.802.4013.8013.802.4013.802.4013.80.48.482.40

.48

.4813.8013.80

ANSIx R

14.68.510.221.627.633.461.119.123.678.036.219.055.3nn9.281.780.8nan

ANSI E/zMomentarymk4.3463.3413.325

14.26815.00114.05820.06614.12714.84617.41614.88619.17316.489nn18.66512.688n10.822na

ANSI ANSIUZ EcMomentary Interrupting5 iPkArating CycleBkrkA kA6.5844.6674.787

22.50424.10533.55222.03223.56029.32024.33329.79627.50761.32861.32726.29221.42331.01018.26728.708

22.884

4.2793.2913.26914.39315.44815.35924.69714.03614.86821.47416.21418.62519.704nn17.51515.86013.533nn

11.4349.2429.38944.47246.90644.02162.56344.01246.40154.38246.46059.91153.311124.888124.71258.03642.56837.18253.36658.033

IEC IECkA kA

ipPh l k

8.085 4.4496.535 3.49431.447 15.81333.168 16.72631.128 15.59322.51515.65716.55219.72116.60821.51319.03045.78845.78920.93815.23923.24513.31321.240

6.639 3.481

lbkA4.4493.4943.450

15.39616.30115.21421.22215.24416.13019.09116.18620.26018.74143.73143.73119.71215.02722.42113.18820.393

lb asymkA4.4873.5053.463

15.90816.92915.73824.01015.68916.67421.67016.81520.50943.78343.78319.76917.59422.43715.39120.4 18

20.806

The IEC 909 Standard calculates both minimum and maxi-mum fault currents for the following:

1) Initial symm etrical short-circuit curre nt 1;2) peak short-circuit current i3) dc aperiodic) short-circuit curr ent i ~ c4) symm etrical short-circuit breaking current 15) steady-state short-circuit current I k

6) asymmetrical short-circuit breaking current I b a s ymFig. 5shows these components of short-circuit current

graphically.X. COMPARINGALCULATIONESULTS

For a typical system shown in Fig. 6, Table I illustratesresults of calculations by both the ANSI and IEC standards.



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630 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29 NO. 3, MAYIJUNE 1993

Table I illustrates calculated results using both standards forthe same problem.Fig. 6is a typical power system design that has been usedas a test problem for evaluation and comparison of ANSIsoftware programs. This test problem is used here to compareANSI results with IEC results.

XI. CONCLUSIONSThe preceding sections have described important concep-tual differences between ANSI and the IEC. Although ANSIsimply applies multiplying factors to machine impedances toaccount for their ac decay in the power system, IEC calculatesthe initial current of each m achine to the short-circuit locationand then calculates the decay separately for each contributionbased on these initial conditions. Additionally, ANSI makesno clear distinction between radial and loop network con tribu-tions, whereas the IEC does. ANSI models generators as localor remote depending on the impedance difference between theshort-circuit location and the generator; IEC considers bothmotors and generators to be subject to neadfar calculationdifferences.REFERENCES

[l] IEEE Application Guide fo r ac-H igh Voltage Circuit Breakers Rates ona Symmetrical Current Basis, ANSI/IEEE Std. C37.010-1979.[2] IEEE Recomm ended Practice fo r Electric Pow er Distribution for Indus-trial Plants Red Book) , ANSIAEEE Std. 141-1986.[3] IEEE Guide or Calculation of Fault Currents orApplication of ac High-Voltage Circuit. Breakers Rated on a Total Current Basis, ANSIAEEE[4] C. N.Hartman, Understanding asymmetry, IEEE Trans. IndustryApplications, vol. IA-21, no. 4, pp. 267-273, July/Aug. 1985.[5] W. C. Huening, Jr., Fault calculations, n IEEE Recom mended Practicefor Electric Power Distribution for Industrial Plants, ANSIAEEE Std.

Std. C37.5-1979.

141-1986.

Interpretationof new american national standards for power cir-cuit breaker applications, IEEE Trans. Industry General Applications,vol. IGA-5, no. 5 Sep./Oct. 1969.International Electrotechnical Commission, International Standard:Short-circuit Current Calculation in Three-phase ac Systems, 1988, 1sted.0 E. Roennspiess, and A. E. Efthymiadis, A comparison of stat icand dynamic short circuit analysis procedures, IEEE Trans. IndustryApplications, vol. 26, no. 3, pp. 463475, MayNune 1990.C. R. St. Pierre, Sample system for three-phase short circuit calcula-tions, IEEE Tran s. Industry Applications, vol. 26, no. 2, pp. 204-211,MarJApr. 1990.

Gene Knight (M81) is a co-founder of SKMSystems Analysis, Inc., Manhattan Beach, CA. Heoversees the technical development of the SKMsoftware, holds multiple software copyrights, andteaches power system analysis classes for the Uni-versity of Wisconsin-Madison. He has publishedseveral IEEE Technical papers on power systemanalysis by computer.Mr. Knight is a registered professional engineer.He has also been a member of the IEEE Violet Bookand Brown Book Committees, the Common DataFormat Committee, and Vice Chairman of the Los Angeles IEEE-IAS chapter.

Harry Sielmg (M81) is a co-founder of SKMSystems Analysis, Inc., Manhattan Beach, CA. He isChief of Engineering for SKh4 and holds multiplesoftware copyrights. Prior to being involved withSKM Systems Analysis, Inc., he was the AssistantManager of Transmission Systems Planning andthe Los Angeles Department of Water and Power.He has published several IEEE technical papers onpower system analysis by computer.Mr. Sieling is a registered professional engineerand a member of Tau Beta Pi.

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