# Losses and efficiency of the transformer

Transformers, like all devices, are not perfect. While ideal transformers have no losses, real transformers have power losses. The output power of the transformer is always slightly less than the input power of the transformer. These power losses are converted into heat, which must be removed from the transformer. There are four main types of loss: resistive loss, eddy current loss, hysteresis loss, and magnetic 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 create the windings. Since higher frequencies cause the electrons to move more towards the outer circumference of the conductor (skin effect), electrical noise, called harmonics, leads to a decrease in the size of the wire and an increase in resistive losses. These losses are the same as the power losses in any conductor and are calculated as follows:

Where P = power (in W), I = current (in A), R = resistance (in ohms).

For example, if the primary winding of a transformer is wound around 100 feet of # 12 copper wire that carries 15 amps, what is the resistive loss in that coil? The resistance of # 12 copper wire is 1.588 ohms / 1000 at room temperature. Therefore, the resistance of 100 feet of wire is 0.1588 ohms.

The primary side of the transformer consumes 35.7 watts of energy, which is lost as heat. If the transformer is not cooled properly, this heat increases the temperature of the transformer and wires. This increased temperature causes an increase in the resistance of the wire and a drop in voltage across the wire. These losses are current dependent and are always present in the primary when energized. The secondary winding sees very small losses of this type during unloading.

## Eddy current losses

Eddy current losses are power losses in a transformer or motor due to currents induced in the metal parts of the system due to changes in the magnetic field. Voltage and current are induced in any conductor in a moving magnetic field. The iron core provides low flux resistance for mutual induction. The magnetic flux induces a current perpendicular to the flux. This means that a current is induced in the core. This current causes the core to heat up. The heat generated by eddy currents increases in proportion to the square of the frequency. For example, the third harmonic (180 Hz) is nine (32) times the thermal effect of the fundamental (60 Hz) frequency.

Making the core from thin sheets of iron bonded together can minimize these losses. Thin layers of sheet metal shorten the current path and minimize eddy currents (see next figure). Each sheet is covered with an insulating varnish that makes these currents flow only inside the individual sheets. This reduces the overall eddy currents throughout the core. These thin sheets are made from silicon-iron or nickel-iron alloys, which are more easily magnetized than pure iron. The use of alloy cores also improves the aging resistance of the core. Sheets are often made from 29 gauge alloy, which is only 0.014 inches thick.

## Loss due to hysteresis

Hysteresis loss is the loss caused by magnetism that remains (lags) in the material after the magnetizing force is removed. Magnetic domains are small patches of magnetic material that act together under the influence of an applied magnetic field. Magnetic domains are magnetic and move in iron under the influence of a magnetic field. When iron is acted upon by a magnetic field of the same polarity, the magnetic domains will be forced to align with the field. When the polarity is reversed twice in each cycle, this reset wastes power and reduces the efficiency of the transformer. This movement of molecules causes friction in the iron, and hence heat is generated as a result. Harmonics can cause the current to reverse more frequently, resulting in higher hysteresis losses.

## Loss due to magnetic flux

Flux losses occur in a transformer when some of the magnetic lines from the primary winding do not pass through the core to the secondary winding, resulting in a loss of power. There are two main reasons why the lines of force travel through the air and not through the core. First, the iron core can become saturated so that the core can no longer receive the lines of force. The flow lines then pass through the air and are not cut by the secondary winding. Second, the ratio of air to core resistance in the unsaturated region is typically around 10,000: 1. This means that for every 10,000 flow lines through the core, there is 1 flow line through the air. Flux losses in a well-designed transformer are usually low.

## Transformer efficiency

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

Where n = transformer efficiency (in%) POUT = transformer output power (in W) PIN = transformer input power (in W).

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

Power transformers typically range from 97 to 99 percent efficiency. The power supplied to the load, plus resistive currents, eddy currents, hysteresis, and flux loss, must equal the input power. The input power is always greater than the output power.