- #1

EQVan

- 6

- 2

- TL;DR Summary
- I know how to solve for phase-to-phase voltages in an unbalanced AC circuit, strictly in terms of phase-to-neutral voltages. I need the inverse -- how to solve for phase-to-neutral voltages in terms of phase-to-phase voltages.

First a disclaimer: I am neither an electrical engineer nor a mathematician. I am a programmer. As part of a simulator project, I've been asked to solve a particular problem -- and I'm in over my head.

Given an unbalanced 3-phase AC circuit, I have learned that I can solve for the phase-to-phase voltages strictly in terms of phase-to-neutral voltages. The formulas are:

Vab = √((|Van|-|Vbn|cos(120°))² + (|Vbn|sin(120°))²)

Vbc = √((|Vbn|-|Vcn|cos(120°))² + (|Vcn|sin(120°))²)

Vca = √((|Vcn|-|Van|cos(120°))² + (|Van|sin(120°))²)

where:

Vab is the phase A to phase B voltage, and

Vbc is the phase B to phase C voltage, and

Vca is the phase C to phase A voltage, and

Van is the phase A to neutral voltage, and

Vbn is the phase B to neutral voltage, and

Vcn is the phase C to neutral voltage.

I have tested these formulas and they seem to give me the correct answers. But what I need is the inverse:

Van = formula in terms of Vab, Vbc and/or Vca

I have tried to do the algebra using the 3 formulae above to solve for Van, and it's just beyond me.

I know of the simple formula:

Vpn = Vpp / √3

but this seems to assume that all the phase-to-phase voltages are the same, an assumption I am not allowed to make.

Are there any electrical engineers out there who would be willing and able to give me a hand with this?

Given an unbalanced 3-phase AC circuit, I have learned that I can solve for the phase-to-phase voltages strictly in terms of phase-to-neutral voltages. The formulas are:

Vab = √((|Van|-|Vbn|cos(120°))² + (|Vbn|sin(120°))²)

Vbc = √((|Vbn|-|Vcn|cos(120°))² + (|Vcn|sin(120°))²)

Vca = √((|Vcn|-|Van|cos(120°))² + (|Van|sin(120°))²)

where:

Vab is the phase A to phase B voltage, and

Vbc is the phase B to phase C voltage, and

Vca is the phase C to phase A voltage, and

Van is the phase A to neutral voltage, and

Vbn is the phase B to neutral voltage, and

Vcn is the phase C to neutral voltage.

I have tested these formulas and they seem to give me the correct answers. But what I need is the inverse:

Van = formula in terms of Vab, Vbc and/or Vca

I have tried to do the algebra using the 3 formulae above to solve for Van, and it's just beyond me.

I know of the simple formula:

Vpn = Vpp / √3

but this seems to assume that all the phase-to-phase voltages are the same, an assumption I am not allowed to make.

Are there any electrical engineers out there who would be willing and able to give me a hand with this?

Last edited: