Calculating the short-circuit current across the terminals of a synchronous generator

Calculating the short-circuit current across the terminals of a synchronous generator

Alternators and motors

Calculating the short-circuit current across the terminals of a synchronous generator is very complicated because the internal impedance of the latter varies according to time.

When the power gradually increases, the current reduces passing through three characteristic periods:

  1. Subtransient (enabling determination of the closing capacity of circuit breakers and electrodynamic contraints), average duration, 10 ms
  2. Transient (sets the equipment’s thermal contraints), average duration 250 ms
  3. Permanent (this is the value of the short-circuit current in steady state).
The short-circuit current is calculated in the same way as for transformers but the different states must be taken account of.
Short-circuit current - three characteristic periods

Short-circuit current – three characteristic periods

The short-circuit current is given by the following equation:

Isc = Ir / Xsc

Xsc - Short-circuit reactance c/c

The most common values for a synchronous generator are:

StateSubtransient X”dTransient X’dPermanent Xd
Xsc10 – 20%15 – 25%200 – 350%


Calculation method for an alternator or a synchronous motor.

  • Alternator 15 MVA
  • Voltage U = 10 kV
  • X’d = 20%

Short-circuit calculation example

All electrical installations have to be protected against short-circuits, without exception, whenever there is an electrical discontinuity; which more generally corresponds to a change in conductor cross-section.

The short-circuit current shall be calculated at each stage in the installation for the various configurations that are possible within the network, in order to determine the characteristics of the equipment that has to withstand or break this fault current.

Reference: Medium voltage design guide – Schneider Electric

About Author //


Edvard Csanyi

Edvard - Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV high power busbar trunking (<6300A) in power substations, buildings and industry fascilities. Designing of LV/MV switchgears. Professional in AutoCAD programming and web-design. Present on

One Comment

  1. Eric Stark
    Jan 13, 2014

    Edvard hi,
    1. Isc is not constant in time (exponentially collapsing on its DC component), and should not be expressed as a constant, unless you define it’s time of occurrence.
    2. The contribution of the reactive part of the load was completely omitted. Why?
    3. There is a difference between 1phase-GND, 2 phases shorting, 3 phases shorting, 2 phases and GND, and 3 phases to GND short circuits. The formulation will be different in each case!

    Kind regards,

    Eric Stark
    Sr. Eng. Trainer & Consultant
    Protection & Control Engineering
    T: 1-416-546-546-1
    LinkedIn profile @:

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