GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 53 of 65

Marks: +1, -0

A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current at

0.9

lagging p.f. load. An ideal reactor is now connected in parallel with load, as a result of which the total lagging reactive power requirement of the load is twice the previous while the real power remains unchanged. The armature current is now ________________ A (rounded off to 2 decimal places).

Your Answer:

Validate

Solution:

{f}_{1}=0.9, \cos ϕ 1=0.9

ϕ_{1}=25.84^{∘}

| {I}_{ {L} 1}|=100 {A}

{I}_{ {L} 1}=100<-25.84^{∘}

(i)

I_{S 1}=I_{L 1}=100<-25.84^{∘}

(ii)

I_{S 2}=I_{L 1}+I_{L}<-90^{∘}

=100<-25.84+I_{L}<-90^{∘}

{Q}_{\;\text "sh reactor "\;}= {Q}_{\;\text "load "\;}

{VI}_{ {L}}= {VI}_{ {L} 1} \sin 25.84

{I}_{ {L}}=100 \sin 25.84

=43.58 {A}

then,

{I} {s} 2=100 ∠-25.84+43.58 ∠-90^{∘}

=100 {cm} 25.84+43.58 {cm} 90^{∘}+100 \sin (-25.84)+ {I} 43.58 \sin (-90^{∘})

=90.00147-87.165

≃125.3 ∠-44^{∘}

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