Transformer Secondary Short-Circuit

A screening estimate of bolted fault current at the transformer secondary terminals.

1. What this check does

Estimates the symmetrical bolted three-phase fault current at the transformer secondary terminals and, if you enter one, compares it with the equipment rating.

2. Inputs used

Transformer kVA, secondary line-to-line voltage, nameplate impedance %Z.
Optional: available fault level of the source in MVA; equipment interrupting or short-circuit rating in kA; transformer X/R and load power factor (regulation and asymmetry); running motor kVA on the secondary (motor contribution).

3. Formulas and assumptions

Full-load current

I_{FL} = \dfrac{\mathrm{kVA} \times 1000}{\sqrt{3}\,V}

Infinite bus

I_{SC} = \dfrac{I_{FL}}{Z\%/100}

Source impedance

Z_s\% = \dfrac{\mathrm{kVA}}{\mathrm{MVA}_{SC} \times 1000} \times 100

On the transformer base.

Finite source

I_{SC} = \dfrac{I_{FL}}{\bigl(Z\% + Z_s\%\bigr)/100}

Motor contribution

I_M = 4\,\dfrac{\mathrm{kVA}_M \times 1000}{\sqrt{3}\,V}

Low-voltage motors, about four times rated current (IEEE 141 / 242 practice).

Asymmetry

I_{\text{asym}} = I\sqrt{1 + 2e^{-2\pi/(X/R)}} \qquad I_{\text{peak}} = \sqrt{2}\,I\left(1 + e^{-\pi/(X/R)}\right)

Regulation

\mathrm{VR}\% = \%R\cos\varphi + \%X\sin\varphi + \dfrac{(\%X\cos\varphi - \%R\sin\varphi)^2}{200}

%R = Z%/√(1+(X/R)²), %X = %R·X/R. Full load, lagging power factor.

Symbols

$\mathrm{kVA}$	Transformer rating	kVA
$V$	Secondary line-to-line voltage	V
$I_{FL}$	Secondary full-load current	A
$Z\%$	Transformer impedance on its own base	%
$\mathrm{MVA}_{SC}$	Available utility short-circuit level	MVA
$Z_s\%$	Utility source impedance on the transformer base	%
$I_{SC}$	Symmetrical three-phase fault current at the secondary	A
$\mathrm{kVA}_M,\ I_M$	Running motors on the secondary; their fault contribution	kVA, A
$X/R,\ \%R,\ \%X$	Transformer X/R and its resistance and reactance in percent
$\varphi,\ \mathrm{VR}\%$	Load power factor angle; voltage regulation no load to full load	°, %

One-line from utility source through transformer to a fault on the secondary bus, with the equivalent circuit of source impedance and transformer percent impedance in series. — **Figure 1.** Source impedance and transformer impedance in series up to the fault.

The infinite-bus result is the upper bound for the transformer alone.
Source and transformer impedances are added as magnitudes, which assumes similar X/R ratios. This is a screening simplification.
Motor contribution is about four times the rated current of the running motors, the common screening value; the equipment rating is compared with the total.
Asymmetry uses the transformer X/R for the whole path; regulation is the full-load value at the power factor entered.
Nameplate impedance is used as given. Actual impedance may be lower within manufacturing tolerance, which increases fault current.

4. What is NOT checked

Secondary cable and bus impedance downstream of the terminals.
X/R multiplying factors against breaker test ratings (see Short-Circuit Duty), single-phase and ground faults.
Arc-flash incident energy and protective device coordination.

5. Reference standards

NEC 2023 110.9, 110.10 — interrupting rating and circuit impedance
IEEE Std C57.12.00 — transformer impedance tolerance

6. Validation cases

Hand-calculated cases run on every change. See Validation.

7. Known issues and changes

See the Engineering Notes. Try the tool: Transformer Secondary Short-Circuit.