Three generators are connected in parallel to a load. The generators have the following characteristics:

Unit

Rating

R $($on its own base$)$

$1$

$600$ MVA

$6\%$

$2$

$500$ MVA

$4\%$

$3$

$400$ MVA

$3\%$

The system is initially operating at $60$ Hz in steady$-$state.

Assuming no sensitivity of the load to frequency changes, find the steady$-$state frequency of the system, if the load is increased by $100$ MW$.$ Under these conditions, what is the change in mechanical power of each generator?

Group of answer choices

dPM$1=37\mathrm{.}9070$ MW$,$ dPM$2=24\mathrm{.}8837$ MW$,$ dPM$3=37\mathrm{.}2093$ MW

dPM$1=27\mathrm{.}9070$ MW$,$ dPM$2=34\mathrm{.}8837$ MW$,$ dPM$3=37\mathrm{.}2093$ MW

dPM$1=28\mathrm{.}9070$ MW$,$ dPM$2=33\mathrm{.}8837$ MW$,$ dPM$3=37\mathrm{.}2093$ MW

dPM$1=27\mathrm{.}9070$ MW$,$ dPM$2=35\mathrm{.}8837$ MW$,$ dPM$3=36\mathrm{.}2093$ MW