4.2 IDMT/TCC Curves & Coordination

The IDMT Curve Equation

Quick Answer: For an IEC 60255-151 inverse definite minimum time curve, trip time t = TMS x k / ((I / Is)^alpha - 1), where TMS is the time multiplier setting, Is is the pickup current, and k and alpha are curve-type constants.

An IDMT characteristic means trip time decreases as current increases, but flattens out at a minimum (definite) time once the current is many times pickup. That is the "inverse" and the "definite minimum" in the name. The three IEC curve families every NETA Level 2 candidate should memorize:

IEEE C37.112-1996 defines equivalent Moderately, Very, and Extremely Inverse curves using a slightly different equation form (with A, B, and p parameters). Most modern numeric relays let you select either the IEC or the IEEE family.

Worked IDMT Calculations

Standard Inverse, pickup 100 A, TMS 0.2, fault 500 A (M = 5):

t = 0.2 x 0.14 / (5^0.02 - 1) = 0.028 / (1.0328 - 1) = 0.028 / 0.0328 = 0.854 s

Extremely Inverse, pickup 100 A, TMS 0.3, fault 1000 A (M = 10):

t = 0.3 x 80 / (10^2 - 1) = 24 / 99 = 0.242 s

These match the published IEC 60255-151 tables. If your injection test gives a time more than about 10 percent off the calculated value, suspect a wrong TMS, a CT ratio mismatch, or a saturated CT.

Reading a TCC Curve

A time-current characteristic (TCC) curve is plotted on log-log paper: current on the X-axis (log scale), trip time on the Y-axis (log scale). A coordination study overlays every device curve in the chain so you can see, at a glance, which device trips first for any given fault current.

Reading a TCC:

1. Find the fault current on the X-axis (e.g., the maximum available fault at the downstream bus).
2. Move up to each device curve.
3. Read the trip time on the Y-axis for each device.
4. The downstream device must clear before the upstream device by at least the coordination time interval (CTI).

The CTI accounts for breaker interrupting time (3 to 5 cycles), relay overtravel, and a safety margin. The industry standard is 0.3 to 0.5 seconds; 0.3 s is the tightest normally accepted, 0.4 s is common, 0.5 s is conservative.

Pickup vs. Time-Dial (TMS) Settings

The pickup (Is) shifts the curve left or right — raising pickup moves the curve right, so the relay operates at higher current. The time multiplier (TMS, or time dial TD on electromechanical relays) shifts the curve up or down without changing its shape. To grade two relays on the same curve family, keep the curve shape identical and increase the upstream TMS so its curve sits above the downstream curve by at least one CTI at the worst-case fault.

Pickup is normally set 1.05 to 1.3 times maximum load current so the relay does not trip on normal overload. The lower end (1.05) is for cables and transformers; the upper end (1.25 to 1.3) is typical for feeders with motor inrush.

RK1 vs. RK5 Fuse Links

Class R (rejection) fuses are rated 250 V or 600 V and come in two current-limiting subclasses:

• RK5 — less current-limiting, time-delay. Cheaper, used where some let-through is tolerable.
• RK1 — more current-limiting, lower peak let-through energy (lower I2t). Preferred for arc-flash reduction and protecting components with low short-time withstand.

On a TCC, the RK1 curve sits below and to the left of the RK5 curve at high currents — it clears faster and lets less energy through. When a specification calls for arc-flash mitigation or a lower incident energy at a panel, RK1 is usually required.

Worked Coordination Example

A 225 A main breaker with a 51 relay (pickup 270 A, TMS 0.5, Standard Inverse) feeds a 100 A feeder breaker with a 50/51 relay (pickup 120 A, TMS 0.3, Standard Inverse). A bolted fault of 4000 A occurs on the feeder.

Feeder 51: M = 4000 / 120 = 33.3 t_feeder = 0.3 x 0.14 / (33.3^0.02 - 1) = 0.042 / 0.0726 = 0.579 s

Main 51: M = 4000 / 270 = 14.8 t_main = 0.5 x 0.14 / (14.8^0.02 - 1) = 0.07 / 0.0554 = 1.264 s

CTI = 1.264 - 0.579 = 0.685 s — well above the 0.3 s minimum, so coordination is selective. The feeder trips first and isolates only the faulted segment; the main stays closed and serves the rest of the switchboard. If the curves overlapped at 4000 A, a fault on the feeder would trip the main and black out every feeder — a coordination failure your TCC review should catch before commissioning.