# What is the Efficiency of Transformer & Its Derivation

Similar to an electrical machine, the efficiency of the transformer is also defined as the same as the ratio of output power and the input power (efficiency = output/input). Electrical devices like transformers are highly efficient devices. We know that there are different types of transformers available in the market based on the application where the full load efficiency of these transformers ranges from 95% to 98.5%. When a transformer is highly efficient, then the input, as well as output, has almost the same value. Thus it is not practical to calculate the efficiency of the transformer by using output/input. So, this article discusses an overview of the efficiency of the transformer.

## What is the Efficiency of Transformer?

The efficiency of the transformer can be defined as the intensity or the amount of power loss within a transformer. Therefore, the ratio of the secondary winding’s power output to the primary winding’s power input. The efficiency can be written like the following.

**Efficiency (η) = (Power Output/Power Input) X 100**

Generally, efficiency can be denoted with ‘η’. The above equation is suitable for an ideal transformer wherever there will be no transformer losses as well as the complete energy within the input gets moved to the output.

Therefore, if transformer losses are considered & if the transformer efficiency is analyzed within practical states, the following equation is mainly considered.

**Efficiency = ((Power O/P) / (Power O/P + Copper Losses + Core Losses)) × 100%**

Or else it can be written as **Efficiency = (Power i/p – Losses) / Power i/p × 100**

**= 1− (Losses/i/p Power) × 100**

So, all the input, o/p, and losses are mainly expressed in terms of power (Watts).

#### Power of a Transformer

Whenever an ideal transformer is considered with no losses, then the transformer’s power will be stable because the voltage V is multiplied through current I is stable.

So, the power within the primary is equivalent to the power within the secondary. If the voltage of the transformer increases then the current will be decreased. Similarly, if the voltage is decreased, then the current will be increased so that the output power can be maintained constant. Therefore the primary power is equal to the secondary power.

**P _{Primary }= P_{Secondary}**

**V _{P}I_{P}cosϕ_{P}=V_{S}I_{S}cosϕ_{S}**

Where ∅_{P} & ∅_{s} are primary as well as secondary phase angles

### Determination of Transformer Efficiency

Generally, the efficiency of a normal transformer is extremely high that ranges from 96% to 99%. So the efficiency of the transformer cannot be decided through high accuracy by measuring input and output directly. The main dissimilarity among the readings of input and output and input of instruments is very small that an instrument error will cause an error of the 15 % orders within the transformer losses.

Additionally, it is not convenient and expensive to include the essential loading devices of the exact ratings of voltage & power factor (PF) to load the transformer. There is also a large amount of power wastage & no information is obtainable from a test regarding the number of transformer losses like iron & copper.

The transformer losses can be determined through the accurate method would be to calculate losses from short circuit & open-circuit tests, so that efficiency can be determined

From an open circuit test, the iron loss like P1 = P0 or Wo can be determined

From the short circuit test, the copper loss on full loads like Pc = Ps or Wc can be determined

Copper loss on a load x times full load = I2^{2} R_{02 }=> x^{2} Pc

Transformer efficiency (η) = V_{2}I_{2} CosΦ / V_{2}I_{2} CosΦ + Pi + x^{2} Pc

In the above equation, the result of instrument readings can be restricted to losses simply so that overall efficiency can be achieved from it is very accurate as compared with the efficiency attained through direct loading.

### Maximum Efficiency Condition of a Transformer

We know that copper loss = I12R1

Iron loss = Wi

Efficiency = 1- Losses/Input

= 1- (I12R1 + Wi/ V1 I1 CosΦ1)

= 1 – (I1 R1/V1 I1 CosΦ1) – (Wi/ V1 I1 CosΦ1)

Differentiate the above equation with respect to I1

dη/dI1 = 0 – (R1/V1CosΦ1) + (Wi/ V1 I12 CosΦ1)

The efficiency will be high at dη/dI1 = 0

Therefore, the efficiency of transformer will be high at

R1/V1CosΦ1 = Wi/ V1 I12 CosΦ1

I12R1/V1I12 CosΦ1 = Wi/ V1 I12 CosΦ1

I12R1 = Wi

Therefore, the transformer efficiency will be high once copper and iron losses are equivalent.

### All-Day Efficiency

As we discussed above that the transformer ordinary efficiency can be given as

**Ordinary Efficiency of Transformer = Output (Watts)/Input (Watts)**

However, in some kinds of transformers, their performance cannot depend on their efficiency. For instance, in distribution transformers, their primaries always energized. However, their secondary windings will supply a slight load most of the time in a day

Once transformer secondary’s will not supply any load, after that only transformer’s core losses are significant & copper losses are not present.

Copper losses are significant only once transformers are loaded. Therefore, for these transformers, losses like copper are mostly less important. So the performance of the transformer can be compared based on the energy used in a single day.

The transformer’s all-day efficiency is less always as compared with normal efficiency of it.

**Factors that affect the efficiency of a transformer** include the following

- The current heating effect in a coil
- Induced eddy current’s Heating Effect
- Iron Core’s Magnetization.
- Leakage of Flux

#### How to Improve the Efficiency of Transformer?

There are different methods to improve the efficiency of transformers like loop area, insulation, coils resistance, and flux coupling.

**Loop area**

**Insulation**

The insulation among core sheets must be ideal to prevent eddy currents.

**Primary and Secondary Coil’s Resistance**

The material of primary and secondary coils must be stable so that their electrical resistance is extremely little.

**Flux Coupling**

Both the coils of the transformer must be wound in such a manner that flux coupling among the coils is utmost as power transfer from one coil to another will takes place during flux linkages.

Thus, this is all about an overview of the efficiency of the transformer. Transformers are electrical devices with high efficiency. So, most of the transformer’s efficiency will range from 95% to 98.5%. Here is a question for you, what are the different types of transformers available in the market?