Sequence Currents in a Power System

[jaus tail]

Homework Statement

It's a solved problem but I don't understand why is there no 30 degree lag from line voltage to lead voltage.

Homework Equations

Phase voltage = Line Voltage / 1.732 and there is 30 degree lag
So shouldn't Ir be at angle 150 degrees.

The Attempt at a Solution

In Y line and phase current is same, so even their phase angle is same?

 

[Baluncore]

This is a three phase unbalanced Y supplying a three phase Y load, not a star to delta transformer.

The question asks specifically for the magnitude of the current in any phase. That suggests you do not need to consider phase angle, only the scalar magnitude. Yet the given solution then accounts for the phase angle.

Why do you believe there should be a 30 degree lag?

 

[jaus tail]

Cause in 3-phase line current leads phase current by 30 degrees.

 

[Baluncore]

Cause in 3-phase line current leads phase current by 30 degrees.

Can you give me a reference that explains the origin of the alleged 30 degree shift.

 

[jaus tail]

Here you go:

As you see, line voltage leads phase by 30 degrees.

I don't understand this. Whenever they substitute they only replace the magnitude and not the phase angle.
Even in this thread,
https://www.physicsforums.com/threads/find-the-capacitance-when-given-the-power-factor.937950/
Post#3, circled part.
i got answer when I substitute only magnitude.
When I substitude phase angle as well(as I think I should), i don't get the answer.
Can you explain why the angles are discarded when substituting in polar coordinates?

Like: A (angle theta1) = B(angle theta 2)
Then if vector A (theta 1) = vector C + vector D
then they replace as:
Magntitude B (theta 1) = Vec C + Vec D

Shouldn't this be:
Mag B (theta 2) = Vec C + Vec D?

 

[Baluncore]

Here is an interesting archived book from 1943. Circuit analysis of A-C power systems, by Edith Clarke. 41MByte.
See; Chap VIII. Unsymmetrical Three-Phase Circuits – Analysis By The Method Of Symmetrical Components. Page 225.
https://ia801609.us.archive.org/12/...cuit-Analysis-Of--A-c-Power-Systems-Vol-I.pdf

 

[Babadag]

?

 

[jaus tail]

I think your RYB are wrong. Y has to lag R by 120 degrees. Your Y is leading R by 120 degrees.

 

[Babadag]

If the fig.8-11 is the correct sketch then according to the arrow convention VRY it has to be R on the head and Y on the tail.

 

[jaus tail]

Yeah you're right. Sorry I overlooked that.

View attachment 219573?

What do you want to ask by this question?
Shouldn't Vrn + Vyn + Vbn always be zero?

 

[Babadag]

You may calculate algebraically the VRN,VYN and VBN using the equations:
VRY=VRN-VYN etc. and VRN+VYN+VBN=0 in complex. Do you?

 

[jaus tail]

I have the line voltages as
RY -- -200 + j0
YB -- +0 + j346
BR -- +200 - j346
Is phase voltage as simple as dividing this by 1.732? Cause then the summation will be zero. But it's unbalanced system, so summation should not be zero
For balanced summation is zero.
I still think in the red circled part it should be 200 angle 150 degrees because of 30 degree lag between line and phase voltage. Phase voltage lags line voltage by 30 degrees.

 

[Babadag]

In my opinion, if you have not a neutral the sum of currents has to be 0 and the sum of voltages
to neutral also [it does not important if they are balanced or not].

 

[jaus tail]

Can you explain why in the circled part in post#1, why have they not included phase lag of 30 degrees?

 

[Babadag]

I think this article author made a mistake confusing the line-to-line voltage with line-to-neutral.
The currents IR,IY and IB are per phase and not per line-to-line.
One has to calculate the voltage phase-to-neutral, at first. By the way the 1Ω per phase impedance it could be only resistance-according to standard symbol.
For instance VRN= 159.6A<141.2degrees and it is not 200/√3 <180.

 

[jaus tail]

But it's star connection. Line current n phase current are same.

 

[Babadag]

What do you have is VRY. What do you need is VRN [IR=VRN/Z] VRN<>VRY/SQRT(3)

 

[jaus tail]

Vrn = Vry/(1.732) and what about the 30 degree phase shift?
Shouldn't it be Vrn = Vry(-30 degrees angle) / 1.732

 

[Babadag]

 

[Babadag]

 

[Babadag]

You may also follow Symmetrical Components-as Baluncore proposed:

 

[jaus tail]

Yes. You've taken the 30 degree in the post. So shouldn't in equation also it be:
Vrn = |Vry|/1.732 and then (cos (-30) + j sin (-30))

I've noticed this in other problems also.
When there are two equations with complex numbers and they use substitution of one variable with other, they only substitute magnitude and not phase.
Like if:
Vector A = ( 2 ) (Vector B) at an angle 30 degrees with A leading B by 30 degrees.
And if
A + B = 0
Then they make it
2B + B = 0, instead of 2B(cos 30 + j sin30) + B = 0.

 

[Babadag]

Sorry. Direct components=positive components and inverse =negative [zero components=0].
The -30 or +30 degrees are for line-to-neutral symmetrical components with respect the symmetrical line-to-line components and not for the actual[total] VRN with respect to VRY.The actual VRN it is the result of vectorial sum of VR1 and VR2 [and VRo=0].

 

[jaus tail]

One question: if phase is unbalanced then Vry, Vyb and Vbr won't be 120 degree phase shift. There'll be some other angle. But will Vrn, Vyn, and Vbn also be at some other angle displacement or will that follow 120 degree phase shift irrespective of balance or unbalance in system?

 

[Babadag]

More or less it is scaled!

 

[Babadag]

At first, I have to apologize as I did not understand well your problem.
Because the text in the o.p. image was very hard to read, I misunderstood what you need is the total current on the phase rather than the sequence current.
Actually what do you need it is only-I think-positive components of these currents.
The phasor diagram presents only the voltage-or current-positions one with respect to another. You may start for the first voltage [VR1 for instance] any where in the diagram that means you can start at 180 degrees as -30. VR1[positive sequence module of VRN] =VRY1[positive sequence of VRY]/sqrt(3) and you may start at 180 degrees[or not important at other angle]. It was very simply indeed.

 

[jaus tail]

Thanks for all the help. The exam is tomorrow.