# Which Transformer is More Efficient When Operates on 50Hz or 60Hz?

**A 50/60 Hz Transformer – Which One is More Efficient and Why?**

A transformer is designed to be operated on both 50Hz and 60Hz frequency. For the Same rating, which one is more efficient when:

- Operates on 50 Hz
- Operates on 60 Hz

**Obliviously! If the rating and parameters of the transformer is same in both cases, a 50Hz transformer is more efficient then 60Hz transformer.**

How? Lets do some calculations.

In previous posts, we showed that in an inductive circuit, when frequency increases, the circuit power factor decreases. Consequently, the transformer output decreases.

Let’s consider the following example.

*Transformer Rating & Parameters*

- kVA Rating = 100kVA
- R = Resistance = 700Ω
- L = Inductance = 1.2 H
- F = Frequency 50/60 Hz

Related Post: Can We Operate a 60Hz Transformer on 50Hz Supply Source and Vice Versa?

**When Transformer Operates on 50 Hz Frequency**

We are interested in the power factor. So lets find it by “Cos θ = R/Z” where Z = Impedance which depends on Inductive Reactance “X_{L}“.

Inductive Reactance X_{L} = 2π*f*L

X_{L} = 2 x 3.1415 x 50Hz x 1.2H

X_{L} = 377 Ω

Impedance = Z = √ (R^{2}+X_{L}^{2})

Z = √ (700^{2}+ 377^{2})

Z = 795 Ω

Power Factor = Cos θ = R/Z = 700/795

Cos θ = 0.88

Transformer Output (Real Power)

kW = kVA x Cos θ

kW = 100kVA x 0.88

kW = 88000 W = 88kW

**When Transformer operates on 60 Hz Frequency**

The same transformer is now connected to the 60Hz frequency. We will do the same calculation as above for 50Hz transformer.

**Inductive Reactance X _{L} = 2πfL **

X_{L} = 2 x 3.1415 x 60 Hz x 1.2 H

X_{L }= 452.4 Ω

Impedance = Z = √ (R^{2 }+ X_{L}^{2})

Z = √ (700^{2}+ 452.4^{2})

Z = 833.5 Ω

Power Factor = Cos θ = R/Z = 700/833.5

Cos θ = 0.839

Transformer Output (Real Power)

kW = kVA x Cos θ

kW = 100 kVA x 0.839

kW = 83900 W = 83.9 kW

- Related Post: What is Motor Efficiency & How to improve it?

**What is the Difference ?**

The power factor is higher of 50Hz operated transformer then 60Hz transformer. Now see the difference in transformer output (in Watts i.e. Real or Active Power)

- Output of the 100 kVA Transformer when operated on 50Hz Supply Frequency = 88kW
- Output of the 100 kVA Transformer when operated on 60Hz Supply Frequency = 83.9kW

88kW – 83.9kW = 4100 W = 4.1kW

It may looks small amount of wattage but If we do the same (as above) for the power transformers with high rating i.e, for 500 kVA or MVA Transformers, the result may be huge as shown below.

*Suppose everything is same as above, without frequency*

*Power Transformer Output in Watts When operates on 50 Hz.*

kW = kVA x Power Factor (Cos θ)

kW = 500 kVA x 0.88 = 44000 W = 440 kW

*Power Transformer Output in Watts When operates on 60 Hz.*

kW = kVA x Cos θ

kW = 500 kVA x 0.839 = 419500 = 419.5 kW

Difference in Real Power i.e. in Watts

440 kW – 419.5 kW = 20500 = 20kW

The above calculation shows that a 50Hz transformer is more efficient with high output power as compared to the 60Hz transformer when the rating and parameters of the transformer is same and there is no insulation problems. In addition, if T/F is not designed to be operated on both 60 and 50 Hz, the more current will flow in case of 50Hz transformer with leads in higher power loss due to “I^{2}R losses”. This is due to the the following reasons:

- When frequency (f) decreases, Inductive reactance (X
_{L}) decreases (X_{L}∝ f). - When Inductive reactance (X
_{L}) decreases, Impedance (Z) decreases (Z ∝ X_{L}). - When Impedance decreases, Current increases (X
_{L}∝ 1/I where I ∝ I/Z).

If a transformer is not designed for both 50 and 60 Hz frequencies as the supply frequency in US is 60Hz while in EU etc are 50Hz, then:

- When a 60Hz transformer is being operated on 50Hz supply source, it should be derated i.e. the supply voltage must be reduced by 1/6 to reduce the peak flux in the core and reduce the heat as well.
- When a 50Hz transformer is being operated on 60Hz supply source, the applied voltage should be 20% increased if there is no problem in insulation.

Again, 50Hz transformer has higher output efficiency than 60Hz transformer with same rating.

Related Posts:

- Is it possible to Operate a 50Hz Transformer on 500Hz source of the same voltage?
- Is it possible to Operate a 500Hz Transformer on 50Hz source of the same voltage?
- Can we replace a 110/220 Turns Transformer with 10/20 Turns?
- What will happen if the primary of a transformer is connected to DC supply?

50Hz transforme is more efficient than 60Hz transformer, because iron losses of this transforme is less than 60Hz transforme.

Definitely 50 Hz becz frequency is inversly praportional to leakage flux