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Procedure for IEEE 1584 based arc flash calculations

Normalized incident energy can be found using the equation below:

*lg E*_{n} = K_{1} + K_{2} + 1.081 * lgI_{a} + 0.0011 * G

Equation 1

where,

*E*_{n} - incident energy in J/cm^{2} normalized for time and distance. The equation above is based on data normalized for a distance from the possible arc point to the person of 610 mm. and an arcing time of 0.2 sec

*K*_{1} = -0.792 for open configurations, and is -0.555 for box configurations / enclosed equipment

*K*_{2} = 0 for ungrounded and high resistance grounded systems, and equals -0.113 for grounded systems

*G* - gap between conductors in millimeters

*I*_{a} - predicted three phase arcing current in kA. It is found by using Equations 2 a) or b) so the operating time for protective devices can be determined.

For 1000V and lower systems:

*lgI*_{a} = K + 0.662 * lg I_{bf} + 0.0966 * V + 0.000526 * G + 0.5588 * V * lgI_{bf} - 0.00304 * G * lgI_{bf}

Equation 2 a

where,

*lg* - is logarithm base 10 (log_{10})

*I*_{a} - arcing current in kA

*K* - equals -0.153 for open configurations. and -0.097 for box configurations

*I*_{bf} - bolted fault current for three phase faults in kA symmetrical rms

*V* - system voltage in kV

*G* - gap between conductors in millimeters.

Solve

*lgI*_{a} = 0.00402 + 0.983 * lg I_{bf}

Equation 2 b

for applications with a system voltage ranging from 1 up to 15kV.

Incident energy can be found using the equation below:

*E = 4.184 * C*_{f} * E_{n} * (t / 0.2) * (610^{x}/D^{x})

Equation 3

where,

*E* - incident energy exposure in J/cm^{2}

*C*_{f} - calculation factor equal to 1.0 for voltages above 1 kV, and 1.5 for voltages below 1 kV

*E*_{n} - normalized incident energy in J/cm2 as calculated by Equation 1 above

*t* - arcing time in seconds

*D* - distance from possible arcing point to the person in millimeters

*x* - distance exponent.

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, and incident energy can be determined using the equation below:

*E = 2.142 * 10*^{6} * V * I_{bf} * (t / D^{2})

Equation 4

where,

*E* is incident energy in J/cm^{2}

*V* is system voltage in kV

*t* is arcing time in seconds

*D* is distance from possible arc point to person in mm

*I*_{bf} is bolted fault current.

For the IEEE Std 1584-2002 empirically derived model, arc flash boundary is calculated using the equation below:

*D*_{B} = [4.184 * C_{f} * E_{n} * (t / 0.2) * (610^{x}/E_{B})]^{1/x}

Equation 5

For the Lee method:

*D*_{B} = [2.142 * 10^{6} * V * I_{bf} * (t / E_{B})]^{1/2}

Equation 6

where,

*D*_{B} - distance of the boundary from the arc point in millimeters

*C*_{f} - calculation factor equal to 1.0 for voltages above 1 kV, and 1.5 for voltages below 1 kV

*E*_{n} - normalized incident energy in J/cm^{2} as calculated by Equation 1

*E*_{B} - incident energy in J/cm^{2} at the boundary distance. It is usually set at 5 J/cm^{2} (1.2 cal/cm^{2} ) for bare skin, or at the rating of proposed personal protection equipment.

*I*_{bf} - bolted fault current for three phase faults in kA symmetrical rms

*t* - arcing time in seconds

*x* - distance exponent

*Ibf* - bolted fault current.