Calculate Base Impedance

The base impedance $Z_{base}$ is calculated using the base voltage and base power as $Z_{base} = \frac{(V_{base})^2}{S_{base}}$. Given $V_{base} = 10 kV$ and $S_{base} = 100 MVA$.

$Z_{base} = \frac{(10 \times 10³)^2}{100 \times 10⁶} = \frac{100 \times 10⁶}{100 \times 10⁶} = 1 \, \Omega$

Calculate Per Unit Resistance

Substitute the actual resistance $R_{actual} = 2 \, \Omega$ and the base impedance $Z_{base} = 1 \, \Omega$ into the per-unit formula $Z_{pu} = \frac{R_{actual}}{Z_{base}}$.

$R_{pu} = \frac{2}{1} = 2 \, \text{pu}$