How the transformer works?

The transformer has two coils wound around the common magnetic core. When an alternating voltage is applied to the primary coil, the current flows through it. The current flowing in the primary coil produces the magnetic flux.
The magnetic flux produced in the primary coil is proportional to the ratio of the applied voltage to the frequency. According to Faraday's law of electromagnetic induction, the EMF is induced in the primary and as per the Lenz' law, the induced EMF always opposes the primary current that is responsible for begetting the EMF.
The voltage induced in the coil can be expressed by the following mathematical expression. 

Where  E= Induced EMF in the primary coil
             Φ= The magnetic flux 
              f= Frequency 
              N= Turns /Phase
The flux travels through the magnetic core and it gets linked to the secondary coil. Practically, all the flux produced in the primary does not link to the secondary. Some parts of the magnetic fluxlinks to the primary coil and other parts of the transformer. The flux that does not link to both primary and secondary coils is known as the leakage flux. The losses in the transformer increase with an increase in the leakage flux. The useful flux that links to the secondary coil induces a voltage in the secondary according to the Faraday's Law of Electromagnetic Induction. The voltage induced in the secondary coil is
Es= -N dΦ/dt
The secondary voltage remains constant if the rate of change of the flux is constant. It is desirable that the flux in the transformer must remain constant.
The Flux density of the CRGO Core:

The transformer designer first checks the rated flux density of the colled rolled grain oriented(CRGO) core. The maximum flux density of the CRGO core is about 1.9 Tesla. If the fluxdensity of the transformer is above 1.9 Tesla, the core of the transformer gets saturated, and it will lead to insulation failure of the laminated core. The designed maximum flux density of the core must be below the maximum rated flux density of the core. The core must not get saturated in any case. The magnetization curve of the different material is as given below.

The flux density of the core can be controlled during the design stage of the transformer. The fluxdensity of the core can be controlled by adjusting the cross-sectional area of the core during transformer designing. The flux through the core is the product of the flux density and the cross-sectional area of the core(Φ=B*A). The flux density of the core can be reduced by increasing the cross-sectional area of the core.

The voltage induced in the primary when the sinusoidal voltage is applied is
E=4.44 ΦfN
Φ=E/4.44f N
The Number of turns in the primary is constant for a given transformer
Φ=K* E/f
The induced voltage is approximately proportional to the applied voltage if the primary impedance is ignored.
Φ=K*V/f   ----------(1)
The flux density in the core of the core is as given below.
B=Φ / A
Where A is the cross section area of the core that is also constant.
B=K1*V/f   -----------(2)
Thus the flux density in the core is directly proportional to the ratio of V/f if the number of turns of the primary is fixed. For on load tap changer transformer, the number of turns is not fixed but changes according to the output voltage requirement so we will also discuss the flux density in the core with the tap changer is not at the center tap position.

The over fluxing in the transformer happens with an increase in the supply voltage or decrease of the supply frequency. If the transformer has tap changer and the number of turns is reduced to increase the secondary voltage the flux density in the core will increase. The designer always takes the margin of increase in the flux due to tap changer operation. Also, the margin of allowable increase of voltage and decrement of the frequency is taken into consideration while designing the transformer.

Reasons for transformer Over fluxing :

The Increase of the supply voltage due to sudden load through.

 The receiving end voltage can be more than the sending end voltage due to the Ferranti effect if the line is lightly loaded.

The transients and overshoots in the electrical network