# Calculation of equivalent circuit parameters’ values

This section describes calculation of equivalent circuit parameters’ values

This section describes the method used to calculate equivalent circuit parameters’ values from SI units to per unit and vice versa.

A distinct base voltage, base impedance and base inductance are assigned to each of the transformer’s windings.

## Single-phase transformers

When calculating equivalent circuit parameters’ values from SI units to per unit, the following expression is used:

${x}^{pu}=\frac{{x}^{SI}}{{x}_{base}}$

When calculating equivalent circuit parameters’ values from per unit to SI units, the following expression is used:

${x}^{SI}={x}^{pu}\bullet {x}_{base}$
Base values:
• Base power is transformer nominal power: ${S}_{base}={S}_{n}$
• Base frequency is transformer nominal frequency: ${f}_{base}={f}_{n}$
• Base voltages are transformer nominal winding voltages: ${V}_{base}^{i}={V}_{n}^{i}$
• Base impedances are calculated in the following way: ${Z}_{base}^{i}=\frac{{\left({V}_{base}^{i}\right)}^{2}}{{S}_{base}}$
• Base inductances are calculated in the following way: ${L}_{base}^{i}=\frac{{Z}_{base}^{i}}{2\pi {f}_{base}}$

In the expressions above, i represents the index number of a transformer’s winding.

## Three-phase transformers

When calculating equivalent circuit parameters’ values from SI units to per unit, the following expression is used:

${x}^{pu}=\frac{{x}^{SI}}{k\bullet {x}_{base}}$

When calculating equivalent circuit parameters’ values from per unit to SI units, the following expression is used:

${x}^{SI}=k\bullet {x}^{pu}\bullet {x}_{base}$

In the expressions above, k is determined by

Base values:
• Base power is transformer nominal three-phase power: : ${S}_{base}={S}_{n}$
• Base frequency is transformer nominal frequency: ${f}_{base}={f}_{n}$
• Base voltages are transformer nominal phase-to-phase winding voltages: ${V}_{base}^{i}={V}_{n}^{i}$
• Base impedances are calculated in the following way: ${Z}_{base}^{i}=\frac{{\left({V}_{base}^{i}\right)}^{2}}{{S}_{base}}$
• Base inductances are calculated in the following way: ${L}_{base}^{i}=\frac{{Z}_{base}^{i}}{2\pi {f}_{base}}$

In the expressions above, i represents the index number of a transformer’s winding.