Formation of $\backslash ($ Y$\_\{\backslash$text $\{$Bys $\}\}\backslash )$ and $\backslash ($ Z$\_\{$B u s$\}\backslash )$ :

Example

Consider the single$-$line diagram of a $4-$bus network belwo.

a$)$ Form $"/$Bus of the original network $($in p$.$u$.)$

b$)$ If the line$2-3$ is opened, what is the new Yous?

c$)$ Elimisate Bus $2$ to obtain the reduced Y$/$bus of the original network. $($Note: Bus $2$ has no generatory$)$ load, hence $\backslash ($ I$\_\{2\}=0\backslash ))$

Line$/$branch data:

$\backslash [$

$\backslash$begin$\{$array$\}\{$cccccc$\}$

$\backslash$frac$\{\backslash$text $\{$ FROM $\}\}\{1\}$ & $\backslash$frac$\{70\}\{2\}$ & $\backslash$frac$\{$R$\}\{0\mathrm{.}01\}$ & & $\backslash$frac$\{$X$\}\{0\mathrm{.}05\}$ & $\backslash \backslash$

$\backslash$cline $\{5-6\}$ & & $3$ & $0\mathrm{.}2($P $\backslash$mu$)\backslash \backslash$

$1$ & $0\mathrm{.}007$ & $0\mathrm{.}04$ & $0\mathrm{.}04\backslash \backslash$

$2$ & $3$ & $0\mathrm{.}01$ & $0\mathrm{.}06$ & $0\backslash \backslash$

$3$ & & $0$ & $-0\mathrm{.}5$ & $0\backslash \backslash$

$2$ & $4$ & $0$ & $0\mathrm{.}06$ & $0$

$\backslash$end$\{$array$\}$

$\backslash ]$

d$)$ Form Zas by inverting the $\backslash \%/$bus in part $($a$)$

e$)$ Form $\backslash (\backslash$mathbb$\{$Z$\}\_\{\backslash$text $\{$aus $\}\}\backslash )$ by using the "modification" approach.