Final answer:
The line current flowing through a three-phase y-connected synchronous generator that is rated 120 MVA, 13.2 kV, and 0.8 power factor lagging is approximately 5,304 A.
Step-by-step explanation:
To calculate the line current flowing through a three-phase y-connected synchronous generator, we can use the formula for power in a three-phase system:
P = √3 * V_L * I_L * cos(φ)
Where:
- P is the total power in watts (W)
- V_L is the line-to-line voltage in volts (V)
- I_L is the line current in amperes (A)
- cos(φ) is the power factor
Given:
- The generator is rated at 120 MVA (MVA stands for Megavolt-Amperes)
- The line-to-line voltage V_L is 13.2 kV (kilovolts)
- The power factor cos(φ) is 0.8 lagging
We then rearrange the formula to solve for I_L:
I_L = P / (√3 * V_L * cos(φ))
Converting the power from MVA to VA to match the voltage units (1 MVA = 1,000,000 VA) and the voltage from kV to V (1 kV = 1,000 V), we have:
I_L = (120 * 1,000,000 VA) / (√3 * 13,200 V * 0.8)
Performing the calculations gives us the line current:
I_L = (120,000,000 VA) / (22,627.417 V)
I_L = 5,304 A (rounded to the nearest ampere)
Therefore, the line current flowing through the generator at the rated conditions is approximately 5,304 A.