TCC curves & grading
The key idea
A time–current characteristic (TCC) curve is a device's promise: at this current, I act in this time. Grading is arranging those promises so the device nearest the fault always acts first, and everything upstream waits — by a deliberate margin.
The idea
Most protective devices are inverse-time: the bigger the current, the faster they act. A small overload is tolerated for minutes; a heavy fault is cut off in a tenth of a second. Drawn on log-log axes — current across, time up — each device becomes a falling curve.
Now put every device between a fault and the source on the same plot. A fault current is a vertical line; where it crosses each curve is that device's operating time. Grading means shaping the curves so those crossing points are in the right order: nearest device first, each upstream device slower by a margin.
The margin is not padding for comfort. It must cover real physical time: the downstream breaker takes tens of milliseconds to actually interrupt, relays overshoot, and both devices carry timing tolerances. In practice the sum lands around 0.2–0.4 s per stage.
Two settings shape each relay's curve:
- Pickup — the current below which it does nothing. It goes above the maximum normal load and below the minimum fault current.
- Time multiplier (TMS) — slides the whole curve up or down in time. This is the grading knob.
Try it
Lower the TMS until the margin collapses — that is the miscoordination grading prevents.
margin at 2.5 kA: 0.59 s (need ≥ 0.3 s)
Graded: at the maximum downstream fault current, the downstream relay operates first and the upstream relay waits 0.59 s longer. Try lowering the TMS until the margin collapses — that is the miscoordination every grading study exists to prevent.
Why it matters
- Grading is measured where the curves are closest — at the maximum fault current of the downstream device. A scheme that looks graded at low current can still cross there.
- The current window comes from the fault study. Pickup below minimum fault current, margin checked at maximum: both numbers come from fault current values. Grading without a fault study is guessing on a logarithmic chart.
- A crossed pair spreads outages. If the upstream relay wins the race, a fault on one feeder takes out the whole busbar above it. The violation is invisible in service — until the day it maps a small fault into a large outage.
The math, if you want itOptional — the page reads completely without it
The IEC 60255 standard inverse curve is:
standard inverse
t = TMS · 0.14( I / Is )0.02 − 1
where Is is the pickup and TMS slides the curve in time. The other families trade steepness for grading room:
very inverse · extremely inverse
t = TMS · 13.5( I / Is ) − 1 · t = TMS · 80( I / Is )² − 1
The widget above draws the standard inverse for both relays.
See it in Phasor
Phasor draws TCC curves from the device settings — IEC and IEEE relay families, fuses and LV trip units — computes the actual margin at every current, and flags each pair that falls below the margin you set for the project.