Three identical steam$-$turbine generators G$1,$ G$2,$ and G $3$ are operating in parallel. Each generator is: $7200$ V$,20$ MVA, $50$ Hz$.0\mathrm{.}85$ PF lagging, $4-$ poles, Y$-$connected. Each of G $1$ and G $2$ has a characteristic power$-$frequency slope of $4$ MW$/$Hz$.$ Generator G $3$ has a slope of $5$ MW$/$Hz$.$ Flag question $(1)$ If the three generators supply a total load of $32$ MW$,$ and the no$-$load frequency of each generator is set to $52$ Hz$,$ Calculate: $-$The system frequency $=$ Hz $-$The power supplied by each generator PG$1=$ MW$,$ PG$2=$ MW$,$ PG$3=(2)$ If the load increases with no changes in the settings of the no$-$load frequencies: $-$Which generator reaches its maximum rated power first? Write only the number of the generator, number $=-$At what system frequency does this limit occur? fsys $=-$How much power does each generator supply at that point? PG$1=$ MW$,$ PG$2=$ MW MW$.$ PG$3=$ MW$?-$What is the total power supplied by the three generators? PGtotal$=$ MW$?$ Three identical steam$-$turbine generators G $1,$ G $2,$ and G $3$ are operating in parallel. Each generator is: $\backslash (7200\backslash$mathrm$\{$~V$\},20\backslash$mathrm$\{$MVA$\},50\backslash$mathrm$\{$~Hz$\},0\mathrm{.}85\backslash$mathrm$\{$PF$\}\backslash )$ lagging, $4$ poles, Y$-$connected.

Each of G $1$ and G $2$ has a characteristic power$-$frequency slope of $\backslash (4\backslash$mathrm$\{$MW$\}/\backslash$mathrm$\{$Hz$\}\backslash ).$ Generator G $3$ has a slope of $\backslash (5\backslash$mathrm$\{$MW$\}/\backslash$mathrm$\{$Hz$\}\backslash ).$

$(1)$ If the three generators supply a total load of $32$ MW $,$ and the no$-$load frequency of each generator is set to $52$ Hz $,$ Calculate:

$-$The system frequency $=$ Hz ;

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

$(2)$ If the load increases with no changes in the settings of the no$-$load frequencies:

$-$Which generator reaches its maximum rated power first? Write only the number of the generator, number $=$

$-$At what system frequency does this limit occur? fsys $=\backslash (\backslash$mathrm$\{$MW$\},\backslash$mathrm$\{$PG$2\}=\backslash )$ MW$,$ PG$3=$ MW$?$

$-$How much power does each generator supply at that point? PGI$=$

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