The input data for a three$-$phase power system is given in Table $1.$

a$.$ Determine the bus admittance matrix $($Ybus$)$

b$.$ Add a shunt capacitive element of $100$ Mvar to one of the buses. Assuming a voltage of $1$ per unit at the relevant bus, does it affect the Ybus matrix? Justify your answer with calculations.

c$.$ Draw a configuration of the system for part b$.$

Table $1-$ Input data for problem $1$ Bus $($From$)$ Bus $($To$)$ R $($p$.$u$.)$ X $($p$.$u$)$ B $($p$.$u$.)450\mathrm{.}020\mathrm{.}040430\mathrm{.}050\mathrm{.}060420\mathrm{.}030\mathrm{.}040\mathrm{.}8250\mathrm{.}040\mathrm{.}050\mathrm{.}66230\mathrm{.}080\mathrm{.}11\mathrm{.}40120\mathrm{.}10\mathrm{.}20\mathrm{.}2130\mathrm{.}060\mathrm{.}041\mathrm{.}01000\mathrm{.}0205000\mathrm{.}040$