Identify given parameters

We have initial impedance $Z_{old} = 0.2$ pu at base values $V_{base1} = 11$ kV and $S_{base1} = 50$ MVA · We need to convert it to $Z_{new}$ for $V_{base2} = 22$ kV and $S_{base2} = 150$ MVA.

$Z_{old}=0.2, V_1=11, S_1=50, V_2=22, S_2=150$

Apply the per-unit base change formula

The formula to change the per-unit impedance with new base values is $Z_{new(pu)} = Z_{old(pu)} \times \frac{S_{new}}{S_{old}} \times (\frac{V_{old}}{V_{new}})^2$.

$Z_{new} = 0.2 \times \left( \frac{150}{50} \right) \times \left( \frac{11}{22} \right)^2$

Calculate the final value

Substitute the values: $Z_{new} = 0.2 \times 3 \times (0.5)^2 = 0.6 \times 0.25 = 0.15$ pu.

$Z_{new} = 0.15$