Volt / turn equation - Design of Transformers

Volt / turn equation

Rating of the transformer per phase kVA / ph = V₁I₁ x 10^-3 = E₁I₁ x 10^-3

 = 4.44 φm f T₁ I₁ x 10^-3

The term φ_m is called the magnetic loading and I₁T₁ is called the electric loading. The required kVA can be obtained by selecting a higher value of φ_m and a lesser of I₁T₁ or vice-versa.

 As the magnetic loading increases, flux density and hence the core loss increases and the

efficiency of operation decreases. Similarly as the electric loading increases, number of turns, resistance and hence the copper loss increases. This leads to reduced efficiency of operation. It is clear that there is no advantage by the selection of higher values of I₁T₁ or φ_m. For an economical design they must be selected in certain proportion. Thus in practice

Where K = 4.44 f x 10³ x K_t  is another constant and kVA is the rated output of the transformer. The constant K depends on the type of transformer-single or three phase, core or shell type, power or distribution type, type of factory organization etc.,

Emperical values of K :

 ( 1.0 to 1.2) for single phase shell type

 1.3 for three-phase shell type (power)

 (0.75 to 0.85) for single phase core type

 (0.6 to 0.7) for three phase core type (power)

 0.45 for three-phase core type (distribution)