Transformers

Ideal Transformer

\begin{matrix} e_{1} = N_{1} \frac{d Φ}{d t}, e_{2} = N_{2} \frac{d Φ}{d t} \\ \frac{e_{1}}{e_{2}} = \frac{N_{1}}{N_{2}} = \frac{V_{1}}{V_{2}} = \frac{I_{2}}{I_{1}} = a \end{matrix}

Exact Equivalent Circuit

Approximate Equivalent Circuit

Connection	Note
$\Large Y - \Delta$	Commonly used to step down voltage. Neutral point on high-voltage side can be grounded, which is desirable in most cases.
$\Large \Delta - Y$	Commonly used to step up voltage.
$\Large \Delta - \Delta$	Advantage: one transformer can be removed for repair and the remaining two can continue to deliver three-phase power at a reduced rating of 58% of the original bank. This is known as the open-delta or V connection.
$\Large Y - Y$	Rarely used due to problems with the exciting currents and induced voltages.