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

  • Thread starter Thread starter eehelp150
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around calculating line-to-line voltages and phase-to-neutral voltages in a balanced three-phase circuit, specifically focusing on the relationships and phase angles involved. Participants explore the implications of given voltage values and their representations in phasor form.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a problem involving the line-to-line voltage between Phase A and C, given as V = 208∠10°.
  • Another participant notes that the equations provided assume VAN as the reference phasor, which may not hold true given the provided VAC value.
  • There is a discussion about the phase difference between VAN and VAC, with one participant suggesting it is 30 degrees.
  • Participants explore the relationship between line and phase voltages, with one suggesting a magnitude of 1/sqrt(3) for the phase voltage.
  • There is uncertainty regarding the correct phase angle for VAN, with calculations leading to different proposed values.
  • Participants discuss the relationship between VAC and VCA, with one asserting that they are anti-parallel phasors, leading to a 180-degree phase difference.
  • Final values for Vab, Vbc, and Van are proposed, with participants confirming the correctness of these values in the context of their calculations.

Areas of Agreement / Disagreement

Participants generally agree on the relationships between the voltages and the calculations involved, but there are uncertainties regarding specific phase angles and the implications of the initial conditions. The discussion remains somewhat unresolved as participants refine their understanding of the relationships.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the reference phasors and the potential for typographical errors in the initial problem statement. The phase relationships and calculations depend heavily on these assumptions.

eehelp150
Messages
235
Reaction score
0

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:
upload_2016-10-24_23-23-24-png.107967.png


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.
 
Physics news on Phys.org
eehelp150 said:
. Are the relevant equations I posted correct?
Yes, but in these equations, VAN is assumed to be the reference phasor. In the question, you have Vac∠10° which means VAN is no longer the reference phasor. In a balanced three phase system, what is the phase difference between VAN and VAC? (Refer the equations you posted).
 
cnh1995 said:
Yes, but in these equations, VAN is assumed to be the reference phasor. In the question, you have Vac∠10° which means VAN is no longer the reference phasor. In a balanced three phase system, what is the phase difference between VAN and VAC? (Refer the equations you posted).
30 degrees?
 
eehelp150 said:
30 degrees?
Yes. So what will be VAN when Vac=208∠10?
 
cnh1995 said:
Yes. So what will be VAN when Vac=208∠10?
208 * sqrt(3) ∠40?
 
eehelp150 said:
208 * sqrt(3) ∠40?
No. What is magnitude relationship between line and phase voltages?
 
cnh1995 said:
No. What is magnitude relationship between line and phase voltages?
1/sqrt(3)?
Would it be 208/sqrt(3) = 120∠40?
 
eehelp150 said:
1/sqrt(3)?
Would it be 208/sqrt(3) = 120∠40?
Correct.
 
cnh1995 said:
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?
 
  • #10
eehelp150 said:
Would Van still be 120<40?
No. Magnitude will not change but phase angle will.
eehelp150 said:
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.
eehelp150 said:
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.
 
  • #11
cnh1995 said:
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?
 
  • #12
eehelp150 said:
Vac = 208<130?
No. Angle of Vca is 10°. What is the angle of Vac? Vac and Vca are anti-parallel phasors.
 
  • #13
cnh1995 said:
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?
 
  • #14
eehelp150 said:
Is it a 90 degree difference? so -80 or 100?
It's a 180 degree difference.
 
  • #15
cnh1995 said:
It's a 180 degree difference.
So:
Vca = 208<10°

Vac = 208<190°
Vab = 208<-110°
Vbc = 208<-230°
 
  • #16
eehelp150 said:
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.
 
  • #17
cnh1995 said:
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?
 
  • #18
eehelp150 said:
so
Vab = 208<-110
Vbc = 208<-230

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

Similar threads

  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
14
Views
6K
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
6
Views
6K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
3
Views
3K
  • · Replies 10 ·
Replies
10
Views
6K
Replies
23
Views
6K