HRC fuse I²t and fuses in series

Time–current and I²t characteristics of an HRC fuse

The time–current characteristic shows the operating time against current on log–log scales. It is inverse: long times for small overloads, a few milliseconds for heavy faults.

For short operating times (less than about 10 ms) heat cannot escape from the element, so melting depends only on the energy I²t delivered:

 Pre-arcing I²t  = ∫₀^tp i² dt   (energy to melt element)
 Arcing I²t      = ∫tp^tt i² dt  (energy during arc)
 Total I²t       = pre-arcing I²t + arcing I²t

 I²t (A²s, log)
  │ total I²t ─────────────
  │          ╱ (rises with voltage; higher at low pf)
  │ pre-arcing I²t ────────
  │ (constant at high current)
  └─────────────────────────► prospective I

• Pre-arcing I²t is practically constant for a given fuse at high currents (fixed by element mass and material).
• Total (let-through) I²t depends on circuit voltage, power factor and prospective current.
• Manufacturers give both values for each rating.

Selection of fuses in series using I²t

For a minor (downstream) fuse F2 and a major (upstream) fuse F1:

 Supply ──[F1]──┬──[F2]── load
               fault after F2

1. Both fuses carry the same fault current.
2. For F1 not to blow or be damaged, the energy let through by F2 in clearing the fault must not melt F1:

 Total I²t of F2  <  Pre-arcing I²t of F1

3. At lower currents (long times) the time–current curves must not cross; the major fuse curve must lie above the minor fuse curve with a margin.
4. Choose F2 from the load current; then choose the smallest F1 that satisfies the I²t rule. In practice a rating ratio of about 1.6–2 : 1 is sufficient for gG fuses.

Example (illustrative values): a 63 A fuse with total I²t ≈ 15 000 A²s and a 125 A fuse with pre-arcing I²t ≈ 30 000 A²s discriminate, since 15 000 < 30 000.

The total I²t of the fuse must also be less than the withstand I²t (k²S²) of the protected cable or semiconductor, so the I²t data also fix the maximum fuse rating for a given cable.