Problem $1$ Three generators are connected in parallel to supply a load. Identical Generators G$1$ and G$2$: $480-$V$,200$ KVA, $2-$pole, $3-$phase, $60-$Hz synchronous generator whose prime mover has a no$-$load speed of $3690$ RPM and a full$-$load speed of $3591$ RPM$.$ Generator G$3$: $480-$V$,150$ KVA, $4-$pole, $3-$phase, $60-$Hz synchronous generator whose prime mover has a no$-$load speed of $1830$ RPM and a full$-$load speed of $1790$ RPM$.($a$)$ Calculate the speed droops of generators G$1,$ G$2,$ and G$3.($b$)$ Find the no$-$load frequency of each generator. $($c$)$ Find the full$-$load frequency of each generator. Now Suppose the Slopes are: Sp$1=$ Sp$2=100$ KW$/$Hz for Generators $1$ and $2,$ and Sp$3=92$ KW$/$Hz for Generator $3.$ The no$-$load frequency for each generator is set to $61\mathrm{.}2$ Hz$.($d$)$ Find the operating$-$frequency of the power system for $405$ KW load. $($e$)$ How will the three generators share the $405$ KW load at this operating frequency? $($f$)$ What is the maximum KVA load, at PF $=0\mathrm{.}9$ lagging, that can be delivered by the generators when each is operating at its rated conditions? Find the no$-$load frequency of each generator in this case if the system frequency is to be $59\mathrm{.}5$ Hz$.$