Why is three phase power the preferred choice in power distribution?

[PhysicsTest]

TL;DR

The phase sequence mentioned in the book is confusing

I saw the information of the text at different places and when i compare it is confusing.

The text is

In some other section

If you see the red lines i have highlighted, in the first section the book refers that the B coil is behind the A coil, but in the 2nd section it refers that in the counter clockwise the voltage is induced in B first than in C. Please help me with this.
The other question is the phasor of the B can it be represented as

.
Which is the standard?

 

[DaveE]

I'm not understanding the contradiction here, or perhaps what it is that's confusing you. If you consider that the winding voltage (noted by it's positive peak, for example) is represented by the Real part of the phase vectors (the projection onto the x-axis) and that those vectors are rotating CCW, as specified then then the phase sequence (in time) is ABCABCAB... So the voltage peak of B lags A; it's behind A in time. Likewise B leads C; it's ahead of C in the time sequence.

There is often some ambiguity in identifying this stuff because of the rotation symmetry (like modulus arithmetic), so much of this sort of communication depends on people's definitions. The overriding point is that there are two possible sequences which need to be named somehow; ABC vs. ACB, which is the same as BCA vs. CBA, etc. I think your confusion is likely more about how things are defined than any real misunderstanding.

Having work for many years with 3-phase stuff, I can assure you that you will continue to be confused by other people's seemingly arbitrary choices. Yes, there are some industry standards, but they are often not followed because in practice you will often just try one way see if that's the order you wanted. For example, you connect your motor with a random order and try it, if it spins backwards, then you switch two of the phases and it will be correct. In cases where you can't afford to guess wrong, then you will have go through all of the documentation and do some other test to verify it will be correct before you turn it on.

In our installation manuals for a product with a water pump, we specify the correct phase order referenced to the wire colors on our power cable with language similar to that in your textbook, specifying the order of the voltage sequence to be applied. I've never heard anyone talk about positive or negative phase sequences, that definition is a little too abstract to rely on in practice. Rather, we describe how it must behave, not what name it has.

edit: 240^o vs. -120^o isn't really an issue for people that understand phasors, we all know what you mean. In practice I mostly see people using the (-180^o, +180^o] range.

 

[DaveE]

The important thing here is to fully understand the concepts, so you can adjust to other people's definitions. For example in mechatronics, motors with other phases, like 90^o or 72^o are common.

 

[Merlin3189]

If you see the red lines i have highlighted, in the first section the book refers that
the B coil is behind the A coil, but in the 2nd section it refers that in the counter clockwise
the voltage is induced in B first than in C.

Summary:: The phase sequence mentioned in the book is confusing
I saw the information of the text at different places and when i compare it is confusing.

The other question is the phasor of the B can it be represented asView attachment 271197.
Which is the standard?

Your last point: I'd be happy with both ways, but I don't know the convention.
I'd guess they keep the magnitude of phase <= 180 degrees.
You need and engineer practised in the art to tell you. (Looks like Dave may be your man.)

 

[PhysicsTest]

Yes I understood now, one related question is

Here we if we see the line voltages, $E_{AB}$ from the diagram i can figure out that $E_A$ is at higher potential compared $E_B$, similarly for other voltages as well. Why did he assume like that?

 

[DaveE]

What is E_A? It's not in your diagram. Remember that voltages are between two points.

 

[PhysicsTest]

What is E_A? It's not in your diagram. Remember that voltages are between two points.

I mean $E_{AN}$ is at higher potential than $E_{BN}$. Why it is assumed?

 

[anorlunda]

I mean $E_{AN}$ is at higher potential than $E_{BN}$. Why it is assumed?

I see nothing in that diagram you posted in #5 that says anything about the magnitudes. It just shows sign conventions.

 

[PhysicsTest]

Correct me if I am wrong, in the below diagram we know A is at higher potential compared Neutral which is at 0V. Hence it is shown as +Ve and Neutral as -Ve. So, if i follow the same method then $E_{AN}$ is at higher potential compared to $E_{BN}$. Ok, after your post now i understand he has taken it as a reference convention, based on the actual voltage it can be either +ve or -ve. Similarly $E_{AN}$ only the reference notation is shown, but actually it will go either +Ve and -Ve.

 

[DaveE]

Because the voltages (whichever one you choose) are all sine waves, at any instant one will be larger than others.

If you mean the more normal definition, measured over several cycles (like RMS, etc.) then almost all 3-phase systems are balanced (all of the good ones, anyway), meaning 3-fold symmetry E_AN=E_BN=E_CN and E_AB=E_BC=E_CA

There are cases where there is 2-Phase distribution with 90^o phase difference, which is then converted (with transformers or autotransformers) into 3-phase delta, where the neutral is not in the middle, i.e. it lacks 3 way symmetry. But these are not common, and, except as a real test of complete understanding of phasors, are not worth worrying about.

 

[anorlunda]

Ok, after your post now i understand he has taken it as a reference convention, based on the actual voltage it can be either +ve or -ve.

That's it. Physically, current flows from plus to minus, but in a circuit you can choose any sign convention you want. If you choose the sign convention to be opposite current flow, the answers just come out to be negative.

Although sign conventions are arbitrary, Kirchhoff's Voltage Law is not. The sum of voltages around any closed loop must be zero. If you apply sign conventions consistently, that is the result.

 

[PhysicsTest]

There are cases where there is 2-Phase distribution with 90o phase difference

I was curious how it looks like and came up below diagram.

The voltages induced in the two wingdings are as shown below. $\sin(\omega t - 90)$ in the B phase, $\sin(\omega t)$ in the A phase winding.

The current through the neutral is
$I_N = I_a + I_b$
$I_N = I\angle0+ I\angle{-90}$
$I_N = I\angle{-45}$
So, the neutral current is not zero. Hence it is kind of wasted. Am I correct?

Few questions are
a. I know for the source the windings should be 90 phase apart to induce the voltages, but is it required that the loads also to be connected 90 phase apart? The question is applicable even for 3 phase systems. Load i mean motor that is main area of interest for me.

 

[DaveE]

I'm not about to defend 2-phase 90^o distribution systems, but I do know they have been built. I suspect it's to save money in the number of wires in the distribution network, at the expense of more stuff (transformers, for example) at the load centers. This is a minimal way to generate multi-phase voltages, you must have two voltage sources with a phase difference ≠ 0, or 180^o to make a rotating magnetic field for motors, etc.

How you make 3-phase delta from two 90^o shifted sources is essentially just trigonometry. You use transformer windings (or perhaps autotransformers) to scale and add the two phasors at 0, 90^o to create a couple more at ±120^o. So -(1/2)sin(ωt) + (√3/2)sin(ωt + π/2) = sin(ωt + 2π/3). for example. Most often the neutral isn't used; if you need wye distribution then a delta-wye transformer is usually employed.

I don't recall ever hearing of people using the two 90^o shifted phases together without reconstructing 3-phase, but I'm sure it has been done somewhere. At this level it's all about cost, and there are lots of other considerations too. However, none of this is common in my experience.

 

[anorlunda]

a. I know for the source the windings should be 90 phase apart to induce the voltages, but is it required that the loads also to be connected 90 phase apart? The question is applicable even for 3 phase systems. Load i mean motor that is main area of interest for me.

To be exact, yes. But there are approximations.

It is common in 3-phase power distribution to split the last mile into three single phase branches. For example, let each serve one of three streets of residential houses. There is no guarantee that the three loads will balance, especially with time variations. But if done right, the three will almost balance and almost can be good enough.

If you drive around in a rural area, just look up at the sky at the wires on the power poles. You may see 3 wires meaning 3-phase power, or 2 wires meaning 1-phase.

Three phase power is the favorite because it can deliver 3x as much power as single phase using only 1.5x times as much wire. (Assuming that all wires in question are the same diameter.)

Try to figure out the same for 2-phase power. What is the ratio of power delivered per mile (or km) of wire if the generating source is far away from the loads and all wires are the same diameter?

In some cases, there are also single-wire-earth-return power distribution systems. But it is rarely used, so there must be a reason why. Considerations other than wire cost must dominate. What other considerations can you think of?