Instant Arc Flash Clearing Time Calculator: Compute from Protective Device Settings & TCC

This article presents an instant arc flash clearing time calculator derived from protective device settings.

Methodology computes Time-Current Characteristic intersections, using TCC curves and device trip thresholds precisely analyzed here.

Instant Arc Flash Clearing Time Calculator from Protective Device TCC Settings

Arcing fault current at protective device (kA)

Inverse-time pickup setting (A)

Time dial / time multiplier setting (TMS) (pu)

Inverse-time curve family (IEC 60255) IEC normal inverse IEC very inverse IEC extremely inverse

Advanced options

Instantaneous pickup setting (kA)

Instantaneous total clearing time (ms)

Breaker interrupting time in inverse region (ms)

Safety margin on time (%)

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Enter fault current and basic protective device settings to obtain the clearing time.

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Calculation method and formulas

This calculator estimates the total arc flash clearing time based on IEC inverse-time overcurrent characteristics and, optionally, an instantaneous trip region.

• Convert arcing fault current to amperes:
  Ifc (A) = Ifc (kA) × 1000
• Current multiple of pickup:
  M = Ifc (A) / Ip (A) (dimensionless)
• Inverse-time relay operating time (IEC 60255, seconds):
  • IEC normal inverse: t_relay = TMS × 0.14 / (M^0.02 − 1)
  • IEC very inverse: t_relay = TMS × 13.5 / (M − 1)
  • IEC extremely inverse: t_relay = TMS × 80 / (M^2 − 1)
• Instantaneous region (if enabled and Ifc ≥ Iinst):
  t_total = t_inst,total (given in milliseconds and converted to seconds)
• Total clearing time in inverse region:
  t_total = t_relay + t_breaker
• Breaker interrupting time:
  t_breaker = specified breaker interrupting time (ms) / 1000
• Optional safety margin:
  t_adj = t_total × (1 + Margin% / 100)

The reported arc flash clearing time corresponds to t_adj (or t_total if margin is zero), expressed both in milliseconds and seconds.

Parameter	Typical range	Engineering note
Arcing fault current at LV breaker	4–65 kA	Depends on system short-circuit level, conductor length and arc impedance.
Inverse-time pickup Ip	0.5–1.0 × CT secondary (e.g., 400–1200 A)	Often coordinated slightly above maximum load and motor inrush.
Time dial / TMS	0.05–1.0 pu	Used to coordinate feeder, transformer and bus protection TCCs.
Breaker interrupting time	40–80 ms	Modern LV molded-case and power breakers typically interrupt within 3–5 cycles.
Instantaneous pickup	8–12 × In	Set high enough to avoid nuisance trips while limiting arc flash energy.

Technical FAQ

Does the calculator include breaker mechanical opening time?

Yes. In inverse-time operation the breaker interrupting time is added to the relay operating time. If no value is entered, a default of 50 ms is used. In instantaneous mode, you directly provide the total clearing time including mechanical operation.

When is the instantaneous region used instead of the inverse-time curve?

If both an instantaneous pickup and a corresponding total clearing time are specified, and the arcing fault current is equal to or above the instantaneous pickup, the calculator assumes instantaneous tripping and uses the provided instantaneous clearing time instead of the IEC inverse-time formula.

What happens if the fault current is close to or below the pickup setting?

If the calculated current multiple M is less than or equal to 1 (fault current not above pickup), the inverse-time element will not operate reliably, and the calculator returns an error. For very small margins above pickup the IEC formulas become numerically unstable and an error is also reported.

Can these results be used directly for arc flash labeling?

The clearing time estimation is suitable for arc flash studies, but full incident energy and PPE level calculations require additional parameters (working distance, enclosure type, system voltage, etc.) and should follow applicable standards such as IEEE 1584 or NFPA 70E.

Arc flash clearing time fundamentals and scope

Arc flash clearing time is the elapsed period from arc initiation to fault interruption by the protective device. It is the principal parameter controlling incident energy, equipment damage, and worker hazard. Calculating clearing time requires accurate device Time-Current Characteristic (TCC) data, the available fault current at the fault location, and any coordination delays introduced by multiple devices. This article provides a rigorous method to compute instantaneous and inverse-time clearing times from protective device settings, including formulas, variable explanations, tables of typical values, and worked examples. Critical distinctions must be observed:

• Bolted-fault current (I_bf) is the prospective short-circuit current ignoring arc impedance.
• Arcing current (I_arc) is the empirical current that actually flows in an arc and is typically lower than I_bf; IEEE 1584 provides methods to estimate it.
• Clearing time (t_clear) is the time at which the protective device removes the fault — for arc flash calculations this is the arc duration used to compute incident energy.

Mathematical representation of Time-Current Characteristics (TCC)

TCCs are commonly modeled either by piecewise manufacturer curves or by parameterized functional forms suitable for analytic computation. Two widely used functional prototypes are:

1) Inverse power-law model (suitable approximation for many fuses and breakers):

t = A * (I / I_p)^B + C

2) Inverse-relay-style model (common for electrical relays with time multiplier settings):

t = TMS * K / ( (I / I_pickup)^P - 1 )

Explanation of variables and typical ranges:

• t — clearing time (seconds).
• I — fault current magnitude used for the device curve (A). This can be I_arc or I_bf depending on method.
• I_p — reference current (A). For the inverse power-law it is commonly the device pickup or rated current.
• I_pickup — pickup current setting for the relay or trip element (A).
• A, B, C — empirical coefficients to fit the manufacturer TCC into a simple analytic expression. Typical example values (for illustrative modeling only):
• MCCB thermal-magnetic approximate fit: A ≈ 0.2, B ≈ -1.2, C ≈ 0.01.
• Cartridge fuse (highly inverse) approximate fit: A ≈ 1.5, B ≈ -3.0, C ≈ 0.0.
• TMS — Time Multiplier Setting (dimensionless) for adjustable electromechanical/electronic relays.
• K, P — curve constants depending on curve family (standard inverse, very inverse, extremely inverse). Example nominals for modeling:
• Standard inverse: K ≈ 0.14, P ≈ 0.02 (use only as manufacturer-supplied equivalent).
• Very inverse: K ≈ 13.5, P ≈ 1.0.
• Extremely inverse: K ≈ 80.0, P ≈ 2.0.

Note: The numeric coefficients provided above are illustrative approximations used for worked examples. For any safety-critical calculation use manufacturer TCC data or applicable standards (IEC/ANSI/IEEE) and verified modeling.

Relationship between available current and TCC input

Two commonly used choices for the independent current in TCC evaluation are:

1. I_bf — Bolted-fault current (prospective short-circuit current). This gives a conservative (shorter) computed clearing time if the device reacts primarily to magnitude rather than arc impedance effects. Many protective devices operate on measured current and thus respond to the arcing current actually flowing in the system.
2. I_arc — Arcing current calculated by empirical methods (IEEE 1584-2018) which accounts for arc impedance, enclosure, gap, and voltage. Using I_arc yields least-conservative incident energy estimates for arc energy output but is more accurate for the physical arc survival time.

Step-by-step algorithm to compute arc flash clearing time from protective device TCC

Follow these deterministic steps for a reproducible calculation:

1. Determine system single-line topology and fault location to compute short-circuit current using network impedances (use IEC 60909 or equivalent method).
2. Compute prospective bolted-fault current I_bf at the fault point.
3. Estimate arcing current I_arc if using IEEE 1584 methodology or retain I_bf if the protective device responds primarily to raw current magnitude and the standard for arc current estimation is not applied.
4. Obtain protective device TCC data (manufacturer curve or numeric table). Identify pickup settings, time multiplier, and instantaneous/short-time elements.
5. Model TCC as an analytic function or use tabular interpolation to find the time t such that the device curve predicts operation at I (I = I_arc or I_bf depending on choice).
6. For multiple upstream protection devices, compute the device expected to operate first (the lowest t at the target fault current) — this is the clearing device. If selective coordination is required, account for clearance by upstream/ downstream device cooperation and possible time delays.
7. Report t_clear = computed clearing time. Use this duration in arc flash incident energy computations and PPE selection per NFPA 70E and IEEE 1584.

Mathematical inversion and root finding

For analytic TCC forms such as t = A*(I/I_p)^B + C, inversion algebraically gives:

I = I_p * ( (t - C) / A )^1/B

However, typical use cases require solving for t given I, which is direct evaluation. For relay-style models where t appears on both sides implicitly (rare), numerical root-finding (Newton-Raphson or bisection) may be used. For tabular manufacturer TCCs the common approach is monotonic interpolation on log-log scale.

Extensive tables of common device settings and empirical values

Practical techniques for implementing an instant arc flash clearing time calculator

Key implementation considerations when coding or writing a calculation tool:

• Curve data ingestion: allow manufacturer TCC tables (time vs current) and analytic coefficients.
• Interpolation: implement log-log interpolation to preserve slope characteristics across decades.
• Arcing current vs bolted current: include an option to compute I_arc from I_bf per IEEE 1584 or to use I_bf directly.
• Multiple protection evaluation: compute clearing times for all protective devices that could clear the fault and select the earliest time.
• Instantaneous/short-time elements: treat these as separate curve segments or threshold times with fixed clearance times.
• Validation: compare computed times versus published manufacturer TCC charts for sanity checks.

Example of interpolation algorithm (conceptual)

• Convert time and current arrays to log10 scale: x = log10(current), y = log10(time).
• For given log-current, find interval and perform linear interpolation on y.
• Return t = 10^{y_interpolated}.

Worked example 1 — Low-voltage MCCB with instantaneous trip element

Scenario:

• System voltage: 480 V three-phase.
• Available bolted-fault current at fault location: I_bf = 25,000 A (25 kA).
• Protective device: Molded Case Circuit Breaker (MCCB) with electronic trip unit, rated 1600 A.
• Settings: long-time pickup (I_p) = 1.0 × 1600 A = 1600 A, instantaneous trip threshold = 10,000 A (10 kA), instantaneous trip operating time (manufacturer max) = 0.03 s.
• TCC modeling: electronic instantaneous trip is dominant because I_bf > instantaneous threshold.

Calculation steps:

1. Compare I_bf with instantaneous threshold: 25 kA > 10 kA → instantaneous element will operate.
2. Because instantaneous element is designed to act non-time-delayed, use manufacturer stated instantaneous operating time. For this device assume t_inst = 0.03 s (typical electronic trip response).
3. Therefore, computed clearing time t_clear = t_inst = 0.03 s.

Discussion:

• If instead the instantaneous threshold were higher than I_bf, we would evaluate the inverse-time long-time or short-time curve at I = 25 kA to compute t_clear.
• Note that if multiple upstream devices exist, an upstream device may have a lower clearing time at this current. The calculator must compare times across devices and pick earliest.

Result:

Clearing time used for arc flash energy computation: t_clear = 0.03 seconds.

Worked example 2 — Fuse clearing time computed from TCC table and arcing-current adjustment

Scenario:

• System voltage: 480 V three-phase.
• Available bolted-fault current at fault location: I_bf = 12,000 A (12 kA).
• Protective device: Type gG HRC fuse rated 200 A located at the panel feeding the bus where arc occurs.
• We will estimate arcing current using a conservative reduction factor and then use a typical fuse TCC table to find clearing time.

Step 1 — Estimate arcing current:

• Using IEEE 1584 methodology would be preferred; for this illustrative calculation assume I_arc = 0.6 × I_bf for enclosed low-voltage conditions (typical empirical reduction factor range 0.5–0.9 depending on geometry).
• Compute: I_arc = 0.6 × 12,000 = 7,200 A.

Step 2 — Compute multiple of fuse rating:

• Multiple = I_arc / I_rated = 7,200 / 200 = 36×.

Step 3 — Use fuse TCC table (illustrative table from manufacturer typical behavior): Interpolation:

• For multiple 36×, we interpolate between 30× and 40× giving typical clearing time ≈ 0.015–0.05 s; take a mid-range estimate ≈ 0.02 s.

Result:

Clearing time t_clear ≈ 0.02 s (approx). This value should be used as arc duration for incident energy calculation unless more precise manufacturer data or IEEE 1584 arcing current calculations are provided.

Alternative approach — analytic fit inversion

If the fuse manufacturer provides an analytic fit in the form t = A*(I/I_rated)^B:

t = A * (I / I_rated)^B

Using illustrative constants A = 1.5, B = -3.0 (as an example):

• t = 1.5 * (36)^-3.0 = 1.5 * (36)^-3 = 1.5 / (36^3) = 1.5 / 46656 ≈ 3.21 × 10^-5 s (0.000032 s) — this demonstrates how sensitive exponent choice is and why analytic constants must come from manufacturer fits. This particular fit is not realistic for all fuse types; use manufacturer coefficients.

Note: The unrealistic small result underscores the importance of using validated manufacturer TCC fit values. For safety calculations always use validated tables or published curves.

Considerations for multi-device systems and coordination

When multiple devices can clear a fault, arc duration equals the earliest operation among them. Therefore:

• Calculate t_clear for all downstream and upstream protective devices using the same fault current basis (I_arc or I_bf consistent across devices).
• The device that trips first determines arc extinction. Check that protective coordination does not intentionally delay the upstream device such that the downstream device clears first.
• If reclosing occurs (automatic reclosers) ensure arc flash calculations consider reclose sequences and dead-time where appropriate.

Standards, authoritative references, and further reading

For professional practice and regulatory compliance consult the following authoritative sources:

• IEEE 1584-2018: "IEEE Guide for Performing Arc-Flash Hazard Calculations" — provides methods for arcing current and incident energy estimation. https://standards.ieee.org/standard/1584-2018.html
• NFPA 70E: Standard for Electrical Safety in the Workplace — incident energy thresholds, PPE, and safety-related work practices. https://www.nfpa.org/70E
• IEC 60909: Short-circuit currents in three-phase AC systems — essential for computing I_bf. https://www.iec.ch
• Manufacturer technical bulletins and time-current curves — e.g., ABB, Schneider Electric, Eaton, Siemens provide validated TCC charts and digital files for modeling.
• IEEE C37 series and ANSI/IEEE relay curve families for understanding relay inverse-time equations.

Validation, uncertainty, and recommended best practices

Best practices to ensure safe, defensible calculations:

1. Always source TCC data from the protective device manufacturer. Do not rely solely on generic approximations for safety-critical decisions.
2. Document whether I_arc or I_bf is used in the calculation and the method used to derive I_arc (IEEE 1584 or other).
3. Perform sensitivity analyses on device settings (pickup, TMS, instantaneous threshold) and arcing current estimation to understand variability in t_clear and incident energy.
4. Use log-log interpolation for tabular TCC data to maintain characteristic slopes across decades of current and time.
5. Maintain conservative assumptions where required by safety policy (e.g., assume arcing current equals bolted-fault current if data is insufficient for a realistic reduction factor).

Summary of algorithmic checklist for an instant arc flash clearing time calculator

• Input: system topology, impedances, voltage, protective device settings/TCC.
• Compute I_bf using network short-circuit method (IEC 60909 or equivalent).
• Compute I_arc if using IEEE 1584 methodology; else decide on current basis.
• For each protective device: evaluate TCC at the chosen current using manufacturer table or analytic model to obtain t_candidate.
• Select t_clear = min(t_candidate) across devices capable of fault clearing at the location.
• Use t_clear as arc duration input for incident energy calculation (NFPA 70E / IEEE 1584).
• Document assumptions, sources, and any interpolation/fitting approaches.

Useful external authoritative links

• IEEE 1584-2018 Guide: https://standards.ieee.org/standard/1584-2018.html
• NFPA 70E information: https://www.nfpa.org/70E
• IEC standards search (60909): https://www.iec.ch/
• U.S. Occupational Safety and Health Administration (OSHA) electrical safety information: https://www.osha.gov/electrical

Closing technical notes and cautions

This document provides a practical and technical methodology to compute arc flash clearing time from protective device settings and TCC data. Always use manufacturer curves and formal standards for final safety compliance and design. Implementations must include conservative validation checks, robust interpolation, and explicit reporting of assumptions. For detailed incident-energy calculations pair the computed t_clear with IEEE 1584 and NFPA 70E procedures to define safe working distances and required PPE.