Three steam generators G $1,$ G $2,$ and G $3$ are operating in parallel. Each generator is a: $20$ MVA, $7200$ V$,\backslash (60\backslash$mathrm$\{$~Hz$\},0\mathrm{.}88\backslash )$ PF lagging, $2-$pole, Y$-$connected synchronous generator.

Generators G $1$ and G $2$ have a characteristic power frequency slope S p$1=$ S p$2=6\mathrm{.}4$ MW$/$Hz$.$ Generator G $\backslash (\backslash$mathbf$\{3\}\backslash )$ has a slope of S p$3=5\mathrm{.}4$ MW$/$Hz$.$

$1-$With $\backslash (\backslash$boldsymbol$\{$f$\}\backslash$boldsymbol$\{$n l $,1\}=\backslash$boldsymbol$\{$f$\}\backslash$boldsymbol$\{$n l $,\},\backslash$mathbf$\{$f$\}\backslash$boldsymbol$\{$n l l$\},\backslash$mathbf$\{3\}=\backslash$mathbf$\{62\}\backslash$mathbf$\{$H z$\}\backslash ),$ when the actual system frequency is $\backslash (\backslash$mathbf$\{60$ ~ H z$\}\backslash )$

$-$The power supplied by each generator PG$1=$ MW$,$ PG$2=$ MW$,$ PG$3=$ MW$?$

$-$What is the maximum power the three generators can supply without exceeding the rating of any of them Pmax$=$ MW$.$

$-$At what system frequency does this limit occur? fsys $=$ Hz$.$

$-$How much power does each generator supply at that point? PG$1=$ MW$,$ PG$2=$ MW$,$ PG$3=$ MW$?$

$-$What is the total power supplied by the three generators? PGtotal$=$ MW