How do you calculate line voltage from phase voltage?

Answer 1

For questions of this type, it seems the main issue may be one of definitions and industry terms. See if this makes sense:

Line voltage is a very ambiguous term. For instance, say you are wiring a doorbell transformer. You feed 120V into the primary, and 18V comes out the secondary. The electrician would say the output is "low voltage" and the input is "line voltage". He simply means the building wiring, or "lines". Now, if you go out to the breaker panel, you will measure 120V from each "leg" to neutral, but you can also measure 240V from leg to leg. It's all line voltage. Line voltage simply means the voltage present in that particular power distribution system.

Now the power in your house is "single phase" (well, in almost all homes, anyway). Single phase is fine for most anything, but motors are a special case. Motors need something to create a rotating magnetic field to get them turning. Single phase power doesn't have anything to do that, so they need some sort of a gimmick, like a capacitor, to create a "phase shift" to get the rotation.

Single phase AC (alternating current) simply means the voltage goes positive then back down to zero, then negative then back up to zero. That's one complete cycle. The cycle is divided into 360 degrees, like a circle. The positive voltage goes from 0 to 180 degrees, and the negative half 180 back to 0.

Now 3-phase power has, you guessed it, 3 hot wires. Each hot wire, when paired with a neutral, is a single-phase source. Heres the big difference: Phase A starts its positive cycle. When it is 120 degrees into the cycle, phase B starts going positive. When Phase B is 120 degrees finished with its cycle, phase C starts going positive. When phase C is 120 degrees into its cycle, that's a total of 360 degrees, and phase A is done with one cycle, and the whole process starts over. Picture 3 people doing "the wave" at a football game. Same principle.

This time difference, or "phase shift" is what makes 3-phase power unique. 3-phase motors use the phase shift directly to produce the rotating magnetic field they need to turn. Think of 3 people in a circle, tossing a ball around. see the "circular" motion? Now picture two people tossing the ball back and forth. No circular motion there. That's the difference between single-phase and 3 phase.

So, electricians use the term "phase" to refer to one of the three hot wires in a 3-phase (also correctly called multiphase or polyphase) power system. The term "phase" voltage is just as ambiguous as "line" voltage. To be accurate, you must specify whether you mean phase-to-phase voltage, or phase-to-neutral voltage.

Confused? if you go into a large commercial building with 3-phase power, many times the incoming panel will have voltmeters on the front. In one building, the first meter will be labeled "phase-to-phase voltage", and the second meter will be labeled "phase-to-neutral voltage". Go into the building NEXT DOOR, and the same meters will be labeled "line-to-line voltage" and "line-to-neutral voltage". See? the terms are used pretty interchangably.

In a 3-phase system, each phase, leg, or line has the same potential, or voltage (except for a very few wierd and pretty outdated systems). If you measure from phase A to Phase B you will get the same reading as B to C, also the same as C to A. So, measuring any two phases will tell you what the line voltage is, but that motor still needs all 3 phases to get the rotation.

To understand the different voltages you find in a 3-phase system, see the related questions for another answer that relates to that subject.

Answer 2

To convert line to line voltages to line to neutral voltages:

VA = [VAB - VCA] / 3

VB = [VBC - VAB] / 3

VC = [VCA - VBC] / 3

Assuming ABC rotation. Depending on how you define "unbalanced", your calculation can change from here. You could define it as 3I2 (symetrical components); this is how I would define based on my experience. If you look in power quality standards, and power quality equipment manuals, you will find several other definitions.

Answer 3

It depends on the system.

For a delta-connected, three-wire, system, the line voltage is exactly the same as the phase voltage.

For a wye-connected, four-wire, system, the line voltage is 1.732 (the square-root of 3) times the phase voltage.

Answer 4

If, by 'fix', you mean 'establish' or 'standardise', then for a three-phase, four-wire, system, the 'line-to-line' (not'phase-to-phase'!) voltage will be 1.732 times the 'line-to-neutral' (not 'phase-to-neutral'!) voltage.