Electrical Engineering

Transformer Equivalent Circuit Calculator

Get every equivalent-circuit parameter of a single-phase or three-phase transformer straight from the short-circuit and open-circuit test readings — plus the single-phase diagram and voltage regulation from no-load to short-circuit.

Transformers Equivalent circuit Short-circuit & open-circuit tests Voltage regulation

Equivalent circuit parameters (from the tests)

Turns ratio a –
Rated I1n – A
Rated I2n – A
Zcc – Ω
%Zcc – %
%Rcc – %
%Xcc – %
cos φ0 –

Referred to Primary

Rcc – Ω
Xcc – Ω
Rfe – Ω
Xm – Ω
Lcc – mH
Lm – mH

Operating point

Secondary U2 – V
Regulation – %
I1 – A
I2 – A
Equivalent circuit diagram
Phasor diagram

About this calculator

A transformer's behavior can be fully characterized, without ever loading it, using two simple tests: the open-circuit (no-load) test and the short-circuit test. Together they give every parameter of the equivalent circuit — the series impedance (Rcc, Xcc) that represents the winding resistance and leakage flux, and the shunt branch (Rfe, Xm) that represents core losses and magnetizing reactance. This calculator does that reduction for you, referred to either side, in either the approximate or exact model, and lets you see the resulting single-phase diagram from no-load all the way to short-circuit.

How to use it

1. Enter the rating

Rated power and both rated voltages. For a three-phase transformer, say whether each rated voltage is line or phase.

2. Enter both tests

Vcc/Icc/Pcc from the short-circuit test and V0/I0/P0 from the open-circuit test, noting which side each was performed on.

3. Pick a model

Approximate (L) for quick regulation estimates, or Exact (T) to solve the full circuit including the magnetizing branch.

4. Move the load slider

0% is the open-circuit condition; the "Short circuit" shortcut sets Zload = 0 (and switches to the Exact model, since Kapp's formula does not hold there).

The formulas

Zcc = Vcc / Icc    Rcc = Pcc / Icc²    Xcc = √(Zcc² − Rcc²)
cos φ0 = P0 / (V0·I0)    Rfe = V0² / P0    Xm = V0 / (I0·sin φ0)
%Zcc = (Zcc · In) / Un × 100    Lcc = Xcc / (2π·f)    Lm = Xm / (2π·f)
ε% = (U20 − U2) / U20 × 100
ε% ≈ (Rcc%·cos φ + Xcc%·sin φ) + (Xcc%·cos φ − Rcc%·sin φ)² / 200

The last line is Kapp's approximate voltage-regulation formula, used by the Approximate (L) model. The Exact (T) model instead solves the full circuit — including the magnetizing branch — as a linear system of phasor equations, with no small-angle approximation.

Worked example

50 kVA, 2400/240 V single-phase transformer

Short-circuit test (primary): Vcc = 48 V, Icc = 20.8 A, Pcc = 617 W → Rcc = 1.426 Ω, Xcc = 1.814 Ω (referred to primary).
Open-circuit test (secondary): V0 = 240 V, I0 = 5.41 A, P0 = 186 W → Rfe = 309.7 Ω, Xm = 44.8 Ω (referred to secondary).
At rated load (100%) and cos φ = 0.8 lagging, both models agree closely: U2 ≈ 235.4 V, a voltage regulation of about 1.9%.

Reading the results

  • %Zcc is the nameplate impedance voltage. The lower it is, the smaller the voltage drop under load, but the larger the short-circuit current (roughly 100 / %Zcc times the rated current).
  • Regulation is positive for lagging loads and can become negative for leading (capacitive) ones, where the secondary voltage rises above its no-load value.
  • Phasor diagram: it is drawn with the same fixed scales for every load (voltages relative to U1, currents relative to 150 % of the rated current), so the vectors grow as you move the slider. A » after a label means the vector is longer than the scale allows and is clipped.
  • Referred to: primed quantities (U2', I2') are referred to the primary; when you choose the secondary as reference it is U1' and I1' that carry the prime.

Frequently asked questions

Why does the frequency input not change the circuit parameters?
Rcc, Xcc, Rfe and Xm come directly from the test readings (V, I, P), so they do not depend on the frequency. It is only used to express the reactances as equivalent inductances, Lcc = Xcc / (2πf) and Lm = Xm / (2πf), shown next to them. The tests must have been run at the transformer's rated frequency, because reactance changes with frequency.
Why is %Zcc the same whether I refer the circuit to the primary or the secondary?
%Zcc expresses Zcc relative to the rated impedance of the side it was measured on. When you refer Zcc to the other side, both the impedance and the rated current/voltage scale by the same turns-ratio factor, so the percentage is unchanged. It's a side-independent number, which is why it's the one most commonly quoted on a nameplate.
How is the load defined for the operating point?
The load is a constant impedance sized to draw the selected % of Sn at the given power factor when the secondary is at its rated voltage. The Exact (T) model solves the circuit with that impedance, so as the secondary voltage sags the delivered current drops slightly (in the worked example, 204.3 A at 100 % instead of 208.3 A). The Approximate (Kapp) model instead fixes the load factor: I2 = (% / 100) · I2n exactly, and only the voltage is corrected through ε.
Why does the exact (T) model split Rcc/Xcc 50/50 between primary and secondary?
The two tests only give the total series impedance, not how much of it sits in each winding. Splitting it evenly is the standard assumption when no further winding data is available. In the Exact (T) model the split has a very small effect on the result (in the worked example, putting the whole impedance on the primary side changes U2 by only about 0.05 V), because the magnetizing branch sits between the two series blocks. In the Approximate (L) model it has no effect at all, since only the total Rcc and Xcc are used.
How is the voltage regulation defined?
Regulation is ε = (U20 − U2) / U20 × 100, where U20 is the secondary voltage at no load. In the Approximate model U20 is the rated secondary voltage and ε comes from Kapp's formula. In the Exact model U20 is the no-load voltage given by the circuit itself, which is a hair below the rated value because the exciting current drops a little voltage across R1 + jX1. That is why the regulation at 0 % load is exactly 0 while U2 can read slightly under the rated voltage.
Does this work for a three-phase transformer bank?
Yes — select "Three-phase" and indicate whether each rated voltage was entered as line or phase. The calculator reduces everything to the single-phase (per-phase) equivalent circuit, assuming a wye/star-equivalent connection and that test power readings are given as the total three-phase power. The voltage you enter for each test is read with the same line/phase setting as the rated voltage of the side where that test was performed.