Fahad's Electrical Encyclopedia — Transformers

Electrical Transformer Efficiency

How do you calculate transformer efficiency from power and losses? And why does it peak when the core loss equals the copper loss? With a worked example.

Trainer Fahad Refai Transformer Calculations Quick read

Transformers are among the most efficient machines ever made by humans: no rotating parts and no friction, so their efficiency exceeds 98-99% in larger sizes. Yet understanding how efficiency is calculated and where it peaks has real practical and economic value.

The Basic Formula

Efficiency η = Output Power / Input Power × 100%
η = Pout / (Pout + Core Loss + Copper Loss) × 100%
Worked Example

A 500 kVA transformer supplies a full load at a power factor of 0.8; its core loss is 1.2kW and its copper loss at full load is 5.5kW:

  • Output power = 500 × 0.8 = 400 kW
  • Total losses = 1.2 + 5.5 = 6.7 kW
  • η = 400 ÷ 406.7 × 100 ≈ 98.35%

When Does Efficiency Peak?

The core loss is constant while the copper loss increases with the square of the load. Mathematically, efficiency is at its maximum at the load level at which the copper loss equals the core loss. That's why distribution transformers — which operate at partial load most of the time — are designed so that their efficiency peak occurs around 50-75% of load, not at full load.

Why Does This Matter to You?

  • A 0.5% efficiency difference in a large transformer operating continuously equals megawatt-hours wasted annually and a real bill.
  • When comparing two offers of the same rating, compare the no-load and load losses in the catalog, not just the price — the cheaper purchase may be the more expensive to operate.
Interview question: At what load is a transformer's efficiency at its highest? Why?

Sample answer: At the load level at which the variable copper loss equals the constant core loss. Because the core loss is constant regardless of load, while the copper loss is proportional to the square of the current, differentiation proves that the ratio of total losses to output reaches its minimum at this equality point. That's why distribution transformers are designed so their efficiency peak occurs at a partial load matching their actual loading pattern.

Common Mistake

Assuming maximum efficiency always occurs at full load. Many transformers are designed for a peak efficiency at 50-75% of load, and operating them continuously at full load means operating in a lower-efficiency, higher-temperature region.

Related Topics

Core (Iron) Loss and Copper Loss in Transformers Open-Circuit Test for Transformers Short-Circuit Test for Transformers Why Is Transformer Capacity Rated in Kilovolt-Amperes (kVA)?

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