Question

A three-phase, 60 Hz,550 V, wye-connected synchronous generator is delivering 250 kW at rated voltage. The excitation voltage E ₐᵣ is 460 V per phase, and the synchronous reactance x ₐᵣ = 1.2Ω. Calculate torque angle δ.

Answer 1

To find the torque angle δ of the synchronous generator, we can use the formula δ = arccos((Eᵢ - Eₐᵣ) / Eₐᵣ), where Eᵢ is the induced emf and Eₐᵣ is the excitation voltage per phase. Substituting the given values, we find that δ is approximately 78.50°.

Step-by-step explanation:

To calculate the torque angle δ, we can use the following formula:

δ = arccos((Eᵢ - Eₐᵣ) / Eₐᵣ)

Where Eᵢ is the induced emf in the generator and Eₐᵣ is the excitation voltage per phase. Since the generator is delivering power at rated voltage, the induced emf Eᵢ is equal to the rated voltage V. Substituting the given values, we have:

δ = arccos((550 V - 460 V) / 460 V) = arccos(0.1957) ≈ 78.50°

Therefore, the torque angle δ is approximately 78.50°.