Hey all,

Attached is my work and attempt on this problem.

I used an equivalent 1-phase circuit diagram to do this problem. I first solved for real power sent using: Psend, 1ph = (Ea,LN * Vt,LN / Xs) * sin(theta), and then multiplied that by 3 to get the 3-phase real power transfer.

Then for solving line current Ia, I just did a simple circuit analysis in dividing the voltage difference between Ea,LN and Vt,LN by the synchronous impedance/synchronous reactance Zs = jXs.

I also did a power calculation check on both the sending end (Ea: synchronous generator) and receiving end (Vt: infinite bus). I was able to confirm that my real power values were all equal between the Psend formula, the real power sent by the synchronous generator, and the real power received by the infinite bus.

I should also point out that

**when a synchronous generator is connected to an infinite bus (electrical grid), the generator's terminal voltage Vt and frequency f is determined by the infinite bus. This is because the infinite bus, which is essentially an entire electrical grid, far overpowers one single generator.** Once a synch gen is connected to an infinite bus, the only parameters left that can change are the internal/induced voltage Ea and the angle of Ea (which can also change torque angle theta).