Given a system of $12$ buses, write python code to calculate the jacobaian matrix. Bus data attached. starter code given, assume bus data is read in correctly, but can be rearranged so that it is in order:

# Takes in bus and line data and returns the admittance matrix

def create$\_$admittance$\_$matrix $($bus$\_$data, line$\_$data$)$:

# Creates numpy array of zeros to populate with admittances

y$\_$matrix $=$ np$.$zeros$(($num$\_$buses, num$\_$buses$),$ dtype$=$complex$)$

for i in range$($len$($line$\_$data$))$:

from$\_$bus $=$ line$\_$data.loc$[$i$,$ 'From'$]$

to$\_$bus $=$ line$\_$data.loc$[$i$,\text{'}$To$\text{'}]$

R $=$ line$\_$data$["$Rtotal$,$ p$.$u$."].$iloc$[$i$]$

X $=$ line$\_$data$["$Xtotal$,$ p$.$u$."].$iloc$[$i$]$

B $=$ line$\_$data$["$Btotal$,$ p$.$u$."].$iloc$[$i$]$

Y $=(1/($R $+1$j$*$X$))$

B$\_$complex $=(1$j$*$B$)/2$

#non$-$diagonals

y$\_$matrix$[$from$\_$bus$-1,$to$\_$bus$-1]=-$Y

y$\_$matrix$[$to$\_$bus$-1,$ from$\_$bus$-1]=-$Y

#diagonals

y$\_$matrix$[$from$\_$bus$-1,$ from$\_$bus$-1]+=$ Y $+$ B$\_$complex

y$\_$matrix$[$to$\_$bus$-1,$ to$\_$bus$-1]+=$ Y $+$ B$\_$complex

return y$\_$matrix

y$\_$matrix $=$ create$\_$admittance$\_$matrix $($bus$\_$data, line$\_$data$)$

# Extract bus types

slack$\_$bus $=$ bus$\_$data$[$bus$\_$data$[\text{'}$Type$\text{'}]==\text{'}$S$\text{'}].$index

pq$\_$buses $=$ bus$\_$data$[$bus$\_$data$[\text{'}$Type$\text{'}]==\text{'}$D$\text{'}].$index

pv$\_$buses $=$ bus$\_$data$[$bus$\_$data$[\text{'}$Type$\text{'}]==\text{'}$G$\text{'}].$index

V $=$ np$.$array$($bus$\_$data$["$V Set"$])$

#print$($V$)$

theta $=$ np$.$zeros$($num$\_$buses$)$