Power System Fault Phasor Diagram

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Homework Statement


Single-line diagram of a two-source power system: source EA at angle δ connects through fault locations F1 and F2 to bus A, then to bus B and source EB at angle 0. Currents IF1 and IF2 point right; voltages VF1 and VF2 are shown at bus A.


Homework Equations


If load is inductive current lags voltage. If load is capacitive voltage lags current

The Attempt at a Solution


Current lags voltage since wire is inductive.
So IF1 lags VF1 and IF2 lags VF2
But book says answer is C
Why should VF1 lag IF1? This will happen only if load is capacitor. But that is not mentioned in question.
 
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  • Single-line diagram of a two-source power system: source EA at angle δ connects through fault locations F1 and F2 to bus A, then to bus B and source EB at angle 0. Currents IF1 and IF2 point right; voltages VF1 and VF2 are shown at bus A.
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Do these faults take place at the same time so there's one solution,
or do they occur individually so there's two separate solutions ?

What direction of current is assumed positive ?

old jim
 
They haven't mentioned anything. Only this question. I found two solutions from internet. One says:
When fault takes place at F1, current is feeding into the BUS A. It is like a generator delivering power to bus A----> So Vf1 lags If1
When fault takes place at F2, F2 point is like a load taking power from generator----> So Vf2 leads If2
So they've said C is the right answer.

Other website said that fault always takes reactive power so Vf1 will lead If1 and Vf2 will lead If2
I also think this should be the right answer but many internet sites said the earlier one is the right answer i.e option C. I didn't understand that underlined part above.
 
I guess the faults take place independently. That is why they say 'if the fault takes place at location F1' in the question.
 
jim hardy said:
What direction of current is assumed positive ?

make that what direction is shown positive ? Look at your diagram.
 
I guess positive current is from left to right. Since voltage at A is leading voltage at B, so active power will flow from A to B (Don't know about reactive power) (assuming Ea = Eb).
 
You're almost there. Draw phasor diagram ?
 
I did that. Still not getting answer C.
Handwritten sketch comparing two fault cases on a two-machine power system: a single-line diagram with lines F1 and F2, and phasor diagrams for the fault current lagging or leading the bus A voltage, with labels Ia, Va, Ia XI, Va + Ia XI = Ea and Vb + Ib 2XI = Ea.

In both cases the fault current lags the voltage at bus A.
 
Attachments
  • Hand-drawn power system diagram with a single-line model at top (EA angle delta, F1, A, F2, B, EB angle 0) and two annotated circuit sketches below, with blue and green phasor diagrams showing Ia lagging Va and Ib less than Ia.
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  • Hand-drawn diagram of a power system with generators Ea and Eb and a line with fault points F1 and F2 at bus A and bus B, plus phasor sketches labelled Va, Ia, Ea, Vb, Ib and 2Xl.
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  • Handwritten sketch comparing two fault cases on a two-machine power system: a single-line diagram with lines F1 and F2, and phasor diagrams for the fault current lagging or leading the bus A voltage, with labels Ia, Va, Ia XI, Va + Ia XI = Ea and Vb + Ib 2XI = Ea.
    upload_2018-1-1_10-25-28.png
    22.4 KB · Views: 643
Haste makes waste. I think your diagram is less than rigorous in assigning current directions.
Hand-drawn single-line diagram of a two-machine power system with a line reactance between each source and bus A and bus B, Ea angle = delta and Eb angle = 0, with blue and red annotations marking fault F1 and fault F2 and a green path showing the current direction.


But current is defined in problem statement as what flows at bus A which is in between the two fault locations.

Single-line circuit schematic with a source E_A at angle δ on the left, bus F1 and bus F2 along a line, bus A between them marked with a vertical bar, currents I_F1 and I_F2 drawn as arrows above the line and voltages V_F1 and V_F2 drawn below.

Will current there not flow toward the fault ?
If so,
In one case does it flow through A left to right , same way arrow is pointing, and in other case through A right to left, opposite the arrow ?
What would that do to its phasor?
 
Attachments
  • Single-line circuit schematic with a source E_A at angle δ on the left, bus F1 and bus F2 along a line, bus A between them marked with a vertical bar, currents I_F1 and I_F2 drawn as arrows above the line and voltages V_F1 and V_F2 drawn below.
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  • Hand-drawn single-line diagram of a two-machine power system with a line reactance between each source and bus A and bus B, Ea angle = delta and Eb angle = 0, with blue and red annotations marking fault F1 and fault F2 and a green path showing the current direction.
    upload_2018-1-1_4-56-22.png
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Wow... This was so difficult. How do I go through all this in the exam. I couldn't have thought of this during the exam.
Hand-drawn sketch of a single-line power system: a source EA at angle δ connects through node F1 and a fault marker to node F2, with labels IF1, IF2, VF1 and VF2, an arrow for actual fault current, and a phasor-style note of If1 equal to negative actual fault current.

Is my above phasor right? What would the Ea be? Is that Va or Vf1?
 
Attachments
  • Hand-drawn sketch of a single-line power system: a source EA at angle δ connects through node F1 and a fault marker to node F2, with labels IF1, IF2, VF1 and VF2, an arrow for actual fault current, and a phasor-style note of If1 equal to negative actual fault current.
    upload_2018-1-1_20-44-37.png
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Keep your thinking simple.
jaus tail said:
What would the Ea be?
What is voltage at location of the fault ? Does EA matter at all ?

jaus tail said:
Is my above phasor right?
With no labels i don't know what it is that you drew.
Red text reading: If1 which is -(actual fault current)


Aha there's your next thought step.
What is the current flowing through A to reach the fault ?
Negating AC current shifts its phase 180 degrees, doesn't it ?

Think in simple steps. Write them out one per line.
That's probably the point of this homework problem.

Good luck in your studies. Remember, success is 1% inspiration 99% perspiration . So orderly disciplined thinking is your best ally.

old jim
 
Attachments
  • Red text reading: If1 which is -(actual fault current)
    upload_2018-1-1_18-48-37.png
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Thanks. Is this the right phasor?
Handwritten-annotated circuit schematic of a power line fault: source E_A angle delta feeds bus A, with line currents I_F1 and I_F2 and a fault to ground carrying I(Fa) and I(Fb), and voltages V_F1 and V_F2 marked, above a phasor diagram with I(F1), I(Fb) and I(Fa) arrows.
 
Attachments
  • Top: single-line schematic of a source EA at angle δ feeding bus F1, then point A with fault current IF1 and IF2, then bus F2 with voltage VF1 and VF2 marked. Bottom: phasor diagram with V(F1) horizontal to the right, I(f1) pointing up in red labelled negative of I(fb), and I(f) due to E(a) and I(f) due to E(b) pointing down in blue.
    upload_2018-1-2_11-2-1.png
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  • Handwritten-annotated circuit schematic of a power line fault: source E_A angle delta feeds bus A, with line currents I_F1 and I_F2 and a fault to ground carrying I(Fa) and I(Fb), and voltages V_F1 and V_F2 marked, above a phasor diagram with I(F1), I(Fb) and I(Fa) arrows.
    upload_2018-1-2_11-6-45.png
    7.5 KB · Views: 633
jaus tail said:
Thanks. Is this the right phasor?
Annotated single-line power system diagram with source E_A at angle δ feeding bus A, currents I_F1 and I_F2, voltages V_F1 and V_F2, a fault branch to ground, and hand-drawn phasor sketches labelled I(Fa), I(Fb), I(F1) and V(f1).

Red line represents what ? I thought the fault was at F1 not at bus A.

I(FA) looks like a reasonable guess since we don't know the angle δ .so can't draw a phasor for VA.If V(f1) is zero why does your Black V(f1) phasor have nonzero length ? Are you saying it's the voltage at the fault, its lowercase "f" distinguishing it from voltage at bus A which has uppercase" F" VF1 ?

Were your fault at bus A then the voltage there would be zero. But there's some fraction of line impedance between Bus A and fault F1 .

Current through A is pushed toward the fault F1 by EB. Voltage at bus A, confusingly named VF1 instead of VBusA, is therefore nonzero.
It'll be some fraction of EB by voltage divider action. So we could draw a phasor for it . We could call it either VBusA, or VF1 .. It'll have same phase as EB just shorter length.

Were your black phasor labelled EB and VF1's phasor just a portion of EB 's i'd like your diagram a lot better.

Brown IF1 looks okay, i think you see that it has to be drawn up not down because of the current directions assigned.

That rigorous attention to detail is what it takes to get through EE. You'd best develop the self discipline now.
It's easy to do. What is difficult is to overcome our desire to leap straight to an answer instead of walking there one little step at a time..
That's mental laziness - recognize it as forbidden fruit .

This problem really boils down to basic circuit analysis. Be attentive to labels and assigned polarities and the algebra will work out.

old jim
 
Attachments
  • Annotated single-line power system diagram with source E_A at angle δ feeding bus A, currents I_F1 and I_F2, voltages V_F1 and V_F2, a fault branch to ground, and hand-drawn phasor sketches labelled I(Fa), I(Fb), I(F1) and V(f1).
    upload_2018-1-2_11-6-45-png.png
    7.5 KB · Views: 586
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Yeah i drew fault at wrong place. Red line should be at a bit left.
 
I understand the pressure of university level coursework. They feed it to you fast.

It seems counterintuitive at first to work slow and methodical . Simple problems can often be done by inspection.
As the coursework subjects grow more complex 'slow and methodical' becomes a must.
Remember the fable of "Tortoise and Hare"..

old jim
 
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