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A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is given
Correct answer is between '1,1.5'. Can you explain this answer?
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A 50 Hz synchronous generator is connected to an infinite bus through ...
fn = 1.19 Hz.Most Upvoted Answer
A 50 Hz synchronous generator is connected to an infinite bus through ...
Solution:
The natural frequency of the electrical system is given as:
f_n = 1 / 2πsqrt(L_eqC_eq)
where L_eq = equivalent inductance and C_eq = equivalent capacitance.
Equivalent inductance:
L_eq = L_g + L_l
where L_g = generator reactance and L_l = line reactance.
L_eq = j0.4 + j0.2 = j0.6 pu
Equivalent capacitance:
C_eq = 2H / (X_d^2)
where H = inertia constant and X_d = synchronous reactance.
X_d = 1 / (1 / X_g + 1 / X_l)
where X_g = generator synchronous reactance and X_l = line reactance.
X_g = X_d - X_l = j0.4 - j0.2 = j0.2 pu
C_eq = 2 x 4 x 10^6 / (0.2^2) = 100 μF
f_n = 1 / 2πsqrt(j0.6 x 100 x 10^-6) = 1.06 Hz
The loaded voltage of the generator is:
V_g = V_nl - I_g X_g
where V_nl = no-load voltage and I_g = generator current.
I_g = P / (V_g cosθ)
where P = generator output power and θ = power factor angle.
At 70% of maximum power transfer capacity:
P = 0.7 x S_max = 0.7 x V_g I_g
I_g = 0.7 x V_g / X_g
cosθ = 0.8
V_g = 1.2 pu
I_g = 0.7 x 1.2 / j0.2 = 4.2 ∠-71.57° A
V_g = V_nl - I_g X_g
1.2 = V_nl + j0.84
V_nl = 1.2 - j0.84 = 1.44 ∠-33.69° pu
The frequency of natural oscillations is given by:
f = f_n / sqrt(1 - (P / P_max)^2)
where P_max = maximum power transfer capacity.
P_max = V_g^2 / (2 X_g)
P_max = 1.2^2 / (2 x 0.2) = 36 MW
f = 1.06 / sqrt(1 - (0.7 / 36)^2) = 1.12 Hz
Therefore, the frequency of natural oscillations is between 1 and 1.5 Hz.
The natural frequency of the electrical system is given as:
f_n = 1 / 2πsqrt(L_eqC_eq)
where L_eq = equivalent inductance and C_eq = equivalent capacitance.
Equivalent inductance:
L_eq = L_g + L_l
where L_g = generator reactance and L_l = line reactance.
L_eq = j0.4 + j0.2 = j0.6 pu
Equivalent capacitance:
C_eq = 2H / (X_d^2)
where H = inertia constant and X_d = synchronous reactance.
X_d = 1 / (1 / X_g + 1 / X_l)
where X_g = generator synchronous reactance and X_l = line reactance.
X_g = X_d - X_l = j0.4 - j0.2 = j0.2 pu
C_eq = 2 x 4 x 10^6 / (0.2^2) = 100 μF
f_n = 1 / 2πsqrt(j0.6 x 100 x 10^-6) = 1.06 Hz
The loaded voltage of the generator is:
V_g = V_nl - I_g X_g
where V_nl = no-load voltage and I_g = generator current.
I_g = P / (V_g cosθ)
where P = generator output power and θ = power factor angle.
At 70% of maximum power transfer capacity:
P = 0.7 x S_max = 0.7 x V_g I_g
I_g = 0.7 x V_g / X_g
cosθ = 0.8
V_g = 1.2 pu
I_g = 0.7 x 1.2 / j0.2 = 4.2 ∠-71.57° A
V_g = V_nl - I_g X_g
1.2 = V_nl + j0.84
V_nl = 1.2 - j0.84 = 1.44 ∠-33.69° pu
The frequency of natural oscillations is given by:
f = f_n / sqrt(1 - (P / P_max)^2)
where P_max = maximum power transfer capacity.
P_max = V_g^2 / (2 X_g)
P_max = 1.2^2 / (2 x 0.2) = 36 MW
f = 1.06 / sqrt(1 - (0.7 / 36)^2) = 1.12 Hz
Therefore, the frequency of natural oscillations is between 1 and 1.5 Hz.
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A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is givenCorrect answer is between '1,1.5'. 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. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is givenCorrect answer is between '1,1.5'. 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. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is givenCorrect answer is between '1,1.5'. 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. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is givenCorrect answer is between '1,1.5'. Can you explain this answer?.
A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is givenCorrect answer is between '1,1.5'. 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. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is givenCorrect answer is between '1,1.5'. 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. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is givenCorrect answer is between '1,1.5'. 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. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is givenCorrect answer is between '1,1.5'. Can you explain this answer?, a detailed solution for A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is givenCorrect answer is between '1,1.5'. Can you explain this answer? has been provided alongside types of A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is givenCorrect answer is between '1,1.5'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A 50 Hz synchronous generator is connected to an infinite bus through a line. The pu. reactances of the generator and the lines are j 0.4 pu and j 0.2 pu respectively. The generator no-load voltage is 1.2 pu and that of the infinite bus is 1.0 pu. The inertia constant of the generator is 4 MW-Sec/MVA. Determine the frequency (in Hz) of natural oscillations if the generator is loaded to 70% of its maximum power transfer capacity and small perturbation is givenCorrect answer is between '1,1.5'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
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