# Transformer Losses and Efficiency

## In this article we will learn about the four main types of transformer losses and calculations for finding the efficiency of a transformer.

Transformers, like all devices, are not perfect. While ideal transformers do not have losses, real transformers have power losses. A transformer's output power is always slightly less than the transformer's input power. These power losses end up as heat that must be removed from the transformer. The four main types of loss are resistive loss, eddy currents, hysteresis, and flux loss.

## Resistive Loss

Resistive loss, or I2R loss, or copper loss, is the power loss in a transformer caused by the resistance of the copper wire used to make the windings. Since higher frequencies cause the electrons to travel more toward the outer circumference of the conductor (skin effect), electrical disturbances called harmonics have the effect of reducing the wire size and increasing resistive loss. These losses are the same as the power losses in any conductor and are calculated as follows:

$$P={{I}^{2}}R$$

where

P = power (in W)

I = current (in A)

R = resistance (in Ω)

For example, if a transformer primary is wound with 100′ of #12 copper wire that carries 15 A, what is the resistive loss in that coil?

The resistance of #12 copper wire is 1.588 Ω/1000′ at room temperature. Therefore, the resistance of 100′ of the wire is 0.1588 Ω.

$$P={{I}^{2}}R={{15}^{2}}\times 0.1588=35.7W$$

The transformer primary wiring consumes 35.7 W of power that is wasted as heat. If the transformer is not cooled properly, this heat increases the temperature of the transformer and the wires. This increased temperature causes an increase in the wire resistance, and the voltage dropped across the conductor. This loss varies with the current and is always present in the primary when it is energized. The secondary sees very little loss of this type when unloaded.

**Note**

*Changes that an electric utility makes to power delivery can affect the operation of in-plant transformers. A new area substation can boost the delivered voltage. New factories or commercial buildings may increase the local load and decrease the voltage available. The taps on in-plant transformers may need to be adjusted.*

## Eddy Current Loss

Eddy current loss is power loss in a transformer or motor due to currents induced in the metal parts of the system from the changing magnetic field. Any conductor that is in a moving magnetic field has a voltage and current induced in it. The iron core offers a low reluctance to the magnetic flux for mutual induction. The magnetic flux induces current at right angles to the flux. This means that current is induced across the core. This current causes heating in the core. The heat produced by eddy currents increases as the square of the frequency. For example, the third harmonic (180 Hz) has nine (32) times the heating effect of the fundamental (60 Hz) frequency.

Constructing the core from thin sheets of iron laminated together can minimize this loss. The thin sheet-iron layers shorten the current path and minimize the eddy currents (see Figure 1). Each sheet is coated with an insulating varnish that forces these currents to only flow within individual laminations. This reduces the overall eddy currents in the entire core. These thin sheets are manufactured from silicon-iron or nickel-iron alloys that can be magnetized more readily than pure iron. The use of alloy cores also improves the age resistance of the core. The sheets are often made from 29-gauge alloy, which is only 0.014′′ thick.

*Image courtesy of All About Circuits. *

## Hysteresis Loss

Hysteresis loss is loss caused by the magnetism that remains (lags) in a material after the magnetizing force has been removed. Magnetic domains are small sections of a magnetic material that act together when subject to an applied magnetic field. Magnetic domains have magnetic properties and move in iron when subjected to a magnetic field. When the iron is subjected to a magnetic field in one polarity, the magnetic domains will be forced into alignment with the field. When the polarity changes twice each cycle, power is consumed by this realignment, and this reduces the efficiency of the transformer. This movement of the molecules produces friction in the iron, and thus heat is a result. Harmonics can cause the current to reverse direction more frequently, leading to more hysteresis loss. Hysteresis is reduced through the use of highly permeable magnetic core material.

## Flux Loss

Flux loss occurs in a transformer when some of the flux lines from the primary do not pass through the core to the secondary, resulting in a power loss. There are two main reasons for flux lines to travel through the air instead of through the core. First, the iron core can become saturated so that the core cannot accept any more flux lines. The lines of flux then travel through the air and are not cut by the secondary. Second, the ratio of the reluctance of the air and the core in the unsaturated region is typically about 10,000:1. This means that for every 10,000 lines of flux through the core, there is 1 line of flux through the air. Flux loss is generally small in a well-designed transformer.

## Transformer Efficiency

The ratio of a transformer's output power to its input power is known as transformer efficiency. The effect of transformer losses is measured by transformer efficiency, which is typically expressed as a percentage. The following formula is used to measure transformer efficiency:

$$\eta =\frac{{{P}_{OUT}}}{{{P}_{IN}}}$$

where

η = transformer efficiency (in %)

P_{OUT} = transformer output power (in W)

P_{IN} = transformer input power (in W)

Example: What is the efficiency of a transformer that has an output power of 1500 W and input power of 1525 W?

$$\eta =\frac{{{P}_{OUT}}}{{{P}_{IN}}}=\frac{1500W}{1525W}=98.36%$$

The efficiencies of power transformers normally vary from 97 to 99 percent. The power supplied to the load plus resistive, eddy current, hysteresis, and flux losses must equal the input power. The input power is always greater than the output power.

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