Three physically identical synchronous generators are operating in parallel. They are all rated

for a full load of $3$ MW at $0\mathrm{.}8$ PF lagging. The no$-$load frequency of generator A is $61$ Hz$,$ and

its speed droop is $3\mathrm{.}4$ percent. The no$-$load frequency of generator B is $61\mathrm{.}5$ Hz$,$ and its speed

droop is $3$ percent. The no$-$load frequency of generator C is $60\mathrm{.}5$ Hz$,$ and its speed droop is

$2\mathrm{.}6$ percent.

$($a$)$ If a total load consisting of $7$ MW is being supplied by this power system, what will the

system frequency be and how will the power be shared among the three generators?

$($b$)$ At what load does one of the generators reach to no$-$load condition? Which generator

reaches to no$-$load condition first?

$($c$)$ At what load does one of the generators exceed its ratings? Which generator exceeds its

ratings first?