Question

To convert a per-unit impedance from "old" to "new" base values the equation to be used is

(a) $Z_{p.unew}=Z_{p.u.old}{\left(\frac{V_{baseold}}{V_{basenew}}\right)}^2\left(\frac{S_{basenew}}{S_{baseold}}\right)$

(b)role="math" localid="1655898634705" $Z_{p.unew}=Z_{p.u.old}{\left(\frac{V_{baseold}}{V_{basenew}}\right)}^2\left(\frac{S_{basenew}}{S_{baseold}}\right)$

(c)role="math" localid="1655898620711" $Z_{p.unew}=Z_{p.u.old}{\left(\frac{V_{baseold}}{V_{basenew}}\right)}^2\left(\frac{S_{baseold}}{S_{basenew}}\right)$

Short answer

Therefore, the correct options are (a) and (b):$Z_{p.unew}=Z_{p.u.old}{\left(\frac{V_{baseold}}{V_{basenew}}\right)}^2\left(\frac{S_{basenew}}{S_{baseold}}\right)$

Step-by-step solution

The general expression to calculate the per unit values of the system.

Power system quantities voltage, current and impedance can be expressed in the per unit quantities by using the expression as

$\mathit{P}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{}\mathit{q}\mathit{u}\mathit{a}\mathit{n}\mathit{t}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{A}\mathbf{c}\mathbf{t}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{q}\mathbf{u}\mathbf{a}\mathbf{n}\mathbf{t}\mathbf{i}\mathbf{t}\mathbf{y}}{\mathbf{B}\mathbf{a}\mathbf{s}\mathbf{e}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{q}\mathbf{u}\mathbf{a}\mathbf{n}\mathbf{t}\mathbf{i}\mathbf{t}\mathbf{y}}$

conversion of the impedance from old to new base value.

The per unit impedance can be expressed as

$$\begin{gathered} Z_{p.u.new}=\frac{Z_{actual}}{Z_{basenew}} \\ {Z}_{p.u.new}=\frac{Z_{p.u.old}{Z}_{baseold}}{Z_{basenew}} \\ {Z}_{p.u.new}=Z_{p.u.old}\left(\frac{V_{baseold}^2}{S_{baseold}}\right)\left(\frac{S_{basenew}}{V_{basenew}^2}\right) \\ {Z}_{p.u.new}=Z_{p.u.old}\left(\frac{V_{baseold}^2}{V_{basenew}^2}\right)\left(\frac{S_{basenew}}{S_{baseold}}\right) \end{gathered}$$

Hence the expression to convert impedance from old to new is .$Z_{p.u.new}=Z_{p.u.old}\left(\frac{V_{baseold}^2}{V_{basenew}^2}\right)\left(\frac{S_{basenew}}{S_{baseold}}\right)$