Electrical Power System Essentials

B.2 THE IDEAL TRANSFORMER

Consider the two-winding transformer as shown in Figure B.1. Two coils are magnetically coupled: the primary winding, for which we use suffix 1, and the secondary winding for which we use suffix 2. The number of turns in the primary and secondary windings are indicated with N₁ and N₂ respectively. The primary winding is connected to a sinusoidal voltage source v₁, while the secondary winding supplies a load current. The resistance of each winding and the losses in the transformer core are for the moment neglected. Furthermore, we assume the permeability of the core to be infinite and all the flux to be confined to circulate within the transformer core as is shown in Figure B.1 (i.e. there is no leakage flux).

The voltage v₁ supplies the current i₁ in the primary winding and this current creates a magnetic flux Φ in the transformer core. According to Faraday's law of induction, the magnetic flux in the core induces an EMF in the primary winding that opposes the applied voltage and it also induces an EMF in the secondary winding. The transformer is connected to a load and the magnitude of the secondary current i₂ depends on the load impedance. As there is no flux leakage, the flux Φ links both the primary and the secondary windings. Ampère's law states that the line integral of the magnetic field H around a closed path C is equal to the current traversing the surface S bounded by that path. Ampère's law for the closed path of flux, shown by the dashed line ...