Work out the voltage regulation of a distribution transformer. Adjust the rated kVA, percent resistance, percent reactance, load and power factor to see the no-load voltage, voltage drop and copper loss update in real time — and watch the secondary voltage rise instead of sag at a leading power factor.
Parameters
Rated capacity S
kVA
Rated secondary voltage V
V
Secondary terminal voltage at full load
Percent resistance %R
%
Voltage drop from winding resistance at rated current
Percent reactance %X
%
Voltage drop from leakage reactance at rated current
Load level
%
Actual load as a fraction of rated capacity
Power factor cosφ
Power-factor type
Lagging = inductive, leading = capacitive
Results
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Voltage regulation VR (%)
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No-load voltage (V)
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On-load voltage (V)
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Voltage drop ΔV (V)
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Copper loss (this load) (kW)
—
Verdict
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Phasor diagram — I·R drop and I·X drop
Taking the on-load terminal voltage V as the reference, the load current at angle φ, the I·R drop along the current and the I·X drop perpendicular to it are added to reach the no-load voltage. Colour shows the magnitude of the regulation (green → orange → red).
Approximate voltage regulation. The + sign is for a lagging power factor and the − sign for a leading one (which can give a negative regulation, i.e. a voltage rise). S/S_rated is the load fraction and φ the power-factor angle.
No-load voltage V_nl and copper loss P_cu at the current load. Copper loss scales with the square of the load. V: on-load voltage.
What is Transformer Voltage Regulation?
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I always thought a transformer just converts the input voltage exactly by its turns ratio. What is "voltage regulation"?
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That is true for an ideal transformer, but a real one is different. The windings have resistance and "leakage reactance", and when load current flows through them the voltage drops internally. So when you connect a load, the secondary voltage sags a little. Put another way, the voltage with the load removed — "no load" — is higher than at full load. That difference, divided by the full-load voltage, is the "voltage regulation".
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I see — so the voltage "droops" when you connect a load. Is that a bad thing?
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The smaller the regulation, the "stiffer" the supply — it holds its voltage well even when the load changes. Household lighting and precision equipment want a stable voltage, so a small regulation is desirable. Try raising the "percent reactance %X" on the left. You will see VR jump up. %X is the size of the leakage reactance, and it is the lead actor in voltage regulation.
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You're right, raising %X increases the regulation. Is there anything besides the amount of current that matters?
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Yes — the "power factor". With an inductive load (motors and the like) the current lags the voltage, a "lagging power factor", and the reactance drop adds to the voltage sag. Move the power factor on the "voltage regulation vs power factor" chart below. You will see that, for the same current, the regulation differs hugely with the power factor.
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Wait — when I switched the power-factor type to "leading", the regulation went negative! Is that a bug?
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No, it is physically correct. With a leading power factor (a capacitive load, like capacitors) the reactance drop works in the opposite direction — it becomes a subtraction. The regulation then goes negative, and the secondary voltage actually RISES under load. In fact, on lightly-loaded distribution lines with many power-factor-correction capacitors, the voltage at the far end can rise too high — the "Ferranti effect". This tool reproduces that phenomenon faithfully.
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When I want to make the voltage regulation smaller, what should I change?
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The most effective move is to choose a transformer with a smaller %X. You can also run a lighter load or improve the power factor. But making %X small means a larger current flows during a short circuit, which makes protection harder. So regulation and short-circuit protection are a trade-off. In the field, engineers switch transformer taps or use an on-load tap changer (OLTC) to compensate the voltage on the spot.
Frequently Asked Questions
Voltage regulation is the rise in a transformer's secondary voltage when its load is removed, expressed as a fraction of the full-load voltage. An ideal transformer would hold its output perfectly constant, but a real one cannot: its windings have resistance and leakage reactance, and the load current flowing through them produces an internal voltage drop (the I·Z drop). As a result, the secondary voltage sags when load is applied, so the no-load voltage is higher than the full-load voltage. That percentage difference is the voltage regulation, and a small value means a "stiff" supply that holds its voltage well.
Using the percent resistance %R and percent reactance %X, the approximate per-cent regulation is VR% ≈ (S/S_rated)(%R·cosφ + %X·sinφ) plus a small second-order term for a lagging power factor, and VR% ≈ (S/S_rated)(%R·cosφ − %X·sinφ) plus a small term for a leading power factor. The first term dominates and the second is a minor correction. With a lagging factor the reactance drop adds to the sag, while with a leading factor it subtracts, making the regulation smaller and sometimes negative.
At a leading (capacitive) power factor the load current leads the voltage, so the reactance drop acts in the opposite sense. When the first term %R·cosφ − %X·sinφ goes negative, the whole regulation becomes negative, meaning the secondary voltage actually RISES under load instead of sagging. This is a real effect seen on lightly-loaded distribution lines fitted with power-factor-correction capacitors, and it is related to the Ferranti effect. A negative regulation is not a calculation error — it is physically correct.
Voltage regulation depends on the percent impedance (%R and %X), the load level and the power factor. To reduce it: (1) choose a transformer with a smaller %X (lower leakage reactance), (2) run the transformer at a lighter load, and (3) improve the power factor (bring a lagging factor toward unity, or go leading). However, a smaller %X means a larger short-circuit current, so regulation and short-circuit protection are a trade-off. In practice, tap changers or on-load tap changers (OLTC) compensate the voltage.
Real-World Applications
Sizing distribution transformers: Pole-mounted transformers and the transformers inside switchgear cubicles must keep the customer's voltage within a defined band. A large voltage regulation means the voltage swings widely between the light load at night and the peak load during the day. At the design stage, engineers estimate the regulation from %R, %X and the expected load — as in this tool — and check that the band is met. If it is not, they adjust the tap position or adopt a transformer with a smaller %X.
Power-factor correction and the Ferranti effect: Factories install power-factor-correction capacitors to bring a lagging power factor toward unity, but if the capacitors are not switched off when the load is light (for example at night), the factor becomes leading and the transformer's secondary voltage — and the voltage at the line end — rises. Setting the power-factor type to "leading" in this tool reproduces the negative-regulation behaviour and makes it intuitive why automatic capacitor switching control is needed.
Parallel operation and load sharing: When two or more transformers run in parallel, ideal load sharing in proportion to the capacity ratio requires equal percent impedances (especially %X). If they differ, the transformer with the smaller percent impedance takes more than its share of the load and may overload on its own. Calculating the voltage regulation is the first step in understanding how much each transformer pulls the voltage down, and it underpins any parallel-operation study.
A pre-study for power-system analysis: Before running a full load-flow study, estimating the voltage regulation of a single transformer gives a first read on the voltage profile of the whole system. If the detailed analysis differs greatly from this estimate, it serves as a sanity check that points to an error in the entered percent impedance or tap setting.
Common Misconceptions and Pitfalls
The most common pitfall is thinking voltage regulation is a single fixed number for the transformer. The regulation is not set by %R and %X alone — the actual value depends strongly on the load level and the power factor. The same transformer has a completely different regulation at full load with a 0.8 lagging power factor than at half load with unity power factor. The "voltage regulation" quoted in a catalogue is usually the value at full load and a specific power factor, so it must be recomputed for the real operating conditions. Move the load level and power factor in this tool and that dependence becomes clear.
Next, assuming a negative regulation is a calculation error. At a leading (capacitive) power factor the reactance-drop term becomes a subtraction, so the regulation can be negative. This means that, far from sagging, the secondary voltage actually RISES when load is applied — a real phenomenon on lightly-loaded distribution lines with many power-factor-correction capacitors. Do not look at a negative regulation and conclude the formula is wrong; understand that with a capacitive load a voltage rise is physically possible.
Finally, the misconception that the smaller %X is, the better. It is true that a smaller %X gives a smaller voltage regulation and a more stable voltage. But %X also limits the short-circuit current. If %X is made too small, a short-circuit fault drives an excessive current that can exceed the breaker rating or mechanically damage the windings. Improving the regulation and limiting the short-circuit current are a trade-off, and in practice %X is set by balancing the two. A distribution transformer's %X is typically designed in the range of a few percent up to about 10 %.
How to Use
Enter the transformer rated kVA (e.g., 50 kVA for a distribution unit) and secondary voltage (typically 400 V or 480 V).
Input the percent resistance (%R) and percent reactance (%X) from the transformer nameplate—for example, %R = 1.2%, %X = 4.5% for a medium-power transformer.
Adjust the load current slider or enter a specific load in kW; the simulator calculates voltage regulation VR = (%R·cos φ + %X·sin φ), no-load voltage, on-load voltage, copper losses, and issues a verdict on acceptability against IEC 60076 limits (typically ±5% for distribution transformers).
Worked Example
A 25 kVA distribution transformer with 400 V secondary, %R = 1.5%, %X = 5.2%, operates at 18 kW load (0.95 PF lagging). The simulator computes: ΔV = (1.5 × 0.95 + 5.2 × 0.312) × 18 / (25 × 4) ≈ 3.8 V drop. On-load voltage = 400 − 3.8 = 396.2 V. Voltage regulation VR = 3.8 / 400 = 0.95%. Copper loss at full load = (1.5 / 100)² × 25 ≈ 0.094 kW. Verdict: PASS—regulation well within ±5% limit.
Practical Notes
Reactive load increases voltage drop: motor starts (high %X sensitivity) cause larger ΔV than resistive loads—use the PF slider to model this distinction.
Older transformers (1980s era) often show %R = 2% to 3%; modern units drop to 1.2% to 1.8%, reducing losses and improving regulation for datacenter or industrial feeders.
For rural distribution at long distances, cascade regulation: a 630 kVA primary transformer with ±2% tap changer feeding a 50 kVA secondary limits secondary swing to ±3%—verify using two simulator runs.