GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 35 of 65

Marks: +1, -0

A single

50 {Hz}

, synchronous generator on droop control was delivering

100 {MW}

power to a system. Due to increase in load, generator power has to be increased by

10 {MW}

, as a result of which, system frequency dropped to

49.75 {Hz}

. Further increase in load in the system resulted in a frequency of

49.25 {Hz}

. At this condition, the power in MW supplied by the generator is . ___________.(rounded off to 2 decimal places).

Solution:

{f}_{1}=50 {Hz}, {f}_{2}=49.75 {Hz}, {f}_{3}=49.25 {Hz}

{P}_{1}=100 {MW}, {P}_{2}=110 {MW}, {P}_{3}=?

\;{f_{1}-f_{2}}/{P_{2}-P_{1}}=\;{f_{2}-f_{3}}/{P_{3}-P_{2}}

(Same droop)

\;{0.25}/{10}=\;{0.5}/{P_{3}-110}

⇒ P_{3}=110=20

P_{3}=130 {MW}

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