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

  • Thread starter eehelp150
  • Start date
In summary, we have the following line-to-line voltages:Line-to-line voltage between Phases A and B: 208∠-110°Line-to-line voltage between Phases B and C: 208∠-230°Line-to-line voltage between Phases A and C: 208∠10°We also have the following phase-to-neutral voltages:Phase-to-neutral voltage for Phase A: 120∠190°Phase-to-neutral voltage for Phase B: 120∠70°Phase-to-neutral voltage for Phase C: 120∠-50°Note: There may be a typo in the prompt, as Vca = 208∠10° would result in
  • #1
eehelp150
237
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.
 
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  • #2
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).
 
  • #3
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?
 
  • #4
eehelp150 said:
30 degrees?
Yes. So what will be VAN when Vac=208∠10?
 
  • #5
cnh1995 said:
Yes. So what will be VAN when Vac=208∠10?
208 * sqrt(3) ∠40?
 
  • #6
eehelp150 said:
208 * sqrt(3) ∠40?
No. What is magnitude relationship between line and phase voltages?
 
  • #7
cnh1995 said:
No. What is magnitude relationship between line and phase voltages?
1/sqrt(3)?
Would it be 208/sqrt(3) = 120∠40?
 
  • #8
eehelp150 said:
1/sqrt(3)?
Would it be 208/sqrt(3) = 120∠40?
Correct.
 
  • #9
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.
 

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

1. What is line-to-line voltage?

Line-to-line voltage, also known as phase-to-phase voltage, is the voltage difference between two different phases in a three-phase electrical system. It is measured in volts (V) and is used to power large motors, generators, and other heavy-duty equipment.

2. How do you find line-to-line voltage?

To find line-to-line voltage, you will need a voltmeter. Connect the red probe to one phase and the black probe to another phase. The voltage reading displayed on the voltmeter will be the line-to-line voltage. Repeat this process for each phase pair to get all the line-to-line voltage readings.

3. Is line-to-line voltage the same as line-to-neutral voltage?

No, they are not the same. Line-to-line voltage is the voltage between two different phases, while line-to-neutral voltage is the voltage between one phase and the neutral wire. Line-to-line voltage is typically higher than line-to-neutral voltage in a three-phase electrical system.

4. What is the purpose of measuring line-to-line voltages?

Measuring line-to-line voltages is essential for ensuring the proper functioning of three-phase electrical systems. It helps identify any imbalances between the phases, which can cause equipment failure or damage. It is also necessary for calculating the power delivered to three-phase loads.

5. What are some common applications of line-to-line voltage measurements?

Line-to-line voltage measurements are commonly used in industrial and commercial settings to power large equipment and machinery. They are also used in power distribution systems, motor control, and other electrical systems that require high power. In addition, line-to-line voltage is used in renewable energy systems, such as wind turbines and solar panels, to convert and distribute power.

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