# 2.2 Voltage Transformation

A transformer’s voltage ratio is expressed in polar form as ae${}^{j\delta}$, where a is the magnitude of the transformation and $\delta$ 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.

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

where

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 $\delta$ 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
Winding
Primary Secondary Phase Shift
Wye Wye $0^{\circ}$
Wye Delta $-30^{\circ}$
Delta Wye $30^{\circ}$
Delta Delta $0^{\circ}$

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