# How is Arc Explosion Energy Calculated?

The key to protection against arc explosion is knowing the arc explosion energy to which the employee will be exposed and the safe working distance.

Measures taken without calculating these values may not have an adequate level of protection and may lead to serious injury or death of the employee.

The formulas specified in the NFPA 70E document are used in arc explosion calculations. The sources, calculation limitations and parameters of these formulas are as in the table below.

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| SOURCE | LIMITATIONS & PARAMETERS | |

D.1 | Lee, “Other Electrical Hazards: Arc Blast Burns” | Calculates incident energy and arc flash limit for arcing outdoors; It is consistent over 600 V and gives consistent results as the voltage increases | |

D.2 |
| Calculates the incident energy for three-phase arcing in systems of 600 V and below; Applies to short circuit currents between 16 kA and 50 kA | |

D.3 | IEEE 1584, Arc Flash Calculation Guide | For Calculates incident energy and arc flash limit: 208 V to 15 kV; three phase; 50 Hz to 60 Hz; Short circuit current from 700 A to 106,000 A; and conductive gaps between 13 mm and 152 mm | |

D.4 | Doan, “Arc Explosion Calculations in DC systems” | Calculates the incident energy for dc systems up to1000V dc |

D.1 Ralph Lee Calculation Method

#### D.1.1 Basic Equations for Calculation of Arc Blast Limit Distance

Arc explosion limit distance is calculated according to the following formula:

D_{c} = Distance in feet that a person can survive receiving a healable injury from arc welding (Skin temperature remains below 80°C)

MVA< sub>bf = Bolted short circuit MVA value

MVA= MVA value of the transformer. For transformers less than 0.75MVA, it should be multiplied by 1.25.

t= Arc explosion time in seconds

#### D.1.2 Calculation of Incident Energy Greater than 600 V for Arc Flash Hazard Analysis

The following equation can be used to estimate the incident energy produced by a three-phase arc outdoors in systems above 600 V. Parameters required to perform calculations;

1)Highest three-phase short circuit current value in the equipment

2)Total protective device breaking time at maximum short circuit current (Above the possible arc location)

3)Arc working distance to the source

4)Voltage voltage between two phases

E= Incident energy, cal/cm²

F= Maximum short circuit current, kA

V= Voltage voltage between two phases, kV

t_{A}=Arc time, sec.

D= Distance to arc source, inches

### D.2 Doughty Neal Calculation Method

#### D.2.1 Calculation of Released Incident Energy

The following equations can be used to estimate the incident energy produced by a three-phase spring in systems of 600 V and below. The results of these equations may not represent the worst case in all cases. It is essential that equations be used only within the limitations specified in the definitions of the variables shown under the equations. Equations should only be used under qualified engineering supervision.

Parameters required to perform calculations;

**1)**Maximum bolted short circuit current, three-phase short circuit current available in the equipment and minimum fault level at which the arc will sustain itself. (Calculations should be made using the maximum value and then at the lowest fault level where the arc is self-driving. For 480 volt systems, the industry self-driving minimum level is considered to be 38% of the maximum short circuit current. Exposure to the highest incident energy, overcurrent This may occur at low levels where it may take seconds or minutes for the device to boot up.)

**2)**Breaking time at the minimum fault level (above the possible arc location) at which the total protective device will withstand the maximum short-circuit current and arc. p>

**3)**Working distance to the arc source

Typical working distances are as follows;

1)Low voltage (600V and below) Control or Distribution Panels-455mm (18 inches)

2)Low voltage (600 V and below) Switchgear Panel – 610mm (24 inches)

3)Medium voltage (above 600 V) Switchgear Panel – 910mm (36 inches)

#### D.2.1.1 Incident Energy Calculation in Open Air

Arc explosion incident energy in open air is calculated according to the following formula:

E_{MA}= Maximum incident energy, cal/cm²

D_{A}= Distance to arc electrodes, inches (for distances greater than 18 inches)

t_{A}=Arcing time, sec.

F= Short circuit current, kA (for the range 16 kA and 50 kA)

#### D.2.1.2 Incident Energy Calculation in a Closed Box

The estimated incident energy for an arc in a cubic box (20 inches per side, one side open) is given in the equation below. This equation can be applied to arc flashes originating from switchgear, motor control centers, or other electrical equipment enclosures.

E_{MB}= Maximum 20 inch cubic box incident energy, cal/cm²

D_{B}= To arc electrodes distance, inches (for distances greater than 18 inches)

t_{A}=Arcing time, sec.

F= Short circuit current, kA (for the range 16 kA and 50 kA)

### D.3 IEEE 1584 Calculation Method

#### D.3.1 System Limits

An equation to calculate the incident energy can be derived empirically using a curve fitting algorithm combined with a statistical analysis of the raw data. Available for systems with the following limits:

- 0.208 kV to 15 kV, Three Phase
- 50 Hz – 60 Hz
- Available short circuit current between 700 A – 106,000 A
- Conductive gaps from 13 mm to 152 mm

#### D.3.2 Arcing Current

Two separate formulas are used to calculate the three-phase arc current at which the arc may occur, for systems below 1 kV and for systems of 1 kV and above.

The following formula is used for applications with voltage below 1 kV.

Ia= Arcing current, kA

K= For open air = -0.153, For closed box = -0.097

I_{bf}= Bolted short circuit current (Symmetrical rms), kA

V= System Voltage value, kV

G= Conductor gap, mm (Table 3.1)

The following formula is used for applications with voltage below 1 kV;

This formula can be used for both open air and closed boxes.

**Table 3.1 Factors for Equipment and Voltage Classes**

Voltage (kV) | Equipment | Conductor Gap (mm) | Exponential Distance Factor, x |
---|---|---|---|

0.208-1 | Outdoor Switchgear Cont. & Mountain. Panels Cables | 10-40 32 25 13 | 2.000 1.473 1.641 2.000 |

>1-5 | Outdoor Switchgear Cables | 102 13-102 13 | 2.000 0.973 2.000 |

>5-15 | Open Air Switchgear Board Cables | 153 13-153 13 | 2.000 0.973 2.000 |

#### D.3.3 Incident Energy at Working Distance – Empirically Derived Equation

Determine the log10 of the normalized incident energy to determine the incident energy using the empirically derived equation. The following equation is based on normalized data for an arc duration of 0.2 seconds and a distance of 610 mm from the possible arc point to the person:

E_{n}= Incident energy, normalized for time and distance, J/cm²

k_{1} = - 0.792 For open air arc explosions,

= -0.555 For closed box arc explosions.

k_{2} = 0 Ungrounded and high resistance grounded systems

= -0.113 Grounded systems

G= Conductor gap (Table 3.1)

E= Incident energy, J/cm²

C_{f} = 1.0, for voltages above 1 kV,

= 1.5, 1 For voltages of kV and below,

E_{n}= Normalized Incident energy

t= Arc time, seconds

x= Exponential distance factor (Table 3.1)

D= Working distance ,mm

#### D.3.4 Incident Energy at Working Distance – Theoretically Derived Equation

The following theoretically derived equation is applicable where the voltage is above 15 kV or the gap is outside the range:

E= Incident energy, J/cm²

V= System voltage

I_{bf}= Three-phase bolted short circuit current

t= Arc time, seconds

D= Working distance, mm

At voltages above 15 kV, arc fault current and bolted short circuit current are considered equal.

#### D.3.5 Arc Explosion Limit

The arc flash limit is the distance at which a person is likely to receive second-degree burns. It is assumed that the risk of second-degree burns begins when the skin is exposed to energy of 5.0 J/cm² – 1.2 cal/cm².

Empirically derived equation;

Theoretical derived equation;

D_{B}= Distance of arc explosion limit from arc point, mm

C_{f }= 1.0, above 1 kV for voltages,

= 1.5, for voltages of 1 kV and below,

E_{n}= Normalized Incident energy

t= Arc time, seconds

x= Exponential distance factor ( Table 3.1)

E_{B}= Incident energy at the arc explosion limit, J/cm² (Normally 5 J/cm²)

V= System Voltage, kV

I_{ bf}= Three-phase bolted short circuit current