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

Home / Technical Articles / 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.

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:

 State Subtransient X”d Transient X’d Permanent Xd Xsc 10 – 20% 15 – 25% 200 – 350%

### Example

Calculation method for an alternator or a synchronous motor.

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

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

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### Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry facilities. Professional in AutoCAD programming.

1. soudagar
Aug 14, 2020

Hii Sir,
While calculating short circuit current of alternator, which reactance you have considered?? Whether transient or subtransient??
1.How to calculate source impedance of an alternator?
2.Impedance of busbar??

2. Vamsi Patwari
May 01, 2018

Also, it is important to understand the KVA rating is off the alternator and not the generator set. Often times manufacturers tend to provide the generator KW/KVA rating which is typically lower than the alternator KW/KVA and could impact your calculations.

Any thoughts about why to use alternator KW rating value when the generator KW rating is smaller and probably can be the bottleneck of the energy being produced?

3. nitin
May 25, 2015

4. nitin
May 14, 2015

Great

5. Ahmed
Jan 14, 2015

Guys,

please note that in the example shown, the maximum fault current has been calculated which is taken into consideration to size the Cable. BB and CBs. the issue of this example to help you determining the Maximum Short Circuit capability of the electric items such as Cables and CBs hence we shall calculate it in the sub-transient phase (3 phase SC which is the worst scenario.)
neglecting the cables impedance, this put the calculations in a safe side.
concerning the power factor, it wasn’t considered unity as some people say, but we shall consider the apparent power in MVA and that what the writer has used as a factor in calculation.
this is the most simple and safe method as the same time to calculate the Short circuit current generated by an Alternator

Ahmed

6. Vince
Jan 07, 2015

The example shown is poor at the very best….it leaves a lot of info out…calculation for the short circuit current is for a LINE current given a delta connected winding……so, it is as follows…
15000000/3X10000=500A which is the PHASE current….showing the 870 indicated that the winding of the machine was delta connected which means you take the 500 and multiply radical 3 which would then equal 866 A which the author confusingly rounded up to 870 A. This divided by .2 (referencing the top end of the range for sub-transient reactance or mid-point for the transient reactance) will then get you 4350 A.

Also, as mentioned by the other commenter, it appears the power factor used was unity and therefore no reactive part considered, if there is any at all. And finally and as mentioned by the other commenter, the calculated current could be either sub-transient or transient since it does change in time. If the intent was to calculate short circuit current, then the reactance in the ‘Permanent Xd’ range should have been used.

This is what is referred to as short circuit current…….it is past sub-transient and transient.

7. 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
RNItechnology
Sr. Eng. Trainer & Consultant
Protection & Control Engineering
T: 1-416-546-546-1
[email protected]
http://www.RNItechnology.com