# Referring Impedances

In a system with multiple voltage levels, it is sometimes necessary convert impedances from one voltage to another, i.e. so that they can be used in a single equivalent circuit. Note that the whole process of referring impedances can be avoided by using the per-unit system.

## Referring Impedances in General

Generally, one can refer an impedance at some voltage to another voltage by the following calculation:

Where is the impedance at voltage ()

- is the impedance at voltage ()

## Referring Impedances across Transformers

The winding ratio of a transformer can be calculated as follows:

Where is the transformer winding ratio

- is the transformer nominal secondary voltage at the principal tap (Vac)
- is the transformer nominal primary voltage (Vac)
- is the specified tap setting (%)

Using the winding ratio, impedances (as well as resistances and reactances) can be referred to the primary (HV) side of the transformer by the following relation:

Where is the impedance referred to the primary (HV) side ()

- is the impedance at the secondary (LV) side ()
- is the transformer winding ratio (pu)

Conversely, by re-arranging the equation above, impedances can be referred to the LV side: