# How to find line current of the generator?

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#### Byk

##### Member
Hi, I was wondering is someone can help with this problem?

A three-phase steam turbine generator rated at 722 MVA, 3600 rpm, 19 kV, has a synchronous reactance of 0.65 Ohm. Eo, the excitation voltage is adjusted to be 13.16 kV. The machine is connected to an infinite bus of 19 kV. If the torque angle is 20 degree calculate:

(i) The active power output of the generator

(ii) The line current

I was able to find P following way:

IPl = (Eo*E*sin(δ))/Xs =
IPl = ((11)(13.16)Sin(20))/(0.65) = 76.17M
IP3Phl = 76.17M x 3 = 228.5M

I tried drawing the diagram and solving for I using KCL but I cannot get correct result.

Can someone please explain to me how to find line current?

I got 6943A.

#### rburns18 PE

##### Member
I got 227.88MW using the equation you used above as well as by finding I_line and using S_3phase = sqrt(3)*V_line*I_line. You assume the excitation voltage is the phase voltage so you don't have to divide by sqrt(3). The 19kV is a line voltage. See my work attached.

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#### Byk

##### Member
I got 227.88MW using the equation you used above as well as by finding I_line and using S_3phase = sqrt(3)*V_line*I_line. You assume the excitation voltage is the phase voltage so you don't have to divide by sqrt(3). The 19kV is a line voltage. See my work attached. View attachment 19983
I am such a doughnut, I forgot to divide 19 kV with sqrt(3).

Hopefully won't make same mistake in the exam.

#### DarkLegion PE

##### Member
I am such a doughnut, I forgot to divide 19 kV with sqrt(3).

Hopefully won't make same mistake in the exam.

I went over my motor stuff yesterday since I bombed this question lol but now I feel a bit more confident. I always forget the sqrt(3) so what I try to do in write the subscripts for all my voltages so I know when I'm getting line and phase

#### rburns18 PE

##### Member
I went over my motor stuff yesterday since I bombed this question lol but now I feel a bit more confident. I always forget the sqrt(3) so what I try to do in write the subscripts for all my voltages so I know when I'm getting line and phase
Where is this question from? I need all the questions I can get

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#### DarkLegion PE

##### Member
Where is this question from? I need all the questions I can get
Not sure where this one is from but I worked some from the complex imaginary books to practice

#### rburns18 PE

##### Member
@Byk where is the original question from?

#### Ampera18 PE

##### Member
What was the Line Current answer?

#### rburns18 PE

##### Member
What was the Line Current answer?
I got 7250A. (See above) the line current I got was then used to find the power so it should be correct

#### Byk

##### Member
@Byk where is the original question from?

Where is this question from? I need all the questions I can get

This one came from one of my coworker's notes. I believe that he got from School of PE class but he doesn't remember since it was a while ago.

I think you can find similar problems in complex imaginary and electric machinery and power system fundamentals.

#### rburns18 PE

##### Member
@Byk thanks, agree there are some in complex as well as the engineering pro guides exams.

#### akyip

##### Member
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).

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