Identify given variables

Identify the old base values ($MVA_{old} = 100$, $kV_{old} = 100$) and the new base values ($MVA_{new} = 400$, $kV_{new} = 400$) along with the existing impedance $Z_{old} = 2$ pu.

$Z_{old} = 2 \text{ pu}, MVA_{old} = 100, kV_{old} = 100, MVA_{new} = 400, kV_{new} = 400$

Apply change of base formula

Use the per-unit impedance transformation formula to calculate the new impedance value based on the new power and voltage bases.

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

Substitute and compute

Substitute the given values into the formula: $Z_{new} = 2 \times (400/100) \times (100/400)^2$. Simplify the expression: $2 \times 4 \times (1/4)^2 = 8 \times (1/16) = 0.5$.

$Z_{new} = 2 \times \left( \frac{400}{100} \right) \times \left( \frac{100}{400} \right)^2 = 2 \times 4 \times \frac{1}{16} = 0.5 \text{ pu}$