Jules: Created page with "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 circui..."

2020-11-22T08:17:48Z

Created page with "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 circui..."

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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|per-unit system]].

== Referring Impedances in General ==

Generally, one can refer an impedance <math>Z_{1}</math> at some voltage <math>V_{1}</math> to another voltage <math>V_{2}</math> by the following calculation:

: <math>Z_{2} = Z_{1} \left( \frac{V_{2}}{V_{1}} \right)^{2} </math>

Where <math> Z_{1} \, </math> is the impedance at voltage <math>V_{1}</math> (<math> \Omega </math>)
:: <math> Z_{2} \, </math> is the impedance at voltage <math>V_{2}</math> (<math> \Omega </math>)

== Referring Impedances across Transformers ==

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

: <math> n = \frac{V_{t2} \left( 1 + t_{p} \right)}{V_{t1}} \, </math>

Where <math> n \, </math> is the transformer winding ratio
:: <math> V_{t2} \, </math> is the transformer nominal secondary voltage at the principal tap (Vac)
:: <math> V_{t1} \, </math> is the transformer nominal primary voltage (Vac)
:: <math> t_{p} \, </math> 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:

: <math> Z_{HV} = \frac{Z_{LV}}{n^{2}} \, </math>

Where <math> Z_{HV} \, </math> is the impedance referred to the primary (HV) side (<math> \Omega </math>)
:: <math> Z_{LV} \, </math> is the impedance at the secondary (LV) side (<math> \Omega </math>)
:: <math> n \, </math> is the transformer winding ratio (pu)

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

: <math> Z_{LV} = Z_{HV} \times n^{2} \, </math>

[[Category:Fundamentals]]

Referring Impedances - Revision history

Jules: Created page with "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 circui..."