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# Short Circuit Ratio Calculation2

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## Short Circuit Ratio Calculation

(OP)
Not familiar with short circuit ratio (X/R) of synchronous generator calculation.

Given generator reactances (Xd, X'd, X''d, ....), time constants, stator/rotor resistance, etc.

How would on compute the short circuit ratio ? (if it is possible with the above info.)

Thanks

### RE: Short Circuit Ratio Calculation

Yes, you could do the calculation given the generator subtransient reactance.

The short circuit ratio (SCr) is different than the X/R ratio. For generator applications, the SC ratio is the reciprocal of the synchronous reactance Xs

SCr = 1/Xs.

Please note that for SC purposes, the sub-transient reactance( X”d) should be used in the calc.

I hope this could help.

### RE: Short Circuit Ratio Calculation

(OP)
Thanks for the reply....When looking at manufacturers data sheets for different generators, the reciprocal of the synchronous reactance or subtransient reactance doesn't give the correct short circuit ratio that was also included on the data sheet.  Could this be the X/R ratio and not the short circuit ratio (as noted above).

------------------------------------------------------------
Example data sheet,

Xd = 2.6265 p.u
Xd = 1.6625 ohms

X''d = 0.1414 p.u
X''d = 0.0895 ohms

short circuit ratio = 0.4947
------------------------------------------------------------

From the info. on the generator data sheets (i.e. Gen. resistances (stator, field), reactances, time constants), can I determine the X/R ratio ?

Thanks again

### RE: Short Circuit Ratio Calculation

Short circuit ratio =
Field Amps for producing rated stator voltage on open circuit/Field Amps for producing rated stator current on three phase short circuit

For 2 pole turbogenerators, it is about 0.5 and for salient pole machines, it varies from 0.9 to 1.1

### RE: Short Circuit Ratio Calculation

Tonyflair,

MG Say (Performance and Design of AC machines) says that the unsaturated reactance is not affected by the operating conditions and hence quoted in the data sheets and is higher than 1/SCR. SCR is defined as reciprocal of synchronous reactance (saturated).
It appears the problem is you are looking at unsaturated reactance and the SCR in the datasheets of generator manufacturer and that explains the discrepancy you are finding. If you can obtain the saturated reactance value from the vendor, it should clear the air.
(the reactance values shall be in PU)

Trust the above is helpful.

"The un

### RE: Short Circuit Ratio Calculation

You should refer to the generator manufacturers decrement curves which indicate how the machine will behave under fault conditions given that this is determined by the AVR transfer function (dont go there).

The AVR often has a short circuit maintenance facility which increases the excitation to maintain terminal volts under fault conditions in order to allow the protection to operate.

Just looking at the electromagnetic characteristics of the machine will not give you the whole picture.

_______________________________________
Regards -

Colin J Flatters
Consulting Engineer & Project Manager

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