Transformer X/R Ratio Calculator

Calculate per-unit resistance (R) and reactance (X) values from transformer nameplate data for network modelling and short circuit analysis.

Transformer Nameplate Data

Calculated Values

Resistance (R)
- p.u.
Reactance (X)
- p.u.
X/R Ratio
-

Additional Values

Impedance (Z) - p.u.
Base Impedance - Ω
R (ohms, HV side) - Ω
X (ohms, HV side) - Ω

Transformer X/R sets the peak current your switchgear has to make. Checking make and break duty across the whole network is a short-circuit study. Short-circuit and power system studies →

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Related: Turn this X/R into a peak make current with the fault waveform tool

Calculation Method

Per-Unit Resistance:

R = PCu / Srated

Where PCu is copper losses in MW and Srated is MVA rating

Per-Unit Reactance:

X = √(Z² - R²)

Base Impedance:

Zbase = V² / S

Where V is in kV and S is in MVA

Actual Impedance:

Zactual = Zp.u. × Zbase

This is the two-winding transformer method of IEC 60909-0:2016, clause 6.3.1, formulas (7) to (9), written per unit. For a maximum fault calculation the standard also applies the impedance correction factor KT of clause 6.3.3, which this tool does not.

Worked Example

An 11 kV, 2 MVA transformer with 6 % impedance and 20 kW load loss.

R = 0.020 MW / 2 MVA = 0.0100 p.u.

Z = 6 / 100 = 0.0600 p.u.

X = √(0.0600² − 0.0100²) = 0.0592 p.u.

X/R = 0.0592 / 0.0100 = 5.92

Zbase = 11² / 2 = 60.5 Ω, so R = 0.605 Ω and X = 3.579 Ω on the 11 kV side

Enter 11, 2, 6 and 20 above to reproduce it. That X/R gives a peak factor of κ = 1.02 + 0.98 e−3/5.92 = 1.61 (IEC 60909-0), so the first peak reaches 1.61 × √2 = 2.28 times the r.m.s. fault current. The fault waveform tool plots that current and the d.c. component at break.

A transformer X/R on its own does not give the X/R at a fault point: the source, cables and other transformers all add their own R and X. Building that network model is part of our short-circuit studies.

Minimum Impedance by Rating

IEC 60076-5:2006, Table 1 gives the recognised minimum short-circuit impedance for two-winding transformers. Use the nameplate value where you have one; these are floors, not typical values.

Rated power (kVA) Minimum impedance (%)
25 to 630 4.0
631 to 1,250 5.0
1,251 to 2,500 6.0
2,501 to 6,300 7.0
6,301 to 25,000 8.0
25,001 to 40,000 10.0
40,001 to 63,000 11.0
63,001 to 100,000 12.5
Above 100,000 Above 12.5, by agreement

Resistance does not scale with the impedance. IEC 60909-0 clause 6.3.1 notes that R/X generally falls as transformers get larger, so X/R rises with rating. Take the load loss from the test report.

Frequently Asked Questions

How do you calculate the X/R ratio of a transformer?

Take the per-unit resistance as the load loss at rated current divided by the rating, and the per-unit impedance as the nameplate impedance divided by 100. The reactance is the square root of Z squared minus R squared, and X/R is X divided by R. This is the method of IEC 60909-0:2016 clause 6.3.1. A 2 MVA, 6 % transformer with 20 kW load loss gives R = 0.010 p.u., X = 0.0592 p.u. and X/R = 5.92.

Why does transformer X/R matter?

X/R sets how slowly the d.c. component of a fault current decays, and so the peak make current. IEC 60909-0 takes the peak factor as kappa = 1.02 + 0.98 e^(-3R/X). At X/R = 5.92 kappa is 1.61; a higher X/R gives a higher peak for the same r.m.s. fault current.

Does X/R increase with transformer size?

Yes. IEC 60909-0 clause 6.3.1 states that R/X generally decreases with transformer size, and that for large transformers the resistance may be neglected when calculating the r.m.s. short-circuit current. It still has to be included for the peak current and the d.c. component.

Which losses should I enter?

The load loss, also called copper loss: the total loss in the windings at rated current, P_krT in IEC 60909-0. Take it from the factory test report. The no-load (iron) loss does not enter the short-circuit impedance.

What impedance should I use if I do not know it?

The nameplate or test report value. Without one, IEC 60076-5:2006 Table 1 gives the recognised minimum impedance by rating, for example 6.0 % for 1,251 to 2,500 kVA. A minimum is a floor, not a typical value, and a lower impedance gives a higher fault level.

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Or call 07951 651 013 or email enquiries@stardeltapower.co.uk