# AC 3-phase conceptual question on AAC article

#### Jaunty

Joined Jun 7, 2015
13
Hello

I have a conceptual question about AC 3-phase power.

I see that

I'm trying to make the connection between this: Eline=sqrt(3)*Ephase

and my reference sheet which has: Vab=sqrt(3)*(Van @ 30 deg)
For the Y-connection, Vab is the line voltage, and Van is the phase voltage, correct?

I see the AAC article doesn't have the 30 deg in there? Why is that?

#### t_n_k

Joined Mar 6, 2009
5,455
The phase displacement between the phase and line voltages would be implicitly assumed without necessarily explicitly stating this as the case. I guess the author has chosen to overlook this fact and is rather focusing on the relative voltage magnitudes. If one is being pedantic, I would agree with explicitly stating both the magnitude and phase relationships - particularly when teaching students who are just being introduced to the concepts involved. In teaching this concept I would personally include the use of phasor diagrams both to demonstrate and to reinforce how the relationships arise.

Last edited:

#### Jaunty

Joined Jun 7, 2015
13
I wish it were as simple as just magnitudes.

That's not the reality though...

I suppose for practical purposes (electricians and such) this might be all you need to think about since the phase is set by the generator hundreds of miles upriver and not going to be off?

#### JoeJester

Joined Apr 26, 2005
4,390
I wish it were as simple as just magnitudes.

That's not the reality though...

I suppose for practical purposes (electricians and such) this might be all you need to think about since the phase is set by the generator hundreds of miles upriver and not going to be off?
You might want to illustrate your reality. Even if the generator is 20 feet away, the phases are still 120 degrees apart. Who snuck into the power plant and re-positioned the physical layout of the generator portion without detection?

#### Jaunty

Joined Jun 7, 2015
13
You might want to illustrate your reality. Even if the generator is 20 feet away, the phases are still 120 degrees apart. Who snuck into the power plant and re-positioned the physical layout of the generator portion without detection?

exactly my point...As long as the generator windings are physically oriented correctly the phases would always remain 120 deg apart.

Thanks for the perspective Joe!

#### t_n_k

Joined Mar 6, 2009
5,455
@Jaunty
Your original post seemed to be asking why the AAC book didn't make mention of the phase voltage and line voltage phase displacements at some point in a distribution system. The location of the primary generator would have no bearing on the phase voltage and line voltage relative phase displacements at some arbitrary location in the distribution network.

#### WBahn

Joined Mar 31, 2012
26,398
The 30 degrees mentioned in the OP is not the phase differences between the phases of the generator.

#### t_n_k

Joined Mar 6, 2009
5,455
The 30 degrees mentioned in the OP is not the phase differences between the phases of the generator.
Yes I think the OP is confusing concepts.
The "reference sheet" of which the OP makes mention in the first post, is presumably indicating that not only should one should be cognizant of the point that while there is a 120 degree displacement of the three individual phase voltages - whether it be the line-to-neutral or the line-to-line voltage sets - one should keep in mind that the three phase sets (line-to-line and line-to-neutral) are displaced by 30 degrees relative to one another.

#### JoeJester

Joined Apr 26, 2005
4,390
my reference sheet which has: Vab=sqrt(3)*(Van @ 30 deg)
I take that to mean, phase to phase voltage (V a-b) = sqrt(3) * phase voltage to neutral (V a-n) @ 30 deg. Am I interpreting the statement properly?

I wish it were as simple as just magnitudes.

That's not the reality though...

#### Jaunty

Joined Jun 7, 2015
13
I take that to mean, phase to phase voltage (V a-b) = sqrt(3) * phase voltage to neutral (V a-n) @ 30 deg. Am I interpreting the statement properly?

Thanks for the responses guys,
Sorry I am probably confused.

As i understand it, in a Balanced system the phase voltages are 120 degrees apart and that's the way it is.

But back to original question:

Is the article stating for a Y-connection, that "Vab=sqrt(3)*Vp" ?

but not "Vab=sqrt(3)*Vp@30 deg" ?

Because these are different answers indeed.

#### t_n_k

Joined Mar 6, 2009
5,455
@Jaunty
They are different to the extent that the AAC book form simply states the relative magnitudes of one (line-to-line voltage) to the other (line-to-neutral voltage). Your formula sheet shows a phasor representation (both magnitude and angle) of the one relative to the other.
I would argue your reference sheet isn't strictly correct unless the angle of the phasor representing Van is actually deemed to be 0 degrees. For completeness one might also suggest that representative phasor expressions for Vbc & Vca be provided.
I notice now also it appears you may have switched from (presumably) rms values to peak values. Or is Vp meant to be the rms line-to-neutral voltage magnitude?
Again to ensure consistency shouldn't one perhaps write...

$$\text {Vab=\sqrt {3}\|Van\|@angle(angle(Van) + 30^o)}$$

|Van| being the magnitude (rms value) of the line-to-neutral voltage.

I would think most people looking at system voltages are generally only interested in the rms values at various points in the system network. The phase angle values are presumably taken for granted - unless one is performing specific analysis in designing systems or performing existing network pedictions such as might arise under fault or unbalanced conditions.

Last edited:

#### Jaunty

Joined Jun 7, 2015
13
Exactly. Thanks t_n_k.

I am still learning the concepts so I wasn't thinking about one having a zero degree reference!

#### MrAl

Joined Jun 17, 2014
8,996
Hi,

When you move between systems you often forget about the original phase reference and take on the new phase reference, unless you specifically need this information. But because loads are usually sensitive only to the new system and dont even have access to the old system, the phase of the loads relative to the new system reference is the only thing that matters so sometimes it is left out entirely.

To state this in terms of both the old system and the new system, if all three phases are shifted by 30 degrees to start and all loads are connected only to the new system, then we dont care what the phase shift is relative to the old system we only care what the phase shift is relative to the new system, and phase A would usually be considered to be zero degrees even though it is 30 degrees apart from the original phase A.

A general way to handle three phase (or more) systems is to first convert everything into a complex form. This means the voltages for all three phases that originally look like:
A: 120v @ 0 degrees
B: 120v @ -120 degrees
C: 120v @ +120 degrees

turn into:
A: Va1+0*j
B: V2a+V2b*j
C: V3a+V3b*j

After doing these simple source transformations using identities:
|V|=sqrt(real^2+imag^2)
Angle=atan2(imag,real)

you can then work the three phase problem as if it was a standard three source problem, just with complex results for voltages, currents, and impedances.

For the final result you end up with one complex number for your quantity:
a+b*j

and you convert this back into magnitude and phase angle.

If you've never done it this way it might look strange, but it is fairly straightforward and helps reduce errors that come up when trying to work in both polar and rectangular systems at the same time.