Identify Relationship

The per unit impedance $Z_{pu}$ is defined as $Z_{pu} = \frac{Z_{actual} \times S_{base}}{V_{base}^2}$. Since the actual impedance $Z_{actual}$ and base power $S_{base}$ are constant, the variation depends solely on the square of the base voltage.

$Z_{pu} \propto \frac{1}{V_{base}^2}$

Apply Change Formula

Using the ratio of the new per unit value to the old per unit value where $V_{base,new} = 1.1 V_{base,old}$:

$Z_{pu,new} = Z_{pu,old} \times \left( \frac{V_{base,old}}{1.1 \times V_{base,old}} \right)^2$

Calculate Final Value

Substitute the given values into the ratio formula: $Z_{pu,new} = 0.242 \times \frac{1}{(1.1)^2}$. Since $(1.1)^2 = 1.21$, we get $0.242 / 1.21$.

$Z_{pu,new} = \frac{0.242}{1.21} = 0.2$