Relay Coordination Calculator — IEEE C37.112 / IEC 60255-151 CTI

Calculate

Select the standard matching your relay model

IEC: SI / VI / EI / LTI

Relay-side pickup current — secondary current at which relay begins timing toward operation

TMS range 0.05–1.0 (step 0.01). Multiplies the base inverse-time curve.

IEC: SI / VI / EI / LTI

Upstream pickup should exceed downstream pickup for proper selectivity coordination

TMS range 0.05–1.0 (step 0.01).

Fault current at which coordination is primarily evaluated — typically maximum bus fault current

Required CTI, relay technology, fault range. Open to change.

Overview

This calculator evaluates time-current coordination between two protective overcurrent relays — typically a downstream relay closer to the load and an upstream relay closer to the source — at a specified fault current level. It computes operating times for both relays using IEEE C37.112 or IEC 60255-151 inverse-time characteristic equations, calculates the actual coordination time interval (CTI = upstream operating time − downstream operating time), compares against the required CTI for selectivity, and classifies the coordination status.

Four architectural features set this calculator apart from simplified TCC viewers. First, multi-level evaluation — coordination is checked at minimum fault, primary fault, and maximum fault levels plus 20 log-spaced intermediate points, surfacing coordination robustness beyond a single operating point. Second, curve-crossing detection — when curve geometry is fundamentally incompatible (upstream operates faster than downstream within the timing region), the calculator flags this as a global override. Third, explicit recommended TDS adjustment with both theoretical target and rounded practical setting per relay resolution grid. Fourth, separation of three time concepts: relay operating time, breaker clearing time, and required CTI.

Designed for protection engineers, electrical design engineers, utility relay technicians, and power system planners doing protection coordination studies for industrial, commercial, and utility distribution systems.

How to Use This Calculator

  1. Select coordination standard — IEC 60255-151 (international) or IEEE C37.112 (North American).

  2. Configure downstream relay (closer to load): curve type, pickup current (A), time dial setting (TMS for IEC / TD for IEEE).

  3. Configure upstream relay (closer to source): same parameters. Upstream pickup should exceed downstream pickup for proper selectivity.

  4. Enter fault current at which coordination is primarily evaluated (A).

  5. Optionally specify required CTI in seconds. If omitted, the calculator defaults from relay technology (Electromechanical 0.40 s, Static 0.35 s, Microprocessor 0.20 s, Mixed 0.30 s per IEEE Std 242).

  6. Optionally enter min/max fault range for multi-level evaluation. Defaults ensure both relays are in timing region.

  7. Click Calculate — get operating times, actual CTI, coordination status, crossing detection, and recommended TDS adjustments.

Use the result to support protection coordination studies and relay setting calculations. Verify final settings against project protection specification and relay model documentation.

Inputs & Outputs

Inputs

  • •Coordination Standard — Options: IEC 60255-151 (International), IEEE C37.112 (North American)
  • •Downstream Curve Type — Options: Standard Inverse / Moderately Inverse, Very Inverse, Extremely Inverse, Long Time Inverse (IEC only)
  • •Downstream Pickup Current (A)
  • •Downstream Time Dial (TMS / TD)
  • •Upstream Curve Type — Options: Standard Inverse / Moderately Inverse, Very Inverse, Extremely Inverse, Long Time Inverse (IEC only)
  • •Upstream Pickup Current (A)
  • •Upstream Time Dial (TMS / TD)
  • •Fault Current (Primary Evaluation Point) (A)
  • •Required CTI (s) (s)
  • •Relay Technology (for default CTI) — Options: Mixed (default CTI 0.30 s), Electromechanical (default CTI 0.40 s), Static / Solid-State (default CTI 0.35 s), Microprocessor (default CTI 0.20 s)
  • •Min Fault Current (optional) (A)
  • •Max Fault Current (optional) (A)

Outputs

  • •Downstream Operating Time (s)
  • •Upstream Operating Time (s)
  • •Actual CTI (s)
  • •Required CTI (s)
  • •CTI Margin (s)
  • •Margin (%)
  • •Pickup Ratio (Up/Down)
  • •Downstream Multiple of Pickup (M)
  • •Upstream Multiple of Pickup (M)
  • •Coordination Status

Formula

Relay Coordination Calculation

IEC 60255-151 operating time:

t = TMS × k / (M^α − 1)

Where M = I / I_pickup (multiple of pickup).

Curve Type k α
Standard Inverse (SI) 0.14 0.02
Very Inverse (VI) 13.5 1
Extremely Inverse (EI) 80 2
Long Time Inverse (LTI) 120 1

IEEE C37.112 operating time:

t = TD × (A / (M^p − 1) + B)
Curve Type A B p
Moderately Inverse 0.0515 0.1140 0.02
Very Inverse 19.61 0.491 2
Extremely Inverse 28.2 0.1217 2

Coordination Time Interval:

CTI = t_upstream − t_downstream

Required CTI defaults (IEEE Std 242):

  • Electromechanical: 0.40 s
  • Static/Solid-State: 0.35 s
  • Microprocessor: 0.20 s
  • Mixed: 0.30 s

Recommended TDS adjustment (slow upstream):

For IEC: new_TMS_up = (t_down + CTI_req) / (k_up / (M_up^α_up − 1))
For IEEE: new_TD_up = (t_down + CTI_req) / (A_up / (M_up^p_up − 1) + B_up)

Round to nearest 0.01 (IEC TMS) or 0.05 (IEEE TD).

What is Relay Coordination

Relay coordination is the practice of setting protective overcurrent relays in series so that the relay closest to a fault trips first, isolating the smallest portion of the electrical system. The goal is selectivity: a fault on a branch circuit should clear by tripping only the branch breaker, not the main breaker or the utility feeder. Each relay in series should provide backup for the relay downstream of it — tripping only if the downstream relay fails to operate, and only after a deliberate time delay (the coordination time interval, CTI) that allows the downstream relay to clear the fault first.

Coordination is achieved by setting each relay's pickup current and time dial setting such that the relay's time-current characteristic curve sits below the curves of all upstream relays. The downstream relay must be both more sensitive (lower pickup) and faster (lower operating time at the same fault current) than upstream relays. The vertical separation between curves at the fault current of interest must meet the required CTI for the relay technology used.

How to Calculate Coordination Time Interval (CTI)

CTI is the time margin between upstream and downstream relay operating times at the same fault current. The calculation steps: (1) compute multiple of pickup for each relay: M = I / I_pickup. M must be greater than 1 for the relay to time toward operation. (2) Apply the curve equation to each relay. For IEC 60255-151: t = TMS × k / (M^α − 1). For IEEE C37.112: t = TD × (A / (M^p − 1) + B). (3) Subtract: actual CTI = t_upstream − t_downstream. (4) Compare against required CTI.

If actual CTI is at least 1.2 × required CTI, the pair has comfortable margin (COORDINATED). If actual CTI is at or just above required CTI but below 1.2 × required CTI, the pair has limited headroom (MARGINAL). If actual CTI is below required CTI, the pair is MISCOORDINATED and requires TDS adjustment.

What is Curve Crossing in Relay Coordination?

Curve crossing is a geometric incompatibility between two relay curves: at some current in the fault range, the upstream relay operates faster than the downstream relay. This defeats selectivity. Curve crossing is fundamentally different from miscoordination, which is an adjustable margin shortfall.

The cause is curve shape mismatch combined with inadequate pickup separation. When two curves of different shape are paired with insufficient pickup ratio, they can intersect in the timing region. TDS adjustment alone may be insufficient for curve crossing because it shifts the curve vertically without changing shape.

This calculator detects curve crossing by sweeping 23 points across the fault range (min_fault, primary_fault, max_fault exact, plus 20 log-spaced intermediate points) and checking whether t_upstream < t_downstream at any qualifying point where both relays are above pickup.

Multi-Level Coordination Evaluation

Coordination at a single operating point is necessary but not sufficient. Two relays can show acceptable CTI at the primary fault and yet have curves that converge at extreme fault currents, producing miscoordination at maximum fault. This calculator evaluates coordination across three discrete levels and 20 log-spaced intermediate points.

Track B classification uses pass-count basis: ROBUST (all three qualifying levels pass), PARTIAL (two of three), or POOR (zero or one of three). A level passes when actual CTI at that level meets required CTI. Levels where the upstream relay is below pickup are classified as UPSTREAM BELOW PICKUP and excluded from pass count — selectivity is trivially preserved at such currents.

Inputs & Outputs

Required inputs: Coordination standard (IEC 60255-151 or IEEE C37.112), downstream curve type / pickup current / time dial, upstream curve type / pickup current / time dial, fault current.

Optional inputs: Required CTI override, relay technology (for default CTI), minimum and maximum fault current for multi-level range.

Outputs: Downstream and upstream relay operating times, actual CTI, required CTI with source, margin in seconds and percent, pickup ratio, multiples of pickup for each relay, multi-level coordination table, recommended TDS adjustments when miscoordinated or marginal.

IEEE C37.112 vs IEC 60255-151 Relay Curves

IEEE C37.112-2018 defines three curve types using the equation t = TD × (A / (M^p − 1) + B): Moderately Inverse (general-purpose), Very Inverse (industrial feeders, motor protection), and Extremely Inverse (transformer primary, fuse coordination). IEC 60255-151:2009 defines four curve types using t = TMS × k / (M^α − 1): Standard Inverse, Very Inverse, Extremely Inverse, and Long Time Inverse (generator and large motor protection). The time-dial ranges differ: IEC TMS is typically 0.05 to 1.0 with 0.01 steps; IEEE TD is typically 0.5 to 15 with 0.05 steps.

Pickup Ratio vs CTI

Pickup ratio and CTI are two independent coordination parameters. Pickup ratio is the ratio of upstream pickup current to downstream pickup current. Engineering-practice starting point: pickup ratio of 1.5 provides adequate margin between relays for typical applications. This is advisory, not a universal rule. CTI is the time margin between operating times at the same fault current. The calculator checks both independently. Pickup ratio is flagged as advisory when below 1.2. CTI is checked at the primary fault and across the multi-level range.

Key Facts

  • Inverse-time relay operating time follows t = TMS × k / (M^α − 1) for IEC 60255-151 or t = TD × (A / (M^p − 1) + B) for IEEE C37.112. The curve has a vertical asymptote at M = 1 (pickup) and approaches a low minimum at high M.
  • Coordination time interval (CTI) = upstream operating time − downstream operating time. For selectivity, actual CTI must meet or exceed required CTI.
  • Required CTI engineering-practice values per IEEE Std 242: 0.40 s for electromechanical, 0.35 s for static, 0.20 s for microprocessor, 0.30 s for mixed technology pairs. These values include breaker clearing time.
  • Pickup ratio (upstream / downstream) engineering-practice starting point is 1.5. Advisory, not a universal rule.
  • Curve crossing — t_upstream < t_downstream within the timing region — is a fundamental geometric incompatibility. TDS adjustment alone may be insufficient; curve type or pickup re-selection often required.
  • Multi-level coordination evaluation surfaces convergence at extreme fault currents that single-point analysis at primary fault misses.
  • Three time concepts in coordination: relay operating time (curve output), breaker clearing time (mechanical + arcing, embedded in required CTI), required CTI (engineering-practice minimum margin for selectivity).
  • Practical relay setting resolution: IEC TMS typically steps in 0.01 increments (range 0.05 to 1.0); IEEE TD typically steps in 0.05 increments (range 0.5 to 15).

Applications

  • Protection coordination studies for industrial plant power distribution with main, feeder, and branch protection layers
  • Utility distribution substations with feeder relays coordinating with downstream reclosers
  • Commercial building electrical systems with main service and branch panel coordination
  • Generator and transformer protection with high-side and low-side overcurrent relays
  • Quick verification of single operating point from full coordination studies in CYME, ETAP, SKM, or EasyPower
  • Confirming whether a proposed TDS tweak moves coordination in the correct direction before re-running the full study
  • Field troubleshooting — verifying whether a relay setting change achieves required CTI at new fault current after system reconfiguration
  • Post-event analysis when upstream tripped simultaneously with downstream during an actual fault

Example Calculation

Example 1 — IEC SI, COORDINATED / ROBUST

Inputs:

  • Standard: IEC 60255-151
  • Downstream: Standard Inverse (SI), pickup 100 A, TMS 0.10
  • Upstream: Standard Inverse (SI), pickup 200 A, TMS 0.25
  • Fault current: 1000 A, Required CTI: 0.20 s (microprocessor)

At primary fault 1000 A:

  • M_down = 1000 / 100 = 10 → t_down = 0.10 × 0.14 / (10^0.02 − 1) = 0.297 s
  • M_up = 1000 / 200 = 5 → t_up = 0.25 × 0.14 / (5^0.02 − 1) = 1.067 s
  • Actual CTI = 1.067 − 0.297 = 0.770 s vs required 0.20 s → margin 0.570 s (285%)

Status: COORDINATED / ROBUST — all three multi-level points pass.

Example 2 — IEC SI, MISCOORDINATED with TDS recommendation

Inputs:

  • Downstream: SI, pickup 100 A, TMS 0.10
  • Upstream: SI, pickup 150 A, TMS 0.10 (same TMS — tight ratio)
  • Fault current: 800 A, Required CTI: 0.30 s

At primary fault 800 A:

  • t_down = 0.10 × 0.14 / (8^0.02 − 1) = 0.327 s
  • t_up = 0.10 × 0.14 / (5.33^0.02 − 1) = 0.413 s
  • Actual CTI = 0.413 − 0.327 = 0.086 s vs required 0.30 s → deficit 0.214 s

Status: MISCOORDINATED

Recommended adjustment (slow upstream): increase upstream TMS to 0.15 (theoretical 0.152, rounded to nearest 0.01).

Standards & References

  • IEEE C37.112-2018 — IEEE Standard Inverse-Time Characteristic Equations for Overcurrent Relays (defines moderately inverse, very inverse, extremely inverse curves for North American practice)
  • IEC 60255-151:2009 — Measuring relays and protection equipment — Part 151: Functional requirements for over/under current protection (defines standard inverse, very inverse, extremely inverse, long time inverse curves)
  • IEEE Std 242 — IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems (Buff Book — source for CTI engineering-practice values)
  • IEEE Std 141 — IEEE Recommended Practice for Electric Power Distribution for Industrial Plants (Red Book — coordination practice context)
  • ANSI/IEEE C37.90 — Standard for Relays and Relay Systems Associated with Electric Power Apparatus

Units

  • Time: seconds (s) and milliseconds (ms) for relay operating times. Smart unit selection: values below 100 ms shown in ms; values at or above 100 ms shown in seconds.
  • Current: amperes (A). Currents above 1000 A shown in kA.
  • Ratios: dimensionless — multiple of pickup (M = I / I_pickup) and pickup ratio (upstream pickup / downstream pickup).
  • No Metric/Imperial distinction — all values are in SI electrical units. IEC and IEEE standards both specify relay equations in SI.

Limitations

  • Calculator handles two-relay pair coordination using inverse-time overcurrent characteristics per IEEE C37.112 or IEC 60255-151. Multi-relay (3+ relays in series) coordination requires sequential pair analysis.
  • Definite-time relays, distance relays, differential relays, directional overcurrent, and impedance-based relays are out of scope.
  • Fault current is assumed to be steady-state symmetrical RMS at the relay location. Asymmetrical fault current decay, DC offset, and CT saturation effects are not modeled.
  • Curve constants are standard published values. Some relay manufacturers offer custom curves — verify against relay manual for critical applications.
  • Calculator does not compute arc-flash incident energy, CT performance under fault conditions, differential relay coordination, or coordination with fuses.
  • CTI values are engineering-practice recommendations per IEEE Std 242. Actual requirements may differ per utility standards, specific relay models, or breaker characteristics.

Common Mistakes to Avoid

  • Using the same TMS/TD on both relays with a tight pickup ratio — nearly always produces miscoordination because the curves are nearly identical in shape
  • Assuming single-point coordination at primary fault means the pair is coordinated across the full fault range — curves can converge at maximum fault
  • Confusing relay operating time with breaker clearing time — breaker clearing time is already included in the required CTI engineering-practice value, not separately added
  • Selecting mismatched curve types without verifying curve crossing — Extremely Inverse downstream with Moderately Inverse upstream is a common crossing scenario
  • Applying rounded TDS to the relay without verifying coordination — rounding from theoretical to practical setting can push actual CTI below required CTI
  • Treating pickup ratio as a pass/fail check — it is an advisory guideline, not a code-required minimum
  • Not verifying coordination at minimum fault current — at low fault levels near pickup, operating times are very long and CTI can be very large (trivial coordination) or very sensitive to small current changes

Frequently Asked Questions

What is coordination time interval (CTI) in relay protection?
CTI is the time margin between upstream and downstream relay operating times at the same fault current. For selective coordination, the downstream relay must clear the fault before the upstream relay operates. Actual CTI = t_upstream − t_downstream must meet or exceed the required CTI for the relay technology used — typically 0.20 s for microprocessor pairs, 0.30 s for mixed, 0.40 s for electromechanical per IEEE Std 242.
What is curve crossing in relay coordination and why does it matter?
Curve crossing occurs when the upstream relay operates faster than the downstream relay at some fault current within the timing region — defeating selectivity at that current level. This is a geometric incompatibility between curve shapes. TDS adjustment alone may be insufficient to resolve curve crossing; curve type or pickup re-selection is often required.
How do I choose between IEC 60255-151 and IEEE C37.112 curves?
Use the standard that matches your relay model. IEC 60255-151 is common outside North America and includes four curve types (SI, VI, EI, LTI). IEEE C37.112 is common in North American utility and industrial practice with three curve types (Moderately Inverse, Very Inverse, Extremely Inverse). Check the relay model documentation — modern numerical relays often support both standards.
When should I slow the upstream relay versus speed the downstream relay?
Slow upstream (increase upstream TDS) is the preferred default — it preserves downstream speed for fast fault clearing and generally carries lower risk of transient false trips. Speed downstream (decrease downstream TDS) is an alternative when the downstream relay has clear speed margin and the application tolerates faster downstream tripping. Always verify operating times at min and max fault currents after any TDS adjustment.
Why does the multi-level table matter if the primary fault point passes?
Single-point analysis at primary fault can miss curve convergence at extreme fault currents. Two relays with comfortable CTI at primary fault can have inadequate CTI at maximum fault because inverse-time curves converge at high multiples of pickup. Multi-level evaluation reveals this pattern before it causes problems in service — particularly common when both relays use extremely-inverse curves.
What is a good CTI for relay coordination?
Required CTI depends on relay technology. For modern microprocessor-to-microprocessor pairs, 0.20 s is engineering practice per IEEE Std 242. For mixed technology (one microprocessor, one electromechanical), 0.30 s is conservative. For electromechanical-to-electromechanical pairs, 0.40 s is standard, occasionally 0.45 s for older installations with longer breaker times. These values include relay tolerance, breaker mechanical operating time, breaker arcing time, and safety margin — do not add breaker time separately. Project-specific requirements may differ; verify against project protection specification.
How do I fix relay miscoordination?
Two adjustment paths: slow upstream (increase upstream TDS) or speed downstream (decrease downstream TDS). The calculator gives both theoretical target and rounded practical value for each. Default preference is slow upstream — preserves downstream speed for fast fault clearing. Apply the rounded practical value (not theoretical) to the relay since real relays support specific resolution grids. Trade-off when slowing upstream: upstream operating time increases across all currents, so verify upstream operating time at maximum fault doesn't exceed equipment damage tolerance. Trade-off when speeding downstream: faster downstream may produce false trips on transients (motor inrush, transformer energization) — verify against transient envelopes.
What causes relay curve crossing?
Curve crossing occurs when curve shapes are fundamentally incompatible for the chosen pickup ratio. Two common causes: (1) mixed curve families where downstream uses a steeper curve (e.g., Extremely Inverse) than upstream — at low M, the downstream curve is very slow while upstream is moderate, producing crossing in the timing region. (2) Inadequate pickup ratio (below 1.2) with mixed curve types — the curves overlap in fault range and intersect. Fix by matching curve types (same family on both sides) or significantly increasing pickup ratio. TDS adjustment alone may be insufficient because it shifts curves vertically without changing shape.
Why is my relay pair coordinated at one fault level but not another?
Different curve shapes converge or diverge with fault current. Two Extremely Inverse curves drop very steeply at high M and converge — CTI shrinks toward zero at maximum fault even when primary fault has comfortable margin. Mixed Very Inverse + Extremely Inverse can converge or cross at high M. The calculator's multi-level evaluation surfaces these patterns. If max fault fails CTI but primary passes, you have COORDINATED / PARTIAL or COORDINATED / POOR — verify whether the failing fault level is realistic for your system. If yes, increase upstream TDS to provide larger separation at extreme currents.
What pickup ratio should I use for relay coordination?
Engineering-practice starting point is 1.5 — upstream pickup at least 1.5 × downstream pickup. This is advisory, not a universal rule. Tighter ratios (1.2 to 1.5) can work with appropriate curve selection and CTI margin analysis. Looser ratios (2.0 and higher) are common in utility coordination where fault current varies widely across feeder positions. Higher ratios produce easier coordination but may compromise upstream sensitivity to remote faults. The calculator flags ratios below 1.2 as advisory (soft check) but does not force a specific ratio — use the ratio that matches your protection philosophy and fault current calculation accuracy.
Why does the calculator show COORDINATED / PARTIAL instead of COORDINATED / ROBUST?
The pair coordinates at the primary fault current with margin (Track A = COORDINATED), but coordination fails at one of the multi-level evaluation points (min or max fault). Track B = PARTIAL means 2 of 3 levels pass. Common cause: curves converge at extreme fault currents, particularly when both curves are extremely inverse (steep slope at high M). Verify whether the failing level is a realistic fault scenario — if max fault is conservative and actual max is below the failure level, coordination is adequate in practice. If the maximum fault is realistic and coordination fails there, increase upstream TDS or reconsider curve selection.
Why is fault below pickup shown as INFEASIBLE?
If the fault current is at or below the downstream relay's pickup, the downstream relay does not time toward operation. Coordination evaluation is meaningless because there is nothing to coordinate at that current — only the upstream relay (if its pickup is also exceeded) would operate. INFEASIBLE indicates the inputs cannot produce a meaningful evaluation, not that the relays are malfunctioning. Verify fault current calculation and pickup settings — typically one of them is incorrect. The calculator surfaces INFEASIBLE rather than producing outputs that look meaningful but aren't.
What is the difference between IEEE C37.112 and IEC 60255-151 curves?
IEEE C37.112 is the North American standard, with three defined curve types (Moderately Inverse, Very Inverse, Extremely Inverse) using equation t = TD × (A / (M^p − 1) + B). IEC 60255-151 is the international standard, with four defined types (Standard Inverse, Very Inverse, Extremely Inverse, Long Time Inverse) using equation t = TMS × k / (M^α − 1). The curve constants differ between standards, so the same curve name (e.g., Very Inverse) produces slightly different shapes in each standard. Time dial setting also differs — IEC TMS range 0.05 to 1.0, IEEE TD range 0.5 to 15. Use the standard that matches your relay model — modern numerical relays typically support both.

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