Identify the per-unit impedance formula

To change the base of per-unit impedance, we use the conversion formula which accounts for both power and voltage level changes.

$Z_{pu(new)} = Z_{pu(old)} \times \frac{S_{b2}}{S_{b1}} \times \left( \frac{V_{b1}}{V_{b2}} \right)^2$

Substitute the given values into the formula

Plug in the known variables: $Z_{pu(old)} = 0.9$, $S_{b1} = 20$, $S_{b2} = 50$, $V_{b1} = 33$, and $V_{b2} = 11$.

$Z_{pu(new)} = 0.9 \times \left( \frac{50}{20} \right) \times \left( \frac{33}{11} \right)^2$

Calculate the ratio values

Simplify the fractions: $\frac{50}{20} = 2.5$ and $\frac{33}{11} = 3$. The square of 3 is 9.

$Z_{pu(new)} = 0.9 \times 2.5 \times (3)^2 = 0.9 \times 2.5 \times 9$

Final multiplication

Perform the final calculation: $0.9 \times 22.5 = 20.25$.

$Z_{pu(new)} = 20.25$