What is transformer efficiency, and how is it calculated?

Short Answer:

Transformer efficiency is the measure of how well a transformer converts input power into useful output power without losing energy. It shows the percentage of input energy that is successfully delivered to the load. A highly efficient transformer wastes very little energy in the form of heat or other losses.

Efficiency is calculated using the formula:
Efficiency (%) = (Output Power / Input Power) × 100
Since transformers mainly lose energy due to core loss and copper loss, their efficiency is usually very high—often above 95%, especially under full load.

Detailed Explanation:

Transformer efficiency and its calculation

Introduction

Transformers are static electrical devices that transfer energy between two or more circuits through electromagnetic induction. During this process, some amount of energy is lost in the form of heat due to core losses and copper losses. Transformer efficiency indicates how effectively the transformer performs this energy transfer. It is a key factor when designing or selecting a transformer for electrical systems, especially in power transmission and distribution where losses can affect system performance and cost.

Definition of Transformer Efficiency

Transformer efficiency is defined as the ratio of the output power to the input power. It tells us how much of the input electrical energy is successfully delivered to the load and how much is lost inside the transformer.

Efficiency (η) = Output Power / Input Power

To express it as a percentage:
Efficiency (%) = (Output Power / Input Power) × 100

Where:

  • Output Power = Power delivered to the load (in watts or kilowatts)
  • Input Power = Total power supplied to the transformer, including losses

Types of Transformer Losses

  1. Core Loss (Iron Loss)
    • Occurs in the core due to alternating magnetic fields
    • Includes hysteresis and eddy current losses
    • Remains almost constant, regardless of load
    • Depends on supply voltage and frequency
  2. Copper Loss
    • Occurs in the windings due to resistance when current flows
    • Varies with the square of the load current (I²R loss)
    • Increases as the load increases

Because of these two losses, the input power is always slightly more than the output power.

Formula for Transformer Efficiency

Let:

  • Pout = Output Power (kW)
  • Pin = Input Power (kW)
  • Losses = Total losses = Core loss + Copper loss

Then:
Efficiency = Pout / (Pout + Losses)
Or
Efficiency = Output / Input × 100%

For full-load efficiency:
η = (Output Power) / (Output Power + Core Loss + Full-load Copper Loss) × 100

For half-load or other conditions, copper loss is calculated accordingly:
Copper Loss at x% load = (x/100)² × Full-load Copper Loss

Example Calculation

If a transformer delivers 95 kW output power and has core loss = 1 kW and copper loss = 2 kW:

  • Input Power = Output + Losses = 95 + 1 + 2 = 98 kW
  • Efficiency = (95 / 98) × 100 = 96.94%

So, the transformer operates with about 96.94% efficiency at that load.

Maximum Efficiency Condition

The efficiency of a transformer is maximum when:
Copper Loss = Core Loss

At this point, the total loss is minimized, and the transformer operates most efficiently. This typically occurs at a specific load (not always full load).

Typical Efficiency Range

  • Distribution Transformers: 95% to 98%
  • Power Transformers: Up to 99%
  • The efficiency depends on load level, transformer design, and maintenance

Why Transformer Efficiency Matters

  • Higher efficiency means less power loss and lower operating cost
  • Reduces heat generation, improving transformer lifespan
  • Important for energy conservation in large-scale systems
  • Improves reliability and performance of the electrical network
Conclusion

Transformer efficiency tells us how well a transformer converts input power into output power with minimal losses. It is calculated by dividing the output power by the input power and is expressed as a percentage. Core and copper losses reduce the efficiency, but well-designed transformers can achieve efficiency levels of 95% or more. Understanding and calculating transformer efficiency is important for ensuring energy savings, reliable operation, and cost-effective power system design.