A 60 Hz, 4 pole turbo generator rated 100 MVA, 13.8 KV has an inertia constant of 10 MJ/MVA. Find the stored energy in the rotor at synchronous speed.  

Explanation:

Stored Energy in the Rotor of a Turbo Generator

Problem Statement: A 60 Hz, 4-pole turbo generator rated 100 MVA, 13.8 kV has an inertia constant of 10 MJ/MVA. The task is to calculate the stored energy in the rotor at synchronous speed.

Solution:

The key to solving this problem lies in understanding the relationship between the inertia constant (H), the apparent power (S), and the stored kinetic energy of the rotor (W_stored) at synchronous speed. The inertia constant is defined as the energy stored in the rotor per unit of the generator's apparent power (MVA rating) at synchronous speed.

Given Data:

• Frequency (f): 60 Hz
• Number of poles (P): 4
• Apparent power (S): 100 MVA
• Inertia constant (H): 10 MJ/MVA
• Voltage rating: 13.8 kV (not needed for this calculation)

Formula:

The total stored energy in the rotor at synchronous speed can be calculated using the formula:

W_stored = H × S

Where:

• W_stored is the total energy stored in the rotor (in MJ).
• H is the inertia constant (in MJ/MVA).
• S is the apparent power rating of the generator (in MVA).

Substituting the Given Values:

W_stored = 10 MJ/MVA × 100 MVA

W_stored = 1000 MJ

Final Answer: The stored energy in the rotor at synchronous speed is 1000 MJ.

Additional Information

To analyze why the other options are incorrect, let us revisit the problem:

Option 1: 10 MJ

This is incorrect. The inertia constant (H) is 10 MJ/MVA, meaning the stored energy per MVA is 10 MJ. Since the generator has a rating of 100 MVA, the total stored energy is 100 times this value, or 1000 MJ. Option 1 does not account for the multiplication by the apparent power of the generator.

Option 2: 100 J

This is incorrect. The unit of energy given in this option (Joules) is inconsistent with the unit of the inertia constant (MJ/MVA). Furthermore, 100 J is an extremely small value for the stored energy in the rotor of a generator rated at 100 MVA. This value is not realistic for the given scenario.

Option 3: 1000 J

This is incorrect. Similar to Option 2, the unit of energy in this option (Joules) is inconsistent with the given data. Additionally, 1000 J is a negligible amount of energy for a generator of this size and rating. The correct answer must be expressed in megajoules (MJ), not joules (J).

Option 4: 1000 MJ

This is the correct answer. As calculated above, the total stored energy in the rotor is 1000 MJ, derived from multiplying the inertia constant (10 MJ/MVA) by the apparent power (100 MVA).

Option 5: (Not provided in the problem)

There is no fifth option in the problem description, so this does not need further analysis.

Conclusion:

The correct option is Option 4: 1000 MJ. This value accurately represents the total stored energy in the rotor of the turbo generator at synchronous speed, based on the given inertia constant and apparent power rating.