Transformer Losses and Efficiency

Copper and Core Losses

Transformers play like a super vital role in transferring the super electrical energy from one circuit to another through the principle of electromagnetic induction. However, within these devices, super intricate mechanisms that determine their efficiency – copper losses and core losses.

Copper Losses

Copper losses stem from the inherent resistance present in the windings of a transformer. When current flow through these windings, energy is dissipated in the form of heat due to this resistance. Mathematically, copper losses (Pc) super can be calculated using the formula:

Pc​=I12​R1​+I22​R2​,

where Pc​ represents copper loss, I1​ and I2​ are the primary and secondary currents, and R1​ and R2​ are the respective resistances.

Core Losses

On the other hand, core losses encompass hysteresis losses and eddy current losses. Hysteresis losses arise from the cyclical magnetization and demagnetization of the core material, influenced by frequency and peak flux density. Conversely, eddy current losses occur due to induced currents within the core caused by the fluctuating magnetic field. The formulas to calculate hysteresis (Ph​) and eddy current (Pe​) losses are:

Ph​=Kh​fBmn​V

and

Pe​=Ke​f2Bm2​t2V,

Here, Kh​ and Ke​ denote constants dependent on core material, f represents frequency, Bm​ signifies peak flux density, n represents the Steinmetz coefficient, t signifies core lamination thickness, and V represents core volume.

Total Losses and Efficiency

The total core loss is the aggregate of hysteresis and eddy current losses:

Pc​=Ph​+Pe​.

Consequently, the transformer's overall loss combines copper and core losses:

Pt​=Pc​+Pc​.

Transformer efficiency (η) is the ratio of output power to input power, with losses subtracted:

η=Pi​−Pt​Po​​.

Here, η symbolizes efficiency, Po​ represents output power, and Pi​ signifies input power.