To compute the efficiency of a transformer, the input power to and the output power from the transformer must be known. The input power is equal to the product of the voltage applied to the primary and the current in the primary. The output power is equal to the product of the voltage across the secondary and the current in the secondary. The difference between the input power and the output power represents a power loss. You can calculate the percentage of efficiency of a transformer by using the standard efficiency formula shown below:
Losses in the transformer arise from:
Winding resistance :
Current flowing through the windings causes resistive heating of the conductors. At higher frequencies, skin effect and proximity effect create additional winding resistance and losses.
Hysteresis losses :
Each time the magnetic field is reversed, a small amount of energy is lost due to hysteresis within the core. For a given core material, the loss is proportional to the frequency, and is a function of the peak flux density to which it is subjected.
Eddy currents :
Ferromagnetic materials are also good conductors, and a solid core made from such a material also constitutes a single short-circuited turn throughout its entire length. Eddy currents therefore circulate within the core in a plane normal to the flux, and are responsible for resistive heating of the core material. The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness.
Magnetic flux in a ferromagnetic material, such as the core, causes it to physically expand and contract slightly with each cycle of the magnetic field, an effect known as magnetostriction. This produces the buzzing sound commonly associated with transformers, and in turn causes losses due to frictional heating in susceptible cores.
Mechanical losses :
In addition to magnetostriction, the alternating magnetic field causes fluctuating electromagnetic forces between the primary and secondary windings. These incite vibrations within nearby metalwork, adding to the buzzing noise, and consuming a small amount of power.
Stray losses :
Leakage inductance is by itself loss less, since energy supplied to its magnetic fields is returned to the supply with the next half-cycle. However, any leakage flux that intercepts nearby conductive materials such as the transformer’s support structure will give rise to eddy currents and be converted to heat.
A three-phase transformer is made of three sets of primary and secondary windings, each set wound around one leg of an iron core assembly.
Connecting Single-Phase Transformers into a Three-Phase Bank:
Power may be supplied through a three-phase circuit containing transformers in which a set of three single phase transformers is used. Using three single phase transformer becomes difficult to handle especially because of size, weight and is less economical to use. When used this way, this arrangement is called a transformer bank.
When a considerable amount of power is involved in the transformation of three phase power, it is more economical to use a three phase transformer. The unique arrangement of the windings and core saves a lot of iron, losses, space and money.
There are two configurations for three phase power:
1) Delta : In this three conductors are connected end to end in a triangle or delta shape.
2) Wye : All the conductors radiate from the center, it means they are connected at one common point. The Wye connected winding is often called a ” Star Connection “. It has four leads, three phase leads and one neutral lead, so it is possible to provide two voltages.
Possible uses of transformer combinations as follows:
- Delta to Delta – use: industrial applications
- Delta to Wye – use : most common; commercial and industrial
- Wye to Delta – use : high voltage transmissions
- Wye to Wye – use : rare, don’t use causes harmonics and balancing problems.