# Two identical synchronous machines with equal inertia constants are connected in parallel order and oscillating simultaneously. The effective inertia

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Two identical synchronous machines with equal inertia constants are connected in parallel order and oscillating simultaneously. The effective inertia constant is 4 MJ / MVA. What will be the inertia constant of each machine?
1. 2 MJ / MVA
2. 16 MJ / MVA
3. 4 MJ / MVA
4. 8 MJ / MVA

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Correct Answer - Option 1 : 2 MJ / MVA

Two machine system:

• In a two-machine system, a synchronous generator is connected to a synchronous motor by a loss-less network.
• Initially, both the machines are in stable condition. When the load on the motor increases suddenly, the electrical input cannot change simultaneously so that the motor will get oscillations.
• When the oscillations are very high when compared to the natural frequency of oscillations the motor has become unstable.
• When the motor has become unstable, the load on the synchronous generator is zero and the generator will make oscillations.
• Then the above two machine system becomes a single machine system.

If the two machines are swinging together then the equivalent inertia constant is given by

Heq = H1 + H2

Explanation:

As given both the machines having the same inertia constant

H1 = H2 = H

Effective inertia constant = 4 MJ/MVA

Heq = 4 MJ/MVA

Heq = H + H

Heq = 2H

4 = 2H

H = 2 MJ/MVA