Electrical Machines - Practical Transformer

Practical Transformer

A practical transformer is one which possesses the following characteristics −

• The primary and secondary windings have finite resistance.
• There is a leakage flux, i.e., whole of the flux is not confined to the magnetic core.
• The magnetic core has finite permeability, hence a considerable amount of MMF is require to establish flux in the core.
• There are losses in the transformer due to winding resistances, hysteresis and eddy currents. Therefore, the efficiency of a practical transformer is always less than 100 %.

The analytical model of a typical practical transformer is shown in Figure.

Characteristics of a Practical Transformer

Following are the important characteristics of a Practical Transformer −

Winding Resistances

The windings of a transformer are usually made up of copper conductors. Therefore, both the primary and secondary windings will have winding resistances, which produce the copper loss or $\mathit{i^{\mathrm{2}} \mathit{R}}$ loss in the transformer. The primary winding resistance $\mathit{R_{\mathrm{1}}}$ and the secondary winding resistance $\mathit{R_{\mathrm{2}}}$ act in series with the respective windings as shown in Figure-3.

Iron Losses or Core Losses

The core of the transformer is subjected to the alternating magnetic flux, hence the eddy current loss and hysteresis loss occur in the core. The hysteresis loss and eddy current loss together are known as iron loss or core loss. The iron loss of the transformer depends upon the supply frequency, maximum flux density in the core, volume of the core and thickness of the laminations etc. In a practical transformer, the magnitude of iron loss is practically constant and very small.

Leakage Flux

The current through the primary winding produces a magnetic flux. The flux $\mathit{\phi _{\mathit{m}}}$ which links both primary and secondary windings is the useful flux and is known as mutual flux. However, a fraction of the flux ($\mathit{\phi _{\mathrm{1}}}$) produced by the primary current does not link with the secondary winding.

When a load is connected across the secondary winding, a current flows through it and produces a flux ($\mathit{\phi _{\mathrm{2}}}$), which links only with the secondary winding. Thus, the part of $\mathit{\phi _{\mathrm{1}}}$, and the flux $\mathit{\phi _{\mathrm{2}}}$ that link only their respective winding are known as leakage flux.

The leakage flux has its path through the air which has very high reluctance. Therefore, the effect of primary leakage flux ($\mathit{\phi _{\mathrm{1}}}$) is to introduce an inductive reactance ($ \mathit{X_{\mathrm{1}}}$) in series with the primary winding. Similarly, the secondary leakage flux ($\mathit{\phi _{\mathrm{2}}}$) introduces an inductive reactance ($ \mathit{X_{\mathrm{2}}}$) in series with the secondary winding as shown in Figure.

However, the leakage flux in a practical transformer is very small (about 5% of $\mathit{\phi _{m}}$), yet it cannot be ignored. Because the leakage flux paths are through the air, which has very high reluctance. Thus, it requires considerable MMF.

Finite Permeability of Core Material

In general, the practical transformers have a core made up of high grade silicon steel, which has a specific relative permeability ($\mathit{\mu _{r}}$). Thus, the core saturates at a certain value of magnetic flux density. Therefore, the core of a practical transformer has finite permeability and hence possesses reluctance in the path of magnetic flux.