Transcript
Introduction to Symmetrical Components
Good afternoon, everyone, and welcome to today’s white paper webinar. Today, we are talking about symmetrical components. I’m gonna show how to use symmetrical components or how to view these in PQ CanvasS, and also talk a little bit about what they are and why you might do this in a power quality recording.
Let’s start from the beginning, and this isn’t a comprehensive course on positive, negative, and zero sequence components. But just briefly, symmetrical components are a way of decomposing an unbalanced set of three-phase phasors, either voltage or current, into a set of balanced phasors.
Understanding Unbalanced Systems
In general, if you have an unbalanced system where you have, as we see in this bottom plot, an A, B, and C vector, this can be voltage or current. We have A, B, and C, and we can see that the lengths of the vectors are different and the phase angles between each of them is different. It’s not 120 degrees between each phasor, and their lengths are different. So the magnitudes and the phase angles are all different. That’s an unbalanced system.
Mathematically, it’s possible to represent this unbalanced system as a linear combination of three different balanced systems, and that’s known as the positive sequence system, the negative sequence system, and the zero sequence system.
Positive, Negative, and Zero Sequence
Each of these is a balanced system in itself. The positive sequence system is a set of vectors that have the same magnitude for all of them, with the phase rotation of ABC around this way. Negative sequence is the same magnitude and same 120 degree phase angles, or the same magnitude within themselves, but the opposite rotation. So we’re going ACB. And then the zero sequence, they’re all in the same direction.
So it’s possible to take any unbalanced system and represent it as a combination of a positive sequence set of vectors, a negative sequence set of vectors, and a zero sequence set of vectors.
Positive Sequence Components
The positive sequence represents the balanced portion of the three-phase system. So if your system is already balanced, then the positive sequence magnitudes will be the same as the magnitudes of the original system. For example, if you have a 120 volt, a two-ought-eight three-phase service and the voltage magnitudes and phase angles are perfectly balanced, all the same, then the positive sequence magnitude will be 120 volts, and the negative sequence magnitudes will be zero.
Ideally, that’s the only portion present. Another property of this is that if you have balanced loads with the same impedance on all three phases, that load will only draw a positive sequence current when it’s given positive sequence voltages. So if you have a balanced voltage system and you’re feeding balanced loads, the currents will also be balanced. This positive sequence voltage is what’s responsible for positive torque in motors. If you have a three-phase induction motor, this is what spins the shaft in the desired direction.
Negative Sequence Components
The negative sequence component is the counter-rotation component. This represents the amount of unbalance in the system. Generally, the magnitude of the negative sequence is much, much smaller, maybe a volt or two instead of 120 volts, compared to the positive sequence. Within the negative sequence set though, remember the magnitudes of all these phasors are the same, but generally small compared to the positive sequence.
Negative sequence voltage will produce counter-torque in a rotating motor, in the shaft of a motor. That slows the motor down. It can create shaft vibration and lead to other sorts of problems in a motor. And negative sequence voltage will produce negative sequence current even if the load is balanced.
Zero Sequence Components
With the zero sequence system, that represents generally neutral current or usually from a fault. So in a three-phase load that’s connected line to line that’s not touching the neutral or drawing power through the neutral, there will be no negative sequence current, and it’s not gonna produce negative sequence voltage. Generally, you get negative sequence issues if the neutral is moving with respect to the phases. And again, that typically only happens during a fault or you have an open three-phase neutral.
Sequence Impedances in Loads
What’s interesting about symmetrical components is that many loads have different positive, negative, and zero sequence impedances. The classic three-phase induction motor has basically infinite zero sequence impedance because it’s not touching the neutral at all. So it draws no negative sequence current and is basically blind to zero sequence current, and it is blind to zero sequence voltage. It doesn’t matter what the neutral does because the motor isn’t connected to the neutral.
For a three-phase motor, the positive sequence impedance is higher than the negative sequence impedance. The positive sequence impedance is the impedance of the motor as it’s running. The negative sequence impedance is generally not seen unless there’s a fault or significant unbalance. And the fact that these impedances are different is why a motor’s current imbalance is usually much higher than the voltage imbalance.
For example, if you have a 1% voltage imbalance and apply that to a standard three-phase motor, the current imbalance that results is gonna be six, eight, nine, or ten times higher, maybe six to ten percent instead of one percent. Different types of loads will have different positive, negative, and zero sequence impedances. And where symmetrical components are normally used are in a fault analysis where you have fault current flowing, and it makes the calculations easier to determine what that fault current is and what phases that’s on because you can think about the positive, negative and zero sequence impedance of the system itself.
Symmetrical Components and Harmonics
There’s another interesting twist when it comes to harmonics. What we’ve talked about is our 60 hertz phasors. Generally when we’re talking about positive and negative sequence, we’re only talking about the 60 hertz component of voltage or current. But of course, we also have harmonic distortion that’s present in systems, and different harmonics are considered positive, negative or zero sequence based on how the phase angles of those harmonics rotate with the 60 hertz fundamental.
Generally the harmonics that we see here are the multiples of three plus one: the first harmonic, the 60 hertz, the seventh harmonic, the 13th harmonic. These are all positive sequence frequencies. They generate positive torque in a motor. Technically the even harmonics that we see are the fourth and the 10th and so forth, are also positive sequence harmonics, but you very rarely see even harmonics in the system. So generally we only think about the odd harmonics here.
Negative sequence harmonics are 5, 11, multiple of three minus one, and then the zero sequence harmonics are also known as triplets: the third harmonic, ninth harmonic, 15th harmonic and so forth.
The most important aspect to remember about symmetrical components and harmonics are the fact that zero sequence harmonics add together in the neutral. Even with balanced loads, if those loads are drawing, say, third harmonic on each of the three phases, that third harmonic current doesn’t cancel on the neutral like positive sequence current would. It adds together in the neutral. And that’s why in many cases, the neutral current is dominated by 180 hertz because the 60 hertz cancels out for the most part in the neutral because it’s positive sequence. But the zero sequence frequencies, which is usually the largest at third harmonic, adds together in the neutral.
Additional Resources
I’ve really just touched on the basics of symmetrical components. It’s, again, more often used in fault analysis rather than power quality. But if you want to learn more about symmetrical components, here is a good set of videos that are available for free on YouTube that goes into a lot more detail on how to compute symmetrical components and why they’re useful in fault current analysis and protection analysis.
Another good set of videos is from Nathan Yerr. He has created some useful videos that help you understand symmetrical components from a geometric perspective. So it’s not as abstract as it might be from just looking at the math.
Voltage Imbalance Factor
One of the key ways that symmetrical components are used is to calculate voltage or current imbalance. You may be familiar with the ANSI C84 method, which is the max deviation from the average divided by the average voltage. That’s an approximation really. The best way of computing voltage imbalance is to use this voltage imbalance factor, which is the ratio of the negative sequence voltage to the positive sequence voltage magnitude.
To do this, of course, first you have to compute the negative and positive sequence voltage, and then you divide. Ideally, if there’s no imbalance in the system, this would be one. The positive sequence voltage is equal to the normal magnitude of the system, like 120 volts or 480 volts. V2 represents the amount of voltage imbalance and hopefully that’s small, just a few volts, and this ratio is under 2 or 3% ideally.
This is the best way of computing voltage imbalance because it uses the same values for line to line or line to neutral measurements. The max deviation from the average divided by the average is really an approximation. This matches more closely with the physical effects of imbalance on motor heating and variable frequency drive front ends. So this is really the best way of computing voltage imbalance and is the most common use of symmetrical components in a power quality analysis.
Another way of using symmetrical components is to measure the customer’s negative sequence current, because with voltage imbalance, if you have a high imbalance at a customer meter base, one question is, well, are they causing that imbalance themselves with their unbalanced load? And one way to assess that is to measure their negative sequence current, which really should be proportional to their contribution to the voltage imbalance.
Viewing Symmetrical Components in PQ Canvass
Let’s jump back to the paper. The first part of the paper talked about what I just did using the text here. But let’s jump to looking at symmetrical components in a PQ recording. And here I’m going to use PQ Canvass to do that. PQ Canvass is our cloud-based system, and I’ve logged into PQ Canvass here, and I have a data file that I’ve loaded.
With PQ Canvass, all your data files are here in the cloud. We can look at active devices, we can look at recordings that are already in PQ Canvass. I’m gonna look at an example that is a good voltage imbalance situation. So here we can look at, for example, the RMS voltage and get a hint that there’s some imbalance. So we can look at the imbalance graph, but I’m gonna show how to look at the symmetrical components directly.
Analyzing Waveform Captures
Here the system is computing this from a waveform capture. So I can pick any waveform capture. Here we see a hard start motor. We have voltage in red, current in blue. Current is basically zero until this motor starts on. It kind of slams right on the line. We can analyze this, as the paper says, by looking at harmonics or vector diagrams, but we can also click on Symmetrical Component Magnitudes.
Here we get a continuous graph of positive, negative, and zero sequence magnitudes. This is done on a 60 hertz basis, one cycle at a time, because it takes a one cycle window to compute those phase angles. But it’s done with a sliding window. So this calculation slides one sample at a time to give you a continuous graph of the symmetrical components versus time.
This graph is still the same timescale as the waveform, 120 milliseconds. The top one is the positive sequence. Then we have the negative sequence and the zero sequence for voltage and for current. And we can see for voltage, we jump up in positive sequence, negative sequence, and zero, and we can see what the current is doing.
Using the Meter Display
What’s also interesting is to look at the meter display. If we click here on Meter, we have the symmetrical components down here at the bottom. So we get a one cycle analysis window we can move around, and PQ Canvass is computing the symmetrical components in addition to all these other parameters for this one cycle under analysis.
Here we have the positive magnitude, 490 volts, negative magnitude, 1.7 volts, zero sequence magnitude, .24, and we have the phase angles for the positive, negative, and zero sequence. The phase angles are not usually used, but they’re there, just in case you need them. Then we have the voltage imbalance ratio. This is 1.7 divided by 4.9273. That’s the voltage imbalance. And we can move this rectangle around and see how this varies.
Steady State vs. Transient Analysis
If you’re looking at steady state voltage imbalance, you want to put this at a steady state portion of the waveform. You wouldn’t wanna put it right here, because that’s in the middle of the disturbance. We want either before the disturbance to catch the baseline steady state before the disturbance happened, or we’d put it on the other end, after things have settled down. So if you’re looking at steady state issues, you keep that in a steady state portion of the waveform.
For the most part, voltage imbalance or looking at negative sequence current for assessing the customer’s contribution of voltage imbalance is a steady state issue. If you’re looking at symmetrical components versus time like this, then you’ll be looking at it as more of a fault current analysis. This is available for any waveform capture that’s in the data file, and you can use this with any recorder that can record waveforms.
Wrap-Up and Future Features
That covers the white paper here. Coming up in a future version of the device firmware will be a way to record symmetrical components directly as strip charts. But in the meantime, you can use the symmetrical components analysis tool in PQ Canvass to look at positive, negative, and zero sequence magnitude and current, both on a steady state basis if you have waveforms, for example, on a periodic basis, as the white paper recommends, or on a transient basis if you put this over a transient.
If anyone has any questions, give us a call at any time at 1-800-296-4120, or send an email to support@powermonitors.com. Everyone, thanks for attending and have a great afternoon.