Protecting utility workers and other working personnel who are exposed to line-to-line voltages above 15kV at live electricity installations is critical. For this reason and to ensure compliance with OSHA regulations, arc flash hazards must be evaluated and studied for every facility with an electrical installation. An arc flash produces extremely high temperatures, intense heat flux and radiation, high sound dB levels, and arc flash blast pressure waves. The intense heat and radiation can ignite clothing and cause severe burns.
Various methods have been proposed to calculate high-voltage arc-flash (HVAF) thermal incident energy levels, including IEEE 1584-2002, the Lee method, and Duke’s HFC Calculator. This article focuses on methods derived from Electric Power Research Institute (EPRI) testing as well as methods based on research by V.V. Terzija and H.J. Konglin. These methods serve as the basis for arc flash calculations in the examples, and we explain in detail how they relate to OSHA and NESC regulatory requirements.
Several key driving factors are responsible for the incident energy caused by a high-voltage arc flash. These include conductor gap, short circuit current, arcing voltage, and exposure duration (arcing time) among others. The effect of each parameter in the calculation is explained to help the reader apply the methods.
In overhead transmission and distribution lines, the gap between conductor and ground is the most likely place for an arc fault. This article focuses on open-air, line-to-ground arc faults; however, three-phase arc faults in enclosed equipment (15 kV to 36 kV) are also discussed because of the proliferation of renewable energy collector systems. We explore the differences between the methods to help clear misconceptions about the regulations and the available methodology for performing HVAF incident energy calculations.
Arc flash has been identified by OSHA’s regulatory bodies as a serious hazard requiring prompt mitigation action. OSHA Article 1910.335 states: “to warn and protect employees from hazards which could cause injury due to electric shock, burns, or failure of electric equipment parts.”
In Section 5(a)(1) of the 1970 Occupational Safety and Health Act, OSHA requires employers to ensure a safe work place for all working personnel: “Employers are required to provide their employees with a place of employment that is free from recognized hazards that are causing or are likely to cause death or serious harm.’”
OSHA 1910.333(a)(1) states:
Live parts to which an employee may be exposed shall be deenergized before the employee works on or near them, unless the employer can demonstrate that deenergizing introduces additional or increased hazards or is infeasible due to equipment design or operational limitations. Live parts that operate at less than 50 volts to ground need not be deenergized if there will be no increased exposure to electrical burns or to explosion due to electric arcs.
The NEC’s NFPA 70E emphasizes the need for identification of arc flash hazards and the required mitigation measures. To paraphrase NFPA 70E-2018, Article 130.5, Arc Flash Risk Assessment: An arc flash risk assessment shall be performed and shall: (1) Determine if an arc flash hazard exists. The risk assessment shall determine: (a) appropriate safety-related work practice, (b) the arc flash boundary, (c) the PPE to be used within the arc flash boundary. (2) Be updated when a major modification or renovation takes place. It shall be reviewed periodically, at intervals not to exceed 5 years, to account for changes in the electrical distribution system that could affect the results of the arc flash risk assessment. (3) Take into consideration the design of the overcurrent protective device and its opening time, including its condition of maintenance.
This article emphasizes the utility industry electrical safety requirements found in OSHA 29 CFR 1910, Subpart R (1910.269). While the utility industry may own and operate many facilities that fall within the scope of NFPA 70E, and thus can follow the guidelines provided there for incident energy calculations, the majority of transmission and distribution systems fall outside this context.
Similar to the arc flash requirements at industrial and commercial facilities, utilities follow NESC (ANSI/IEEE C2-2017) for guidance on equipment that falls outside the scope of NFPA 70E. Section 410A3 states:
Effective as of January 1, 2009, the employer shall ensure that an assessment is performed to determine potential exposure to an electric arc for employees who work on or near energized parts or equipment. If the assessment determines that a potential employee exposure greater than 2 cal/cm2 exists, the employer shall require employees to wear clothing or a clothing system that has an effective arc rating not less than the anticipated level of arc energy.
The standard further states:
When an arc flash analysis is performed, it shall include a calculation of the estimated arc energy based on available fault current, the duration of the arc (cycles), and the distance from the arc to the employee.
To summarize, regulatory requirements state that a safe workplace must be provided in industrial and commercial applications (governed by NFPA-70E) and in utility transmission and distribution applications (governed by NESC). However, although some standards list specific HVAF methods as examples that produce reasonable results, they are certainly not a requirement.
For example, OSHA 1910.269 Appendix E, Section III, Table 2 and Table 3 provide examples of specific methods that can be used to reasonably calculate HVAF incident energy. However, OSHA has clarified by means of an official letter of interpretation that, “OSHA never intended that the calculation methods currently listed in the Appendix would be the only methods employers could use to comply with the standard.” In fact, Note 1 to 29 CFR 1910.269(1)(8)(ii) specifically provides that “[a]n employer may choose a method of calculating incident heat energy not included in appendix E” as long as the method used “reasonably predicts the incident energy to which the employee would be exposed.” This information, which is quoted directly from an interpretation letter from the U.S. Department of Labor, Occupational Safety and Health Administration, is the main reason to explore alternative methods that could provide reasonable incident energy estimations from electric arcs.
Research and standards developed in previous decades focused mainly on how to calculate arc flash incident energy for enclosed, three-phase, low- and medium-voltage systems (0.208 to 15.0 kVLL). Far less detailed information has been published or highlighted regarding thermal energy produced by long conductor gaps, which are more prevalent in high-voltage systems. To validate the methods available at the time (and also because of the requirement placed on utilities in 2009), EPRI requested a comprehensive set of tests and experiments. This led to the development of the empirical equations that could be used to validate existing methods.
The experimentally derived equations (1) to (5) from EPRI TR-1022632 provide a method to calculate incident energy and can be effectively used to determine the heat flux and incident energy for open-air, line-to-ground arc faults in overhead power distribution and transmission systems. The first equation defines the voltage gradient, which is a function of the gap and arc current.
Equation (1) must be solved in conjunction with equation (2) using basic iterative routines.
Eave Average voltage gradient (kV / m)
G Length of the gap between conductors (m)
Iarc Arc current in (kA rms)
The arc voltage (rms) can be determined using equation (2) with the voltage gradient and length of the gap between conductors.
Varc Arc voltage (Volts rms)
The arc power is easily determined once an iterative process has determined the values of the arc current and voltage.
Parc Arc power (MW)
The energy flux equation (4) accounts for the effect of the gap and arc current on the heat transfer at a particular working distance.
Ф Thermal energy flux (cal/(s*cm2)
D Working distance (feet)
The incident energy equation (5) can be corrected based on statistical analysis of the energy measurements.
W Thermal incident energy (cal/cm2)
T Arc exposure duration (seconds)
n Statistical multiplying factor
σ Standard deviation
Similar to the method from EPRI TR-1022632, other international research efforts have led to the development of alternate representations of the long-gap arcs in open air. Similar equations based on the research by Terzija and Konglin can be used to determine the arc voltage gradient, arc current, arc resistance, arc power, and energy as described by equation (6) through equation (11).
Rarc Arc resistance (Ohms)
Ua Arc voltage magnitude (Volts)
Iarc Arc current (Amps)
Ea Arc voltage gradient (Volts/meter)
L Gap length (meters)
Substituting equation (7) into equation (6):
Use equation (9) to determine Ua:
B Voltage gradient (volts/meter)
Iarc Arc current (amps)
The arc power and energy are found using equation (10) and equation (11):
Tarc Arc exposure duration (seconds)
The incident energy can be determined using equation (7) and equation (8) developed based on R. Wilkins for various combinations of a and k (which are a function of the box size and electrode orientation), and x (which is a function gap and arc current magnitude):
For arcs in open air, equation 12 is applied because the arc freely expands compared to arcs that are confined to enclosed equipment.
For arcs within enclosed equipment (i.e., switchgear) the box size is taken into account in order to determine the Wilkins reflectivity factors a and k. These values are used to account for the reflectivity effect of the enclosure.
E Incident energy (Joules/cm2)
Earc Arc energy (Joules)
d Working distance (mm)
a Wilkins “a” reflectivity coefficient
k Wilkins “k” reflectivity coefficient
x Distance exponent coefficient
Parameters a, k, and x are determined based on a matrix of combinations of gap between conductors, which are optimized based on evaluation of the results.
The basic premise of the two methods — which from this point forward are referred to as the EPRI and Terzija/Konglin methods — is that HV arcs in open air can be represented mathematically using rms equivalents of the arc voltage and current. These rms-equivalent current and voltage gradients can be derived using spectrum analysis of the measured waveforms of open-air, single-phase arcs. The harmonic spectrum obtained from fast Fourier transform (FFT) can be used to create rms waveforms for the voltage, which can be somewhat equivalent to those of a square waveform. Typical high-voltage waveforms can be approximated as a square wave (Figure 1).
According to Terzija/Konglin, the voltage gradient can be approximated using a square waveform; however, according to EPRI, the voltage gradient experiences variation, and thus a square waveform model cannot possibly model all combinations of arc current and gap between conductors. An example of this is shown in Figure 2, where the instantaneous voltage waveform does not quite resemble a square wave but has continuous decay from the point where the arc ignites until the point where the arc extinguishes because of zero crossing.
Figure 2 includes the arc voltage waveform. A square waveform was superimposed on the arc voltage waveform to show that the actual waveform is similar to a square waveform but varies significantly depending on the gap and current. The EPRI method in equation (1) through equation (5) includes the effect of various gaps and arc currents. The same effect can be added to equation (7) for the Terzija/Konglin method to be sensitive to different gap lengths.
The models presented apply to single-phase, open-air arc faults, which statistically have the highest probability of occurring in high-voltage power systems. However, three-phase arcing faults also occur in enclosed equipment operating at voltages higher than 15 kV (outside the range of IEEE 1584 2002 or 2018) for which incident energy calculations need to be performed. There is no standard to address the calculations of three-phase arcs above 15 kV, but two methods have emerged as potential solutions.
The first method is to adapt calculation methods like the ones from EPRI and Terzija/Konglin to conservatively simulate three-phase enclosed arcs. The second proposed method based on T. A. Short utilizes an extension of the IEEE 1584-2002 method equations to determine the incident energy in enclosed three-phase equipment. To convert the single-phase arc to a multi-phase arc, a multiplier of 1.75 to 2.5 is proposed. The dimensions of the enclosure, the electrode configuration, and the working distance are all factors that affect the conversion factor.
Calculation Method Comparisons
The methods described above are only two of several methods that can be used to establish a reasonable estimation of the incident energy generated by a single-phase arc in open air. OSHA 1910.269 Appendix E, Section III, Table 2 and Table 3 provide additional examples of reasonable methods to determine the incident energy levels from flames and electric arcs required for the selection of PPE. Appendix E does not intend to make direct recommendations or imply that the listed methods are to be used exclusively to determine the incident energy. The intent of these tables is to provide examples of methods that can yield reasonable results.
The word “reasonable” was added to these tables in response to a statement in IEEE 1584-2002, which lists the Lee method as acceptable to determine the arc-flash incident energy for systems with voltages higher than 15 kV. Ironically, the reference to the Lee method was removed from the latest edition of IEEE 1584-2018 because the inclusion of this text in Appendix E generated confusion — it was misinterpreted as a requirement. In fact, alternative methods based on actual test results were used to refine some of the results listed in Appendix E and may be included in future revisions of the OSHA regulations.
To prove that several available methods yield similar and reasonable results, comprehensive comparative analysis was performed to observe how the incident energy results of each method vary across parameter sweeps that comprise different gaps, voltages, short-circuit currents, and working distances. This section only provides a small sample of the thousands of comparisons completed for six different methods (including one that cannot be disclosed since it is not a publicly available application and thus has been omitted from the comparisons). A good starting reference for a comparative analysis is to follow the calculations done to generate the data in Table 410-2 and Table 410-3 of NESC C2-2017. Figure 3 compares the five methods:
- Theoretically-derived Lee (included for illustration purposes)
- Duke Heat Flux Calculator
- ArcPro V3.0.
The voltage range is 1.0 kV to 46 kV, the working distance is 15 in, and gaps vary according to the footnotes in Table 410-2. The short-circuit current is 5.0 kA for all calculations. The arc exposure duration is varied to show a normalized 4 cal/cm2 exposure and is taken from the table. The electrode material is stainless steel (thus, the electrode erosion effect is not considered).
The comparison shows that between 1.1 to 46 kV, the variation between results is approximately 1.6 cal/cm2 or less (from highest to lowest). The horizontal line represents the normalized target energy value of 4 calories. The Lee method produces a hyperbolic result nearly 20 times higher, in most cases, and proves to be unreasonable for all applications above 15 kV.
Figure 4 shows further comparisons for longer gaps and higher short-circuit currents. This comparison was made based on the parameters selected to generate NESC C2-2017, Table 410-3. The voltage varies between 1.0 to 500 kV, the working distances and gaps between conductors are determined based on the minimum approach distance, and the voltage of the equipment uses the details provided in the footnotes of Table 410-3. Equation (14) and equation (15) were used to establish some of the working distances and gaps between conductors:
GapLG Gap between conductors (mm)
WDLG Working distance for line-to-
MinAppDist Minimum approach distance
w/out tools (ft)
VLL Voltage Line-to-Line (kV)
In Figure 4, only four methods are compared, since it is impractical to include the Lee method. The data trend shows that the results of all four methods decrease or increase depending on the changes in gap and working distance required for higher voltages. The results of all four methods are higher than the 4-calorie reference value between 121 and 362 kV. The highest incident energy difference between methods is approximately 1.16 cal/cm2 or less.
The trends are similar for other incident energy reference values and other combinations of gaps and short-circuit currents. NESC C2-2017 Table 410.3 includes higher incident energy reference values. Figure 5 shows a comparative analysis of the results for 20 kA of available short-circuit current with an 8-calorie reference frame. Similar to the trend established in Figure 4, the incident energy results of the longer gap results tend to be generally higher than the reference. The highest incident energy difference between methods is 2.2 cal/cm2 or less.
As mentioned previously, three-phase enclosed arcs are of high interest, particularly between 15 and 36 kV. Figure 6 shows the comparative analysis of four methods when applied to this condition. Typical dimensions for medium-voltage switchgear were used for the comparison. The height, width, and depth are 1143 mm, 762 mm, and 762 mm, respectively, for voltage levels above 15 kV. For 5 kV equipment, 914 mm was used for all three dimensions. A working distance of 36 in was used for all comparison samples. The arc exposure duration was 200 ms for all samples. The short-circuit current is 10 kA. The gap between conductors varied between 4 and 12 in (4 in at 5 kV, 6 in at 15 kV, 9 in at 25 kV, and 12 in at 35 kV).
The EPRI, Terzija/Konglin, and ArcPro single-phase arc to multi-phase arc results were adjusted using a 2.0 multiplier factor. The incident energy obtained from ArcPro appears to have been converted using a constant 1.75 multiplier to go from three-phase arc in open air to three-phase enclosed conditions. The EPRI and Terzija/Konglin methods were converted to enclosed conditions using reflectivity factors developed based on R. Wilkin and other proprietary sources of information that cannot be referenced.
The variation in incident energy calculations is much higher for three-phase enclosed arcs and can be as high as 50 percent from high to low based on the Figure 6 comparisons. The variation comes from the dimensions of the enclosure, the orientation of electrodes, the distance between the electrodes and the back wall, the distance between the electrodes and the bottom surface of the enclosure, and the working distance. To account for some of these additional sources of variation, the reflectivity factors applied to the EPRI and Terzija/Konglin methods were designed to produce more conservative results.
The new IEEE 1584-2018 standard introduced a new enclosure-size correction factor, but at first sight, the new IEEE 1584-2018 equations do not appear capable of being extended for application on voltages above 15 kV (unlike their predecessors). It appears that the arc current equations collapse, producing unrealistic results at input voltages higher than 22 kV. However, if the input voltage is held at a max of 22 kV, it may be possible to extend the comparative analysis to include this new method as shown in Figure 7. Note that the results of the IEEE 1584-2018 method were obtained using the following assumptions:
- Horizontal conductor in a box (HCB)
- Dimensions of 914 mm x 914 mm x 914 mm for 5 kV
- Dimensions of 1143 mm x 762 mm x 762 mm for 15 kV and higher
- Gaps of 4 in at 5 kV, 6 in at 15 kV, 9 in at 22 kV, and 12 in at 22 kV (No arc current solution is feasible at input voltages greater than 22 kV.)
This final comparison shows that variations in electrode orientation in medium-voltage equipment have a significant effect that may not be captured well with single-phase arc models that are adapted to three-phase enclosed conditions. Figure 7 also shows that additional conservative factors may be adequate to conservatively estimate the incident energy because of many parameter variations that can introduce significant effect in the thermal incident energy transfer.
The comparative analysis performed to determine which method was capable of providing reasonable incident energy results was extensive. Another sample of this effort can be observed in Figure 8, which was recreated based on the comparative analysis performed in Ammerman, Gammon, Sen, and Nelson. Figure 8 originally included only the results of the Duke Heat Flux Calculator, ArcPro V2.0, and IEEE 1584-2002 results for a three-phase, open-air fault. The chart presented here includes the two additional methods applied under identical input parameters. The gap between conductors is 6 in, which is important for this comparison since it shows that even under short-length gaps, all four models can yield very close results. Furthermore, the x-axis represents the available fault current, which varies from 5 kA to approximately 45 kA (very high for high-voltage applications). The working distance used in the comparison was 30 in and the arc exposure duration (arc time) was set at 0.2 seconds.
The correlation between the EPRI method and ArcPro V2.0 results is no more than 1.0 cal/cm2 for the 45 kA result. It can also be observed that the lowest value is that of the Terzija/Konglin method. This could be expected, since this method was developed to represent long gap lengths. No conversion factor is used in any of the single-phase arc methods to convert the result to a multi-phase arc.
The main purpose for Part 1 of this article was to explore and compare various methods to calculate the incident energy from HV and MV electric arcs. Analyzing the results presented in Figure 3, Figure 4, and Figure 5 demonstrates that several methods can be used to calculate the incident energy generated by open-air, line-to-ground arc faults for systems within the range of NESC tables 410-2 and 410-3.
In Part 2 of this article, key driving factors that directly affect the arc flash incident energy will be discussed in detail along with PPE considerations for different scenarios. A real-life case study will be analyzed to drive home the importance of high-voltage arc flash studies for utility applications.
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Albert Marroquin, BSEE, PE, IEEE Senior Member, is Vice President, Validation & Verification, and Senior Principal Electrical Engineer at ETAP. A registered Professional Engineer in the state of California, he is the main designer and product manager for ETAP’s ac and dc arc flash products, a working group member of IEEE 1584 and IEEE 1458, and an active attendee at NFPA 70E seminars and meetings.
Abdur Rehman, BSEE, MSEE, PE, is the Relay Operations Supervisor at Puget Sound Energy, where he leads a team of relay technicians who maintain, troubleshoot, and commission protection systems throughout PSE territory. Abdur brings a wealth of high-voltage experience in protection engineering and has performed various power system studies, high-profile incident investigations, troubleshooting, and RCAs.
Ali Madani, BSEE, is the lead Power Systems Engineer at AllumiaX Engineering. Ali has performed various power systems studies including modelling, short circuit, coordination, and arc flash studies for a variety of low- and medium-voltage facilities.