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Transformer Efficiency
All day Efficiency & Condition for maximum Efficiency
Table of Contents
Efficiency of Transformer
Formulas for Transformer Efficiency
Condition for Maximum Efficiency of Transformer
All Day Efficiency of Transformer
Efficiency of Transformer
Transformer efficiency may be defined as the ratio between Output and Input.

Transformer Efficiency = Output / Input

On specified power factor and load, the transformer efficiency can be found by dividing its output on Input (similar to other electrical machines i.e. motors, generators etc). But the values of both Input and Output should be same in unites (i.e. in Watts, kilowatts, megawatts etc)

But note that a transformer has very high efficiency because the losses occur in transformer are very low. Since the Input and Output almost equal, therefore measurement of input and output is practically not possible. The best way to find the transformer efficiency is that, first determine the losses in transformer and then calculate the transformer efficiency with the help of those losses calculation.

You may also read: EMF Equation Of a Transformer
Transformer Efficiency, All day Efficiency & Condition for maximum Efficiency

Formulas for Transformer Efficiency
Efficiency = ? = Output / Input

Efficiency = ?= Output / (Output + Losses) ….. (As Input = Output +Losses)

Efficiency = ?= Output / (Output +Copper Losses + Iron Losses)

You may also find the Efficiency by the following formula

Efficiency = ?= Output / Input

Efficiency = ? = (Input – Losses) / Input ….. (As Output = Input – Losses)

Taking LCM

Efficiency = ? = 1 – (Losses /Input)

As we know that the rating of Transform is expressed in kVA not in kW. But the efficiency doesn’t depend on VA i.e. it would be expressed in Power Watts (kW) not in kVA. Although, the Losses are directly proportional to VA (Volt-Amperes), thus, efficiency depends on Power factor on every kind of VA load. And the efficiency would be maximum on unity (1) Power factor.

You may also read: Power Transformers Maintenance, Diagnostic & Monitoring
Good to Know

We can also find transformer efficiency by determining:

Core losses by open circuit test or No Load test, and
Copper losses by short circuit test.
Condition for Maximum Efficiency of Transformer
We know that,

Copper Loss = WC = I12 x R1 or I22 x R2

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

Suppose to the primary side of transformer…

Primary Input = P1 = V1 x I1 Cos?1

Efficiency = ? = Output / Input

Efficiency = ? = (Input – Losses) / input ….. (As Output = Input – Losses)

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

Efficiency = ? = (P1 – WC – WI) / P1

Efficiency = ? = (V1 x I1 Cos?1 – I12 x R1 – WI) / V1 x I1 Cos?1

Taking LCM

Efficiency = ? = 1- (I12 x R1 / V1I1 Cos?1) – (WI / V1 x I1 Cos?1)

Or

Efficiency = ? = 1- (I1 x R1 / V1 Cos?1) – (WI / V1 x I1 Cos?1)

Differentiate both sides with respect to I1

D? / dI1 = 0 – ( R1 / V1 Cos?1) + (WI /V1 x I12 Cos?1)

D? / dI1= – ( R1 / V1 Cos?1) + (WI / V1 x I12 Cos?1)

For Maximum Efficiency, the value of (D? / dI1) should be Minimum i.e.

D? / dI1 = 0

The above Equation can be written as

R1 / (V1 Cos?1) = (WI /V1 x I12 Cos?1)