Incident Energy and Arc Flash Boundary Calculation per IEEE Std 1584-2018

Thermodynamic and Electrophysical Foundations of the Electrical Arc in Power Systems

An arc flash represents one of the most violent fault manifestations in power engineering. It consists of a disruptive electrical discharge through an ionized dielectric medium (gas or air) driven by a potential difference sufficient to overcome the dielectric strength of the medium or initiated by a loss of insulation induced by contamination, transient overvoltages, mechanical failure, or human error during energized switching operations. Unlike a bolted short circuit, where the dissipated energy is dominated by the impedance of the conductors and the source, an arc flash fault converts electrical energy into thermal, luminous, acoustic, and mechanical energy through the formation of a high-energy-density plasma.

The physics of plasma arc is governed by thermal and collisional ionization. When the local current density exceeds the critical thresholds of thermionic and electric-field emission, air molecules ($N _2$, $O _2$) dissociate their diatomic bonds and lose electrons, reaching the plasma state. Saha's ionization equation describes the degree of ionization $\alpha$ of the gas as a function of absolute temperature $T$ and partial electron pressure $P_e$:

Where $m_e$ is the electron mass, $k_B$ is the Boltzmann constant, $h$ is Planck's constant, and $\mathcal{E}_i$ is the ionization potential characteristic of the gas mixture. In the core of the electric arc, temperatures reach ranges between $10\,000 K$ and $20\,000 K$ ($\approx 18\,000\,^\circ C$), frequently exceeding the temperature of the sun's surface. At these extreme temperatures, energy transfer to the surrounding environment occurs predominantly through non-linear black-body radiation, governed by the Stefan-Boltzmann law corrected by the spectral emissivity of the plasma $\epsilon_p$:

Where $\sigma = 5.670374 \times 10^{-8} W/(m ^2\cdot K ^4)$. This radiation encompasses the far-ultraviolet (UV-C), visible, and near-infrared spectrums, causing instantaneous third-degree thermal burns to human skin and actinic keratoconjunctivitis in the ocular system without appropriate personal protective equipment (PPE).

Simultaneously with the thermal phenomenon, the volatilization of electrode material (typically copper or aluminum) generates an explosive volumetric expansion. Solid copper has a density of $8\,960 kg/m ^3$; upon vaporizing at arc temperatures, the volumetric expansion ratio reaches a factor of approximately 1:67,000. This sudden phase transition vaporizes kilograms of metal in milliseconds, injecting liquefied molten metal and copper vapor into the plasma. The volume change and rapid temperature rise generate an acoustic and mechanical overpressure wave (arc blast) whose local peak pressure $Ppeak$ is dynamically related to the rate of rise of the arc current $diarc/dt$ and the dissipated energy per unit volume $Evol$:

Where $\gamma$ is the adiabatic expansion coefficient of the ionized gas and $Venclosure$ is the internal volume of the enclosure confining the arc. The resulting overpressure can exceed $100 kPa$ ($\approx 10 t/m ^2$), collapsing switchgear structures, projecting shrapnel, exceeding the tympanic membrane rupture threshold ($\approx 35 - 50 kPa$), and causing severe mechanical trauma to exposed personnel.

The hydrodynamic behavior of the plasma is strongly determined by Lorentz forces ($\mathbf{J} \times \mathbf{B}$). The interaction between the three-dimensional current density $\mathbf{J}$ and the self-induced magnetic field $\mathbf{B}$ generates directional plasma jets. Depending on the physical orientation of the electrodes within the metal enclosure, these forces propel the plasma column directly toward the front of the compartment, thermally coupling the convective-radiative flux toward the operator, or direct it redundantly/divergently toward the sides or rear.

Normative Evolution and Mathematical Architecture of IEEE Std 1584-2018

The IEEE Std 1584-2002 standard established the first widely accepted analytical methodology for predicting arc current and incident energy. However, it was based on a limited empirical model derived from a reduced set of laboratory tests that accounted for only two basic geometric configurations: electrodes in open air (Open Air) and vertically oriented electrodes inside a metallic enclosure (In Box). This simplification proved inadequate for representing the actual geometric topology of modern low- and medium-voltage switchgear, significantly overestimating or underestimating the actual incident energy depending on the ejection direction of the plasma.

The revision IEEE Std 1584-2018 constitutes a landmark in forensic engineering and experimental research following more than a decade of development and the execution of over 2,000 controlled tests. It incorporates five standardized electrode configurations and a continuous mathematical model based on multi-variable polynomials that adjust energy according to the actual physical dimensions of the enclosure, conductor gap, working distance, and nominal system voltage.

Validity Limits and Boundary Conditions

The empirical mathematical model of IEEE Std 1584-2018 is strictly applicable under the following operational and physical topology boundary conditions:

• Nominal line-to-line voltage ($Vsystem$): Three-phase alternating current, from $208 V$ to $15\,000 V$.
• System frequency ($f$): $50 Hz$ or $60 Hz$.
• Three-phase bolted short-circuit current ($Ibf$):
  • For voltages between $208 V$ and $600 V$: $0.5 kA \le Ibf \le 106 kA$.
  • For voltages between $601 V$ and $15\,000 V$: $0.2 kA \le Ibf \le 50 kA$.
• Electrode/busbar spacing ($G$):
  • For voltages from $208 V$ to $600 V$: $6.35 mm$ to $76.2 mm$ ($0.25 in$ to $3.0 in$).
  • For voltages from $601 V$ to $15\,000 V$: $19.05 mm$ to $254 mm$ ($0.75 in$ to $10.0 in$).
• Working distance ($D$): Greater than or equal to $305 mm$ ($\ge 12 in$).
• Enclosure dimensions:
  • Maximum Height or Width: $1\,219.2 mm$ ($48 in$).
  • Maximum Depth: $1\,219.2 mm$ ($48 in$).
  • Front opening area: Unconfined or fitted within the empirical size model boundaries.

Mathematical Formulations of Arcing Current ($Iarc$)

Unlike the 2002 model which utilized a direct logarithmic equation, IEEE Std 1584-2018 evaluates the three-phase RMS arcing current ($Iarc$) at three intermediate reference voltage levels: $600 V$, $2700 V$, and $14\,300 V$. For any voltage within the application range, a non-linear polynomial interpolation based on the source's symmetrical bolted short-circuit current ($Ibf$) is executed.

The general equation to determine the arcing current at a specific reference voltage level ($Vref \in \{600, 2700, 14300\} V$) is defined on a logarithmic scale by:

Where coefficients $k_0$ through $k_9$ vary depending on the selected electrode configuration (VCB, VCBB, HCB, VOC, HOA). Once the arcing currents at the three reference levels ($I_{arc,600}$, $I_{arc,2700}$, and $I_{arc,14300}$) are calculated, the final arcing current at the nominal system voltage $Vsystem$ (in $kV$) is obtained via interpolation:

For systems with $0.208 kV \le Vsystem \le 0.600 kV$:

For systems with $0.600 kV < Vsystem \le 2.700 kV$:

For systems with $2.700 kV < Vsystem \le 14.300 kV$:

Arcing Current Variation Factor and Minimum Arcing Current ($I_{arc\_min}$)

A fundamental change in the 2018 standard is the elimination of the fixed $15\%$ arcing current reduction rule prescribed by the 2002 edition to check the operating speed of protective devices in their inverse zone. IEEE Std 1584-2018 introduces the concept of the Arcing Current Variation Factor ($VarCF$), which analytically calculates the expected minimum arcing current ($I_{arc\_min}$) based on plasma impedance dynamics and phase variations during the fault:

This reduced current $I_{arc\_min}$ is highly critical. In many systems with time-dependent overcurrent relays (IEEE/IEC inverse-time curves) or circuit breakers operating in their thermal-magnetic region, a reduced arcing current can shift the device operating point to significantly longer clearing times ($Tclearing$), dramatically increasing the total accumulated incident energy.

Incident Energy Calculation Algorithm and Arc Flash Boundary

Incident energy ($E$) is defined as the total amount of radiant and injected thermal energy per unit area at a specified working distance ($D$) from the arc source. Its standardized unit in safety engineering is calories per square centimeter ($cal/cm ^2$) or Joules per square centimeter ($1 cal/cm ^2 = 4.184 J/cm ^2$).

Incident Energy Normalization and Enclosure Size Factor

The calculated incident energy for a baseline arcing time of $0.2 seconds$ ($12 cycles$ at $60 Hz$) and a standard distance of $610 mm$ ($24 inches$), denoted as intermediate or normalized energy ($E_{1000,Vref}$), is computed at the three reference voltages ($0.6 kV$, $2.7 kV$, and $14.3 kV$):

Where $b_0 \dots b_5$ are empirical constants dependent on electrode configuration, and $Ese$ represents the geometric factor corrected for enclosure size (Enclosure Size Effect). IEEE Std 1584-2018 parameterizes the enclosure based on its height ($H$), width ($W$), and depth ($Dp$). If the dimensions differ from standard baseline reference enclosures, an equivalent size and enclosure correction coefficient ($CF$) are calculated:

The factor $CF$ corrects for energy reflected by the internal walls of the metallic box toward the front opening. For small enclosures, internal reflections concentrate radiation flux and increase $CF > 1.0$, whereas in large-volume structures, the plasma expands internally, reducing the frontal concentration factor.

Final Incident Energy Equation

By interpolating energy at the nominal system voltage $Vsystem$ and adjusting for the protection device's actual clearing time ($T$, in seconds) and the worker's actual working distance ($D$, in $mm$), the final incident energy $E$ is obtained:

Where $C_f$ is the voltage correction factor ($C_f = 1.5$ for $Vsystem \le 1.0 kV$ and $C_f = 1.0$ for $Vsystem > 1.0 kV$), and $x$ is the working distance exponent, which is not a fixed constant of value $2.0$ (as in the inverse-square law for point sources), but a continuous function computed from enclosure and electrode geometric parameters:

Derivation of the Arc Flash Boundary ($AFB$)

The Arc Flash Boundary ($AFB$) is defined as the physical distance from the potential arc point where transmitted incident energy attenuates to precisely the threshold energy for the onset of a second-degree burn on human skin, standardized by NFPA 70E and IEEE 1584 as $Eth = 1.2 cal/cm ^2$ ($5.024 J/cm ^2$).

By analytically solving for distance $D$ in the general incident energy equation and setting $E = Eth$, the rigorous mathematical expression for the $AFB$ boundary (expressed in $mm$) is derived:

Any unqualified individual or personnel lacking appropriate thermal PPE must remain outside this boundary radius $DAFB$ while equipment is energized and operating under fault-prone conditions.

Comparative Thermal and Geometric Analysis: Electrode Configurations

The inclusion of five geometric electrode configurations in IEEE Std 1584-2018 eliminated estimation biases present in the prior version. Relative busbar orientation and the presence of insulating barriers radically alter plasma current emission vectors caused by magnetic forces as well as radiative patterns.

Configuration	Geometric and Physical Description	Plasma Mechanism and Force Vector ($\mathbf{J} \times \mathbf{B}$)	Relative Incident Energy Multiplier	Typical Application in Industrial Equipment
VCB	Vertical Conductors in Box. Vertical electrodes terminating inside a metallic box open at the front.	The arc travels toward the lower tips of the electrodes. Electromagnetic force drives plasma toward the back of the enclosure, which bounces and exits diffusely toward the front.	$1.0\times$ (Baseline)	Medium-Voltage Metal-Clad switchgear, air circuit breakers in main distribution switchboards.
VCBB	Vertical Conductors with Insulated Barrier in Box. Vertical electrodes terminating on a non-conductive insulating barrier.	The arc attempts to move downward but strikes the insulating barrier. This forces plasma to bow outward, directing the thermal-magnetic blast straight toward the front door.	$1.25\times - 1.80\times$	Low-voltage Motor Control Centers (MCCs), load-break switches with phase/back barriers, soft starters.
HCB	Horizontal Conductors in Box. Horizontal electrodes placed inside a metallic box pointing toward the opening.	Current in parallel horizontal bars creates a Lorentz force ($\mathbf{J} \times \mathbf{B}$) that ejects the plasma column directly toward the front, acting as a "thermal cannon."	$2.00\times - 3.50\times$	Main horizontal distribution busbars, transformer-to-switchgear bus ties, distribution busways.
VOC	Vertical Conductors in Open Air. Vertical electrodes arranged in open air without a confining enclosure.	Plasma expands freely in three dimensions. Heat dissipates spherically, reducing radiation density per unit area.	$0.20\times - 0.45\times$	Overhead distribution lines, open-air substation switchyards, bare busbars without enclosures.
HOA	Horizontal Conductors in Open Air. Horizontal electrodes arranged in open air.	Magnetic forces eject plasma longitudinally along the electrode axis in free space. Transmitted energy is higher than VOC but lacks box reflection.	$0.40\times - 0.75\times$	Outdoor horizontal disconnect switches, high-voltage transformer bushings, exposed cable terminations.

As deduced from the comparative analysis, the HCB configuration represents the most severe fault scenario within enclosed installations. A design that fails to account for horizontal bar orientation in a switchboard can underestimate incident energy by over $200\%$ if a VCB topology is erroneously assumed.

Forensic Analysis of Electromechanical Faults and Dielectric Impact

To understand the origin of arc flashes in power installations, forensic engineering analyzes fault sequences that transform a safe operating state into a catastrophic thermal event. A typical destructive fault event in medium-voltage switchgear ($13.8 kV$) or motor control centers ($480 V$) transitions through well-defined physical phases:

Insulation Degradation Mechanism and Electrical Tracking

The most frequent root cause of unintended internal arcs is the formation of surface conduction paths on organic or polymeric insulation (epoxy, glass-reinforced polyester). In industrial environments characterized by high relative humidity, saline moisture contamination, or conductive dust deposits (carbon, metallic filings), a partial ionization process known as electrical tracking initiates. Micro-leakage currents dry and carbonize insulation material, leaving a graphite track of high conductivity. Upon the occurrence of a switching surge or atmospheric discharge, the carbonized path collapses dielectrically, triggering the initial spark.

Once the interstitial air gap between phases or phase-to-ground is ionized, arc resistance drops from megohms down to a fraction of an ohm ($Rarc \approx 0.01 - 0.1 \Omega$), establishing a three-phase arcing current.

Thermomechanical Destruction Sequence in Switchgear

1. Sub-transient (0 to 10 ms): The arc establishes at the point of primary insulation breakdown. Current reaches its asymmetrical peak value ($Ipk$). Rapid air heating increases enclosure internal pressure at rates of $dP/dt > 50 kPa/ms$. Sheet-metal enclosure panels experience elastic and plastic deformation; if the switchgear is non-arc-resistant (per IEEE C37.20.7), front doors or rear covers fail due to bolt shearing, blasting direct incandescent gases outward.
2. Volatilization Transient (10 to 50 ms): Copper vapor at $25\,000 K$ saturates the enclosure volume. Adjacent solid insulation undergoes pyrolysis, releasing hydrocarbon combustible gases that feed the oxidizing mixture. Parallel busbars experience massive electrodynamic forces ($F \propto Iarc^2 / d$), flexing and shattering insulating supports, transforming original single-phase-to-ground faults into high-power three-phase arcs.
3. Steady-State Thermal Destruction (> 50 ms): Continuous radiation melts supporting copper, steel, and bronze structures. Metallic components drip in a liquid state. If overcurrent protection fails to clear the source due to current transformer (CT) saturation or improper breaker clearing delays, the switchboard suffers total destruction from widespread fire and loss of physical compartmentation integrity.

Protection Clearing Failure Pathologies

A severe error in arc flash hazard evaluation is assuming that clearing time ($T$) equals the nominal instantaneous relay setting. Multiple forensic factors cause protection system failures in rapidly interrupting the arc:

• Current Transformer (CT) Saturation: The high DC aperiodic component at short-circuit inception, combined with a high system $X/R$ ratio, can drive the CT iron core into deep saturation. Secondary current supplied to the relay becomes severely distorted and attenuated in RMS magnitude, preventing instantaneous element ($50$) pick-up. Consequently, the fault is cleared by the time-delay unit ($51$), multiplying arcing time by a factor of $10\times$ to $50\times$.
• Inadequate Calculation with Minimum Arcing Current ($I_{arc\_min}$): If the instantaneous setting of a Molded Case Circuit Breaker (MCCB) is calibrated near the bolted short-circuit current ($Ibf$), actual arcing current ($Iarc$ or $I_{arc\_min}$)—being lower due to plasma impedance—will fail to cross the magnetic trip threshold. The breaker clears the fault in its thermal region (bimetallic curve), extending clearing time from $16 ms$ (1 cycle) to several seconds, escalating incident energy to lethal levels ($E > 40 cal/cm ^2$).

Advanced Mitigation Strategies and Engineering Design

Incident energy mitigation in electrical installations revolves around two main axes: reducing arcing duration ($T$) and reducing or limiting short-circuit current ($Ibf$ / $Iarc$). NFPA 70E enforces a hierarchy of risk controls where physical hazard elimination (working under verified de-energized conditions) is top priority, followed by engineering controls.

Arc Duration Reduction Systems

Because incident energy is directly proportional to exposure time ($E \propto T$), modern protection technology focuses on eliminating intentional selective coordination delays when an open arc fault occurs.

Optical Arc Flash Protection Systems (Arc Flash Relays)

These systems utilize point fiber-optic sensors or distributed bare fiber cables installed inside switchgear compartments, connected to an ultra-fast relay (e.g., IEC 60255 standard). The relay evaluates a dual-criterion logic: simultaneous detection of a high-intensity light flash (photodiodes) and an overcurrent threshold exceeded via a fast CT or Rogowski coil. When both conditions are met, the relay outputs a solid-state trip signal (IGBT/Triac) to the circuit breaker trip coil in under $1 ms$ to $2 ms$, limiting total clearing time strictly to breaker mechanical opening speed ($30 ms - 50 ms$).

Zone Selective Interlocking (ZSI)

In ZSI schemes, electronic trip units or relays of downstream and upstream circuit breakers communicate over a dedicated data bus or discrete signals. When a fault occurs on the main switchgear bus, downstream devices do not sense short-circuit current and send no restraint signal upstream. The main upstream breaker interprets the lack of restraint as a fault inside its own direct zone, instantly bypassing its short-delay time setting ($SDT$) and tripping without delay ($t < 50 ms$), thereby protecting the switchboard.

Arc Reduction Maintenance Systems (ARMS / Maintenance Switch)

An Arc Reduction Maintenance System (ARMS) temporarily alters the protection relay trip curve via a physical selector switch or remote signal activated by operators prior to performing maintenance work. Upon activating ARMS mode, time-delayed functions ($I^2 t$ curves) are disabled, enabling a non-delayed analog instantaneous trip set below the calculated minimum arcing current ($I_{arc\_min}$). This ensures that any arc initiated by operator error is cleared in the fastest possible mechanical time.

Current Limitation and Physical System Modification

• Current-Limiting Fuses (CLF): High-interrupting-capacity fuses (Class J, RK1, L, E) contain silver elements surrounded by high-purity quartz sand. Under severe faults, the fuse operates within the first quarter-cycle (less than $4 ms$), melting the element and extinguishing the arc in the quartz, attenuating peak current to a lower let-through value ($Ip$). Incident energy produced under a current-limiting fuse operating in its current-limiting range is negligible ($E < 1.2 cal/cm ^2$).
• High-Resistance Grounding (HRG): In low- and medium-voltage industrial power systems, inserting a resistor between transformer neutral and ground limits single-phase ground-fault current to typically between $1 A$ and $10 A$. Given that $95\%$ of arc flashes initiate as phase-to-ground faults, an HRG system prevents the fault from escalating into a cataclysmic three-phase arc, allowing continuous operation and controlled fault location without an instantaneous trip.
• Arc-Resistant Switchgear (IEEE C37.20.7): Structures designed with mechanical relief plenums and discharge ducts that direct the overpressure blast wave and incandescent gases away from occupied spaces (e.g., out through the electrical room roof). They comply with Type 1, Type 2 accessibility ratings (protection around front, sides, and rear perimeters) and Type 2B or 2C sub-classifications (maintaining protection even with control or instrument compartments open).

Practical Implementation and Simulation in Vexten Suite

Modern power system engineering workflows require the integration of high-precision multiphysics simulation tools for arc flash calculations. The Vexten Suite platform consolidates short-circuit analysis (IEEE 141 / IEC 60909), cable thermal capacity (IEC 60287 / NEC 310), and a specialized arc flash module under the comprehensive architecture of IEEE Std 1584-2018 within a unified numerical calculation environment.

Systematic Calculation Methodology in Vexten Suite

1. Power Network Modeling and Short-Circuit Simulation: Vexten Suite constructs the system nodal admittance matrix ($\mathbf{Y}_{bus}$) to compute three-phase symmetrical and asymmetrical bolted short-circuit currents ($Ibf$) across all buses and nodes, factoring in dynamic contributions from induction motors and synchronous machines according to IEEE C37.010 / IEC 60909.
2. Conductor Verification and Thermal Derating Factors: Power cables are validated using the IEC 60287 / NEC 310 calculation engine, ensuring harmonic and grouping derating maintain cable impedance within true operational margins, directly impacting fault loop impedance.
3. Clearing Time Extraction from TCC Curves: The protection coordination module in Vexten Suite automatically evaluates Time-Current Characteristic (TCC) curves for each upstream protective device. The software intersects both nominal arcing current ($Iarc$) and minimum arcing current ($I_{arc\_min}$) with device tolerance bands to deterministically extract exact clearing times $Tnominal$ and $Tmax$.
4. Execution of IEEE 1584-2018 Numerical Engine: Vexten Suite executes iterative evaluation across the five electrode configurations, processes enclosure physical dimensions ($H, W, D_p$), determines distance exponents $x$ and enclosure size correction factor $CF$, and generates the final Incident Energy ($E$) matrix and Arc Flash Boundary ($AFB$).

Numerical Case Study and Comparative Simulation

Below is the rigorous analytical and numerical development for a critical node in a low-voltage industrial distribution switchboard simulated in Vexten Suite.

System Input Parameters:

• Nominal system voltage ($Vsystem$): $0.480 kV$ ($480 V$, $60 Hz$).
• Three-phase bolted short-circuit current ($Ibf$): $35.0 kA$.
• Busbar/electrode spacing ($G$): $25.4 mm$ ($1.0 in$).
• Nominal working distance ($D$): $457.2 mm$ ($18.0 in$).
• Actual enclosure dimensions: Height $H = 508.0 mm$ ($20 in$), Width $W = 508.0 mm$ ($20 in$), Depth $D_p = 508.0 mm$ ($20 in$).
• Burn threshold energy level ($Eth$): $1.2 cal/cm ^2$.

Evaluated Simulation Scenarios:

• Case 1: VCB electrode configuration with conventional overcurrent protection set with a short time delay: $T = 0.35 s$ ($21 cycles$).
• Case 2: HCB electrode configuration (horizontal busbars) maintaining conventional protection: $T = 0.35 s$.
• Case 3: HCB electrode configuration optimized by implementing Vexten Suite's optical arc protection module: $T = 0.05 s$ ($3 cycles$).

Numerical Equation Development in Vexten Suite:

Step 1: Calculation of Arcing Current ($Iarc$) at 600 V Reference:

Utilizing IEEE 1584-2018 standardized polynomial coefficients for VCB and HCB configurations at $Ibf = 35.0 kA$ and $G = 25.4 mm$:

For VCB configuration:

For HCB configuration:

Applying voltage correction to $Vsystem = 0.480 kV$:

Step 2: Evaluation of Enclosure Size Factor ($CF$) and Exponent ($x$):

With enclosure dimensions ($508 \times 508 \times 508 mm$), the module computes a box reflection concentration factor $CF \approx 1.18$ (as the enclosure is smaller than standard reference baseline dimensions), and a distance exponent $x \approx 1.64$ for VCB and $x \approx 2.05$ for HCB.

Step 3: Calculation of Incident Energy ($E$) and Arc Flash Boundary ($AFB$):

Evaluation Case 1 (VCB, T = 0.35 s):

Evaluation Case 2 (HCB, T = 0.35 s):

Evaluation Case 3 (HCB with Ultra-Fast Optical Protection, T = 0.05 s):

Comparative Matrix of Processed Results in Vexten Suite:

Calculated Parameter	Case 1: VCB ($T = 0.35 s$)	Case 2: HCB ($T = 0.35 s$)	Case 3: HCB + Optical Protection ($T = 0.05 s$)
Arcing Current ($Iarc$)	$27.05 kA$	$28.41 kA$	$28.41 kA$
Min. Arcing Current ($I_{arc\_min}$)	$23.26 kA$	$24.15 kA$	$24.15 kA$
Enclosure Size Factor ($CF$)	$1.18$	$1.18$	$1.18$
Distance Exponents ($x$)	$1.64$	$2.05$	$2.05$
Incident Energy ($E$)	$18.64 cal/cm ^2$	$45.32 cal/cm ^2$	$6.47 cal/cm ^2$
Arc Flash Boundary ($AFB$)	$2.43 m$ ($95.6 in$)	$3.15 m$ ($124.0 in$)	$1.21 m$ ($47.7 in$)
PPE Category (NFPA 70E)	Category 3 ($25 cal/cm ^2$)	Extreme Hazard ($> 40 cal/cm ^2$)	Category 2 ($8 cal/cm ^2$)

The numerical results quantitatively demonstrate the extreme sensitivity of the IEEE Std 1584-2018 model to electrode configuration and protection clearing times:

1. Transitioning from vertical (VCB) to horizontal (HCB) configuration for the same tripping time of $0.35 s$ increased incident energy from $18.64 cal/cm ^2$ to $45.32 cal/cm ^2$ (a $143\%$ increase), crossing the critical threshold of $40 cal/cm ^2$. Above this value, NFPA 70E considers the condition an unacceptable risk for energized work due to the lethal hazard of mechanical pressure waves (arc blast).
2. Implementing the mitigation analyzed in Vexten Suite via optical arc flash relays (Case 3), reducing clearing time to $0.05 s$ ($50 ms$), drastically reduced incident energy in the horizontal configuration from $45.32 cal/cm ^2$ down to just $6.47 cal/cm ^2$. This intervention reduced the required PPE category from non-permitted/extreme to Category 2, safeguarding operational personnel and engineering staff within the facility.