zero sequence voltage for line to line voltage

[mivey]

How can you have three L-L voltages that do not form a closed delta?

I can't hardly see how with a transformer. You would have to have something stuck between the two metering leads. Maybe with an impedance stuck between the delta windings? Suppose we had a bank of single phase transformers in a delta connection, and there was a bad terminal or crimp causing a high resistance connection. Would this cause a "broken delta" type situation on the transformer and the meter reading? What would be the situation with the zero sequence then? I'm not sure. It would be interesting to see where the voltages from nisri came from. Maybe they are the readings across the secondary broken delta coils. It could also be like you said, that the readings have a time displacement.

...three L-L voltages that can form, as vectors, an equilateral triangle...

True. This triangle would not necessarily be the same as a real set of transformer windings.

If you can read these JPEGs, note the Physical Meaning starting at the bottom of the first image.

Thanks Al. I could make out enough to follow what they were saying, I think.

Also, the convention is to have positive vector rotation. Do you see any application of a negative rotation? Would you worry about getting the vector sequence a-b-c on the front end or just recognize that a negative vector rotation will have the positive and negative sequences swapped and the zero sequence flipped 180 degrees?

 

[al hildenbrand]

Do you see any application of a negative rotation?

At this point in my career, I don't have to wrangle the math. I like the notion that the real world assymmetrical quantity rotation is turned only into a vector label reversal in the symmetrical component notation.

I would worry the notion if I were Nisri and coding a calculation program.

 

[jghrist]

It would be interesting to see where the voltages from nisri came from. Maybe they are the readings across the secondary broken delta coils. It could also be like you said, that the readings have a time displacement.

A sample waveform from IEEE 1159.2 is at http://grouper.ieee.org/groups/1159/2/wave9.xls

These appear to be discrete measurements (256 points per cycle) of L-L voltages. If you add Phase A-B Voltage, Phase B-C Voltage, and Phase C-A Voltage (columns B-D), you don't get zero. You get a peak value as high as the peak phase values.

I can't explain how this comes about. If you measure from the same three points, the voltages have to add to zero if they are at the same time.

 

[mivey]

A sample waveform from IEEE 1159.2 is at http://grouper.ieee.org/groups/1159/2/wave9.xls

I could not find the values that nisri used. I found no phasor angles in the files listed here. But, this graph may explain the problem:

 

[nisri]

mivey,

That is one of the sample waveform that enclosed in the ieee webpage. I get the phase angle by finding the fundamental component of the voltages. I'm using STFT (short time fourier transform) to do this process.

The data that I've given in this forum is taken from sample no 7 (if I'm not mistaken :grin: ).

As you can see, the data is labelled as an abc sequence phases, but when I'm calculating the angle, I've got it in acb sequence phases. Can it be possible if they have labelled it incorrectly (seems impossible)? I think, I need to recheck back my code..:grin:

Anyway, thanks with all the opinions from all of you guy..I can see some solution or idea why my graph or data look like what I've got. I'm not really sure the right answer for my problem but I agree with Mivey (really agree). Thanks mivey and everybody...thank you so much...

 

[nisri]

Attached is the result that I've obtained from the coding that I've coded..

Green >> Zero Sequence
Red >> Negative sequence
Blue >> Positive Sequence

This is the previous result that I've got when using the standard formula for the symmetrical component :
Vab=V0+V1+V2
Vbc=V0+a^2*V1+a*V2
Vca=V0+a*V1+a^2*V2

When I try to use the solution suggested by mivey, I've got the same result, but with a higher value of the zero sequence component..I think because it's being multiplied by the sqrt of 3.

 

[jghrist]

Here is Wave7, with the zero-sequence (Vab+Vbc+Vca)/3 calculated. It's not really zero-sequence, because sequence values only apply to sinusoids. Applying the zero-sequence formula to the fundamental component is valid, but since the fundamental component is not the entire measurement, this could be the reason that there is a zero-sequence.

The puzzling thing is that the instantaneous values of (Vab+Vbc+Vca)/3 are not zero. At about t=0.034, both Vab and Vbc are practically zero, but there is a large Vca measurement. How can you measure no voltage from A to B, no voltage from B to C, and a large voltage from C to A?

The phase sequence doesn't bother me. This could either be a real reverse sequence or misnaming the voltages. Some utilities (Duke Energy and Georgia Power for instance) use a reverse phase sequence, at least on their transmission system.
View attachment 1421

 

[mivey]

In my post #12, there were 3 typos and in my post #13, there was an error (too much playing around and too much chicken scratch). I have put the correct numbers in bold brackets. Sorry for any confusion:

From #12:

Now if you transform an unbalanced 120<0, 125<120, 120<240 {120<0, 125<-120, 120<120} set of wye voltages, you get:
V0=1.7<-120, V1=121.7<0, V2=1.7<120

If you take the delta voltages for these wye values and transform them you get:
VAB=212.2<30.7,VBC=212.2<-90.7,VCA=208<150
with a transform of
V0=0, V1=210.7<30, V2=2.9<90

And for one more: transform these 120<0, 120<125, 120<240 {120<0, 120<-125, 120<120} set of wye voltages, you get:
V0=3.5<147.5, V1=120<0, V2=3.5<27.5

If you take the delta voltages for these wye values and transform them you get:
VAB=212.9<2.75,VBC=202.4<-92.5.7,VCA=208<150 {VAB=212.9<27.5,VBC=202.4<-92.5.7,VCA=208<150}
with a transform of
V0=0, V1=208<28.3, V2=6<-2.5

From #13:

Now let's take our nice delta from before of
VAB=207.85<30,VBC=207.85<-90,VCA=207.85<150
which transformed to:
V0=0, V1=207.85<30, V2=0
and open the delta like this:
VAB=210<30,VBC=207.85<-90,VCA=207.85<150
gives us a transform of:
V0=120.62<0.17, V1=120<-0.34, V2=120.62<120.17 {the correct transform is V0=0.72<30, V1=208.6<30, V2=0.72<30 but I posted the transform of VAB=207.85<30,VBC=207.85<-90,VCA=210<30}

[edit: thanks to stikeh for the PM asking about the transform]

 

[wirenut1980]

Here is Wave7, with the zero-sequence (Vab+Vbc+Vca)/3 calculated. It's not really zero-sequence, because sequence values only apply to sinusoids. Applying the zero-sequence formula to the fundamental component is valid, but since the fundamental component is not the entire measurement, this could be the reason that there is a zero-sequence.

The puzzling thing is that the instantaneous values of (Vab+Vbc+Vca)/3 are not zero. At about t=0.034, both Vab and Vbc are practically zero, but there is a large Vca measurement. How can you measure no voltage from A to B, no voltage from B to C, and a large voltage from C to A?

The phase sequence doesn't bother me. This could either be a real reverse sequence or misnaming the voltages. Some utilities (Duke Energy and Georgia Power for instance) use a reverse phase sequence, at least on their transmission system.
View attachment 1421

The waveform looks like around the time 0.034 there is a single line to ground fault resulting in sagging voltage on V_ab. What does not make sense is why at least one other phase to phase voltage is not sagging as well. The single line to ground fault would result in a zero sequence current and voltage. Something does not look right...Is the waveform an output from your program?

 

[jghrist]

It is a sample waveform from IEEE 1159.2 at http://grouper.ieee.org/groups/1159/2/wave9.xls

 

[mivey]

typo

typo

{Sigh} I debated on posting this as it doesn't seem to be a big deal but:

And for one more: transform these 120<0, 120<125, 120<240 {120<0, 120<-125, 120<120} set of wye voltages, you get:
V0=3.5<147.5, V1=120<0, V2=3.5<27.5

I did not really calculate the positive sequence as it was not interesting and should be close to the original balanced value. But for those interested in something other than rough math:roll: , the value is:
V1=119.898482342<-1.66619627954

If you take the delta voltages for these wye values and transform them you get:
VAB=212.9<2.75,VBC=202.4<-92.5.7,VCA=208<150 {VAB=212.9<27.5,VBC=202.4<-92.5.7,VCA=208<150}

I posted the same typo twice. VBC=202.4<-92.5.7 is really VBC=202.4<-92.5 :roll: :roll: