Transformers and Distribution
Turns ratio, losses and efficiency, regulation, kVA sizing, inrush, short-circuit current and distribution layout.
How a transformer works
Two coils wound on a common iron core are linked by the alternating magnetic flux. The voltage across each coil is proportional to its number of turns, and the power in equals the power out (less losses), so the currents are in inverse ratio:
V₁ ÷ V₂ = N₁ ÷ N₂ = I₂ ÷ I₁
Ratings: kVA, impedance and losses
A transformer is rated in kVA (not kW), because its heating depends on the current and the voltage, whatever the power factor of the load. The nameplate also gives the voltages and the tapping range, the impedance (percent voltage drop at rated current with the secondary shorted, usually 4 to 6 percent for distribution units), the no-load (iron) loss Pfe that is always present when energized, the load (copper) loss Pcu at full load that varies with the square of the load, the vector group and the cooling class (ONAN for oil, AN for dry-type).
Worked example: a 100 kVA distribution transformer
Worked example: 11 kV to 400 V, 100 kVA, 4 percent impedance
- Turns ratio = 11 000 ÷ 400 = 27.5.
- Rated currents: secondary Is = S ÷ (√3 Vs) = 100 000 ÷ (1.732 × 400) = 144.3 A; primary Ip = 5.25 A.
- The workshop: the press motor takes 14.2 kVA (AC Power Basics) and the other loads total 45 kVA with a demand factor of 0.75 (they never all run together): total 14.2 + 33.8 = 48.0 kVA, a loading of 48 percent: a good size, with room for growth.
- Resistive and reactive parts of the impedance: R = Pcu ÷ S = 1.75 percent, X = √(4² − 1.75²) = 3.60 percent. In ohms (referred to 400 V) the transformer is Z = 0.04 × 400² ÷ 100 000 = 0.064 Ω.
- Inrush at switch-on: the magnetizing current spikes to 8 to 12 times the rated primary current for a few cycles: about 52 A here. The protection on the primary must ride through it.
Efficiency and regulation
η = x S cos φ ÷ (x S cos φ + Pfe + x² Pcu)
Worked example: efficiency and voltage regulation
- Pfe = 350 W and Pcu = 1 750 W: at full load, power factor 0.9, η = 90 ÷ (90 + 0.35 + 1.75) = 97.72 percent.
- Best efficiency at x = √(350 ÷ 1 750) = 0.447: 98.29 percent. A transformer that is lightly loaded is wasting the iron loss; it loses 6 594 kWh a year at the workshop’s 48 percent load (about 791 at 0.12 per kWh).
- Voltage regulation (the drop from no-load to load) ≈ R% cos φ + X% sin φ at a lagging power factor: 1.75 × 0.85 + 3.60 × 0.527 = 3.4 percent at full load, so the 400 V no-load secondary delivers 386 V under full load. Tapping the primary (typically ±2.5 and ±5 percent) raises the secondary by 10 V per step to compensate.
Short-circuit current
The impedance limits the fault current: Isc = Irated ÷ Zpu. For the 100 kVA unit, Isc = 144.3 ÷ 0.04 = 3 608 A at the terminals (25 times rated), assuming an infinite supply behind it. Every breaker and fuse downstream must be able to break this current; cable impedance reduces it along the run (see Protection, Earthing and RCDs). A bigger transformer or a lower impedance gives a higher fault level.
Winding connections and vector groups
The three primary and secondary windings are connected in star or delta, and the combination sets the phase shift between them, written as a vector group. The usual distribution transformer is Dyn11: delta on the high-voltage side (it traps third harmonics and gives a stable earth reference) and star with an accessible neutral on the low-voltage side, with a phase shift of 30° (the 11 means 11 o’clock). Transformers can be paralleled only if their voltage ratio, vector group, impedance (within about 10 percent) and phase sequence match; unequal impedances make the small unit take more than its share.
Other transformers
| Type | What it does | Notes |
|---|---|---|
| Distribution (oil or cast resin) | steps 11 or 33 kV down to 400 V | resin is dry, fire-safe and used indoors; oil is cheaper and more overload-tolerant |
| Isolation transformer | separates a circuit from the supply (1:1), for safety and noise | a 1 kVA unit at 230 V carries 4.3 A; the secondary is not earthed, so a single fault does not cause a shock |
| Autotransformer | a single winding with a tap; smaller and more efficient for small ratios | no isolation; 400 V to 230 V uses a ratio of 0.58 and carries only 43 percent of the power through the magnetic circuit |
| Control and instrument transformers | small supplies for control circuits; current transformers (CTs) and voltage transformers (VTs) for metering | never open the secondary of a live CT: the voltage rises dangerously |
| Drive and rectifier transformers | supply large converters | higher ratings for harmonic currents (K-factor) |
Related
- Previous: Three-Phase Systems. Next: Induction Motors and Drives.
- Inductors, Transformers and Relays for small transformers.
- System Integration for panels and supplies.
- Electrical Power: the whole guide.
FAQ
Why are transformers rated in kVA?
Because the copper loss depends on current and the iron loss on voltage, whatever the power factor. A 100 kVA transformer can supply 100 kW at unity power factor or only 85 kW at 0.85.
Can a transformer be run overloaded?
For short periods an oil-filled unit tolerates some overload, depending on its thermal time constant and ambient temperature (IEC 60076-7 gives the loading guide), but the life halves for every 6 to 8 K of winding temperature above the design value.
What is no-load loss?
The iron loss (hysteresis and eddy current) present whenever the transformer is energized: it runs 8 760 hours a year regardless of load.
Why does a transformer hum?
Magnetostriction: the core changes shape slightly with the flux, at twice the supply frequency (100 Hz). Loose laminations or harmonics make it louder.
References
- IEC 60076 (power transformers), IEEE C57 series, IEC 60076-20 and EU Regulation 548/2014 (ecodesign limits on losses).
- Wildi, T., Electrical Machines, Drives and Power Systems, Pearson; Fitzgerald, A. E., et al., Electric Machinery, McGraw-Hill.
- Harlow, J. H., Electric Power Transformer Engineering, CRC Press.
Last reviewed: October 2026. Losses and impedance are typical for a 100 kVA distribution transformer.