Identify the per-unit change formula

To change the base of per-unit impedance, we use the conversion relationship based on the definitions of per-unit values: $Z_{pu} = \frac{Z_{actual}}{Z_{base}}$ where $Z_{base} = \frac{(kV)^2}{MVA}$.

$Z_{pu,new} = Z_{pu,old} \times \frac{MVA_{new}}{MVA_{old}} \times \left( \frac{kV_{old}}{kV_{new}} \right)^2$

Substitute the given values

Substitute $Z_{pu,old} = 2$, $MVA_{new} = 400$, $MVA_{old} = 100$, $kV_{old} = 100$, and $kV_{new} = 400$ into the formula.

$Z_{pu,new} = 2 \times \left( \frac{400}{100} \right) \times \left( \frac{100}{400} \right)^2$

Calculate the result

Simplify the expression: $2 \times 4 \times (1/4)^2 = 8 \times (1/16) = 0.5$.

$Z_{pu,new} = 8 \times \frac{1}{16} = 0.5$