Transformer Losses

Practical power transformers, although highly efficient, are not perfect devices. Small power transformers used in electrical equipment have an 80 to 90 percent efficiency range, while large, commercial powerline transformers may have efficiencies exceeding 98 percent. The total power loss in a transformer is a combination of three types of losses. One loss is due to the DC resistance in the primary and secondary windings. This loss is called copper loss or PR loss. The two other losses are due to eddy currents and to hysteresis in the core of the transformer. Copper loss, eddy-current loss, and hysteresis loss result in undesirable conversion of electrical energy into heat energy.

Copper Loss

Whenever current flows in a conductor, power is dissipated in the resistance of the conductor in the form of heat. The amount of power dissipated by the conductor is directly proportional to the resistance of the wire, and to the square of the current through it. The greater the value of either resistance or current, the greater is the power dissipated. The primary and secondary windings of a transformer are usually made of low-resistance copper wire. The resistance of a given winding is a function of the diameter of the wire and its length. Copper loss can be minimized by using the proper diameter wire. Large diameter wire is required for high-current windings, whereas small diameter wire can be used for low current windings.

Copper loss can be calculated using the formula for power lost as heat:

Copper loss = I²R

The effect of this is that if the current (I) is doubled, for example, the amount of copper loss will quadruple, since the relationship between copper loss and current is one of a square law. However, if the resistance of the winding is halved, the copper loss is also halved, since the relationship between copper loss and resistance is linear.

It must also be remembered that any change in resistance of a winding (by adjacent wires fusing together in an overheating transformer for example) will have an inverse relationship on the current flow through the winding. Thus, if an overheating transformer has wires fusing together, such that its resistance halves, the current will double (Ohm's Law). The compound effect on the copper loss, of halving resistance and doubling the current, from the above formula, is to increase the loss by a factor of 2.

Eddy-Current Loss

The core of a transformer is usually constructed of some type of ferromagnetic material because it is a good conductor of magnetic lines of flux.

Whenever the primary of an iron-core transformer is energized by an alternating-current source, a fluctuating magnetic field is produced. This magnetic field cuts the conducting core material and induces a voltage into it. The induced voltage causes random currents to flow through the core which dissipates power in the form of heat. These undesirable currents are called to minimize the loss resulting from eddy currents, transformer cores are laminated. Since the thin, insulated laminations do not provide an easy path for current, eddy-current losses are greatly reduced.

Hysteresis Loss

When a magnetic field is passed through a core, the core material becomes magnetized. To become magnetized, the domains within the core must align themselves with the external field. If the direction of the field is reversed, the domains must turn so that their poles are aligned with the new direction of the external field.

Power transformers normally operate from either 60 Hz or 400 Hz alternating current. Each tiny domain must realign itself twice during each cycle, or a total of 120 times a second when 60 Hz alternating current is used. The energy used to turn each domain is dissipated as heat within the iron core. This loss, called hysteresis loss, can be thought of as resulting from molecular friction. Hysteresis loss can be held to a small value by proper choice of core materials.

Eddy current loss and hysteresis loss are both losses from the magnetic core of the transformer. Due to the effect of the back-EMF increase, when the transformer load increases, the magnetic flow within the core of the transformer is approximately constant, regardless of the load on the transformer, therefore the eddy current and hysteresis losses are also fairly constant as transformer load increases. Copper loss, on the other hand, is a heat loss in the windings of the transformer, and this increases on a square law, with the current flowing through the windings.