Choice of flux density in transformer design

The maximum flux density $B_m$ in the core is chosen as high as possible to reduce the size and cost of the core, but it is limited by iron loss, magnetising current, noise and the type of steel.

Factors deciding $B_m$

1. Core loss and efficiency: hysteresis loss ∝ $B_m^{1.6}$ and eddy loss ∝ $B_m^2$. Higher $B_m$ means more iron loss and lower all-day efficiency.
2. Magnetising current: near the knee of the B–H curve the mmf rises sharply, so $I_0$ and its harmonics increase.
3. Type of transformer: distribution transformers are energised 24 h, so a lower $B_m$ is used to keep iron loss low. Power transformers can use higher values.
4. Grade of steel: cold-rolled grain-oriented (CRGO) steel has low loss and high permeability along the grain, so it allows higher $B_m$ than hot-rolled steel.
5. Over-voltage and frequency: margin is kept so the core does not saturate at overvoltage or reduced frequency.
6. Noise: magnetostriction hum increases with $B_m$.

Usual values

So $B_m$ is a compromise between a small core (high $B_m$) and low iron loss, low no-load current and low noise (low $B_m$).