DC-Arc Models and Incident-Energy Calculations

1810 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 46, NO. 5, SEPTEMBER/OCTOBER 2010

DC-Arc Models and Incident-Energy CalculationsRavel F. Ammerman, Senior Member, IEEE, Tammy Gammon, Senior Member, IEEE,

Pankaj K. Sen, Senior Member, IEEE, and John P. Nelson, Fellow, IEEE

Abstract—There are many industrial applications of large-scaledc power systems, but only a limited amount of scientific literatureaddresses the modeling of dc arcs. Since the early dc-arc researchfocused on the arc as an illuminant, most of the early data wasobtained from low-current dc systems. More recent publicationsprovide a better understanding of the high-current dc arc. Thedc-arc models reviewed in this paper cover a wide range of arcingsituations and test conditions. Even with the test variations, acomparison of dc-arc resistance equations shows a fair degree ofconsistency in the formulations. A method for estimating incidentenergy for a dc arcing fault is developed based on a nonlineararc resistance. Additional dc-arc testing is needed so that moreaccurate incident-energy models can be developed for dc arcs.

Index Terms—DC-arc modeling, dc-arc resistance, dc incident-energy calculations, dc-system hazard risk category evaluation,free-burning arcs in open air, volt–ampere (V –I) characteristics.

I. INTRODUCTION

A RC physics is complex, and the physical constants areparticularly hard to clearly define for real-world arcing

faults in power systems. Therefore, the present knowledge hasbeen largely developed based on the observation and analysis ofelectrical measurements. The volt–ampere (V –I) characteris-tics of electric arcs, which are dependent on test parameters, areessential to defining the complex arc phenomenon in power sys-tems. Early researchers often failed to specify test conditions,the configuration type, and if ac or dc arcs had been initiated.Since the V –I characteristic is dependent on test conditions,including gap width and relative current magnitude, it can bedifficult to assess the early published work for accuracy andcoherence.

High current magnitudes (on the order of kiloamperes),typical of arcing faults in power systems, are commonly viewedas being quasi-stationary because the large thermal inertia inthe arc discourages changes in arc temperature and conduc-tance. Even though the dynamic nature of the arc generatesa time-varying arc length, arc voltage equations have been

Manuscript received June 22, 2009; accepted January 24, 2010. Date ofpublication July 12, 2010; date of current version September 17, 2010. Paper2009-PCIC-185, presented at the 2009 IEEE Petroleum and Chemical IndustryTechnical Conference, Anaheim, CA, September 14–16, and approved forpublication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS bythe Petroleum and Chemical Industry Committee of the IEEE Industry Appli-cations Society.

R. F. Ammerman and P. K. Sen are with Colorado School of Mines, Golden,CO 80401 USA (e-mail: [email protected]; [email protected]).

T. Gammon is with John Matthews & Associates, Cookeville, TN 38502USA (e-mail: [email protected]).

J. P. Nelson is with NEI Electric Power Engineering, Arvada, CO 80001 USA(e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIA.2010.2057497

Fig. 1. Series-electrode arc classification [2].

developed from the quasi-stationary V –I characteristics. Thispaper provides an overview of the most commonly used andpublished arc equations and develops dc-arc-resistance models.A simulation study is performed to compare the formulas whichare relevant with present dc-arc research. Additionally, basedon these models, dc arcing-fault incident-energy calculationsare presented to assess the level of risk involved when workingaround high-current dc apparatus. The discussion begins with abrief summary of free-burning arcs in open air.

II. FREE-BURNING ARCS IN OPEN AIR

As Sweeting and Stokes observed, “The vast majority ofthe literature deals with arcs that have been constrained orstabilized.” They also noted that “The bulk of the arc literatureis based on single-phase opposing electrodes, where the currentcomes from one side and flows across to the other side” [1].Series electrodes have historically received the majority ofattention because this is the configuration utilized to designpower-system protective devices like circuit breakers and fuses.In this context, arcs are often divided into two main cate-gories: axisymmetric and nonaxisymmetric. An axisymmetricarc burns uniformly, while nonaxisymmetric arcs are either in a“state of dynamic equilibrium or continuous motion” [2]. Fig. 1shows some of the commonly used arc classifications.

The “wall-stabilized” arc is constrained to a cylindricalshape. At low currents (below 10 A), the geometry of a free-burning arc would look similar to the diagram on the right sideof the figure. As shown, the actual arc length is longer thanthe electrode gap. Convective forces cause the arc plasma tobow upward; the resulting shape helps to explain the originof the term “arc” used to describe this complex electricalphenomenon.

0093-9994/$26.00 © 2010 IEEE

AMMERMAN et al.: DC-ARC MODELS AND INCIDENT-ENERGY CALCULATIONS 1811

Fig. 2. Electric-arc characterization [3], [4].

Free-burning arcs in open air are the exclusive focus ofthis paper. In industrial applications, high-current free-burningarcing faults are extremely chaotic in nature. The arc movesrapidly so that its length and geometry are constantly changing.The contributing factors to the dynamic nature of high-currentfree-burning arcs are the following:

1) thermal convection;2) electromagnetic forces;3) burn back of electrode material;4) arc extinction and restriking;5) plasma jets.

III. CHARACTERISTICS OF AN ARC

As shown in Fig. 2, an arc consists of three regions: the anoderegion, the plasma column, and the cathode region. The elec-trode regions (anode and cathode) form the transition regionsbetween the gaseous plasma cloud and the solid conductors.

As shown in Fig. 2, an arc is also commonly associatedwith a voltage profile. The voltage gradient across the arcplasma depends on the actual arc length; the arc may deviatefrom the gap width between the electrodes. Less deviationis expected for short gap widths, series electrodes, and lessturbulent conditions.

A number of researchers have postulated that the voltagegradient in the plasma column of an arc is nearly independentof the arcing current. For example, Browne found that thevoltage gradient in the arc column is nearly independent of thearc current for magnitudes above 50 A and is approximately12 V/cm (30.5 V/in) for arcs in open air [5]. Browne’s researchinvestigated arc behavior in both dc and ac circuits. In 1946,Strom published that “the voltage gradient in the arc is affectedvery little by current magnitude” [6]. Strom found that, forarc gap widths from 0.125 to 48 in (0.32 to 122 cm), the arcvoltages averaged 34 V/in (13.4 V/cm) during arc tests, whichproduced peak ac currents ranging from 68 to 21 750 A. Table Isummarizes the results of Strom’s findings. These numbers arecomparable to Browne’s finding.

TABLE ISTROM’S AVERAGE VOLTAGE GRADIENT [6]

Fig. 3. Arcing voltage and current characteristic [5], [7].

Fig. 4. DC-arc test circuit configuration [8].

A. Arc V –I Characteristics

Fig. 3 shows the quasi-static V –I characteristic for an arcof “fixed” length. In the low-current region (identified by thedotted line), the arc voltage drops as the arc current increases;as a result, the arc power (P = V I) tends to remain relativelyconstant in this region. For “larger” currents, the arc voltageincreases slightly with increasing arc current. (A transitioncurrent, which defines the boundaries between the low- andhigh-current regions, is presented later). With wall-stabilizedarcs, the arc plasma is only partially ionized in the low-currentregion, whereas the plasma becomes fully ionized above somethreshold current [2]. A similar transition in the level of ioniza-tion is observed for free-burning arcs.

B. Arc Modeling Using Static V –I Characteristics

Fig. 4 shows a typical test circuit used to measure thecharacteristics of a dc arc. In this diagram, the gap width,not the actual arc length, between the electrodes is labeled as“L.” The arc length is difficult to measure. Many equations


Fig. 5. DC equivalent-circuit model.

use arc length. A number of experimenters probably assumedthat the arc length was equal to the gap width. The lengthof the arc approximates the gap width when series electrodes,low currents, and short gap widths are involved. Otherwise, thearc length may be considerably longer than the gap width. Inmany early papers, it is not clear when arc length is definedas an equation parameter if the equation is based on the gapwidth or an estimated arc length. Most equations are probablybased on gap width since gap width is a measurable parameter.However, it must be remembered that the impedance of the arcis governed by the actual arc length.

The arc’s physical processes are complex and chaotic innature, and it is very difficult to develop theoretical modelsusing arc physics. Consequently, an arc is often representedwith an equivalent electrical circuit (a “black-box” approach).In some cases, this representation is sufficient because theobjectives are to determine arc current, power, and energy.Fig. 5 shows the simplified dc equivalent-circuit representationof the arc.

IV. DC-ARC V –I CHARACTERISTICS AND EQUATIONS

Much of the early arc research was focused on the useof an arc as an illuminant. Low-current arcs were relativelystable, while their high-current counterparts were consideredunpredictable and dangerous. This belief, coupled with theavailability of low-power dc supplies, explains why most earlyarc research focused on low-current dc arcs, which exhibitedinverse V –I characteristics. This section highlights some ofthe early and selected key publications; it also provides acomparison of methods used to model a dc arc.

A. Ayrton Equation

Ayrton formulated the first known equation used to modelthe electrical properties of a steady-state arc [9]. Developed in1902, (1) was derived for arcs in air initiated between carbonelectrodes separated by a few millimeters

Varc = A + BL +C + DL

Iarc. (1)

The constant A represents the electrode voltage drop, Bdescribes the voltage gradient, and L is the arc length; C and Dare constants, which model the arc’s nonlinear characteristic.

Fig. 6. Sample of arc characteristic curves [8].

B. Steinmetz Equation

In 1906, Steinmetz derived a semiempirical V –I equationbased on carbon and magnetite arc experiments [10]

Varc = A +C(L + D)

I0.5arc

. (2)

In (2), A, C, and D are constants, and L is the arc length.For a 25.4-mm (1-in) arc with carbon electrodes, the equationis defined as

Varc = 36 +130(1 + 0.33)

I0.5arc

. (3)

C. Nottingham Equation

In the mid 1920s, Nottingham conducted arc research thatproduced a similar inverse characteristic [11]

Varc = A +B

Inarc

. (4)

The constants A and B are dependent on the arc length andthe electrode material. The arc current is raised to a power n,where n varies as a function of the electrode material. For arclengths ranging from 1.0 to 10.0 mm (0.0394 to 0.394 in), theequation for copper electrodes is specified in (5). Also, note thatthe exponent n is different from the previous two equations

Varc = 27.5 +44

I0.67arc

. (5)

Fig. 6 shows a sample of some typical V –I characteristics ofarcs with 6-mm (0.236-in) arc lengths and different electrodes.For constant arc lengths, the Nottingham equation has the samegeneral structure as the Ayrton and Steinmetz formulas.

The early arc formulas are based on a limited number oflow-current test results. The empirical constants were actuallydependent on electrode materials, gap lengths, and gaseousmediums. No standard testing procedure had been established,and experimental procedures did not follow consistent testingprotocols. Consequently, many of the findings have been con-sidered inconclusive.


D. Van and Warrington Equation

In 1931, Van and Warrington performed a series of tests onhigh-voltage ac systems for arcing currents between 100 and1000 A and electrode distances which spanned several feet [12].The V –I characteristic of a stable arc was determined as

Varc =8750L

I0.4arc

. (6)

In (6), L is the arc length in feet. Van and Warrington con-firmed the early research performed by Ayrton and Steinmetzby showing that arc voltages are proportional to the arc lengthand decrease with increasing arcing current. The inverse char-acteristic was probably exhibited in this current range becauseof the large gap distance between the electrodes.

E. Miller and Hildenbrand

In 1972, Miller and Hildenbrand published a dc-arc modelbased on an energy-balance concept [13]. As a first approxi-mation, they recommended using the empirical relationship in(4) developed by Nottingham. They emphasized that A, B, andn are not absolute constants but depend on the arc conditions,specifically, electrode material, arc length, and gas species andpressure. Furthermore, they referenced Cobine’s statement thatconstants are difficult to accurately determine even for a givenset of conditions [14]. Ignatko conducted a series of ac-arctests which generated arc currents ranging from 5 to 150 kAfor arc gaps between 5 and 200 mm (0.197 and 7.87 in).Ignatko determined that the total electrode (cathode and anode)drop remained practically constant and measured 23.5 V forcopper, 26.5 V for steel, and 36 V for tungsten [15]. Ignatko’sresults confirm earlier work reporting a 20- to 40-V drop at theelectrodes [5].

F. Hall, Myers, and Vilicheck

In 1978, a group of researchers conducted tests to evaluatefaults on dc trolley systems [16]. Over 100 dc-arc tests wereconducted using a 300-V dc supply. Arcing currents rangedfrom 300 to 2400 A, and electrode gap widths ranged from4.8 to 152 mm (3/16 to 6 in). The relationship between thearc voltage and the arc current, shown in Fig. 7, is based on anumber of arc tests with a 9.5-mm (3/8 in) gap. The relationshipbetween the arc current and the arc voltage in a dc trolleysystem was determined to match the form defined in (4).

G. Stokes and Oppenlander Model

Stokes and Oppenlander performed perhaps the most exhaus-tive study of free-burning vertical and horizontal arcs betweenseries electrodes in open air [17]. “Current and voltage sig-nals have been recorded for arcs burning with exponentiallydecaying currents from 1000 to 0.1 A, and 50-Hz arcs forsinusoidal currents with amplitudes decaying from 20 kA to30 A [17].” Figs. 8(a) and (b) and 9 show that the minimumvoltage needed to maintain an arc depends on current magni-tude, gap width, and orientation of the electrodes. Stokes and

Fig. 7. DC-arc voltage versus current in 9.5-mm (3/8 in) gap [16].

Fig. 8. (a) Minimum arc voltage for horizontal arcs [17]. Minimum voltagecharacteristics for copper electrodes. Continuous lines are measured. Brokenlines are calculated based on power characteristics. Gap widths for curvesfrom bottom to top: 5, 20, 100, and 500 mm (0.20, 0.79, 3.94, and 19.7 in).(b) Minimum arc voltage for horizontal arcs [17]. Stokes and Oppenlander datapresented on a linear scale (500-mm (19.7-in) gap).

Oppenlander formulated the minimum arc voltages for serieselectrodes. DC arcs in an industrial setting are likely to beinitiated between parallel electrodes, which are characterizedby longer arc lengths and higher arc voltages.


Fig. 9. Minimum arc voltage for vertical arcs [17]. Minimum voltage char-acteristics for aluminum electrodes. Continuous lines are measured. Brokenlines are calculated based on power characteristics. Gap widths for curves frombottom to top: 5, 20, 100, and 500 mm (0.20, 0.79, 3.94, and 19.7 in).

The current associated with the transition point for eachgap width is clearly marked on the figures by the solid linewith dots. The transition current is defined as It = 10 + 0.2zg ,where the length of the gap zg is expressed in millimeters [17].The curves show the inverse V –I characteristic for an arc witha current that is lower than the transition point. For currentsabove the transition point, the arc voltage shows a very slowrise in voltage values. Stokes and Oppenlander modeled the arcvoltage for arcing currents above a transition point. “This setof data, totaling some two million current and voltage points,was reassembled to current–voltage characteristics [17].” Theresult is

Varc = (20 + 0.534zg)I0.12arc . (7)

Equation (7), written in terms of arc resistance, becomes

Rarc =20 + 0.534zg

I0.88arc

. (8)

H. Paukert’s Compilation of LV Arcing-Fault Data

Paukert compiled published arcing-fault data from sevenresearchers who conducted a wide range of arc tests. Some testswere dc, and some tests were ac. Some configurations werevertical, and others were horizontal. Arcing currents rangedfrom 0.3 A to 100 kA, and electrode gaps ranged from 1 to200 mm (0.039 to 8 in) [18]. The survey data are summarizedin Fig. 10.

Based on the collected data, Paukert formulated arc-voltageand arc-resistance equations for various electrode gap widths;these equations are listed in Tables II and III. Table II presentsan inverse V –I characteristic for low-current arcs, and Table IIIpresents positive V –I characteristic for currents above 100 A.

Good agreement was found between the measurements ofStokes and Oppenlander and the test results compiled byPaukert, as shown in Fig. 11(a) and (b). The best agreement isfound in the higher current range, which is greater than 100 A.Paukert concludes his analysis with the following words: “Al-

Fig. 10. Paukert’s compilation of arcing-fault data [18].

TABLE IIEMPIRICAL ARC FORMULAS FOR Iarc < 100 A [18]

TABLE IIIEMPIRICAL ARC FORMULAS FOR 100 A < Iarc < 100 kA [18]

though the author’s approximation formulas for minimal arcvoltage and minimal arc resistance have been found to be ingood agreement with other authors’ results, the uncertaintyconnected with the determination of actual arc length willhamper their successful application for exact calculation [18].”

I. Sölver

Like earlier researchers, Sölver recognized the complex-ity of the relationship between the arc current, arc voltage,


Fig. 11. (a) Comparison of V –I characteristic formulas for vertical arcs[18]: full lines—measurements of Stokes and Oppenlander [17], very full thicklines—Paukert [18], and broken lines–theory of Lowke [19]. (b) Comparison ofV –I characteristic formulas for horizontal arcs [18]: full lines—measurementsof Stokes and Oppenlander [17], very full thick lines—Paukert [18], and brokenlines—theory of Lowke [19].

Fig. 12. Current–voltage characteristics for dc arcs in air, with copperelectrodes [20].

and arc length. Fig. 12 shows experimental results for dcarcs between copper electrodes separated by widths of up to200 mm (7.87 in). For lower current values, the arc voltage hasan “inverse” relationship with the arc current; as the arc currentsincrease, the arc voltages tend to flatten and become relativelyconstant (independent of the current). When the arc is short, the

arc voltage is primarily determined from the electrode voltagedrops, which is around 20 V. “When the arcs are long and thecurrent is not too low, the arc voltage tends to be on the orderof 10 V/cm [20].”

The dc-arc models presented in this section share the follow-ing characteristics.

1) Arc resistance is nonlinear.2) Arc resistance is dependent on multiple factors:

a) gap length;b) electrode material;c) arc-current magnitude;d) electrode configuration.

The need for additional testing is evident. More testing wouldlead to the development of better equations for dc arcing and dc-arc resistance. Section V provides a comparative analysis of theexisting arc-resistance equations.

V. ARC-RESISTANCE MODEL COMPARATIVE STUDY

The following models are used in the comparative study tocalculate arc resistance. The models developed by Paukert andby Stokes and Oppenlander are included because they representa large number of test data, including dc arcs.

1) Nottingham: Equation (5), based on test data from dcarcs, with lengths ranging from 1.0 to 10.0 mm (0.0394to 0.394 in). His sample curves show arc currents up to10 A.

2) Stokes and Oppenlander: Equation (8), based on expo-nentially decaying dc currents from 1000 to 0.1 A anddecaying single-phase 50-Hz amplitudes from 20 kA to30 A. The gap widths ranged from 5 to 500 mm (0.20to 19.7 in) between series electrodes. Copper electrodeswere tested in a horizontal configuration, and aluminumelectrodes were tested in a vertical configuration.

3) Paukert: (Table III), based on test data from dc and single-phase ac arcs. Based on readings of Fig. 10, the dc-arctests were conducted for arc currents of up to approxi-mately 50 A (covered in Table II only). Rieder initiateddc arcs between copper electrodes spaced between 1 and160 mm (0.0394 and 6.30 in).

Figs. 13 and 14 show comparisons between the arc-resistanceformulas. Fig. 13 shows a comparison of the three approachesfor a gap length of 10 mm (0.394 in).

The Nottingham formula described in (5) is only applicableto electrode gaps in the range of 1–10 mm (0.0394–0.394 in),so it is not included in the sensitivity study shown in Fig. 14.

Fig. 15 shows the relationship between arc resistance, gaplength, and sensitivity to arc current.

Fig. 13 shows that the three models are somewhat consistent.Fig. 14 shows that the V –I relationships developed by Paukertand by Stokes and Oppenlander exhibit more deviation withlarge gap widths. Some additional observations include thefollowing.

1) Arc resistance is nonlinear.2) Arc resistance decreases with increasing arc current.3) Arc-resistance drop approaches a constant value at high

current magnitudes.


Fig. 13. DC-arc resistance comparative study (10-mm electrode gap).

Fig. 14. DC-arc resistance comparative study (sensitivity to electrode gap).

Fig. 15. DC-arc resistance comparative study (Stokes and Oppenlander/Paukert formula comparison).

4) Arc resistance changes rapidly at low current magnitudes(< 1 kA).

5) Paukert predicts larger arc resistances (almost by a factorof 1.5) than what Stokes and Oppenlander predict.

6) For a given arc current, the arc resistance increases lin-early with the electrode gap.

VI. ARC ENERGY

The law of “conservation of energy” principle requires thatenergy is conserved during an arcing fault; therefore, the elec-trical energy input is equal to the energy released in the formof heat, pressure, sound, light, and electromagnetic radiation.Arc-resistance models may be a convenient way to estimate theelectrical energy delivered during an arcing fault.

A. Theoretical Arc-Energy Fundamentals

For steady-state dc systems, power is determined as follows:

Power = VdcIdc. (9)

Generally speaking, the power for dc or single-phase ac arcscan be expressed as

Parc = VarcIarc = I2arcRarc. (10)

Since energy is a function of time, the energy associated withan arc is approximated as

Earc ≈ I2arcRarctarc. (11)

The arc duration (tarc) is measured in seconds. It shouldbe noted that dc arcs do not pass through current zero everyhalf cycle, which makes low voltage (LV) single-phase ac arcssusceptible to self-extinction [21].

B. DC-Arc Incident-Energy Estimates

Since electric arcs involve extremely complex processes,modeling electric arcs with theoretical physics is difficult, andmodel parameters depend on test and environmental conditions.Arcing faults in an industrial workplace may be initiated undera wide range of conditions. Arcing, by nature, is a dynamicprocess, and industrial arcing faults are much more dynamic,random, and turbulent than constrained arcs initiated in a con-trolled environment (for example, a laboratory setup). Conse-quently, semiempirical models are an effective way of modelingarcing faults in power systems and calculating incident energy.

1) Open-Air Arc Exposures: A large battery-bank installa-tion in a nuclear power plant is an example of an open-air dc-arcflash hazard. For this type of exposure, the heat transfer dependson the spherical energy density, as described in (12), where drepresents the distance from the arc (in millimeters).

Es =Earc

4πd2. (12)

This formula is based on radiant-heat transfer, and not all arcenergy will be transferred as radiant heat. In (12), the energydensity varies with the inverse square of the distance from thearc source.


TABLE IVOPTIMUM VALUES OF a AND k [22]

Fig. 16. Incident energy (open air) versus arc duration for 32-mm (1.25-in)gap and 457-mm (18-in) working distance.

2) Arc-in-a-Box Exposures: When a dc arc is initiatedwithin a piece of switchgear, the enclosure tends to have afocusing effect on the incident energy. Wilkins proposed anapproach for three-phase ac arcs where the spherical energy-density component is replaced by a value E1 that takes intoaccount the focusing effect of an enclosure [22]. In other words,the term E1 also represents the additional energy reflected bythe back and sides of the enclosure

E1 = kEarc

a2 + d2. (13)

Table IV lists Wilkins’ optimum values of a and k for thethree equipment classes described in the IEEE 1584 guide [23].

The use of (12) and (13) to compare the arcs initiated inenclosures with those in open-air arc exposures shows thatthe arc-in-a-box case results in an increase of incident energydirected toward a worker.

C. DC-Arc Incident-Energy Release

Figs. 16 and 17 approximate the incident energies associatedwith dc arcing faults of 2, 6, and 10 kA across a gap of 32 mm(1.25 in). The arc power was calculated from the arc-resistanceequation (8). Incident energy at 457 mm (18 in) was determinedby (12) and (13). The LV switchgear values for a and k inTable IV were used to calculate the incident energies associatedwith an enclosure. The resulting incident-energy levels arecompared with the hazard risk categories defined in National

Fig. 17. Incident energy (arc-in-a-box) versus arc duration for 32-mm(1.25-in) gap and 457-mm (18-in) working distance.

Fig. 18. DC system one-line diagram.

Fire Protection Association 70E [24]. For the selected enclo-sure type and test distance, the incident energies calculatedfor enclosures are 2.2 times larger than the incident energiescalculated for open air.

VII. DC DISTRIBUTION SYSTEM: CASE STUDIES

Two case studies of a large power plant illustrate a methodfor estimating the potential dc-arc flash hazard associated withhigh-current batteries. The one-line diagram in Fig. 18 showsoperational units feeding a 250-V dc bus through rectifiers.The bus is backed up with 258-V battery banks. The dc-supplysources include batteries, rectifiers, and battery chargers; anyof these sources might sustain a dc arcing fault, depending onsystem operating conditions and the fault location. The dc busserves a variety of loads, such as motors, inverters, relay coils,and lamps.

For the fault calculations presented in this section, it isassumed that a fault occurs on the dc bus while being supplied


Fig. 19. Double-string battery circuit model.

TABLE VDC SYSTEM SPECIFICATIONS AND PARAMETER VALUES

TABLE VIITERATIVE SOLUTION RESULTS

by the battery bank. It is further assumed that the fault-currentcontribution from any dc motors is negligible. The dc steady-state circuit model for the double-string battery system isshown in Fig. 19. For the single-string system, one battery isremoved. Table V lists the system specifications and circuit-model parameters for the case studies. The reactive (inductiveand capacitive) dynamic response of the batteries lasts approx-imately 15 ms after the fault occurs and is neglected [25]. Theeffect of the battery charger is also transitory and neglected inthe calculations. Furthermore, any nonlinear battery-dischargecharacteristics are not considered in this work.

The bolted-fault currents, listed in Table VI and associatedwith the double-string and single-string battery banks, werecalculated using the nominal battery voltage and the totalsystem resistance. The arcing-fault current for each case wasdetermined using an iterative solution of (8) and the circuit

Fig. 20. Incident energy (open air) versus arc duration for 20-mm (0.79 in)gap and 457-mm (18 in) working distance.

model shown in Fig. 19. As an initial guess, the arc current wasset to be equal to 50% of the bolted-fault current and convergedrapidly. The arc gap width was defined as 20 mm since a 250-Vsource has limited voltage potential to sustain arcs across largegap widths. The arc current and arc resistance for each systemare provided in Table VI.

For the single-string and double-string systems, the batterybanks lack upstream overcurrent circuit protective devices, soimmediate dc-arc interruption is not likely for sustainable gapwidths. Equations (11) and (12) were used to calculate theincident energies at 457 mm (18 in). The incident energies,plotted as a function of time and shown in Fig. 20, meritconcern. In particular, the magnitude of the incident energy forthe double-string battery bank increases quickly as a function oftime and reaches Hazard Category 4 soon after 1.1 s. A higherrisk of serious burn is certainly associated with the double-string battery bank. These cases were calculated for a dc arcingfault which occurs at the 250-V bus. However, if an arcing faultinitiates between battery terminals, chemical burns present anadditional hazard.

VIII. CONCLUSION

The models presented in this paper have been based on testsconducted over more than a century by different researchersin different countries and under very different protocol. Con-sidering the wide range of testing methods and conditions, theresults are remarkably similar. At low current levels, the V –Icharacteristic is inversely proportional and nonlinear. At higharcing-current levels, the analysis in this paper has shown thatthe arc-resistance voltage-drop approaches a constant value. Inan effort to quantify the risks associated with high-current dcsystems, a method has been presented to estimate the incident-energy levels possible during an arcing fault. Results from acase study demonstrated that the risks associated with high-current dc systems may be significant.

Arcing behavior is highly variable, and the existing dc-arc models cannot accurately and reliably assess all the


characteristics of dc arcs. Additional arc testing is needed todevelop more accurate V –I characteristics and better dc-arc re-sistance models. Extensive testing in a controlled environmentis needed to study the incident-energy levels associated withdc arcing faults. A hazard risk assessment is needed to identifywhere dc arcing faults might be initiated in industrial powersystems. The relative severity of the arc flash hazard posed bydifferent types of dc power equipment must be identified.

ACKNOWLEDGMENT

The authors would like to thank G. Leask of Bruce Power,Ontario, Canada, for his assistance in providing the dc systeminformation presented in the case studies, and to the manyreviewers of this paper for their detailed and constructivecriticism.

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[16] P. M. Hall, K. Myers, and S. W. Vilcheck, “Arcing faults on direct currenttrolley systems,” in Proc. 50th WVU Conf. Coal Mine Electrotechnol.,Morgantown, WV, 1978, pp. 1–19.

[17] A. D. Stokes and W. T. Oppenlander, “Electric arcs in open air,” J. Phys.D, Appl. Phys., vol. 24, no. 1, pp. 26–35, Jan. 1991.

[18] J. Paukert, “The arc voltage and arc resistance of LV fault arcs,” in Proc.7th Int. Symp. Switching Arc Phenom., 1993, pp. 49–51.

[19] J. J. Lowke, “Simple theory of free burning arcs,” J. Phys. D, Appl. Phys.,vol. 12, no. 11, pp. 1873–1886, Nov. 1979.

[20] C. E. Sölver, Electric Arcs and Arc Interruption. Götenburg, Sweden:Chalmers Univ. Technol., 2006, EEK 195 High Voltage Technol-ogy, Lecture 7. [Online]. Available: http://193.140.122.139/high_voltage/elkraft/www.elkraft.chalmers.se/GU/EEK195/lectures/Lecture7.pdf

[21] T. Gammon and J. Matthews, “Conventional and recommended arc powerand energy calculations and arc damage assessment,” IEEE Trans. Ind.Appl., vol. 39, no. 3, pp. 594–599, May/Jun. 2003.

[22] R. Wilkins, “Simple improved equations for arc flash hazard analysis,” inProc. IEEE Elect. Safety Forum, Aug. 30, 2004, pp. 1–12.

[23] IEEE Guide for Performing Arc-Flash Hazard Calculations, IEEE Std.1584-2002, 2004.

[24] Standard for Electrical Safety in the Workplace, NFPA 70E-2004, 2009.[25] Battery Short Circuit Current, C&D Technologies, Inc., Blue Bell, PA,

Document # RS1468.

Ravel F. Ammerman (SM’09) received the B.S. de-gree in engineering (electric power/instrumentation)from the Colorado School of Mines, Golden, in1981, the M.S. degree in electrical engineering(power/control) from the University of Colorado,Denver, in 1987, and the Ph.D. degree in engineeringsystems (electrical specialty—power systems) fromthe Colorado School of Mines, in 2008.

He has over 28 years of combined teaching, re-search, and industrial experience. He is currentlywith the Colorado School of Mines. He has coau-

thored and published a number of award winning technical articles, published inarchival journals. His research interests include arc flash hazard analysis, elec-trical safety, computer applications in power system analysis, and engineeringeducation.

Dr. Ammerman is a member of the IEEE/NFPA Arc Flash CollaborativeResearch and Testing Project Team.

Tammy Gammon (SM’06) received the Ph.D.degree from the Georgia Institute of Technology,Atlanta, in 1999.

She was an Assistant Professor with the NorthCarolina State Engineering Program, University ofNorth Carolina at Asheville, from 1999 to 2003. Shehas been with John Matthews & Associates, Inc.,Cookeville, TN, as a Senior Electrical Engineer since2003. The firm specializes in forensic engineering(fires of electrical origin, electrical shock, and arcflash burns) and evaluates the safety of electrical

products and equipment. The firm is experienced in utility and distributionpower issues and in designing electrical and lighting systems for buildings.She is also currently the Research Manager for the IEEE/NFPA Arc FlashCollaborative Research Project. She has taught a wide range of power andmechatronic courses.

Dr. Gammon is a Registered Professional Engineer in the State of NorthCarolina.

Pankaj K. (P. K.) Sen (SM’90) received the Ph.D.degree from the Technical University of Nova Scotia(Dalhousie University), Halifax, NS, Canada, in 1974.

He has over 44 years of combined teaching, re-search, and consulting experience. Currently, he isa Professor of engineering and the Site Directorfor the NSF Power Systems Engineering ResearchCenter (www.PSerc.org), Colorado School of Mines,Golden. He has published over 120 papers on avariety of subjects related to power systems engi-neering, electric machines and renewable energy,

protection, grounding, and safety and has supervised over 120 graduate stu-dents. His current research interests include application problems in powersystem engineering, renewable energy and distributed generation, arc flashhazard, electrical safety, and power engineering education. He is a member ofthe IEEE/NFPA Arc Flash Collaborative Research and Testing Project Team.

Dr. Sen is a Registered Professional Engineer in the State of Colorado.

John P. Nelson (S’73–M’76–SM’82–F’98) receivedthe B.S.E.E. degree from the University of Illinois,Urbana, in 1970, and the M.S.E.E. degree from theUniversity of Colorado, Boulder, in 1975.

He is the Founder/CEO of NEI Electric PowerEngineering, Inc., Arvada, CO. He spent ten yearsin the electric utility industry and the last 29 yearsas an electrical power consultant. He has authorednumerous papers (over 30) involving electric powersystems, grounding and protection, and protection ofelectrical equipment and personnel safety. Many of

those papers are also published in the IEEE TRANSACTIONS ON INDUSTRYAPPLICATIONS and IEEE Industry Applications Magazine. He has taughtgraduate and undergraduate classes at the University of Colorado, Denver, andColorado School of Mines, Golden, along with a number of IEEE tutorials andseminars.

Mr. Nelson has been active in IEEE Industry Applications Society/Petroleum and Chemical Industry Committee for 27 years. He is a RegisteredProfessional Engineer in the State of Colorado and numerous other states.

Documents

DC-Arc Models and Incident-Energy Calculations