Book Problem $9\mathrm{.}1.$

A single machine connected to an infinite bus has the following faulted and postfault equations.

Faulted: $0\mathrm{.}0133($d$^(2)\backslash$sigma $)/($dt$^(2))=0\mathrm{.}91-3\mathrm{.}24$sin$\backslash$delta $,$t$>$tclV$(\backslash$delta $,\backslash$omega $)$VcrA$2,$A$30\mathrm{.}0133($d$^(2)\backslash$sigma $)/($dt$^(2))=0\mathrm{.}91,0.$

Postfault: $0\mathrm{.}0133($d$^(2)\backslash$sigma $)/($dt$^(2))=0\mathrm{.}91-3\mathrm{.}24$sin$\backslash$delta $,$t$>$tcl$.$

The prefault system is the same as the postfault system.

$($a$)$ Find V$(\backslash$delta $,\backslash$omega $)$ and Vcr using the u$.$e$.$p formulation.

$($b$)$ Explain stability test of $($a$)$ using the equal$-$area criterion. Sketch the areas A$1,$ A$2,$A$3.$

$($c$)$ Find tcr using Vcr$.$

$($d$)$ Find tcr using PEBS method.

Some problems provide results. You can use them to check your results.