$2.$ Consider the network with meters at locations as shown in Figure $1$ on page $2.$ The measurement values and standard deviations $(\backslash (\backslash$sigma $\backslash ))$ of the meters are given in Table $1$ on page $2.$ All branch impedances are in per unit $($pu$)$ on a $100$ MVA base.

Use the DC power flow model in your calculations.

Note: Question No$.2$ continues on page $2.$

Table $1$

$($a$)$ Is the network observable? Explain.

$($b$)$ If a measurement of generation output at Bus $\backslash (3,\backslash$mathrm$\{$M$\}\_\{3\}=92\backslash$mathrm$\{$MW$\}\backslash )$ with $\backslash (\backslash$sigma$=0\mathrm{.}015\backslash$mathrm$\{$pu$\}\backslash ),$ is included in the measurement set of Table $1,$ what will happen to the observability of the network? Explain.

$($c$)$ Compute the estimated states and measurements if any of the network in parts $($a$)$ and $($b$)$ is observable.