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A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia constant of H = 7.5 MJ/MVA. If the mechanical power input is 552 MW and the electrical power output is 400 MW and stator copper loss is assumed to be negligible, then the angular acceleration is _____ mech degree/sec 2 .?
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A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia cons...
**Given data:**
- Generator rating: 500 MVA
- Voltage rating: 22 kV
- Frequency: 60 Hz
- Number of poles: 4
- Inertia constant: H = 7.5 MJ/MVA
- Mechanical power input: 552 MW
- Electrical power output: 400 MW
- Stator copper loss negligible
**Calculating the electrical power input:**
The electrical power input to the generator can be calculated using the formula:
P_e = P_out + P_copper_loss
Since the stator copper loss is negligible, P_copper_loss = 0.
Therefore, P_e = P_out = 400 MW.
**Calculating the mechanical torque:**
The mechanical power input to the generator can be calculated using the formula:
P_m = P_e + P_mech_loss
Since the stator copper loss is negligible, P_mech_loss = 0.
Therefore, P_m = P_e = 400 MW.
The mechanical torque can be calculated using the formula:
T_m = P_m / (2 * π * f)
Where f is the frequency in Hz.
Substituting the given values:
T_m = 400 MW / (2 * π * 60 Hz) = 400 x 10^6 W / (2 * π * 60 s^-1) = 106.10 Nm.
**Calculating the angular acceleration:**
The mechanical power input can also be calculated using the formula:
P_m = T_m * ω_m
Where ω_m is the angular velocity in rad/s.
The angular velocity can be calculated using the formula:
ω_m = 2 * π * f / p
Where p is the number of poles.
Substituting the given values:
ω_m = 2 * π * 60 Hz / 4 = 30 π rad/s.
Substituting the values of P_m and ω_m into the equation:
400 MW = 106.10 Nm * 30 π rad/s
Simplifying the equation:
400 x 10^6 W = 3183.1 Nm/s * π rad/s
400 x 10^6 W = 9993.9 Nm/s
Therefore, the angular acceleration is 9993.9 Nm/s divided by the inertia constant H.
**Calculating the angular acceleration in mech degree/sec^2:**
To convert the angular acceleration from rad/s^2 to mech degree/sec^2, we need to multiply it by a conversion factor.
1 rad/s^2 = 180/π mech degree/sec^2
Therefore, the angular acceleration in mech degree/sec^2 is:
9993.9 Nm/s * (180/π) = 572,957.795 mech degree/sec^2.
Therefore, the angular acceleration is approximately 572,958 mech degree/sec^2.
- Generator rating: 500 MVA
- Voltage rating: 22 kV
- Frequency: 60 Hz
- Number of poles: 4
- Inertia constant: H = 7.5 MJ/MVA
- Mechanical power input: 552 MW
- Electrical power output: 400 MW
- Stator copper loss negligible
**Calculating the electrical power input:**
The electrical power input to the generator can be calculated using the formula:
P_e = P_out + P_copper_loss
Since the stator copper loss is negligible, P_copper_loss = 0.
Therefore, P_e = P_out = 400 MW.
**Calculating the mechanical torque:**
The mechanical power input to the generator can be calculated using the formula:
P_m = P_e + P_mech_loss
Since the stator copper loss is negligible, P_mech_loss = 0.
Therefore, P_m = P_e = 400 MW.
The mechanical torque can be calculated using the formula:
T_m = P_m / (2 * π * f)
Where f is the frequency in Hz.
Substituting the given values:
T_m = 400 MW / (2 * π * 60 Hz) = 400 x 10^6 W / (2 * π * 60 s^-1) = 106.10 Nm.
**Calculating the angular acceleration:**
The mechanical power input can also be calculated using the formula:
P_m = T_m * ω_m
Where ω_m is the angular velocity in rad/s.
The angular velocity can be calculated using the formula:
ω_m = 2 * π * f / p
Where p is the number of poles.
Substituting the given values:
ω_m = 2 * π * 60 Hz / 4 = 30 π rad/s.
Substituting the values of P_m and ω_m into the equation:
400 MW = 106.10 Nm * 30 π rad/s
Simplifying the equation:
400 x 10^6 W = 3183.1 Nm/s * π rad/s
400 x 10^6 W = 9993.9 Nm/s
Therefore, the angular acceleration is 9993.9 Nm/s divided by the inertia constant H.
**Calculating the angular acceleration in mech degree/sec^2:**
To convert the angular acceleration from rad/s^2 to mech degree/sec^2, we need to multiply it by a conversion factor.
1 rad/s^2 = 180/π mech degree/sec^2
Therefore, the angular acceleration in mech degree/sec^2 is:
9993.9 Nm/s * (180/π) = 572,957.795 mech degree/sec^2.
Therefore, the angular acceleration is approximately 572,958 mech degree/sec^2.
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A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia constant of H = 7.5 MJ/MVA. If the mechanical power input is 552 MW and the electrical power output is 400 MW and stator copper loss is assumed to be negligible, then the angular acceleration is _____ mech degree/sec 2 .?
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A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia constant of H = 7.5 MJ/MVA. If the mechanical power input is 552 MW and the electrical power output is 400 MW and stator copper loss is assumed to be negligible, then the angular acceleration is _____ mech degree/sec 2 .? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia constant of H = 7.5 MJ/MVA. If the mechanical power input is 552 MW and the electrical power output is 400 MW and stator copper loss is assumed to be negligible, then the angular acceleration is _____ mech degree/sec 2 .? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia constant of H = 7.5 MJ/MVA. If the mechanical power input is 552 MW and the electrical power output is 400 MW and stator copper loss is assumed to be negligible, then the angular acceleration is _____ mech degree/sec 2 .?.
A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia constant of H = 7.5 MJ/MVA. If the mechanical power input is 552 MW and the electrical power output is 400 MW and stator copper loss is assumed to be negligible, then the angular acceleration is _____ mech degree/sec 2 .? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia constant of H = 7.5 MJ/MVA. If the mechanical power input is 552 MW and the electrical power output is 400 MW and stator copper loss is assumed to be negligible, then the angular acceleration is _____ mech degree/sec 2 .? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia constant of H = 7.5 MJ/MVA. If the mechanical power input is 552 MW and the electrical power output is 400 MW and stator copper loss is assumed to be negligible, then the angular acceleration is _____ mech degree/sec 2 .?.
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A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia constant of H = 7.5 MJ/MVA. If the mechanical power input is 552 MW and the electrical power output is 400 MW and stator copper loss is assumed to be negligible, then the angular acceleration is _____ mech degree/sec 2 .?, a detailed solution for A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia constant of H = 7.5 MJ/MVA. If the mechanical power input is 552 MW and the electrical power output is 400 MW and stator copper loss is assumed to be negligible, then the angular acceleration is _____ mech degree/sec 2 .? has been provided alongside types of A 500 MVA, 22 kV, 60 Hz four-pole turbo- generator has an inertia constant of H = 7.5 MJ/MVA. If the mechanical power input is 552 MW and the electrical power output is 400 MW and stator copper loss is assumed to be negligible, then the angular acceleration is _____ mech degree/sec 2 .? theory, EduRev gives you an
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