Short-circuit current calculation per IEC 60909-0 — the equivalent voltage source method

The guide on prospective short-circuit current and Icu sizing cites IEC 60909-0 as the standard that defines the concepts of Ik'' (initial symmetrical short-circuit current) and Ip (peak short-circuit current), but does not go into the calculation method itself. This guide covers that method: the equivalent voltage source method that IEC 60909-0 prescribes for calculating short-circuit currents in low-voltage and high-voltage networks.

The premise: one equivalent source at the fault location, no load currents

IEC 60909-0 does not calculate short-circuit currents by modeling the actual operating state of the network just before the fault (with all actual voltages at every node and all actual load currents). Instead, the standard introduces an equivalent voltage source with a fixed, standardized magnitude at the fault location itself, and represents all other active sources in the network (the grid itself, generators, motors) by their internal impedance without a driven voltage source. This is a deliberate simplification: instead of needing to know the exact but unknown pre-fault loading condition, the method produces a calculation that depends solely on the network impedances and one standardized source voltage.

The voltage factor c: cmax and cmin

To account for the spread in actual operating voltage (which normally lies within a certain bandwidth around the nominal voltage) and other uncertainties, IEC 60909-0 multiplies the nominal voltage by a voltage factor c, which differs by voltage level and by calculation purpose:

cmax is used to calculate the maximum short-circuit current — determining the required switching and breaking capacities (Icu/Icn) of protective devices.
cmin is used to calculate the minimum short-circuit current — determining whether protective devices (fuses, circuit breakers, differential relays) actually operate fast enough for a fault at the farthest point of a circuit.

For low-voltage networks, IEC 60909-0 typically gives a value around 1.05 for cmax (networks with a permitted voltage tolerance of ±6%) or 1.10 (networks with a permitted tolerance up to +10%/−6%), and a value of 0.95 for cmin. It is essential to state, for every calculation, which c-value was used and why, since Icu sizing and protection selectivity serve fundamentally different purposes and therefore require different c-values.

Note: cmax and cmin in practice produce two separate calculations for the same network — one for sizing the breaking capacity (using cmax), and one for checking the operating times of protective devices for a fault at the farthest point (using cmin). Using these two values interchangeably for the wrong purpose leads to an incorrect conclusion in both directions.

Combining the network impedance: grid, transformer, cable, motor

The equivalent voltage source method requires that all impedances between the supplying source and the fault location be combined into one resulting impedance (with a resistive and a reactive component):

The impedance of the supplying grid at the connection point, typically derived from the short-circuit power at that point as stated by the grid operator.
The impedance of each transformer in the supply chain, derived from the short-circuit voltage percentage (uk%) and the rated power of the transformer.
The impedance of each cable or line, depending on cross-section, material, length, and (for AC) the reactance per unit length.
Where rotating machines (motors, generators) are present near the fault location: their contribution to the short-circuit current, which can initially be significant but decays rapidly (motors feed current back during the first cycles after the fault from their own stored magnetic energy, also known as motor back-feed).

These impedances are combined in series and parallel, just as in an ordinary AC network calculation, into the resulting impedance Zk at the fault location, from which Ik'' then follows directly from the equivalent source voltage divided by this impedance (multiplied by the relevant factor).

From Ik'' to Ip: the peak factor κ (kappa)

Ik'' is the symmetrical rms value of the short-circuit alternating current immediately after the fault occurs. The actual instantaneous peak value of the current in the first half-cycle — the peak short-circuit current Ip — is higher, because an aperiodic DC component arises when the fault does not occur exactly at the voltage zero crossing. IEC 60909-0 calculates Ip by multiplying Ik'' by a peak factor κ, which depends on the R/X ratio (resistive versus reactive component) of the resulting network impedance: the smaller this ratio (the more inductive the network), the larger κ and therefore the higher the relative peak compared to Ik''. This peak value determines the required dynamic (making capacity) strength of switchgear and busbars, in addition to the thermal strength determined by Ik'' and the clearing time.

Practical relevance

When substantiating a short-circuit current calculation for an installation under NEN 1010 — for example to verify the breaking capacity (Icu) of a main distribution board, or to check the clearing time per chapter 434/435/436 — it must be explicitly recorded which voltage factor (cmax or cmin) was applied for which purpose, and which impedance contributions were included (with or without motor back-feed, for example). Short-circuit calculation software typically implements IEC 60909-0 directly, but the result is only reliable if the entered impedance data (grid short-circuit power, transformer uk%, cable lengths and cross-sections) is correct.

Common mistakes

Mixing up cmax and cmin — cmax belongs to sizing breaking capacities (maximum short-circuit current), cmin to checking protective device clearing times (minimum short-circuit current); applying the wrong value for the wrong purpose leads to an unwarrantedly optimistic or unwarrantedly pessimistic conclusion.
Confusing Ik'' with Ip — Ik'' is the symmetrical rms short-circuit alternating current, Ip is the asymmetrical instantaneous peak value including the DC component; only Ip is relevant to the required making capacity (dynamic strength) of equipment.
Applying the peak factor κ without regard to the actual R/X ratio of the network — using a generic κ value from a table without checking the actual impedance composition of the specific installation can produce a peak value that is too low.
Forgetting motor back-feed in installations with significant connected motor power near the fault location, causing both Ik'' and Ip to be underestimated.