Two generators, G$1$ and G$2,$ are connected to a common bus and participate in load sharing. The droop settings of the generators are:

$-$ G$1$: R$1=4\backslash \%,$ rated power $\backslash (\backslash$mathrm$\{$Pl$\}=200\backslash$mathrm$\{$MW$\}\backslash ),$

$-$ G$2$: R$2\backslash (=5\backslash \%\backslash ),$ rated power P$2=300$ MW$.$

$1.$ Derive the power$-$frequency characteristics of each generator.

$2.$ If the total load increases by $50$ MW $,$ calculate the change in power output $\backslash (\backslash$Delta $\backslash$mathrm$\{$P$\}1\backslash )$ and $\backslash (\backslash$Delta $\backslash$mathrm$\{$P$\}2\backslash ).$

$3.$ Explain how droop settings affect load sharing between generators.