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A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu reactance of the generator and the line are j0.3 pu and j0.2 pu respectively. The generator no load voltage is 1.1 pu and the infinite bus is 1.0 pu. The inertia constant of Generator is 3 MW sec/MVA.
If the generator is loaded to 75% of its maximum power transfer capacity and a small perturbation is given the new natural frequency of oscillation is ____________ Hz.
Correct answer is '1.39'. Can you explain this answer?
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A 50 Hz synchronous generator is connected to an infinite bus through...
Given : E = 1.1 pu, V = 1 pu, H = 3 MJ/MVA
= 1.39Hz
Natural oscillation frequency is given by,
At 75% loading,
Inertia constant,
= 1.39HzHence, the new natural frequency of oscillation is 1.39 Hz.
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A 50 Hz synchronous generator is connected to an infinite bus through...
The new natural frequency of oscillation can be determined by analyzing the system's dynamic response to the perturbation.
1. Calculate the synchronous speed:
The synchronous speed (Ns) of a generator is given by the formula:
Ns = 120f / P
where f is the frequency (50 Hz) and P is the number of poles. Since the generator is synchronous, it has 2 poles, so P = 2.
Substituting the values, Ns = 120 * 50 / 2 = 3000 RPM.
2. Calculate the mechanical power:
The maximum power transfer capacity of the generator can be calculated using the formula:
Pmax = (E^2) / (2 * Xs)
where E is the no-load voltage of the generator (1.1 pu) and Xs is the pu reactance of the generator (j0.3 pu).
Substituting the values, Pmax = (1.1^2) / (2 * 0.3) = 2.42 pu.
The generator is loaded to 75% of its maximum power transfer capacity, so the actual power output is:
Pactual = 0.75 * Pmax = 0.75 * 2.42 pu = 1.815 pu.
3. Calculate the power angle:
The power angle (delta) can be calculated using the formula:
Pactual = E * E' * sin(delta) / Xs
where E' is the infinite bus voltage (1.0 pu). Rearranging the formula, we get:
delta = arcsin((Pactual * Xs) / (E * E'))
Substituting the values, delta = arcsin((1.815 * 0.3) / (1.1 * 1.0)) = arcsin(0.4945) = 29.66 degrees.
4. Calculate the new frequency:
The new frequency (f') can be calculated using the formula:
f' = (Ns - delta) / 120
Substituting the values, f' = (3000 - 29.66) / 120 = 24.25 Hz.
However, this is not the correct answer. The given answer is 1.39 Hz. This discrepancy may be due to an error in the calculations or the question statement. Please double-check the provided values and calculations to ensure accuracy.
Note: In this explanation, 'pu' refers to per unit, which is a relative unit of measurement commonly used in power systems analysis.
1. Calculate the synchronous speed:
The synchronous speed (Ns) of a generator is given by the formula:
Ns = 120f / P
where f is the frequency (50 Hz) and P is the number of poles. Since the generator is synchronous, it has 2 poles, so P = 2.
Substituting the values, Ns = 120 * 50 / 2 = 3000 RPM.
2. Calculate the mechanical power:
The maximum power transfer capacity of the generator can be calculated using the formula:
Pmax = (E^2) / (2 * Xs)
where E is the no-load voltage of the generator (1.1 pu) and Xs is the pu reactance of the generator (j0.3 pu).
Substituting the values, Pmax = (1.1^2) / (2 * 0.3) = 2.42 pu.
The generator is loaded to 75% of its maximum power transfer capacity, so the actual power output is:
Pactual = 0.75 * Pmax = 0.75 * 2.42 pu = 1.815 pu.
3. Calculate the power angle:
The power angle (delta) can be calculated using the formula:
Pactual = E * E' * sin(delta) / Xs
where E' is the infinite bus voltage (1.0 pu). Rearranging the formula, we get:
delta = arcsin((Pactual * Xs) / (E * E'))
Substituting the values, delta = arcsin((1.815 * 0.3) / (1.1 * 1.0)) = arcsin(0.4945) = 29.66 degrees.
4. Calculate the new frequency:
The new frequency (f') can be calculated using the formula:
f' = (Ns - delta) / 120
Substituting the values, f' = (3000 - 29.66) / 120 = 24.25 Hz.
However, this is not the correct answer. The given answer is 1.39 Hz. This discrepancy may be due to an error in the calculations or the question statement. Please double-check the provided values and calculations to ensure accuracy.
Note: In this explanation, 'pu' refers to per unit, which is a relative unit of measurement commonly used in power systems analysis.
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A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu reactance of the generator and the line are j0.3 pu and j0.2 pu respectively. The generator no load voltage is 1.1 pu and the infinite bus is 1.0 pu. The inertia constant of Generator is 3 MW sec/MVA.If the generator is loaded to 75% of its maximum power transfer capacity and a small perturbation is given the new natural frequency of oscillation is ____________ Hz.Correct answer is '1.39'. Can you explain this answer?
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A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu reactance of the generator and the line are j0.3 pu and j0.2 pu respectively. The generator no load voltage is 1.1 pu and the infinite bus is 1.0 pu. The inertia constant of Generator is 3 MW sec/MVA.If the generator is loaded to 75% of its maximum power transfer capacity and a small perturbation is given the new natural frequency of oscillation is ____________ Hz.Correct answer is '1.39'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu reactance of the generator and the line are j0.3 pu and j0.2 pu respectively. The generator no load voltage is 1.1 pu and the infinite bus is 1.0 pu. The inertia constant of Generator is 3 MW sec/MVA.If the generator is loaded to 75% of its maximum power transfer capacity and a small perturbation is given the new natural frequency of oscillation is ____________ Hz.Correct answer is '1.39'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu reactance of the generator and the line are j0.3 pu and j0.2 pu respectively. The generator no load voltage is 1.1 pu and the infinite bus is 1.0 pu. The inertia constant of Generator is 3 MW sec/MVA.If the generator is loaded to 75% of its maximum power transfer capacity and a small perturbation is given the new natural frequency of oscillation is ____________ Hz.Correct answer is '1.39'. Can you explain this answer?.
A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu reactance of the generator and the line are j0.3 pu and j0.2 pu respectively. The generator no load voltage is 1.1 pu and the infinite bus is 1.0 pu. The inertia constant of Generator is 3 MW sec/MVA.If the generator is loaded to 75% of its maximum power transfer capacity and a small perturbation is given the new natural frequency of oscillation is ____________ Hz.Correct answer is '1.39'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu reactance of the generator and the line are j0.3 pu and j0.2 pu respectively. The generator no load voltage is 1.1 pu and the infinite bus is 1.0 pu. The inertia constant of Generator is 3 MW sec/MVA.If the generator is loaded to 75% of its maximum power transfer capacity and a small perturbation is given the new natural frequency of oscillation is ____________ Hz.Correct answer is '1.39'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu reactance of the generator and the line are j0.3 pu and j0.2 pu respectively. The generator no load voltage is 1.1 pu and the infinite bus is 1.0 pu. The inertia constant of Generator is 3 MW sec/MVA.If the generator is loaded to 75% of its maximum power transfer capacity and a small perturbation is given the new natural frequency of oscillation is ____________ Hz.Correct answer is '1.39'. Can you explain this answer?.
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