10.1.1 Transformer Theory

Elementary theory is developed from the viewpoint of a 3-phase three-leg concentric-cylindrical two-winding transformer, with the primary low-voltage winding next to the core and the secondary high-voltage winding outside the primary winding. This corresponds to a generator-step-up transformer of moderate kVA. Most of the information is also applicable to single-phase transformers with windings on two legs, 3-phase transformers with five-leg cores, transformers with the primary winding outside the secondary winding, three-winding transformers, substation transformers, etc.

Sinusoidal voltage is induced in windings by sinusoidal variation of flux

(10-1)

where a _c=square inches cross section of core, B=lines per square inch peak flux density, E= rms volts, =frequency in hertz, and N=number of turns in winding.

The induced voltage in the primary (excited) winding approximately balances the applied voltage. The induced voltage in the secondary (loaded) winding approximately supplies the terminal voltage for the load.

Voltage ratio is the ratio of number of turns ("turn ratio") in the respective windings. The rated open-circuit (no-load) terminal voltages are proportional to the turns in the windings, but under load the primary voltage usually must be somewhat higher than the rated value if rated secondary voltage is to be...