Losses in Transformer — Types, Formulas & How to Reduce Them
No machine in the world is 100% efficient — every electrical machine has some losses. A transformer, despite being a highly efficient static device (typically 95–99%), also suffers from energy losses that reduce its output power. Understanding these losses is essential for designing efficient transformers and predicting their performance under varying load conditions.
Types of Losses in Transformer
Since a transformer is a static machine with no moving parts, it does not have mechanical losses like friction or windage. The losses in a transformer are purely electrical and magnetic in nature:
- Copper Loss (Variable Loss) — depends on load current
- Iron Loss (Constant Loss) — depends on supply voltage and frequency
- Stray Loss — due to leakage flux
- Dielectric Loss — in insulation (negligible at low voltages)
Copper Loss (I²R Loss)
Copper loss occurs due to the resistance of the primary and secondary windings. When current flows through the winding conductors, heat is produced according to Joule's law. This energy dissipated as heat is called copper loss or I²R loss.
Where:
- I₁, I₂ = Primary and secondary currents
- R₁, R₂ = Resistance of primary and secondary windings
Copper loss can also be expressed in terms of equivalent resistance referred to one side:
Key Point: Copper loss varies as the square of the load current. At half load, copper loss is only 25% of its full-load value. This is why copper loss is also called variable loss.
Copper loss is measured using the Short Circuit Test of the transformer.
Iron Loss (Core Loss)
Iron loss occurs in the magnetic core of the transformer due to the alternating magnetic flux. It is the sum of two components — hysteresis loss and eddy current loss.
Key Point: Iron loss remains practically constant from no-load to full-load because the flux in the core depends on the applied voltage (which remains constant), not on the load current. This is why iron loss is also called constant loss.
Iron loss is measured using the Open Circuit Test of the transformer.
Hysteresis Loss
Hysteresis loss occurs due to the repeated reversal of magnetization in the transformer core. When the core is subjected to an alternating magnetic field, the magnetic domains in the core material must realign every half cycle. The energy consumed in this molecular friction is dissipated as heat.
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| B-H Curve (Hysteresis Loop) of Transformer Core |
The hysteresis loss is given by Steinmetz's empirical formula:
Where:
- η = Steinmetz hysteresis coefficient (depends on core material)
- Bmax = Maximum flux density (Tesla)
- f = Frequency of supply (Hz)
- V = Volume of core (m³)
The area enclosed by the B-H curve (hysteresis loop) represents the energy lost per cycle per unit volume. Materials with a narrow hysteresis loop (like CRGO silicon steel) have lower hysteresis loss.
Eddy Current Loss
When the alternating magnetic flux links with the transformer core, it induces an EMF in the core body according to Faraday's Law of Electromagnetic Induction. This induced EMF causes circulating currents within the core material called eddy currents. These currents produce I²R heating in the core resistance, resulting in eddy current loss.
Where:
- Ke = Eddy current constant
- t = Thickness of each lamination
- f = Frequency of supply
- Bmax = Maximum flux density
Key Point: Eddy current loss is proportional to the square of lamination thickness. This is why transformer cores are made of thin laminated sheets (0.35–0.5 mm) insulated from each other, rather than a solid block.
Stray Loss & Dielectric Loss
Stray Loss: A small portion of the magnetic flux does not confine itself to the core — it leaks into surrounding metallic parts (tank, clamps, bolts). This leakage flux induces eddy currents in these parts, causing stray loss. In large power transformers, stray loss can be 10–15% of total losses.
Dielectric Loss: The insulating materials (oil, paper, pressboard) experience molecular polarization under alternating electric stress. This causes a small dielectric loss. It is significant only in high-voltage transformers (above 33 kV).
Comparison Table — Copper Loss vs Iron Loss
How to Reduce Transformer Losses
Transformer Efficiency & Condition for Maximum Efficiency
The efficiency of a transformer is defined as the ratio of output power to input power:
The condition for maximum efficiency is:
This means a transformer operates at maximum efficiency when its variable loss (copper loss) equals its constant loss (iron loss). For most distribution transformers, this occurs at about 50–75% of full load — which is why they are designed to operate most efficiently at typical loading conditions rather than at full load.
Frequently Asked Questions
1. Why does a transformer have no mechanical losses?
A transformer is a static device with no rotating parts. Unlike motors and generators, there is no friction, windage, or bearing loss. Only electrical (copper) and magnetic (iron) losses occur.
2. Which test determines copper loss and iron loss?
The Open Circuit (OC) Test determines iron loss because it is conducted at rated voltage with no load current. The Short Circuit (SC) Test determines copper loss because it is conducted at rated current with reduced voltage.
3. Why is the transformer core laminated?
Lamination breaks the path of eddy currents. Since eddy current loss is proportional to the square of lamination thickness (Pe ∝ t²), using thin insulated sheets drastically reduces eddy current loss compared to a solid core.
4. At what load does a transformer have maximum efficiency?
Maximum efficiency occurs when copper loss equals iron loss. For a transformer with full-load copper loss Pcu(FL) and iron loss Pi, the load fraction for max efficiency is: x = √(Pi / Pcu(FL)). Typically this is 50–75% of full load.
5. Why is transformer rating given in kVA instead of kW?
Copper loss depends on current (I²R) and iron loss depends on voltage (V). Neither depends on the power factor of the load. Since losses are independent of power factor, the transformer's capacity is rated in kVA (= V × I) rather than kW (= V × I × cosφ). Read more: Why Transformer Rating is in kVA Instead of kW