Transformer Open-Circuit and Short-Circuit Tests: Extracting the Equivalent Circuit

Begin With the Test Boundary

This guide concerns a single-phase transformer at a declared sinusoidal frequency. Record the winding energized, open or shorted terminal condition, tap, RMS terminal voltage, RMS current, real input watts, ambient and winding temperature, and measuring-instrument accuracy. Perform tests only under a qualified, current-limited procedure with appropriate isolation and protection. The short-circuit test deliberately uses a small fraction of rated voltage; applying rated voltage to a shorted winding is dangerous. For three-phase units, per-phase and connection conversions must be defined separately; the single-phase equations below cannot be applied to line readings without that conversion.

Unlike the Transformer Load and Loss Guide, which starts with rating and load, this workflow starts from test observations to extract model parameters. It does not replace a dielectric, temperature-rise, short-circuit withstand, or production acceptance test.

Open-Circuit Test: Excitation Branch

Leave the opposite winding open and apply the specified test-side voltage at the stated frequency with a controlled source. Often the lower-voltage winding is energized for practical instrumentation, but the connection must match the equipment rating and approved procedure. Measure V0, I0, and P0 simultaneously. The apparent input power is V0 I0, so a physically consistent measurement has 0 ≤ P0 ≤ V0 I0. The open winding carries no load current, but the energized winding still carries I0; its copper loss and meter burden may matter when P0 is small.

For example, V0 = 120 V RMS, I0 = 0.200 A RMS, P0 = 12 W, and f = 60 Hz give apparent power 24 VA and power factor 0.5. Then Ic = 0.100 A, Im = sqrt(0.04 - 0.01) = 0.1732 A, Rc = 1200 Ω, Xm ≈ 692.8 Ω, and Lm ≈ 1.838 H, all referred to the energized side. Use the Transformer Magnetizing Current Calculator for the ideal Lm-to-Im relation after extracting Lm; the calculator does not infer Lm from three raw open-circuit meter readings. If P0 approaches V0 I0, the reactive remainder approaches zero and the inferred Lm becomes ill-conditioned. Recheck power factor, instrument range, and the approximation before reporting a large inductance.

Controlled Short-Circuit Test: Series Branch

With the specified secondary safely shorted, increase the applied voltage from zero only until the intended test current is reached. Measure Vsc, Isc, and Psc on the energized winding. Low applied voltage normally keeps core flux and core loss small relative to the load-dependent loss, but that is an approximation. Do not assume Psc is exactly the sum of DC winding I²R: leads, contacts, stray flux, AC conductor effects, temperature, and meter uncertainty can contribute. Check 0 ≤ Psc ≤ Vsc Isc before taking a square root.

At Vsc = 12 V, Isc = 5 A, and Psc = 30 W, Zeq = 2.4 Ω, Req = 1.2 Ω, and Xeq = sqrt(2.4² - 1.2²) ≈ 2.078 Ω on the energized side. If an ideal turns ratio is 2:1 from measured side to opposite side, the same branch referred to the opposite side is one quarter of those impedance values. Do not compare the 2.4 Ω test-side impedance directly with a secondary load resistance without referring one of them. A case with Req greater than Zeq is not a negative-reactance transformer; it signals inconsistent readings or an invalid simplified model.

Use the Model for Regulation and Loss Checks

Refer the series branch to the load side and use load-side RMS current and the specified displacement power factor. For a sinusoidal lagging load, a small-drop approximation is ΔV ≈ I(R_eq cosφ + X_eq sinφ). For a leading load, the reactance term changes sign. This is a voltage-drop estimate, not a guarantee of full-load terminal voltage. Source regulation, saturation, harmonics, winding temperature, and load crest factor can make the measured result differ. Measure no-load and actual loaded terminal voltage at the same input voltage and frequency, then use the Transformer Voltage Regulation Calculator with its stated denominator convention.

For a screening loss budget, use corrected open-circuit real power as an estimate of excitation-related real loss near the same voltage and frequency, and corrected short-circuit real power as an estimate of rated-current load loss near the same winding temperature. Scale only the copper-like component with current squared; stray loss and harmonics may not obey the same rule. Input-output efficiency still requires real watts on both sides or a loss model with every material loss accounted for. The Transformer Efficiency and Loss Calculator closes the real-power balance, but cannot decide which measured watts belong to core, copper, lead, or stray loss. The Core Loss Guide covers material and waveform effects that a single open-circuit test point cannot extrapolate reliably.

Measurement and Reporting Checklist

Repeat measurements after warm-up, at the intended frequency, and with instrument ranges that resolve low power factor. Report raw readings alongside derived parameters, correction assumptions, and uncertainty. Compare predicted current and regulation with safe loaded measurements rather than presenting the fitted circuit as a certificate of transformer safety.

Common Mistakes

• Applying rated voltage to a shorted winding.
• Treating I0 as pure reactive magnetizing current.
• Treating every open-circuit watt as core loss without checking copper and meter burden.
• Reporting measured-side impedance as if it were already load-side impedance.
• Mixing RMS current and peak voltage in an equivalent circuit.
• Using Psc/Isc instead of Psc/Isc squared for resistance.
• Taking sqrt(Zeq squared minus Req squared) when inconsistent readings make it negative.
• Assuming one test point predicts saturation and harmonic behavior.
• Using cold short-circuit data to predict hot full-load loss without correction.
• Claiming the short-circuit test measures destructive fault withstand.

Engineering Source

The New Jersey Institute of Technology transformer laboratory procedure presents the open- and short-circuit measurements, equivalent-circuit extraction, and regulation check. Its apparatus and voltage steps are lab-specific; use the approved procedure and ratings for your own hardware.