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If the initial acceleration power of a 100 MVA, 50 Hz synchronous generator having H= 5 MJ/MVA is Xpu, the initial acceleration in elec-deg/s2 and the inertia constant in M J-s/ele-deg respectively will be
- a)31.4X, 18
- b)1800X, 0.056
- c)X/1800, 0.056
- d)X/31.4, 18
Correct answer is option 'B'. Can you explain this answer?
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If the initial acceleration power of a 100 MVA, 50 Hz synchronous gene...
From swing equation,
Also, inertia constant,
Also, inertia constant,
Most Upvoted Answer
If the initial acceleration power of a 100 MVA, 50 Hz synchronous gene...
Solution:
Given parameters are:
Synchronous generator rating = 100 MVA
Frequency = 50 Hz
Inertia constant H = 5 MJ/MVA
Initial acceleration power = Xpu
We know that the formula for initial acceleration in electrical degrees per second square is given by:
θ'' = (Xpu × S) / (2H × f)
where,
Xpu = Initial acceleration power
S = Generator rating in MVA
H = Inertia constant in MJ/MVA
f = Frequency in Hz
θ'' = Initial acceleration in electrical degrees per second square
Now, substituting the given values in the above formula, we get:
θ'' = (Xpu × 100) / (2 × 5 × 50)
θ'' = (Xpu × 1) / (1 × 50)
θ'' = Xpu / 50
The formula for the inertia constant in MJ-s/electrical degree is given by:
H = (2πf × E'' × S) / (1000 × θ'')
where,
E'' = Induced emf per phase per unit synchronous reactance
S = Generator rating in MVA
θ'' = Initial acceleration in electrical degrees per second square
f = Frequency in Hz
H = Inertia constant in MJ/MVA
Now, substituting the given values in the above formula, we get:
H = (2π × 50 × 1 × 100) / (1000 × Xpu/50)
H = 1800Xpu
Therefore, the initial acceleration in electrical degrees per second square is 1800Xpu and the inertia constant in MJ-s/electrical degree is 0.056.
Hence, the correct answer is option B.
Given parameters are:
Synchronous generator rating = 100 MVA
Frequency = 50 Hz
Inertia constant H = 5 MJ/MVA
Initial acceleration power = Xpu
We know that the formula for initial acceleration in electrical degrees per second square is given by:
θ'' = (Xpu × S) / (2H × f)
where,
Xpu = Initial acceleration power
S = Generator rating in MVA
H = Inertia constant in MJ/MVA
f = Frequency in Hz
θ'' = Initial acceleration in electrical degrees per second square
Now, substituting the given values in the above formula, we get:
θ'' = (Xpu × 100) / (2 × 5 × 50)
θ'' = (Xpu × 1) / (1 × 50)
θ'' = Xpu / 50
The formula for the inertia constant in MJ-s/electrical degree is given by:
H = (2πf × E'' × S) / (1000 × θ'')
where,
E'' = Induced emf per phase per unit synchronous reactance
S = Generator rating in MVA
θ'' = Initial acceleration in electrical degrees per second square
f = Frequency in Hz
H = Inertia constant in MJ/MVA
Now, substituting the given values in the above formula, we get:
H = (2π × 50 × 1 × 100) / (1000 × Xpu/50)
H = 1800Xpu
Therefore, the initial acceleration in electrical degrees per second square is 1800Xpu and the inertia constant in MJ-s/electrical degree is 0.056.
Hence, the correct answer is option B.
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If the initial acceleration power of a 100 MVA, 50 Hz synchronous generator having H= 5 MJ/MVA is Xpu, the initial acceleration in elec-deg/s2 and the inertia constant in M J-s/ele-deg respectively will bea)31.4X,18b)1800X, 0.056c)X/1800, 0.056d)X/31.4, 18Correct answer is option 'B'. Can you explain this answer?
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