Equivalent circuit of transformers with control of voltage and phase angle

This paper presents a methodology aimed at obtaining the equivalent circuit of regulating transformers. This aspect is insufficiently treated in most current textbooks in which the equivalent circuit of a tapped transformer is not well justified. The document shows how to obtain the equivalent circuit of a regulating transformer with control of voltage magnitude and phase angle, and how to apply it using either physical quantities or per unit (pu) quantities. The resulting equivalent circuit is adequate for steady-state calculations under balanced conditions and neglects transformer core parameters. The usage of per unit values can be made by selecting the base quantities in an arbitrary manner, which is an obvious advantage when the turns ratio must be estimated.

Research highlights
► It is possible to consider more than one equivalent circuit and that the selection of the most adequate representation depends on the case under study.
► The equivalent circuit of the most general regulating transformer (i.e., that with control of voltage magnitude and phase angle) includes a voltage-controlled current source, which cancels out when the phase angle is not controlled.
► The calculations with parameters in per unit can be made by selecting system base values in an arbitrary manner.
► The calculation of the transformer parameters is different if the transformer impedance must be reduced to the primary or to the secondary side. This fact is emphasized in very few textbooks. The selection of one or the other side depends on the side at which the transformer taps are installed.