In short. A time-current curve plots how long a protective device takes to operate at each current. Putting the curves of every device in a path on one log-log chart shows at a glance whether the device nearest the fault trips first, and whether equipment damage curves stay safely to the right.
Formula, physics, then the chart
Heating in a conductor follows I² × t, so a longer-lasting overload can be tolerated at low current and only a very short one at high current. Protective devices imitate this: inverse-time elements trip slowly at small overloads and quickly at large currents. The TCC plot shows this trade on both axes in logarithmic scale.
Heat ∝ I² × t
Regions of a device curve
| Region | Behaviour | Purpose |
|---|---|---|
| Long-time | Inverse, trips in seconds to minutes | Overload protection |
| Short-time | Fixed or I²t delay, tens to hundreds of milliseconds | Allows downstream devices to clear first |
| Instantaneous | No intentional delay | Severe faults |
What is plotted
- Device curves with tolerance bands (minimum and maximum operating times).
- Full-load current and motor starting curves.
- Transformer inrush point and damage curve.
- Cable thermal withstand (I² × t limit). See cable protection.
- Maximum and minimum fault currents as vertical lines. See maximum and minimum studies.
- Generator damage and decrement curves.
How to check coordination on the plot
- Draw the fault-current lines first.
- Check that each downstream curve lies to the left of (faster than) the upstream curve for all currents up to the downstream fault level.
- Check the time gap between tolerance bands, not between central curves.
- Check each device curve lies left of the equipment damage curve it protects.
- Check curves stay right of load and inrush points so there is no nuisance tripping.
- Repeat with the generator-only fault levels.
Typical problems seen on plots
- Curves that cross in the instantaneous region, so both devices trip.
- An upstream breaker with no short-time delay, giving no selectivity.
- A fuse and relay with different curve shapes that cross at high current.
- Instantaneous setting below transformer inrush.
Moving from drawing to evidence
A plot shows the intended behaviour. Field evidence closes the loop: relay event records, injection test results and as-left settings. If a trip occurs, compare the recorded operating time with the curve. A growing difference between test and design values is a signal for investigation. See protection records.
Illustrative example
A 630 A feeder breaker and a 1,600 A incomer are plotted. At a 12 kA fault, the feeder breaker trips in about 20 ms, and the incomer’s short-time band begins at 300 ms, a clear gap. At the generator-only fault level of 3.2 kA, the feeder breaker is in its short-time region at about 150 ms and the incomer still waits. The plot also shows that the incomer’s curve stays below the busbar withstand, so the settings are accepted.
Reading a TCC plot
A time-current characteristic plots operating time (vertical, log scale) against current (horizontal, log scale). Lower-left is fast and sensitive; upper-right is slow and robust. A coordinated system has curves that nest without crossing, downstream devices to the left and below.
What goes on the plot
| Item | Shown as |
|---|---|
| Protective devices | Curves with pickup, delay and instantaneous region |
| Transformer inrush | Point, typically 8 to 12 times rated for 0.1 s |
| Transformer damage | Curve or ANSI frequency-based limit |
| Cable damage | I²t line |
| Motor starting | Starting current and time |
| Generator decrement | Decaying fault curve |
| Maximum and minimum fault | Vertical lines |
Checks on the plot
- The device curve is above full-load and motor-start current.
- It is below the cable and transformer damage curves.
- It operates at the minimum fault current.
- The upstream curve is slower than the downstream by the required margin across the full current range up to the maximum fault.
Common issues
- Instantaneous regions overlapping, which makes both devices trip.
- Curves plotted on different voltage bases.
- Generator decrement curve ignored, so the relay does not pick up on a decayed fault.
Where full selectivity is impossible, accept partial selectivity knowingly and record it. See coordination workflow.
Common mistakes
- Spacing central curves rather than tolerance bands.
- Ignoring damage curves.
- Plotting only the utility case.
What to send us
Send device models and settings. Send your application details. See also coordination and selectivity.
Questions engineers ask
Why log-log scale?
It lets very small and very large currents and times fit on one chart, with inverse curves close to straight lines.
What is a damage curve?
The limit of what a cable, transformer or motor can withstand before thermal or mechanical damage.
How much time gap is enough?
Enough that tolerance bands do not overlap, using manufacturer data for the devices involved.
Can software do this?
Yes, but the engineer must still check the assumptions and read the result.
This guide gives general principles. Settings must be confirmed with manufacturer curves.