2.2 Voltage Transformation

A transformer’s voltage ratio is expressed in polar form as aejδ{}^{j\delta}, where a is the magnitude of the transformation and δ\delta is its phase shift.

2.2.1 Transformation Ratio

Each transformer is categorized by a nominal operating point, i.e. its nameplate primary and secondary voltage. The nominal magnitude of the voltage ratio is determined by examining the real part of Equation 1 at nominal operating conditions.

anom=VpVs{a}_{nom}=\frac{{V}_{p}}{{V}_{s}} (11)


Vp is the nominal primary voltage.

Vs is the nominal secondary voltage.

When voltages are expressed in per unit, the nominal value of a is always one.

2.2.2 Phase Shift

In the general case, an arbitrary angular shift δ\delta may be introduced by a multiphase transformer bank. However, omitting phase shifters (angle regulating transformers) from the system model, reduces the angle shifts across balanced transformer configurations to effects introduced by the connections of the windings. Table 2 describes the phase shift associated with common transformer connections.

Table 2: Transformer Phase Shifts
Primary Secondary Phase Shift
Wye Wye 00^{\circ}
Wye Delta -30-30^{\circ}
Delta Wye 3030^{\circ}
Delta Delta 00^{\circ}

When phase shifters are ignored, the user does not have to specify δ\delta explicitly. It may be inferred from Table 2.