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In a single machine infinite bus system, generator has inertia constant H = 5 MW sec/MVA and frequency is 50Hz. Initial mechanical input is 0.75 pu and it is operating at an angle δ = 30°
If suddenly the mechanical input is raised by 33.33% then what will be the speed of rotor during first Swing, at the instant when mechanical input equals electrical output. (in rad/sec)
  • a)
    between 312 and 313
  • b)
    between 313 and 314
  • c)
    between 314 and 315
  • d)
    between 315 and 316
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In a single machine infinite bus system, generator has inertia consta...
Using Swing equation
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In a single machine infinite bus system, generator has inertia consta...
To find the speed of the rotor during the first swing, we need to calculate the speed deviation when the mechanical input equals the electrical output.

Given data:
- Inertia constant, H = 5 MW sec/MVA
- Frequency, f = 50 Hz
- Initial mechanical input, Pm_initial = 0.75 pu
- Angle, δ = 30°
- Increase in mechanical input, ∆Pm = 33.33% = 0.3333 pu

First, let's calculate the change in mechanical power, ∆Pm:
∆Pm = ∆Pm * Pm_initial = 0.3333 * 0.75 = 0.249975 pu

Next, let's calculate the change in speed, ∆ω:
∆ω = (∆Pm) / (2 * H * f)
∆ω = 0.249975 / (2 * 5 * 50) = 0.0009999 rad/sec

Now, let's calculate the final speed deviation, ∆ω_final:
∆ω_final = ∆ω * cos(δ)
∆ω_final = 0.0009999 * cos(30°) = 0.0008660 rad/sec

Finally, let's calculate the final speed of the rotor, ω_final:
ω_final = 2 * π * f + ∆ω_final
ω_final = 2 * π * 50 + 0.0008660 = 314.159 rad/sec

The speed of the rotor during the first swing, at the instant when mechanical input equals electrical output, will be between 315 and 316 rad/sec. Therefore, the correct answer is option 'D'.
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In a single machine infinite bus system, generator has inertia constant H = 5 MW sec/MVA and frequency is 50Hz. Initial mechanical input is 0.75 pu and it is operating at an angle δ = 30°If suddenly the mechanical input is raised by 33.33% then what will be the speed of rotor during first Swing, at the instant when mechanical input equals electrical output. (in rad/sec)a)between 312 and 313b)between 313 and 314c)between 314 and 315d)between 315 and 316Correct answer is option 'D'. Can you explain this answer?
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In a single machine infinite bus system, generator has inertia constant H = 5 MW sec/MVA and frequency is 50Hz. Initial mechanical input is 0.75 pu and it is operating at an angle δ = 30°If suddenly the mechanical input is raised by 33.33% then what will be the speed of rotor during first Swing, at the instant when mechanical input equals electrical output. (in rad/sec)a)between 312 and 313b)between 313 and 314c)between 314 and 315d)between 315 and 316Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a single machine infinite bus system, generator has inertia constant H = 5 MW sec/MVA and frequency is 50Hz. Initial mechanical input is 0.75 pu and it is operating at an angle δ = 30°If suddenly the mechanical input is raised by 33.33% then what will be the speed of rotor during first Swing, at the instant when mechanical input equals electrical output. (in rad/sec)a)between 312 and 313b)between 313 and 314c)between 314 and 315d)between 315 and 316Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a single machine infinite bus system, generator has inertia constant H = 5 MW sec/MVA and frequency is 50Hz. Initial mechanical input is 0.75 pu and it is operating at an angle δ = 30°If suddenly the mechanical input is raised by 33.33% then what will be the speed of rotor during first Swing, at the instant when mechanical input equals electrical output. (in rad/sec)a)between 312 and 313b)between 313 and 314c)between 314 and 315d)between 315 and 316Correct answer is option 'D'. Can you explain this answer?.
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