Generator reactances Xd″, Xd′ and Xd — why a generator fault current is not constant

The [guide on short-circuit current calculation per IEC 60909-0](/guides/nen-1010/kortsluitstroomberekening-iec-60909-impedantiemethode) uses a generator's subtransient reactance Xd″ as the source for the initial symmetrical short-circuit current Ik″. This article covers the background of that reactance, and why it is only one of three different reactances a synchronous generator passes through during a short circuit.

Three reactances, three time windows

A synchronous generator behaves fundamentally differently from a network with a fixed impedance when a sudden short circuit occurs at its terminals: the machine's effective reactance changes over time, and with it the magnitude of the fault current the machine delivers. This happens in three recognisable phases:

Phase	Reactance	Time window (order of magnitude)	Characteristic
Subtransient	Xd″	first ~1-2 cycles (tens of ms)	Smallest reactance → highest fault current
Transient	Xd′	up to ~1-2 seconds	Medium reactance → decaying but still elevated fault current
Synchronous (steady-state)	Xd	sustained fault	Largest reactance → lowest, final fault current

Immediately after the fault occurs, induced eddy currents in the damper winding and the rotor core strongly damp the magnetic field, so that the machine behaves as if it has a small reactance Xd″ — this produces the highest initial fault current. As these damping currents decay (with a time constant T″d, typically on the order of tens of milliseconds), the effective reactance increases to Xd′, dominated by the more slowly decaying current in the field winding itself (time constant T′d, typically on the order of a second or more). Only once this transient effect has also decayed does the full synchronous reactance Xd remain — considerably larger than Xd″ and Xd′ — and the generator delivers its final, steady-state short-circuit current.

Why Xd is so much larger than Xd″

As an approximation, for a typical large synchronous generator Xd″ is smallest (roughly on the order of 10-25% on the machine's own base), Xd′ lies in between (roughly 20-35%), and Xd is largest (often 100% or well above). Because fault current is inversely proportional to reactance, this means the final, steady-state short-circuit current of a generator can be much lower than the initial current — for a generator without boosted excitation (forcing) from the voltage regulation system, the steady-state fault current can even fall close to, or below, the machine's rated current.

Note: the exact values of Xd″, Xd′, Xd and the associated time constants T″d, T′d and T′d0 are machine-specific data supplied by the manufacturer (typically on the test report or nameplate datasheet); this article covers the principle of the three phases, not universal figures that apply to every generator.

Why this matters for generator protection

This decaying fault current — often referred to as the generator's decrement — has a direct consequence for the setting of overcurrent protection on a generator feeder: an ordinary time-current protection (ANSI 50/51) set based on the high subtransient initial current may, by the time it is actually meant to trip, be faced with a fault that has already decayed to the transient or even synchronous level — possibly below the pickup threshold. For this reason, generator output protection is often implemented with a voltage-dependent overcurrent characteristic (ANSI 51V: voltage-restrained or voltage-controlled), which automatically lowers the pickup threshold as terminal voltage sags during the fault — remaining sensitive to a fault whose current has decayed to near, or even below, normal operating current.

Practical relevance

When coordinating generator protection with upstream and downstream protection devices, the generator's full decrement curve must be taken into account — not just the high subtransient initial value used in a single IEC 60909-0 Ik″ calculation. A protection setting based solely on Ik″ can miss a longer-sustained fault whose current has already decayed, unless voltage-dependent or differential protection is explicitly taken into account (see the generator differential protection (ANSI 87G) guide).

Common mistakes

Assuming a generator delivers a constant short-circuit current the way a network with fixed impedance does — the current actually decays through three phases as Xd″ transitions to Xd′ and finally Xd.
Applying only the subtransient reactance Xd″ (as used in an IEC 60909-0 Ik″ calculation) to the setting of a time-delayed overcurrent protection that is only meant to trip after the subtransient phase — the transient or synchronous reactance is decisive there, not Xd″.
Applying an ordinary, non-voltage-dependent overcurrent protection on a generator feeder without assessing whether the steady-state fault current (based on Xd) remains above the pickup threshold.
Neglecting the time constants T″d and T′d when assessing how quickly the fault current transitions from one level to another — these time constants, together with Xd″/Xd′/Xd, determine the full shape of the decrement curve.