# Impedance ratio

#### Ainsley Whyte

##### Senior Member
Can someone explain impedance ratio X/R, Really i am working on replacement of a sub- station and was ask for the X/R Ratio to check short circuit current.The truth is the substation is very old from the 60 s therefore information is very difficult to get regarding to this switch gear and i need to determined the current MVA ratings with the plan to increase MVA ratings for more loads.

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#### Russs57

##### Senior Member
Well, you know what X/R means.....so I'm guessing what you really want is some firm numbers to work from when factual information isn't available.

Probably about the best you can do is reference a standard like : IEEE Std. 242 – IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems.

A web page like this might help a little. It does suck to have engineering come down to "educated guesses". Just err on the side of caution.

This one has some historical info.

Doubt I helped any but good luck.

#### Hv&Lv

##### Senior Member
It does suck to have engineering come down to "educated guesses". Just err on the side of caution.
I was told many years ago I don’t have to get the exact answer, just make sure I’m “close enough”

#### Ainsley Whyte

##### Senior Member
Now that I have my short circuit current and my impedance ratio, how can i calculate my MVA size for a switch gear ? of course I have the
the single line diagram.

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#### paulengr

##### Senior Member
Now that I have my short circuit current and my impedance ratio, how can i calculate my MVA size for a switch gear ? of course I have the
the single line diagram.
Wrong direction.

Impedance of the transformer is based on the size, system voltage, and %Z. Impedance is a result, not an input. Given voltage and assuming ANSI standard %Z we can calculate MVA backwards but that’s not how it’s done.

MVA is determined by a load study. You are looking at a short circuit study. Typically first we determine the required load. In an upgrade situation it is more common to measure load then estimate the new load. Short circuit studies play a role in determining AIC, as inputs to coordination studies, to stability studies, and as inputs to arc flash studies. Theoretically we can get to AIC then go back and modify %Z on the transformer spec (alter the core and copper loss ratios) but this is rarely actually done. Usually we just use ANSI standard %Z as a consequence, not a variable.

#### Julius Right

##### Senior Member
If you have the peak short-circuit current-from the utility- you can calculate X/R. If you know the d.c. component current you may calculate X/R.
From IEEE Std 551/2006 IEEE Recommended Practice for Calculating Short-Circuit Current in Industrial and Commercial Power Systems
Ipeak=√2.Iac,rms.[1.02+0.98.e^(-3/(X/R)]
Idc=√2.Iac,rms.[0.02+0.98.e^(-3/(X/R)]
Extracting X/R=3/ln[(Ipeak/√2/Iac-1.02)/0.98]
Iac,rms= a.c. component of short-circuit current

#### NewtonLaw

##### Senior Member
Now that I have my short circuit current and my impedance ratio, how can i calculate my MVA size for a switch gear ? of course I have the
the single line diagram.
If you are attempting to determine the short circuit duty in MVA for a particular circuit breaker or switchgear, Utilities simply calculate the available short circuit current based on the maximum system design for example, my substations are designed for a maximum fault duty of 20,000 amps. If I choose to use 15 kV switchgear, the fault duty MVA would be 520 MVA = 20 kA X 15 kV X 1.7321. Thus the typical fault rating would likely be 600 MVA.

The importance of the X/R ratio for the fault is to allow you to determine the asymmetrical fault current. Many standards allow you to just use the symmetrical fault up to a certain X/R ratio since part of the standard many require an assumed X/R of say 6, 10, 15 etc. based on the applied standard. For substation switchgear and the associated circuit breakers, it is best to know the actual asymmetrical fault level if you are doing the design specification. Hope this helps.