4.5.1 Calculate Arc Current
Calculate arc current for every required equipment or bus using one of the empirical formulae recognized by the NFPA-70E (NFPA, IEEE, or other standards). These are described in Chapter 3. The arc current may be a function of the bolted fault current, the open circuit voltage, the type of enclosure and the gap between conductors depending on the calculation method selected.
4.5.2 Consider a range of Arc Current
4.5.2.1 Tolerance due to Random Variation based on IEEE-1584
To cover the variance that can occur in arcs, IEEE procedure suggests the following.
1. Calculate the maximum expected bolted fault condition.
2. Calculate the minimum expected bolted fault condition. The minimum bolted fault current could be a light load condition with many motor loads or generators not running.
3. Calculate the arcing current at 100% of IEEE 1584 estimate for the above two conditions.
4. Calculate the arcing current at 85% of IEEE 1584 estimate for the two above conditions.
5. At these four arcing currents calculate the arc flash incident energy and use the highest of the incident energies to select PPE. The minimum fault current could take longer to clear and could result in a higher arc flash incident energy level than the maximum-fault current condition. The fault current in the main fault current source should be determined since the current in this device may determine the fault clearing time for the major portion of the arc flash incident energy.
Note: Although IEEE recommends considering a range of 85% to 100% of the estimated arc current, IEEE test data shows that the measured values of arc current vary from 67%
of the estimate to 157% of the estimate. Further analysis of the IEEE test data was performed by the authors and the results are discussed in detail in Appendix A. Careful application of tolerances is required for the following reasons:
i. The tripping time of inverse-time protective devices is influenced by the arc current.
ii. The incident thermal energy is more sensitive to arcing time than it is to arc current.
iii. A more realistic and reasonably conservative estimate of arcing time can be obtained by proper selection of tolerances of arc current.
The following section provides guidelines based on statistical analysis of test data for various voltage levels and enclosure types.
4.5.2.2 Tolerance due to Random Variation based on Actual Data
Because of the random nature of arc currents, the actual arc current may take any value within a range of possible values. The calculated arc current is only a single estimate within the range possible values. The calculated arc current or the highest possible arc current may not necessarily produce the highest incident energy to which workers may be exposed. The arcing time may depend upon the arc current due to the tripping characteristics of the protective device. Therefore, the incident energy may be greater for smaller arc currents if the contributing branch current of the arc current lies in the inverse-time section of trip characteristics.
Chapter 4. Practical Steps to Arc-flash Calculations
Table 4.5: Minimum and maximum tolerances for arc currents obtained from IEEE 1584 test data for confidence level of 95%.
Voltage Enclosure Type Minimum Arc Current
Maximum Arc Current
LV Open -26.5% 26.0%
LV Box -26.9% 33.0%
MV Open -6.7% 10.2%
MV Box -20.8% 12.3%
When considering the range of the calculated arc current, the simplest way is to take a tolerance. This tolerance is a percentage of the calculated arc current. The tolerance is obtained from statistical analysis of the test data. The tolerances differ for IEEE 1584 method and NFPA 70E methods. For further description see Appendix A. Table 4.5 provides tolerances for IEEE 1584 arc current estimate for a confidence level of 95%. A confidence level of 95% means that there is a probability of 95% that the arc current will be in the tolerance range. To be more conservative, you could also take a confidence level of 99%. This would widen the tolerance range.
Example
For a 0.48 kV equipment in open air, the calculated arc current (Iarc) using IEEE 1584 estimate was 40 kA. What is the possible range of the arc current?
From Table 4.5 the minimum and maximum tolerances of arc current are –27.5% and +31.9% respectively.
Minimum arc current = Iarc * (100 + Min. Tolerance %)/100
= 40 * (100 – 26.5) / 100 = 29.4 kA.
Maximum arc current = Iarc * (100 + Max Tolerance %)/100
= 40 * (100 + 26.0) / 100 = 50.4 kA.
Variation of Arcing Current with Arc Gap
If the exact arc gap (or gap between conductors) was used in obtaining the arc current estimates, then further adjustments need not be applied. However, if the gap is an average value or an assumed value, then the possible range of arc current may need to be adjusted. Appendix A describes in detail the effect of gap on the arc current. The gap is used in calculations in the IEEE 1584 equations. NFPA 70E does not take the gap into account. Table 4.6 provides the sensitivity of arc current to gap. For every mm of difference in gap the arc current value is modified by the sensitivity amount. The voltage across an arc gap is roughly proportional to the length of the gap. Higher voltage means higher arc power for the same arc current. Since the arc resistance is non-linear, the
resistance is not directly proportional to the gap length. Therefore statistical approach is preferred in the evaluation of the effect of variation of arc gap length on arc current. The procedure given below should be used only for small differences in arc gap, as with most other sensitivity analyses.
Table 4.6 Sensitivity of arc current to gap for IEEE 1584 method Voltage Enclosure Sensitivity (% / mm)
LV Box -1.0%
LV Open -0.7%
MV - Not Required
Example
The exact gap between conductors for various devices are not known. For low voltage box, it was generally observed that the gap ranged from 25mm to 40mm with an average of 32mm. There are two ways to deal with this. The first method is to obtain two estimates for arc current, one for the least gap and the other for the highest gap. The second method is to adjust the IEEE estimate for the average gap using the sensitivity shown in Table 4.6. Let us say that the arc current for 32mm gap was found to be 40 kA.
Arc current for min. gap = Iarc * (1+sensitivity*(Min. gap – Average gap)/100)
= 40 * (1-1.0*(25-32)/100)
= 42.8 kA.
Arc current for max. gap = Iarc * (1+sensitivity*(Max. gap – Average gap)/100)
= 40 * (1-1.0*(40-32)/100)
= 36.8 kA.
If the variation in gap is small, then extensive analysis need not be carried out.
4.5.2.3 Limits for Arc Currents
After calculating the range of possible arc current, it is necessary to check whether the calculated values are within the practical range. Check for the following:
• Upper limit: It is not possible for the arc current to be greater than the bolted fault current because of the additional impedance of the arc. Therefore, after applying adjustments for random variations and for gap variations, if the upper limit of the range of arc current is greater than the bolted fault current, then discard that value and take the bolted fault current as the upper limit.
Chapter 4. Practical Steps to Arc-flash Calculations
Example
For a bolted fault current of 50 kA at medium voltage equipment in box, the arc current was calculated to be 49 kA using IEEE 1584 equations. To account for random variations tolerance data from Table 4.5 was applied. This takes the upper limit of arc current to 12.3% greater than the estimated value. Therefore, the upper limit of the arc current was calculated to be 49*(100+12.3)/100 = 55 kA. This is higher than the bolted fault current (50 kA), and therefore, is not possible. Take the upper limit of arc current as 50 kA.
• Lower Limit: Arcs do not sustain when the current is very low. For 480-volt systems, the industry accepted minimum level for a sustaining arcing fault current is 38% of the available three-phase fault current21. Test data accompanying IEEE Standard 1584 shows arc sustaining for 0.2 seconds at 0.208 kV at a current of 21% of bolted fault current. Table 4.7 shows the minimum arc current as a percentage of bolted fault current obtained during tests. The lower limit of arc current is not yet clear. Until further information is obtained, it may be reasonable to use Table 4.7 as the cut-off minimum arc current as a percentage of the bolted fault current.
Table 4.7: Adjusted minimum arc current as a percentage of bolted fault currents*.
Voltage (kV)
Min Measured Iarc % of Ibf
0.2/0.25 21%
0.4/0.48 21%
0.6 28%
2.3 51%
4.16 64%
13.8 84%
*The adjustment is based on maximum measured values taken normalized to the bolted fault current.
4.5.3 Calculate Branch Currents Contributing to the Arc Current
This is done using the branch current contributions to the bolted fault current obtained from section 4.4.2. To calculate the contributing currents to the arc fault, use equation (4.1).
Ix,arc = Ix,BF * Iarc / IBF (4.1)
Where,
Ix,arc = Current through branch x for arc fault Ix,BF = Current through branch x for bolted fault IBF = Bolted fault current.
Arc currents have been observed to be non-sinusoidal due to the non-linear nature of the arc resistance. The harmonic contribution of different branches may vary, however, the fundamental component can be approximated using the method describe above. It has been observed that although the voltage waveform is highly distorted, the arc current however has low harmonic content. Therefore the linear relation (4.1) is a reasonable approximation.
Section 4.5.2 describes taking upper and lower bounds of the range of arc current. The branch contribution must be calculated for each case. These are later used to determine the trip time of protective devices.