Relay
A relay is an electrically operated switch — and in power-system engineering, the device that watches for faults and tells the circuit breaker when to open. This page covers relay meaning, the IDMT trip-time formula, the full ANSI standard relay numbers reference (IEEE C37.2), the differences between electromechanical and digital relays, and a calculator for the most common protection function: time-overcurrent (function 51).
Use the IDMT relay calculator
The most common protection function — ANSI 51, time-overcurrent — uses the IEC 60255-151 inverse-time characteristic. Enter the fault current, the pickup setting, the time multiplier (TMS), and the curve type, and the calculator returns the trip time in seconds. Used for relay coordination studies during commissioning and after any feeder modification.
Trip time t = TMS · ( β / (M^α − 1) + L ), where M = I / I_set is the multiple of pickup. Lower TMS = faster trip; lower curve constants α and β = faster trip at high M. Typical TMS range 0.05–1.0 in 0.05 steps.
The IDMT trip-time formula
Inverse Definite Minimum Time (IDMT) overcurrent relays follow the closed-form expression below. Slope and shape are set by two constants β and α specific to each standardised curve.
- t
- trip time after pickup, s
- TMS
- time multiplier setting (engineer-chosen 0.05–1), —
- I
- fault current through the relay CT, A
- I_set
- pickup current setting, A
- β, α
- curve constants from the standard, —
- L
- IEC: 0; IEEE C37.112: nonzero per curve, —
Multiplying by TMS scales the entire curve up or down, allowing the protection engineer to coordinate this relay against upstream and downstream devices. The β / (M^α − 1) term is the inverse-time shape; the higher M is, the faster the trip. At M = 1 (current at pickup) the denominator is zero and the relay never trips — there must be a margin, typically M ≥ 1.5, for the relay to operate predictably.
Standards: ANSI, IEEE C37.2, IEC 60255
Three standards govern protective relays in modern power systems:
- IEEE C37.2 (originally ANSI C37.2) — Standard Electrical Power System Device Function Numbers, Acronyms, and Contact Designations. Assigns a unique number 1 – 99 to each protection function (the "ANSI relay numbers"), plus suffix letters for variations. Used universally on US protection schematics and increasingly internationally.
- IEC 60255 series — Measuring relays and protection equipment. The cornerstone for European and international relay specifications, often abbreviated IEC255 relay in older datasheets. IEC 60255-151 defines the inverse-time overcurrent characteristic curves used by every relay time calculator; IEC 60255-1 the general requirements; IEC 60255-21 the vibration, shock, and seismic test requirements.
- IEEE C37.112 — Inverse-Time Characteristic Equations for Overcurrent Relays. The American counterpart to IEC 60255-151 with a slightly different mathematical form (additive constant L). Both standards are supported by every modern multi-function relay; pick whichever matches the existing protection scheme on the bus.
ANSI standard relay numbers (IEEE C37.2)
The full IEEE C37.2 list assigns 1 – 99 to every protective relay function. Below are the most common relay numbers you will see on a single-line diagram or protection schematic — these are the protective relay codes the protection engineer reads at a glance. Function 51 is the time-overcurrent that the calculator above computes. Function 52 is the circuit breaker itself; 87 is differential protection; 86 is the lockout relay that holds the breaker open until manually reset. With relay numbers explained this way, even a multi-line bus protection diagram becomes readable. The full ANSI relay numbers PDF is published by IEEE Standards.
| No. | Name | Description |
|---|---|---|
| 1 | Master Element | Initiating device that operates other devices |
| 2 | Time-Delay Starting / Closing | Time-delay start of equipment in a sequence |
| 3 | Checking / Interlocking | Permits sequence to proceed only if conditions are correct |
| 12 | Overspeed | Operates on excessive speed of a machine |
| 14 | Underspeed | Operates on subnormal speed of a machine |
| 21 | Distance Relay | Functions when impedance reaches a preset value |
| 24 | Volts per Hertz | Overexcitation; voltage / frequency above setpoint |
| 25 | Synchronism-Check | Verifies two AC sources within voltage/phase tolerance |
| 27 | Undervoltage | Operates on AC voltage below pickup |
| 32 | Directional Power | Power flow in a specified direction (reverse-power) |
| 37 | Undercurrent / Underpower | Operates on current or power below pickup |
| 38 | Bearing Protection | Bearing temperature or vibration excessive |
| 40 | Field (Loss-of-Field) | Synchronous machine loss-of-excitation protection |
| 46 | Negative-Sequence / Unbalance | Detects unbalanced 3-phase currents (motor protection) |
| 47 | Phase-Sequence Voltage | Confirms correct phase rotation of the supply |
| 49 | Thermal (Machine / Transformer) | Operates on temperature rise (RTD or thermal model) |
| 50 | Instantaneous Overcurrent | Trips immediately when current exceeds pickup |
| 51 | AC Time Overcurrent (IDMT) | Inverse-time overcurrent (the IDMT relay this calculator handles) |
| 52 | AC Circuit Breaker | The circuit breaker itself, not a relay (control function) |
| 59 | Overvoltage | Operates on AC voltage above pickup |
| 63 | Pressure Switch | Operates on transformer Buchholz / sudden pressure rise |
| 64 | Ground Detector | Detects insulation failure to ground |
| 67 | Directional Overcurrent | Overcurrent + direction (line protection) |
| 79 | AC Reclosing Relay | Auto-recloses circuit breaker after trip |
| 81 | Frequency | Operates on under- or over-frequency |
| 86 | Lockout Relay | Trips and locks out CB until manually reset |
| 87 | Differential Protection | Trips on current difference between zone boundaries (transformer / generator / bus) |
| 94 | Tripping / Trip-Free | High-speed trip relay; "trip-free" prevents reclose if fault present |
Suffix letters customise the function: N for neutral / ground (51N = time-overcurrent ground), G for generator, T for transformer, P for phase, X for auxiliary. Numbers above 99 are reserved for plant-specific functions; numbers 100 – 199 are sometimes used for HV substation telecontrol.
Worked example: feeder overcurrent coordination
A 22 kV feeder breaker with an IDMT relay set to I_set = 100 A, TMS = 0.1, IEC standard inverse curve. A bolted three-phase fault produces 600 A at the relay CTs. Compute the trip time and verify selectivity against a downstream fuse rated 50 A with a clearing time of 0.5 s at 600 A.
| Step | Calculation | Result |
|---|---|---|
| Multiple of pickup M | I / I_set = 600 / 100 | 6.0 |
| Curve constants (IEC standard) | β = 0.14, α = 0.02, L = 0 | — |