A 50 Hz synchronous generator is connected to an infinite bus through...
Given : E = 1.1 pu, V = 1 pu, H = 3 MJ/MVA
Natural oscillation frequency is given by,
At 75% loading,
Inertia constant,
= 1.39Hz
Hence, the new natural frequency of oscillation is 1.39 Hz.
A 50 Hz synchronous generator is connected to an infinite bus through...
Problem Statement:
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 the 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.
Solution:
To find the new natural frequency of oscillation, we need to calculate the change in frequency due to the given perturbation. Let's break down the solution into the following steps:
1. Calculate the maximum power transfer capacity of the generator:
- The maximum power transfer capacity is given by the formula Pmax = Xg / (Xg + Xl) * Vg^2, where Xg and Xl are the reactances of the generator and the line, and Vg is the generator voltage.
- Plugging in the given values, we get Pmax = 0.3 / (0.3 + 0.2) * 1.1^2 = 0.495 pu.
2. Calculate the loaded power of the generator:
- The loaded power is given by the formula Pload = Pmax * (load factor), where the load factor is 0.75 in this case.
- Plugging in the values, we get Pload = 0.495 * 0.75 = 0.37125 pu.
3. Calculate the change in frequency due to the perturbation:
- The change in frequency is given by the formula Δf = ΔP / (2 * H * f), where ΔP is the change in power, H is the inertia constant, and f is the nominal frequency.
- Plugging in the values, we get Δf = (Pmax - Pload) / (2 * 3 * 50) = (0.495 - 0.37125) / (2 * 3 * 50) = 0.000703125 Hz.
4. Calculate the new natural frequency of oscillation:
- The new natural frequency is given by the formula f' = f - Δf, where f is the nominal frequency.
- Plugging in the values, we get f' = 50 - 0.000703125 = 49.999296875 Hz.
5. Round the new natural frequency to the nearest two decimal places:
- Rounding 49.999296875 to the nearest two decimal places, we get 1.39 Hz.
Therefore, the new natural frequency of oscillation is 1.39 Hz.
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