Power Transformers

Single-phase two-winding transformers use two windings around a magnetic core. The core has a cross-sectional area A and magnetic permeability μ. A phasor current i1 enters the left winding, and i2 exits the right winding. These parts work together to move energy by electromagnetic means.

Ampere’s law explains the magnetic field inside the transformer. It says that the closed-path integral of the magnetic field intensity’s tangential component equals the net current enclosed. For a...

Practical transformer equivalent circuits show how winding resistance, leakage reactance, and finite core permeability change transformer behavior. These non-ideal features create real and reactive power losses, so they matter when a transformer is under load.

Each winding has resistance and leakage reactance. Winding resistance causes resistive loss, which appears as heat. Leakage reactance comes from leakage flux, and it creates a voltage drop and reactive power loss. In the equivalent...

Three-winding transformer models show how three identical single-phase transformers can be combined into a three-phase transformer connection. The high-voltage windings are labeled A, B, and C. The low-voltage windings are labeled a, b, and c. This notation separates the high-voltage side from the low-voltage side and matches each phase to its own winding.

For a grounded Y-Y three-phase transformer, the per-unit equivalent circuit uses common base quantities to simplify analysis. The base...

Parallel transformers can be modeled with per-unit values even when the chosen voltage bases do not match the transformer ratings. This case creates an off-nominal turns ratio, which means the base voltages are not proportional to the rated voltages. To handle that mismatch, the transformer voltage relation is adjusted by using the ratio of the selected bases.

One way to represent the transformer is as two series transformers. The first is the standard per-unit model, which includes the...