Transcript
Introduction
Good afternoon, everyone, and welcome to today’s white paper webinar. Today we’re talking about the types of advanced measurements you can make with just some basic information. We’ll walk you through how to compute some metrics like real reactive power, apparent power, and some more advanced metrics like THD and symmetrical components from just a handful of parameters that you can get from a PQ recorder or sometimes from a relay at a substation or maybe a cap bank controller or even a voltage regulator or a fault current indicator.
So it can be really handy to be able to derive or compute some of these metrics from basic measurements of RMS voltage and current in 60 hertz voltage and current, where the magnitude and the phase angle. That really allows us to compute a lot of things that you might not expect.
Setting Up the PQ Recorder
To start with, we’ll show you here what you would need to enable in a PQ recorder. Figure one shows the setup for a PMI recorder. The key is recording RMS voltage and current and the magnitude and phase angles of the 60 hertz component or the first harmonic.
If there’s no harmonic distortion, then the RMS value of the voltage and current is basically the same as the 60 hertz fundamental. But if there’s any sort of waveform distortion, they become different. And that RMS value has a lot of information. Fundamentally, looking at the difference between the RMS value, which includes information from all frequencies, and the 60 hertz fundamental allows you to compute some interesting parameters.
You will also want to record real power to get other sorts of power metrics. Real power in the recorder is the instantaneous product of voltage and current, summed over a cycle. That’s something you can’t derive from the RMS voltage and current or 60 hertz fundamentals absent fact. So these four measurements—the RMS voltage, current, real power, and 60 hertz fundamental voltage and current harmonic magnitudes and phase angles—are all we need to compute many other parameters.
Total Harmonic Distortion
The first thing we look at is total harmonic distortion. Computing a voltage or a current THD with the traditional method is basically take the Fourier transform and you want to go through the harmonic subduce. You want five hertz bands all way up to the 51st harmonic, and all of those are expressed as the ratio of the fundamental.
For the purposes of this, we can get a pretty good approximation. What we do in ours actually is take the square of the RMS minus the square of the fundamental magnitude, subtract them, and then take that of the ratio of the fundamental again. So that gives us a pretty close approximation here. Times 100 gets you the THD for that.
PMI recorders, mentioned that we default sample. It is 256 samples a cycle, so that 127th of the theoretical maximum harmonic that we can compute. So if you want to go beyond the IEEE specification, take that into effect, you can.
Symmetrical Components
Symmetrical components, as you can see here, there’s a previous white paper that was dedicated specifically to this whole task. With that one, I made a spreadsheet that you can download, an Excel spreadsheet that goes along with this, so that you could export the readings directly from ProVision and import them into the left half of the spreadsheet, and it would compute all of the values for you.
The purpose of this paper is more along the lines of providing algebraic definitions for these measurements for users that want to make the minimal recording and then do these computations themselves. The symmetrical components, again, it’s a linear algebraic equation. Pretty straightforward. In compute, you’ll get positive, negative, zero sequence voltages or currents depending on what you’re measuring. And then you can also compute imbalance from those magnitudes and phases that you get out of. Those are all complex outputs. This operation here, all the multiplication outputs are gonna give you complex outputs.
Power Measurements
Apparent power, again, that’s a pretty simple computation. You’ve already recorded RMS voltage and current. It’s just a product of those.
Displacement power factor is the angular displacement between the 60 hertz voltage and current phases. We’ve got both of those phases. We can take the cosine of the difference of those and get displacement power factor.
Reactive power: we can take our apparent power measurement that we made earlier, and then we can take sine of the theta, that same differential we found before, and we get the reactive power off of that.
The real power, as Chris already mentioned, that’s a different kind of measurement. That’s why we’re having you record that outside of the 60 hertz values. And then distortion power factor is a measure of THD at a load decreases. So it’s simply the fundamental magnitude divided by the RMS. Pretty simple measurement.
Worked Examples and Algebraic Computations
The rest of the paper is just basically working out the algebraic computations for each of these different measurements. We’ve put out a series of tables and values and worked these out by hand. As you can see, they’re very simple. They were worked out on the blackboard, and then converted to LaTeX and then passed on through our marketing team to format them. So pretty much a 0% chance of error in transposing any of this.
The point of all of these was to try to work all these out piece by piece so you can see that you can derive these yourselves, use Python script to export some of the data and compute them with Python or turn around and do them in your own spreadsheet. Again, if you go back to the link we provided here, you can go back and get the Excel spreadsheet and modify that too with these equations and algorithms.
Saving Space and Streaming Options
The other thing to bring up here is these are, by hand computing these instead of having the recorder compute these, you can save up a lot of space on the unit. So if you don’t have, for instance, a cell modem or ability to stream recording data, this is a convenient way to extend the lifetime of a recording itself.
But if you have something like a Seek or a Bolt or something that has direct streaming access to PQ Canvas, simple thing to do is just turn on all your recordings, all your recording measures, and let them stream to PQ Canvas, and they’re already there for you to analyze directly in a web browser or on your phone or wherever you have it.
Like Caleb said, if you have a modern recorder or you are streaming to the cloud with the Seek or the Bolt or the Guardian, you can simply enable these and have the recorder compute these for you and you don’t need to make these secondary computations. The recorder can measure these directly and stream it, and there’s no memory limitation.
But this is handy if you have an older recorder with limited memory or if you have spot measurements that you’re pulling from something else like a relay or cap bank controller that can give you a reading, like a one-second reading of some of these measurements, and you want to know, for example, the voltage imbalance or the THD, and the relay can’t give you that directly, but it can give you RMS values and 60 hertz values, then this is very handy to be able to compute these advanced metrics from the limited measurements that something out in the field can give you.
It’s one thing to have the algebra here, but it’s also very handy to have worked out examples so that you know how to translate algebra like this into the real numbers here. So we show you both and some worked through examples.
Contact Information
If anyone has any questions, give us a call anytime at 1-800-296-4120 or send an email to support@powermonitors.com. Thanks for attending, everyone. Have a great afternoon.