## Magnetic Hysteresis

The phenomenon of magnetization lagging behind the field producing it is called magnetic hysteresis. It is derived from Greek word hysteresis (to lag). Every Ferromagnetic material used in transformer cores exhibits hysteresis phenomena. The hysteresis curve of a magnetic material is shown in the figure

Hysteresis losses in Transformer

By applying external magnetic field the magnetic material will get magnetized. The extent the material gets magnetized depends on the applied field and the permeability of the material (µr). The magnetization, flux density inside material.

B = µor*H, M = (µr-1)*H

Ferromagnetic materials have high magnetic permeability’s and hence can be magnetized used. Starting from zero external field, as the external field is increased the magnetization increases till it reaches saturation. After the field inside the material reaches saturation field further there will not be any increase in thee magnetization even after the external field is increased.

Now if we decrease the field the flux density decreases. But at zero external fields there exists remanent magnetization inside the material. In order to make the flux density inside the material zero we should apply magnetic filed in the direction opposite to the field applied before. The external field that should be applied to make the flux density inside the material zero is called coercive field denoted by Hc. It is obvious from the B-H curve that magnetization and the flux density inside the material lag behind the applied field.

## Explanation of Hysteresis

Magnetic hysteresis can be explained as follows: Ferromagnetic materials such as iron consist of domains in their internal structure. The size of the domain will be ranging from 1 micro m to 1 mm. These domains consist of a number of magnetic dipoles which are parallel with respect to one another inside the domain. Every atom in ferromagnetic material has contains of unpaired spinning electrons which acts as magnetic dipoles. Hence every atom has non zero magnetic moment associated with it. Due to random orientation of domains at no applied magnetic field the net magnetization in a ferromagnetic material will be zero.

When an external magnetic field is applied all these domains orient in the direction of magnetic field which gives rise to net magnetic field. Now the external field is removed, after the removal of external filed most of the domains again orient randomly. But some of the domains retain their orientation due to crystal defects (dislocations) giving rise to permanent magnetization. As the applied magnetic field intensity varies periodically, the hysteresis loop is traced once. To make the field inside the material zero an external magnetic field opposite to the direction of magnetization of iron should be applied. So in order to achieve this demagnetization and magnetization of domains extra work is being done which is termed as hysteresis loss.

## Quantification of Hysteresis Loss

The total area inside the hysteresis loss is a measure of hysteresis losses of core. The work done on the core to neutralize the field inside core appears as hysteresis loss. The hysteresis losses of core per unit volume of core is given as

$Hysteresis&space;loss/unit&space;volume=&space;\int_{0}^{\beta&space;_{max}}H.dB$

Hence the total hysteresis losses = Total area inside hysteresis loop*volume of core.

Therefore the materials with less area inside the hysteresis loop are preferred for transformer cores.

According to Steinmetz’s formula, the heat energy dissipated due to hysteresis is given by

Wh=ηβmax1.6 , and,

Hysteresis loss is thus given by

Ph≈ Whf ≈ηfβmax1.6

Where,

f is the frequency,

η is the hysteresis coefficient and

βmax is the maximum flux density, the empirical exponent of which varies from about 1.4 to 1 .8 depending on the material used for core but is often given as 1.6 for iron.

## Remedies to reduce hysteresis loss

Air core transformer eliminates loss due to hysteresis in the core material but has more leakage flux. Air core provides very low inductance in most situations. Hence it is not a plausible solution.

Another remedy is to use soft magnetic materials with low hysteresis, such as silicon steel, steel alloys, Mn-Zn ferrite,. Soft magnetic materials are optimal to be used in transformer core because of following advantages

• High saturation magnetization, hence the core saturation happens at higher magnetic fields
• They are characterized by Low coercivity and remanent magnetic flux density, which means low hysteresis losses.
• High resistivity
• High magnetic permeability’s e.t.c.