Hysteresis Loss in Transformer

Hysteresis loss in transformer can be explained in different ways. We will discuss two of them, one is physical explanation and the other is mathematical explanation.

Physical Explanation of Hysteresis Loss

The magnetic core of transformer is made of ′Cold Rolled Grain Oriented Silicon Steel′. Steel is very good ferromagnetic material. This kind of materials are very sensitive to be magnetized. That means, whenever magnetic flux would pass through, it will behave like magnet. Ferromagnetic substances have numbers of domains in their structure. Domains are very small regions in the material structure, where all the dipoles are paralleled to same direction. In other words, the domains are like small permanent magnets situated randomly in the structure of substance. These domains are arranged inside the material structure in such a random manner, that net resultant magnetic field of the said material is zero. Whenever external magnetic field or mmf is applied to that substance, these randomly directed domains get arranged themselves in parallel to the axis of applied mmf. After removing this external mmf, maximum numbers of domains again come to random positions, but some of them still remain in their changed position. Because of these unchanged domains, the substance becomes slightly magnetized permanently. This magnetism is called " Spontaneous Magnetism". To neutralize this magnetism, some opposite mmf is required to be applied. The magneto motive force or mmf applied in the transformer core is alternating. For every cycle due to this domain reversal, there will be extra work done. For this reason, there will be a consumption of electrical energy which is known as Hysteresis loss of transformer.

Mathematical Explanation of Hysteresis Loss in Transformer

Determination of Hysteresis Loss

Consider a ring of ferromagnetic specimen of circumference L meter, cross - sectional area a m² and N turns of insulated wire as shown in the picture beside,

Let us consider, the current flowing through the coil is I amp,

Magnetizing force,

Let, the flux density at this instant is B,
Therefore, total flux through the ring, Φ = BXa   Wb

As the current flowing through the solenoid is alternating, the flux produced in the iron ring is also alternating in nature, so the emf (e′) induced will be expressed as,

According to Lenz,s law this induced emf will oppose the flow of current, therefore, in order to maintain the current I in the coil, the source must supply an equal and opposite emf. Hence applied emf ,

Energy consumed in short time dt, during which the flux density has changed,

Thus, total work done or energy consumed during one complete cycle of magnetism,

Now aL is the volume of the ring and H.dB is the area of elementary strip of B - H curve shown in the figure above,

Therefore, Energy consumed per cycle = volume of the ring X area of hysteresis loop.
In the case of transformer, this ring can be considered as magnetic core of transformer. Hence, the work done is nothing but the electrical energy loss in transformer core and this is known as hysteresis loss in transformer.