How Do You Calculate Line-to-Line Voltages in a Balanced 3-Phase Circuit?

[eehelp150]

Homework Statement

Assuming balanced 3 phase circuit and abc positive phase sequence:
The RMS value of line-to-line voltage between Phase A and C is V = 208∠10°

Find the line to line voltage between Phases A and B (magnitude + angle)
Find the line to line voltage between Phases B and C (magnitude + angle)
Determine the phase to neutral voltage Van, Vbn, Vcn ((magnitude + angle)

Homework Equations

These were in my professor's notes:

The Attempt at a Solution

I have no idea how to do this. Are the relevant equations I posted correct? Any hints would be appreciated.

 

[cnh1995]

. Are the relevant equations I posted correct?

Yes, but in these equations, V_AN is assumed to be the reference phasor. In the question, you have V_ac∠10° which means V_AN is no longer the reference phasor. In a balanced three phase system, what is the phase difference between V_AN and V_AC? (Refer the equations you posted).

 

[eehelp150]

Yes, but in these equations, V_AN is assumed to be the reference phasor. In the question, you have V_ac∠10° which means V_AN is no longer the reference phasor. In a balanced three phase system, what is the phase difference between V_AN and V_AC? (Refer the equations you posted).

30 degrees?

 

[cnh1995]

30 degrees?

Yes. So what will be V_AN when Vac=208∠10?

 

[eehelp150]

Yes. So what will be V_AN when Vac=208∠10?

208 * sqrt(3) ∠40?

 

[cnh1995]

208 * sqrt(3) ∠40?

No. What is magnitude relationship between line and phase voltages?

 

[eehelp150]

No. What is magnitude relationship between line and phase voltages?

1/sqrt(3)?
Would it be 208/sqrt(3) = 120∠40?

 

[cnh1995]

1/sqrt(3)?
Would it be 208/sqrt(3) = 120∠40?

Correct.

 

[eehelp150]

Correct.

I mistyped something in the prompt.
Vca = 208<10 (could this be a typo?)

Would Van still be 120<40? This is the "phase to neutral" voltage, correct?
How would I find Vab, Vbc?

 

[cnh1995]

Would Van still be 120<40?

No. Magnitude will not change but phase angle will.

I mistyped something in the prompt.
Vca = 208<10

So what would be Vac? Find Vac and use the relation between Vac and Van from your equations.

How would I find Vab, Vbc?

What is the angle between Vac and Vab? What is the angle between Vac and Vbc? Refer the equations again. But first find Vac from Vca.

 

[eehelp150]

No. Magnitude will not change but phase angle will.

So what would be Vac? Find Vac and use the relation between Vac and Van from your equations.

What is the angle between Vac and Vab? What is the angle between Vac and Vbc? Refer the equations again. But first find Vac from Vca.

Van = 120<-20?
Vac = 208<130?
Vab = 208<10?
Vbc = 208<-80?

 

[cnh1995]

Vac = 208<130?

No. Angle of Vca is 10°. What is the angle of Vac? Vac and Vca are anti-parallel phasors.

 

[eehelp150]

No. Angle of Vca is 10°. What is the angle of Vac? Vac and Vca are anti-parallel phasors.

Is it a 90 degree difference? so -80 or 100?

 

[cnh1995]

Is it a 90 degree difference? so -80 or 100?

It's a 180 degree difference.

 

[eehelp150]

It's a 180 degree difference.

So:
Vca = 208<10°

Vac = 208<190°
Vab = 208<-110°
Vbc = 208<-230°

 

[cnh1995]

Vac = 208<190°

If the angle of Vac=θ, then θ=180-angle of Vca.
Edit: I am imagining all this in my head without drawing it on paper and this is a mistake. Yes, angle of Vac is 190 degrees.

 

[eehelp150]

If the angle of Vac=θ, then θ=180-angle of Vca.
Edit: I am imagining all this in my head without drawing it on paper and this is a mistake. Yes, angle of Vac is 190 degrees.

so
Vab = 208<-110
Vbc = 208<-230

Van = 120<190+30
Vbn = 120<(190+30)-120
Vcn = 120<(190+30)-240These correct?

 

[cnh1995]

so
Vab = 208<-110
Vbc = 208<-230

Van = 120<190+30
Vbn = 120<(190+30)-120
Vcn = 120<(190+30)-240These correct?

Yes.