Transcript
Measuring Power in Delta Circuits
Good afternoon, everyone, and welcome to today’s webinar. Today we’re gonna talk about measuring power in delta circuits, and talk in particular about why it’s not mathematically possible to measure individual phase powers in a delta, and why, especially in PM recorders, you can only get total power. That’s really mathematically all you can reliably compute in the face of unbalanced loading conditions without making assumptions.
This paper is by David Horning. David can talk a little bit, and I can wrap it up here. When you have a three-phase delta system, you don’t have the means to measure on each phase. That would take a lot of assumptions and math. So we do, as Chris said, put the total power on channel one.
What Is a Three-Phase Power System?
So what is a three-phase power system? As the paper says, you get power through three live connections, and these are good when you have large power draws with large motors. It’s a more efficient way to deliver the large power.
As David was saying, the loads are connected line to line, and the voltage is higher there, so it’s more efficient, less conductors for the same amount of power. But what you’re measuring with the CTs is the combination of these internal windings.
Why You Can’t Measure Individual Phase Power
So you have the CTs here. You can’t measure inside the delta, inside the transformer to get those individual phase currents. You can only measure the sum of these currents. And if that’s where you’re measuring, outside of the transformer, information is lost at that point mathematically.
Now, you can measure the total power coming out of this black box by measuring all three currents, but you can’t measure the power inside each winding individually. And of course, if the transformer windings are all identical and the loads for line to line are all identical, then everything’s balanced and the power from each winding is the same also. And so each phase winding would be identical.
Where that breaks down is if the load across each phase is not identical. That means, for example, if something’s connected A to B that’s drawing more power than A to C and C to A, the phase-to-phase voltage that has the most load is getting contributions from two different windings. And how that mixes depends on all the details, and you can’t see inside the delta to measure individual winding currents. So fundamentally, that means that you can only measure total power.
Unbalanced Systems and the Two Wattmeter Method
As David said, that’s a common case where you have a delta circuit, you have delta connected loads. The voltages aren’t completely balanced. The loads aren’t completely balanced. The transformer windings may not even be completely balanced. You could even have an open delta where one winding is missing, and so then it’s a very unbalanced system. So in all those situations, you can only measure total power, but the total power is accurate.
And this is known as the two wattmeter method. Blondel’s Theorem goes into the mathematical detail, and we have another white paper on that kind of derivation if you wanna see more of the math behind that. With two wattmeters, and two voltages, two currents, you can compute the total power completely because of certain mathematical properties, but there’s not enough information to compute three individual phase powers.
Now, you can make some assumptions on the circuit and come up with three individual phase numbers, and there are some recorders out there that try to do that, but those are assumptions, and can be very misleading. You don’t really know if it’s right or wrong. So really the only thing you can mathematically determine in this situation is the true total power.
How PMI Recorders Display Total Power
Now, in a PMI recording, that total power is input into the channel one slot. So for example, here in this graph, the real power is a three-channel recorder, and so we have, in theory, three channels. The first channel is where the total power lives, and that’s the total three-phase power. The other two phases are just recorded to zeros. So there’s no useful information there. The first slot in the memory is for the total power.
Viewing Delta Power in PT Canvass
And I can show this here in PT Canvass so you can see what it looks like doing this interactively. Here is an example of a delta connected recorder. You can look at the interval. We can look at, for example, voltage and current and see that we do indeed have three-phase voltages of 40 volt service.
But if we try to look at the power, we’ll see that we only have total power on channel one. So if you look at real power, for example, here’s the real power on channel one, and we’re at roughly 15, 20, 30 kilowatts. The other channels have zeros filled in because there’s no information there. So really, channel one is where the information lives, and that’s the total power.
And this is a bit easier to visualize in the total power graph that we can see that gives you individual real reactive and apparent power. So here we have total real power on the top plot, apparent power in volt amps here, reactive power var is there, and then total power factor is here on the bottom.
So this is probably the better graph to see power, especially in a three-phase delta circuit, because you only have total power anyway. And so this graph doesn’t show you all those zero plots. This gives you real reactive and apparent power all on the same plot. We can easily see that we’re in 20, 30 kilowatts. We’ve got some power excursions where loads are cycling.
Summary and Contact Information
But if you see a strip chart where you have zeros for the other channels besides channel one, that’s a three-phase delta hookup. And mathematically the recorder can only give you total power. It’s not possible to see inside the delta in the windings and measure these currents, and so you can only get total power. And again, in the paper we show that, but there is, if you go to our website or look at the other papers, you can see Blondel’s Theorem.
In fact, you can even go into PT Canvass, go into the help and use our white paper search. Tell me Blondel’s Theorem, and this will show you white papers based on that.
If anyone has any questions, give us a call anytime at 1-800-296-4120 or send an email to support@powermonitors.com.
