In our other article All-day Efficiency of Transformer, we have learned what is all-day efficiency and how to calculate it. In this article, we want to know the efficiency of a transformer and the calculation formula.

## What is the Transformer Efficiency?

A transformer's ordinary or commercial efficiency is defined as the ratio of output power to input power.

**Efficiency = η = Output / Input**

Efficiency = η= Output / (Output + Losses)

As Input = Output + Losses

If we go into more detail about the **transformer losses**, just remind the previous articles about the transformer loss calculation.

Transformer Copper Loss the ,

**WC = I12 x R1 or I22 x R2**

Transformer Iron Loss,

**WI = Hysteresis Loss + Eddy Current Loss = WI = WH + WE**

Suppose to the primary side of transformer…

Primary Input = P1 = V1 x I1 Cosθ1

Efficiency = η = Output / Input

Efficiency = η = (Input – Losses) / input

(As Output = Input – Losses)

Efficiency = η = (Input – Copper losses – Iron Losses)/Input

Efficiency = η = (P1 – WC – WI) / P1

Efficiency = η = (V1 x I1 Cosθ1 – I12 x R1 – WI) / V1 x I1 Cosθ1

Efficiency = η = 1- (I12 x R1 / V1I1 Cosθ1) – (WI / V1 x I1 Cosθ1)

Or

Efficiency = η = 1- (I1 x R1 / V1 Cosθ1) – (WI / V1 x I1 Cosθ1)

Differentiating both sides w.r.t I1.

Dη / dI1 = 0 – ( R1 / V1 Cosθ1) + (WI /V1 x I12 Cosθ1)

Dη / dI1= – ( R1 / V1 Cosθ1) + (WI / V1 x I12 Cosθ1)

For maximum efficiency, the value of (Dη / dI1) should be minimum i.e.

Dη / dI1 = 0

Thus, the above equation can be rewritten as:

R1 / (V1 Cosθ1) = (WI /V1 x I12 Cosθ1)

Or, WI = I12 x R1*or * I22 x R2

Iron Loss = Copper Loss

Thus, the transformer will give the maximum efficiency when its copper loss is equal to iron loss:

I2 = √ (WI / R2)

The value of output current (I2) is the factor that makes it possible to equal the value of copper loss and iron loss (i.e. copper loss = iron loss).

### The range of transformer efficiency

The transformer's efficiency is generally in the range of 95 – 99 %. The efficiency can be as high as 99.7% for great power transformers with very low waste. Ideally, the efficiency of the Transformer should be hand 100%, but practically it is not possible due to various types of losses such as core losses or ohmic loss.

### Case Study of Transformer Efficiency

### Transformer Efficiency at Full Load

### Maximum Efficiency of Transformer

#### Output KVA Corresponding to Maximum Efficiency

- Working Principle of Transformer;
- Transformer Construction;
- Core-type Transformers;
- Shell-type Transformers;
- Elementary Theory of an Ideal Transformer;
- E.M.F. Equation of Transformer;
- Voltage Transformation Ratio;
- Transformer with losses but no Magnetic Leakage;
- Transformer on No-load;
- Transformer on Load;
- Transformer with Winding Resistance but no Magnetic Leakage;
- Equivalent Resistance;
- Magnetic Leakage;
- Transformer with Resistance and Leakage Reactance;
- Simplified Diagram;
- Total Approximate Voltage Drop in Transformer;
- Exact Voltage Drop;
- Equivalent Circuit Transformer Tests;
- Open-circuit or No-load Test;
- Separation of Core Losses;
- Short-Circuit or Impedance Test;
- Why Transformer Rating in KVA?;
- Regulation of a Transformer;
- Percentage Resistance, Reactance, and Impedance;
- Kapp Regulation Diagram;
- Sumpner or Back-to-back-Test;
- The efficiency of a Transformer;
- Condition for Maximum Efficiency;
- Variation of Efficiency with Power Factor;
- All-day Efficiency;
- Auto-transformer;
- Conversion of 2-Winding Transformer into Auto-transformer;
- Parallel Operation of Single-phase Transformers;
- Questions and Answers on Transformers;
- Three-phase Transformers;
- Three-phase Transformer Connections;
- Star/Star or Y/Y Connection;
- Delta-Delta or ∆/∆ Connection;
- Wye/Delta or Y/ Connection;
- Delta/Wye or ∆/Y Connection;
- Open-Delta or V-V Connection;
- Power Supplied by V-V Bank;
- Scott Connection or T-T Connection;
- Three-phase to Two-Phase Conversion and vice-versa;
- Parallel Operation of 3-phase Transformers;
- Instrument Transformers;
- Current Transformers;
- Potential or Voltage Transformers.

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