Session Eight: Calculating Arc and Incident Energy in an ...

[Pages:5]Session Eight: Calculating Arc and Incident Energy in an Arc Flash ? Where Do the Equations Come From?

Session Eight: Calculating Arc and Incident Energy in an Arc Flash ?

Where do the Equations Come From?

Prof Jerry Walker

Director, Walmet Technologies (Pty) Ltd jerrywalker@walmet.co.za Visiting Professor, Department of Power Engineering, Vaal University of Technology

Abstract

This paper gives a brief overview of the first formulas and methods developed since it was first recognised that Arc Flashes play a major role in electrical accidents, to the accepted methods and formulas used in present National and International Standards. It also highlights the deficiencies and constraints in the different methods. The formulas for the calculation of the incidence energy at a specific distance (arc flash boundary) are given but not discussed. The other popular methods described in NFPA 70E are not discussed in this paper as it will normally not be used in South Africa.

Introduction

The last decade or two has seen a great increase in the awareness of arc flash hazards and the injuries that result from the lack of adequate personnel protective equipment and safety systems. However, arcing faults and injuries have been around from the early days with the use of electricity. So why is it just recently that actions are being taken to define and protect against this hazard?

One factor is the exposure. There has also been an increase in the number of facilities and users taking power directly at high voltages to take advantage of the lower rates available, and reduction or elimination of facilities charges. As a result, facilities employees are exposed to higher voltages and fault duties (fault levels) than ever before.

Another aspect of the exposure is the increased emphasis on system reliability and reducing downtime.

A third factor is the liability and costs associated with incidents in terms of lawsuits, lost production and repair costs.

As understanding of the arc-flash hazard has grown, several methods for calculating the arc-flash hazard have been developed. Two of these methods will be examined in this paper, namely the theoretical model and the calculation methods presented in SANS 984 (IEEE Std 1584TM).

Theoretical Model

Ralph H. Lee developed a theoretical model for calculation of arc-flash energy in a paper published in 1982. Prior to this, arcing faults had been recognized as

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Session Eight: Calculating Arc and Incident Energy in an Arc Flash ? Where Do the Equations Come From?

damaging to electrical equipment and as a potential safety hazard, but Lee's [1] work was one of the first, if not the first, to quantitatively assess the relationships between the energy produced by arcing faults, the working distance, and the potential hazard to exposed workers. Lee recognized that arcing faults are sources of intense heat and used heat transfer equations to determine the effect of this heat energy on human skin. Equations were presented that allowed for calculation of "just curable" and "fatal" burn distances based on the value of bolted fault current and the fault clearing time.

In his paper he defines the 1.2 cal/cm2 (5 J/cm2) "curable burn level" that is still used today and the calculations to determine the curable burn distance for an arc in air.

At the time, no testing had been performed to investigate the relationship between bolted fault current and arcing fault current, so Lee concluded that the arcing energy calculations should be based on the worst-case condition, i.e., when the voltage across the arc is equal to half the system voltage.

For cases where voltage is over 15 kV, or gap is outside the range of the model, the theoretically derived Lee method can be applied

(1)

Where: E is incident energy (J/cm2)

V is system voltage (kV)

t is arcing time (seconds)

D is distance from possible arc point to person (mm)

Ibf is bolted fault current

For voltages over 15 kV, arc fault current is considered to be equal to the bolted fault current.

Later testing showed that actual incident energy levels reached a maximum of 79% of the theoretical value in a 600 V system and only 42% in a 2400 V system, as the voltage across the arc was actually less than that required to produce maximum arc power. The results of the theoretical model tend to be conservative for any system, but are even more conservative for systems operating at 1 kV or higher.

Further work and publications provided equations to determine incident energy based on the fault level, working distance and the clearing time for arcs in air and in an enclosure on a 600 volt system

EMA = 5271 x DA-1.9593 x tA x (0.0016F2 ? 0.0076F + 0.8939)

(2)

EMB = 1038.7 x DA-1.4738 x tA x (0.0093F2 ? 0.3453F + 5.9675)

(3)

Where: EMA = incident Energy (cal/cm2) for an arc in open air EMB = incident Energy (cal/cm2) for an arc in a box (20 inches maximum) DA, DB = distance from the arc in inches

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Session Eight: Calculating Arc and Incident Energy in an Arc Flash ? Where Do the Equations Come From?

F = bolted Fault Current (kA)

tA = time of arc exposure (seconds)

A more accurate calculation of arcing fault current is however required to achieve more accurate results. In addition, since the theoretical model does not take into account other important factors, such as whether the arcing fault occurs in open air or inside an equipment enclosure, it is not suitable for calculation of incident energy levels or flash-hazard boundaries in a typical industrial or commercial facility although equations (2) and (3) cater for the calculations at voltages less than 600 volt. The model is still useful, however, for calculating energy levels in situations where no other method has been developed. Equations based on Lee's work are included in IEEE 1584 to cover system types that are not otherwise covered by the IEEE 1584 equations, such as open-air transmission or distribution systems, open-air substations, or systems operating above 15 kV.

Arc Flash Boundary

Lee determined the arc flash boundary as:

(4)

Where:

DB is the distance of the boundary from the arcing point (mm)

EB is incident energy in J/cm2 at the boundary distance

t is time (seconds)

Ibf is bolted fault current

EB can be set at 5.0 J/cm2 for bare skin

SANS 984 (IEEE Std 1584)[4]

IEEE Std 1584, IEEE Guide for Performing Arc-flash Hazard Calculations, presents the most comprehensive set of equations to date for calculating incident energy levels and flash-protection boundaries. Empirical equations are given that cover systems at voltage levels ranging from 208 V to 15 kV and for available bolted fault currents ranging from 700 A to 106 kA, sufficient to cover the majority of low-voltage and medium-voltage installations. The equations are rather complex if calculations are to be performed by hand, though the equations are easily implemented in a spreadsheet or in other computer software.

This guide is based on extensive set of test data. The data includes all suitable data from previous testing and the programs conducted or witnessed by representatives of the IEEE Std 1584:2002 working group. This model is designed for systems having:

-- Voltages in the range of 208 V - 15 000 V, three-phase. -- Frequencies of 50 or 60 Hz. -- Bolted fault current in the range of 700 A - 106 000 A. -- Grounding of all types and ungrounded. -- Equipment enclosures of commonly available sizes.

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Session Eight: Calculating Arc and Incident Energy in an Arc Flash ? Where Do the Equations Come From?

-- Cable and conductors in air, with gaps between conductors of 13 mm 152 mm.

-- Faults involving three phases.

There are two principal stages in arc flash calculations: (a) calculation of the r.m.s. arcing current IARC so that the operating time of protective devices can be found (b) calculation of the incident energy density E at a distance d so that a safe working distance or the required personal protective equipment can be determined.

In IEEE 1584a the following equation is given for the calculation of IARC (originally for system voltages under 1kV).

log10 IARC = KA+0.662log10IBF+0.0966V+0.000526g+0.5588Vlog10IBF -

0.00304glog10IBF

(5)

where:

KA = -0.153 or -0.097 (open or box configuration)

IBF = bolted 3-phase symmetrical fault current, kA

V = system voltage, kV

g = gap between arcing electrodes, mm.

It is shown [3] that for bolted fault currents (using equation (5)) less than 1.489kA, irrespective of system voltage, the effect of the gap length is reversed (incorrectly), giving higher arcing currents for longer gaps. Although at 0.48kV the situation improves for bolted fault currents above 1.489kA, the effect of the anomaly is still significant for much higher values. Other anomalies occur at higher voltages. For example, if V > 0.783 kV and g=32mm, the arcing current exceeds IBF at IBF = 100kA.

For higher voltage systems the IEEE 1584 equation is

log10 IARC = 0.00402 + 0.983 log10 IBF

(6)

It is also shown [3] that applying equation (6) gives arcing currents higher than

the bolted fault current for IBF < 1.724kA.

The second stage of the IEEE 1584 method requires the calculation of a normalized incident energy density En using:

log10 En = K1 + K2 + 1.081 log10 IARC + 0.0011g

(7)

where:

K1 = -0.792 or -0.555 (open or box configuration)

K2 = 0 or -0.113 (grounded or ungrounded system)

This equation is based on data normalized for an arc time of 0.2 seconds and a distance from the possible arc point to the person of 610 mm.

Finally, convert from normalized:

(8)

Where: E is incident energy (J/cm2)

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Session Eight: Calculating Arc and Incident Energy in an Arc Flash ? Where Do the Equations Come From?

Cf is a calculation factor 1.0 for voltages above 1kV, and 1.5 for voltages at or below 1kV En is incident energy normalized 15 t is arcing time (seconds) D is distance from the possible arc point to the person (mm) x is the distance exponent from Table 4 in IEEE 1584. This is then adjusted to the actual fault duration (linearly) and for the distance d using a power-law with a "distance exponent" X, which depends on the equipment type. Arc Flash Boundary IEEE 1584:2002 give the arc flash boundary as:

(9)

Where: DB is the distance of the boundary from the arcing point (mm) Cf is a calculation factor

1.0 for voltages above 1 kV, and 1.5 for voltages at or below 1 kV, En is incident energy normalized EB is incident energy in J/cm2 at the boundary distance t is time (seconds) x is the distance exponent from Table 4 (SANS 984). EB can be set at 5.0 J/cm2 for bare skin

References

[1] Ralph H Lee, The Other Electrical Hazard, Electric Arc Blast Burns, Paper IPSD 81-55 Industry Application Society Annual Meeting, Philadelphia, PA, October 5 ? 9, 1981

[2] Data Bulletin, R11/11, 03/2012, Schneider Electric USA, Inc. 3700 Sixth St. SW Cedar Rapids, IA 52404 USA, 1-888-778-2733

[3] Improved Method for Arc Flash Hazard Analysis, R. Wilkins, M. Allison and M. Lang, IEEE Industrial and Commercial Power Systems Technical Conference, May 2004.

[4] SANS 984:2010 IEEE guide for performing arc-flash hazard calculations.

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