A short circuit cannot be described with a single number. Documents therefore carry at least two, they look similar, and they are regularly swapped for one another.
Two numbers, one short circuit
The initial symmetrical short-circuit current I″k is the RMS value of the AC component at the moment the fault occurs. It is the reference quantity of short-circuit calculation to IEC 60909-0 and the figure that appears in most documents.
The peak short-circuit current iₚ is the crest value of the first half-cycle. It arises because a fault struck at an unfavourable instant carries a decaying DC component that superimposes on the AC. iₚ is not an RMS value but a peak, which makes it considerably larger.
What each number governs
| I″k | iₚ | |
|---|---|---|
| Type of value | RMS | peak |
| Governs | breaking capacity of protective devices, thermal stress | dynamic withstand of busbars, supports, terminals |
| Appears in data sheets as | Icu, Ics (IEC 60947-2), Icw | Ipk (IEC 61439-1) |
| Magnitude | reference value | roughly 2.5 times as large |
These are requirements on different components. A circuit breaker whose rated breaking capacity matches I″k says nothing about whether the busbar next to it withstands the force of the first half-cycle.
The factor between them is κ
A single equation connects the two.
iₚ = κ · √2 · I″k
The √2 converts RMS to peak. The factor κ accounts for the DC component and depends on the R/X ratio at the point of fault. IEC 60909-0 gives it as κ = 1.02 + 0.98 · e^(−3R/X).
In low-voltage installations downstream of a distribution transformer κ is typically around 1.8, which makes iₚ about 2.5 times I″k. In systems with a smaller resistive component κ approaches 2 and the factor rises to almost 2.8.
Put the other way round, take a number from a document without knowing which of the two it is, and you can be out by more than a factor of two. In either direction.
Where the mix-up gets expensive
The dangerous case is mistaking it downwards. If a document states a value that is in fact I″k and it is read as iₚ, the dynamic stress is assessed a factor of 2.5 too low. Busbar supports are then sized for a force that will be exceeded several times over in the event. This never shows in operation. It shows only in the one short circuit the installation was supposed to be built for.
The reverse case only costs money. Mistake iₚ for I″k and you buy switchgear with a breaking capacity you do not need.
What belongs in the documentation
A short-circuit value without a statement of which one it is has no use. Plant documents therefore need both the symbol (I″k or iₚ) and the point in the network the value applies to. A value at the transformer’s low-voltage terminals is a different one from the value at a sub-distribution board thirty metres away.
For a first estimate, three nameplate figures are enough, namely rated power, nominal voltage and short-circuit voltage uₖ. The transformer short-circuit current calculator takes them and states explicitly which of the two quantities the result is.
