Transcript
Introduction to Symmetrical Components from PQ Data
Good afternoon, everyone, and welcome to today’s white paper webinar. Today we’re going to be showing you how to get symmetrical component data from recorded strip chart magnitude and phase angle information.
It’s possible to compute positive, negative, and zero sequence components with the 60 hertz phase angle and magnitudes for either volts or for current. And to make life a little easier, we’ve created custom templates in ProVision to extract that data in an Excel spreadsheet to paste this into seamlessly to have this all computed for you.
Configuring the Recorder
First, I can show here we have the white paper that shows you how to configure the Revolution or other PQ recorder. Here in figure one, to get the data in the first place, you need 60 hertz magnitude and phase angle. So here in figure one, we show how to do that.
You want to record at least the first harmonic, that of course being the fundamental. So here in this selected harmonics box, you enter at least a one. You could record other harmonics. You could put a range, say 1-31 or comma separated harmonic numbers here, but at the very minimum, you need the first harmonic recorded to get symmetrical components.
And then you want magnitude for volts and generally for current. And this is the rare situation where phase angles are important. You need the phase angle for the 60 hertz fundamental to compute the symmetrical components. In many cases, for just pure harmonic studies, you don’t really need phase angles. But for this purpose, you do need the phase angle for the fundamental.
So once you have this initialized, you can send this template to a Revolution, a Seeker, a Bolt or a Guardian, even a Tensor, to get this information recorded at whatever strip chart interval you’d like.
Downloading and Exporting the Data
Then when you download the data, you have a recording that has trend data at this selected interval for magnitude and phase angle for each of the selected harmonics. And we have a template or a graphing template that you can download. There’s a link here at the bottom of the white paper to download this, which will then allow you to either graph this in ProVision, but more importantly for this purpose, export this as a CSV file that you can then paste directly into our handy spreadsheet.
Demonstration in ProVision
So I’m going to switch over to ProVision and demonstrate how to do this. So here I have ProVision loaded. I have a data file that has harmonics recorded here. In this recording, we actually have more than just the first harmonic. We have all harmonics up to, I believe, the 15th harmonic. But we’re going to concentrate just on the 60 hertz components here to look at symmetrical components.
Now, we have a custom template that I’ve already preloaded into ProVision called VMAGS and PHASES. This is the 60 hertz fundamental for voltage and for current. You’re going to double-click that. Here, this is just for voltage on this particular one. We have the three magnitudes. We have A, B, and C voltage. They’re around 120 volts because it’s the 60 hertz fundamental. And here we have phase angles. This one doesn’t drift very much, pretty well-regulated. But this data really isn’t meant to be looked at in ProVision graphically. The intent here is to export this and use it in the spreadsheet.
So to do that, we go to Report and Custom Graph Reports, and I’ve got a lot of templates in this version of ProVision. Here at the bottom is the one I most recently imported into ProVision, VMAGs, VPHASES. And this is just a tabular view of that graph we just looked at. Here are the magnitudes and phase angles for the 60 hertz component, and you can see that VMAG, VPHASE, and this one means first harmonic. If you had other harmonics defined in this template, this would be a lot wider.
But we want to take this out of ProVision and put it into our Excel spreadsheet. So I can simply right-click and export it as a CSV file, and this launches an export. I can save this on the desktop, and now I have a CSV file that is essentially this exact report.
Pasting Data into the Spreadsheet
Now, we can use our handy spreadsheet to compute symmetrical components. I will take this export, open this in Excel. So here is the data right out of ProVision. Again, it looks almost exactly like the report in ProVision. I’m just going to simply copy those columns and paste it into this spreadsheet that we downloaded from the white paper.
And now we see the symmetrical components here in the spreadsheet. You missed it. Yeah. I gotta paste it in the right spot. Paste it in, starting in column A, where it says, “Paste data here.”
Now we have the correct data. We have the original data that we pasted in here in this section. And over here, we have some intermediate calculations. These are the raw calculations for the symmetrical components, and Caleb can describe the theory behind these complicated formulas in Excel.
Spreadsheet Output: Symmetrical Components and Unbalance
And the bottom line is this, columns here in J through P. This is the positive magnitude, negative magnitude, and zero sequence magnitude, and these are the phase angles for the symmetrical components. And then here is the imbalance as a percentage. This is the negative sequence over the positive sequence.
Now here we’ve pasted voltage into the spreadsheet. You could also do the same thing for current, in which case you get the current symmetrical components and the current imbalance. You can paste either voltage or current into here, or you could paste them both if you duplicate these columns.
So here we have a time series. We have a row for each data point. Here’s the timestamp. And this is the interval data for the entire recording. So as far down in is the recording, and from graphs, we can plot here in Excel the symmetrical components directly, or we can look at the unbalance if that was the end goal. Or even look at the symmetrical component phase angles. But in most situations, the magnitudes are more important than the phase angles for these components. Or unbalance may be the most important piece here. And we can see the unbalance is a little, actually a little bit high here in this recording.
Summary of the Workflow
With this white paper, you have an easy way of getting trend data for positive, negative, and zero sequence voltage or current components, and including unbalance by simply recording the 60 hertz phase angle and magnitude, and then exporting that data directly into the spreadsheet, which is formatted in a way that you can take it right out of ProVision and put it right into the spreadsheet.
The Math Behind the Spreadsheet
Now, if you want to know more about the math behind how the spreadsheet works, this starting point is an earlier white paper of ours that just talks more about the math behind symmetrical components in the first place. I have this one pulled up. So Caleb also wrote this paper, and at the end of the paper, he gives the mathematical definitions of these components. Now, the tricky part here for this paper is how you go from this linear algebra into raw Excel formulas.
Reconstructing Complex Phasors in Excel
So if we go back to the spreadsheet, I’m going to make it so you can see both these at once. Here are these intermediate calculations. Caleb, you want to chime in on how this works?
Well, I’ll give a go here. I’m software engineer here at PMI, and I run the software engineering department, and I’m very much a Unix guy. So when Chris approached me and says, “Hey, you know how we’ve got all of these Python and other scripts and tools where we can compute symmetrical components? What if we did this in a spreadsheet?” First thought was, I’m not sure we can actually do that. Turns out you can, and this is the proof. So I was very shocked and amazed. I’ve put together probably 10 spreadsheets in my entire life to find out that it supports complex arithmetic, complex functions within Excel.
Let’s see. We’ve got the original paper. Chris mentioned that we need to record both the magnitudes and phases. Those are strip charts of the time series points, and what we end up doing is using trigonometric identities to recompose that complex 60 hertz phasor, where we get our real and imaginary portions by taking the cosine of that phase angle and multiplying that by the magnitude that we recorded, that fundamental magnitude, and the sine of the phase angle by the magnitude gives us that imaginary portion. So that gives us the reconstructed complex phasor.
The Symmetrical Component Transform
If we go to the actual definition here, our matrix is our transform here for the symmetrical components. VA, VB, VC are channel one, two, and three voltages. So remembering that these are actually the 60 hertz phasors, these complex phasors. So VA times one, VB times A, VC times A2, which we’ve defined down here, are these complex values, and then of course unity for one. And so what you have to do is multiply those together and then divide by three, and that gives you the complex output. Complex input, complex output here.
So that gives you a complex number. That is the positive component. And then VA times one, VB A2, VC A gives you the negative sequence, and then VA, VB, VC gives you the zero sequence.
Implementing the Math in Excel
In the spreadsheet here, this is the portion right here where we’re reconstructing this complex phasor, and we’re doing that by taking the cosine. So ProVision exports all the phase angles in degrees, and so we need to convert those to radians. So we’re taking the phase difference here, and we’re taking that and converting it to radians, and we’re taking the cosine of that. And that’s going to give us our imaginary portion times the magnitude here. That’s that C23.
So we’re taking that raw fundamental magnitude, multiplying it by that phase angle of the fundamental phase angle, and then converting that to radians, of course. And then the same thing with the sine to get the imaginary, and now we have this complex defined, complex value for channel one. Same thing for channel two. We’re doing the same thing here. Channel three, we’re doing the same thing here. So now we have channel one, two, and three 60 hertz phasors defined as complex numbers.
And then to get the positive magnitudes, now remember, this is where it gets a little hairy. Kinda gotta get a running start to read through this. So remember from over here, it’s the VA plus VB times A, plus VC times A2 divided by three. And if you look here closely, you’ll see here’s that IMdiv. That’s the outer division. That’s where we’re going to divide by three. So we kinda work our way backwards and back again to the beginning here.
So we divide by three if you look in the outermost. Then we gotta take the sum, because remember, it’s a sum. You multiply a vector by a matrix. It gets VA times one plus VB times A plus VC times A2, right? So now here’s our complex sum, and then we’re taking the products of, again, A, V sub A times one, V sub B times A, and V sub C times A2. So here’s our products of those, products of those, products of those. Then we’re taking the sum of those products, which are defined by the linear algebra, and then we take the scalar one-third, and we’re going to do our imaginary division by three. Now, this we do for our positive, our negative, and our zero sequences.
Defining A and A2 Constants
Now up here, we have these complex numbers that are defined as A and A2. That’s our minus one half and square root three over two, and then that should be negative F and negative root three over two. Those are defined here as well, and you can see those derivations out here if you want to get into those. So we need to use those. Those are part of those multiplications in here. Remember, that’s V sub A times A, or V sub B times A, and V sub C times A2. And those are that A and A2 number there.
Computing Magnitudes and Phase Angles
So now we have all the complex phasors and complex values and complex sequences over here. And then in order to compute the magnitudes, we just literally take the magnitude. Just add the abs of the complex number, gives the magnitude. And for the phase, we can take the arctangent of the real over the imaginary portion, and then we’ll multiply by 180 over pi to get degrees from radians that we had in the previous one. So lots of very tedious little bits that come along here. Looks mind-bending when you look at it here.
If you understand the fundamentals of how we’re converting here, of just the simple linear algebra of multiplying this vector by this matrix step by step, it comes out as small, individual, indivisible, very easily manageable, digestible chunks.
Wrap-Up and Practical Applications
Well, thanks, Caleb, and you can see how easy that was. Yeah, it’s a breeze. It’s a breeze. We recommend using the spreadsheet. No need to make it tedious. We did the tedious work for you, but this is a straightforward way of getting symmetrical component data out of power quality data.
It’s not that commonly used in the PQ world, but it is helpful sometimes, especially if you’re looking at the true unbalance, a negative sequence over a positive sequence, or you’re trying to look at the customer contribution to unbalance, and so you care about their negative sequence current, or you want to know your absolute negative sequence voltage for various reasons. So those are the primary reasons why you’d do this from a power quality standpoint.
Well, if anyone has any questions, give us a call anytime at 1-800-296-4120 or send us an email to support@powermonitors.com. Everyone, thanks for attending and have a great afternoon.