Cable Damage Curves — Decisive Engineering

In Module 2 you coordinated breakers against each other. The question this module asks is one level harder: did you coordinate them well enough that nothing burns up while the right breaker is opening?

A breaker opening cleanly is good. A breaker opening cleanly after the cable insulation between it and the fault has already melted is a fire waiting to happen.

This lesson is about the cable side of that question. The next lesson is about transformers.

What a damage curve is

For a power cable, the damage curve answers:

Given an RMS fault current flowing through me, how long can I carry it before my insulation reaches its short-circuit thermal limit?

The physics is simple — the conductor heats up as I²·t (Joule heating), and the cable insulation has a maximum temperature it can reach before degrading permanently.

The empirical ICEA formula expresses this as:

   I² · t  =  K · Cmils²

where I is the fault current in amperes, t is the maximum time the cable can endure that current, Cmils is the conductor area in circular mils, and K is a constant depending on the conductor material (copper vs. aluminum) and the insulation thermal class (THWN 75°C, XHHW 90°C, etc.).

Solving for time: t = K · Cmils² / I². On a log-log TCC plot, that shape is a straight diagonal line with slope −2. Every cable damage curve is one of those lines. The size of the cable shifts the line up or down; the insulation class shifts it as well.

What the curve means on the plot

Below the damage line: the cable is safe — current low enough or time short enough that the conductor temperature stays below the insulation’s withstand limit.

Above the damage line: the cable insulation degrades. Repeated events here cause permanent damage even if the cable doesn’t fail catastrophically the first time.

The protection rule is straightforward:

The protective device upstream of a cable must trip below the cable’s damage curve at every current the cable might see. If the device’s trip curve ever rises above the damage line, the cable is unprotected at that current.

A working scenario

The widget below has a 1/0 AWG copper THWN feeder cable (150 A continuous ampacity) protected by a 600 A LVPCB with instantaneous turned OFF. The LVPCB’s INST OFF is a normal setting when this feeder is one stage up in a coordination cascade — it gives downstream devices the maximum possible time to clear.

A 600 A device over a 150 A conductor isn’t a normal protection arrangement — outside the NEC’s tap-rule allowances, a 1/0 cable would be protected at or near its 150 A ampacity. We pair them deliberately here to make the damage-curve mismatch easy to see.

The amber dashed line is the cable’s damage curve.

Look at the plot at 20,000 A:

The LVPCB’s curve sits at its 0.3 s S-delay shelf.
The cable’s damage curve sits at about 0.08 s.

The cable damages before the breaker opens. At any current above roughly 10 kA — below the available bolted-fault current at this bus — this combination is unprotected.

Three fixes — pick your poison

Each fix has a real consequence in the rest of the design.

Fix A — Upsize the cable

Drag the conductor size slider on the cable. Step from 1/0 up through 4/0 and 250 kcmil. Watch the damage curve rise. By 250 kcmil the curve has moved up far enough that the LVPCB’s S-delay shelf is cleanly below it at every fault current.

Cost: copper. A 1/0 feeder is significantly cheaper than 250 kcmil on a long run. But upsizing solves the protection problem without touching the coordination cascade.

Fix B — Turn instantaneous back on

Drag the LVPCB’s I pickup off zero. Try 12× = 7,200 A.

Above 7,200 A the LVPCB now drops to its instantaneous floor (≈0.02 s) — well below the cable damage curve at any fault current. The cable is protected.

Cost: instantaneous-on usually means lost coordination with the downstream device. Whatever cable feeder this LVPCB was protecting above is now likely to trip simultaneously with the branch device on high faults. You’ve moved the problem.

Fix C — Switch insulation class

Drag the insulation switch from THWN (75°C) to XHHW (90°C).

XHHW insulation can survive a higher short-circuit temperature (250°C vs. 150°C), which moves the damage curve up. For the same cable size, you buy a meaningful chunk of margin.

Cost: a different cable. Sometimes available, sometimes not. Often the cost premium is small enough to pay for itself.

The protection engineer’s mental model

When the curves are on the plot in front of you, the question stops being theoretical:

Curve relationship	What it means	What you can do
Protective device curve always below cable damage curve	Cable is fully protected	Done
Protective device curve crosses cable damage curve above max available fault	Cable is protected within the system’s actual fault levels	Document it; accept it
Protective device curve crosses cable damage curve within max available fault	Cable is unprotected at some real fault current	Upsize, upgrade insulation, or change device settings

Most working protection studies live in the middle row. The available short-circuit current at any given bus is bounded — you don’t actually have to protect against currents higher than the service can deliver. The skill is knowing where that bound is, and proving the protection curve stays below the damage curve up to it.

Aluminum

Switch the cable to aluminum. The damage curve drops noticeably. Aluminum has lower thermal capacity than copper (the ICEA constant drops by roughly a factor of 0.4), so an aluminum cable of the same size damages sooner under the same fault current.

In practice, when you spec an aluminum feeder you also upsize it — aluminum at one or two trade sizes larger than the copper equivalent recovers the lost damage margin, and you save money even after the upsize.

What’s next

Lesson 8 adds the transformer damage curve — a more interesting shape than the simple I²·t line. Transformers have both thermal limits (similar to cables) and mechanical limits (the winding forces during a through-fault), and the damage envelope reflects both.