Chapter six, three phase metering. When considering three phase power generation you can assume that is made up of three single phase generators connected together on one terminal that generated voltage vectors or phasers are 120 degrees apart, rotating counterclockwise, the load can be connected in various configurations. In this case we show a Wye connected load. Remember from previous chapter that energy meters, regardless of their makeup, mechanical or electronic, are considered to be made up of meter elements. A potential coil or a voltage transducer and an add converter make up a half of the element of the meter. A current coil or a current transducer plus an A to D converter and make up the other half element of the meter.

Together that make up a single element of a meter that can be used to measure power and energy consumption by a single phase load. Multi element meters regardless of whether they are mechanical or electronic can be made up of two or three elements. Each element reads the average power which is the RMS voltage times the rms current times the cosine of the angle between them, which are then summed to give the arithmetic total reading of all of the elements. Let's look at a three phase wide connected load. Now that we have a simple model for a three phase generator, we can replace it with a three terminal generator the generated voltage phasers are 120 degrees apart and the y connected load is made up of three impedances set one set two set three. In order to meter the load we simply need to meter the individual power to each of the load impedances then arithmetically some the three meters.

That is we use three watt meters or a three element watt meter, each element measuring the face to neutral voltage across the load and the current to each of the load as in the diagram here and then we sum the meters or the elements. As I said we could use a three element meter to accomplish the same thing. Each element measures the face to neutral voltage across The load and the current into the load. The digital processing unit then sums the total consumption. Before proceeding into the next set of metering type installations, especially for three phase metering, we have to understand that utilities have installed or will be installing hundreds of thousands of these meters in their utility system. So that as a cost saving measure, they try to keep the numbers of one meters down and certainly the cost of the watt meter is down and if you reduce the number of elements in a watt meter, certainly the cost will go down because the cost will go up as you introduce more elements into the meter.

And if you have fewer elements than you have fewer CTS and pts that have to be connected and the associated wiring. So all in all, there is a general trend or has been a general trend to reduce the amount of elements involved in a metering system. So what we're going to see in the next few installations is some approximations that are made that are acceptable from a billing standard such that the costs will be kept down. And we will be trying to reduce the number of white meters or certainly the number of elements in a watt meter in metering three phase systems. In a utilities three phase system, often referred to as an infinite boss, because utilities tend to be very large and they're interconnected with each other. So that the infinite bus refers to the fact that the voltages regardless of The loads remain relatively unchanged.

In other words, they are going to be equal and 120 degrees apart just about at all times. If we look at the voltages here, if we look at voltage V one, the vector would look something or the phasor would look something like this, then voltage v2, or v2 to neutral would be 120 degrees legging that voltage and look somewhat like this. And voltage three would look something like this. When the voltages are added together because they're equal and 120 degrees apart, the vector sum or phasor, some of the voltages will add to zero. And for the next stage in metering three phase system, we'll use this identity Where the voltages of a three phase system will add to zero in order to make reductions in the number of elements used in a meter. Let's go back to the three phase a metered load that we had up a few slides back where we had y connected load to this system with three watt meters measuring the power consumption of that y connected load.

And we could say that the total power to the load is made up of the sum of wahpeton One, two and three. So wt is equal to W one plus w two plus w three. And we know that the individual white meters are made up of the product of the current and voltage in each of the phases. In other words, I one v one plus i two, B two plus pi three v three is equal to wt We know that each element is reading the power average equation, which is the root mean square of the voltage time through square of the current times a cosine of the angle between them. We also know that because we're dealing with an infinite plus that v1 plus v2 plus v3 is equal to zero, or we can say that v2 is equal to the quantity minus v1 minus V three.

Then if we substitute v2 into our formula, we will get that I one plus v one plus i two times the quantity minus v one minus V three plus i three v three. all we've done is a mathematical substitution here which is allowed. Now we can collect like terms in in this equation. We see that the formula tells us that we only need to walk meters, two meters this system, and that is we collect like terms. In terms of v1 and v3, we see that the total power consumption by that load can be metered with two meters, one using the voltage of free one, and the current is one minus i two, and the voltage of the three and the current of i three minus i two. And the total would be the sum of those two watt meters or two elements that would be used to meter this wide connected load.

As I said this formula tells us that we can use a two element one meter, one element using voltage one and the sum of the current side one minus side two and the other element using voltage v two and the sum of the current side three minus side two. Let's see how this formula will apply to the industry standard 34 over Seven. The meter elements look like this where element one is the bottom element of what's in our diagram. And element two is the top element of the diagram, as we see here, using a three CT and direct connected potentials. Instead of numbering, the standard uses letters but the formula and relationships are the same. The A n is the potential as shown here in red, going through element number one so it's the half element used for potential of element number one.

The current from will Line a is shown here or I subscript a and it goes through element number one in a positive manner. The cn is shown here, and it is the potential connection for element number two. I see takes the current from the current transformer associated with the sea phase, and it puts the current through element number two in a positive manner. Now, I B or the B phase current goes through both elements and it leaves the CP using I'm associating it with a dark green and you can see it goes up and through element number two backwards, which means it's being subtracted, or minus b through element number one, it comes back down, but doesn't return directly to the CT but goes up and backwards through element number two, which gives it a minus b. For element number two, which is shown in the light green here, after it goes through element number two backwards, it returns back to the CT and continues the circuit flow.

If the current and voltage phasers are plotted, the resultant currents through each element are 60 degrees apart. The resultant voltages are 120 degrees apart, this 60 degree 122 20 degree configuration is a standard for correct metering arrangement and you'll see this in several of our meeting or in metering arrangements. This set up using this standard setup 3407 is what we would call non blondell compliant. And we'll explain that once we get into the blondell section of this chapter, which is later on. The standard 3408 is the same type of metering. Only this time we're using an S base meter, which is a socket or plug in type metering.

The elements are to look like they're turned sideways. But this would be element number one, and this would be element number two how Ever all the connections in CTS feeding the meter are the same as before for the a base meter. Now this type of mirroring both with a socket base in the a base meter using three CTS, and then manipulating the current so that you can subtract one from the other is easy to do if you have current transformers and they allow you to do this. If you did not have current transformers, in other words, if you had a direct connected watt meter, you could not connect the currents together. You couldn't make up by one minus i two because you'd have to connect the primary phases together which would short circuit dumb and it just wouldn't work. So in using this formula, how would You'll be able to use a two element meter, or less than a three element meter in order to meter.

This type of situation. Well, it's done using a two and a half element here. And you'll see that in the next slide. If we were to use a two and a half element meter, it would allow us to sum the currents if they are directly connected. That is there is no CTS. Now you remember what a two and a half element meter looks like it has two current inputs and they both share the potential coil.

So you're allowed to take I one through one of the coils and you can pump it to backwards through the other element and then have it Go through backwards through the other one here. And the other element as well, allowing us to use the same formula wt is equal to W one plus w three, which is v one, I one minus i two, plus the three times the quantity is three minus i two. So, what meter w one would look like this and it still gives us the average power one meter three still gives us the average power using the currents here in the formula. So, again, we've satisfied the equation for calculating the total average power for this setup. However, this time we are using a two and a half element meter. And again and I'll state this and explain it later.

This is a non blonde Dell compliant setup. It is accurate enough for our purposes, but it is not blondell compliant setup. Let's look at our three phase four wire load again. And let's apply just a pure a purely resistive load this is just to make things look a little bit simpler. The eye one current phaser would look like this. The eye to phaser would like I one by 100 120 degrees and look like this.

Eye three current vector would lie guy two by 120 degrees and look like this. The I one minus i two current phaser would look like This and the eye three minus side two current phaser would look like this. In actual fact, the load does not have to be a Wye configuration. Since the calculations only deal with current and voltages to the load this metering will work for any three phase four wire load. Again, if the current and voltage phasers are plotted together the resultant currents through each element are at 60 degrees or 60 degrees apart and the resultant voltages to those to those elements are 120 degrees apart. So this gives us the characteristic of Accurate metering, which is usually plotted with voltages and currents at 120 and 60 degrees apart.

If there is non resistive elements, in other words reactive elements such as inductance or capacitance in this circuit, there will be a shift of the currents either in a forward or reverse direction compared to the voltages, however, the currents will still be 60 degrees and the voltages will still be 120 degrees. Remember this reduction in the number of watt meters two instead of three was based on the fact that the voltages were balanced. This is purely a cost saving measurement and is also a non blondell compliant setup. nearing any three phase four wire load with three watt meters or a three hour watt meter is the best and more most accurate where the total power consumption wt is given by the sum of the individual watt meters or elements w one plus w two plus w three and element number one is fed with the ADA neutral voltage times z a phase current element number two is fed with the beat a neutral voltage times the B phase current and element number three is fed with the C to neutral voltage times the C phase current.

Using direct connected potentials to the meter and CTS and a three element meter measurement Canada standard 30 418 is a cost effective way to meter a three phase four wire load using solid state meters today, solid state meters the price of salt solid state meters has come down drastically. With the development of them over time, so it makes sense to use a three element meter now instead of approximating the total with a two element meter or a two and a half element meter, and with this setup, the voltage just no longer need to be balanced metering a three phase three wire, delta load, the Delta load is made up of three individual loads connected phase two phase as shown in this slide. This time we're labeling the phases are wb or red white and blue. Two meter the load we would use three watt meters or a three element watt meter, each, the watt meters or elements are connected such that each watt meter or element measures the current through the load and the voltage drop across each load.

Red to white, white to blue and blue to red voltage, the total power consumed is the arithmetic sum of the three watt meters. So, as I said, the total load will be the summation of the individual watt meters, W one w two w three are the individual elements of a three element watt meter. Substituting the voltage drop across each load and the current through the load for the W one w two w three we get this equation. Remember that in a three phase load the voltages we'll add the voltage phasers will add to zero as indicated Here. If we would like to get the blue to red voltage in terms of the other two voltages, then we can write that the blue, the red voltage is equal to the quantity minus voltage read the white minus the voltage white to blue. We can now go back to the equation above and substitute the term that we just found for the blue to red voltages, and we get this equation here.

We can expand what's inside the brackets mathematically and we end up with this equation. And we can further rearrange the terms not doing anything magical other than math, mathematical manipulation. And we would end up collecting like terms we would end up with The total power can be monitored by actually two meters or a two element meter, with we're measuring the red to white voltage times the current through Zed one minus the current through Zed three plus the voltage white to blue, and times the current through set to minus the current through Zed three. So we haven't done much more than mathematical manipulation at this point. But we will recall that the current the red face current is equal to eyes and one minus eyes and three which is current jobs current law really. So we can substitute that in our equation.

Similarly, by kerchief 's current law minus I B is equal to two minus i said three. So we can put i minus IB in our equation. So now our total equation or our or equation for total power consumption is given by the red the white voltage times the red phase current plus the white to blue voltage times minus the blue phase current. Now we can rewrite that equation and get rid of the negative sign and you'll notice that we just changed the polarity of the white to blue voltage to the blue to white voltage, and we end up with an equation that is the total power consumed by this load is the red the white voltage times a red face current plus the blue to white volt edge times of blue phase current. This formulas tells us that we only need two meters or one two element meter to measure the power consumption in a three phase three wire load.

One meter element uses the red white phase two phase voltage with the red phase current. The other meter or element uses the blue the white phase two phase voltage with the blue phase current. Since the measurement of power to the load only uses face to face voltages and phase currents, the load configuration doesn't matter as long as there is only three wires to the load that is no neutral look looking at the voltage and current phasers See that we are using the red the white and white to blue voltages with the red and white phase currents. The resultant currents each out of each element are 120 degrees apart. The resultant voltages of each element are 60 degrees apart. This is the 60 degree 120 degree configuration that is standard for correct metering arrangements.

Let's look at a measurements Canada standard 3301 which is metering a three phase three wire low with load with a self contained meter or directly connected the first element sees the voltage A to B plus C a phase current the second element, we'll see the voltage seem to be using the C phase current. And of course, the standard uses ABC for their three phases, whereas we develop the formula red, white and blue are our W and B, which matches up to what you see here. And metering any three phase three wire wire load using a self contained or an Essbase meter, such as measurement Canada here uses 3302 the first element would be on the left, the second element would be on the right and measuring the same quantities as an a base meter which we just looked at in the previous slide. And for a higher voltage higher current circuit using PTs and CTS, such as measurement Canada standard 3311 shows here, the same equation holds true where the first element takes in the voltage A to B with the read phase current.

And the other element takes voltage C to B with the C phase current. And of course, you have to take into consideration the turnover ratio of the CTS and pts when you're coming out with your final answer. So far we've been sampling excerpts from the measurement Canada's standard connection diagrams and connections for metering systems. Anything From single phase to three phase system to wire three wire for wire systems, they're all listed here on the Government of Canada website, they can be found at this location. And just about every metering system in Ontario and certainly Canada adheres to this standard so that we can continually refer to it and make sure that our connections are correct and our stack. The website has two sections and Appendix A, which is 87 pages of electricity metering installations with color coded connections, and you can leave through them we've gone through several of them here in this chapter Appendix B is measurement Canada's standard color codes for electrical metering installations.

Now, these color codings don't necessarily or they for sure don't affect the actual metering themselves. But what they do is they make it easier for those that are maintaining the system to understand how the wires are connected without having to go and separate out the bundles and have to reconnect or re bundle them together after maintenance is done. The actual wired connections to a meter are also standardized. And most of the systems use what they call test blocks for the purposes of connecting and disconnecting the current and potentials to and from The meters these test blocks are designed such that you can inject current or measure current and inject voltages or disconnect voltages by opening and closing suspicious. These test switches are also designed to take test plugs which allow you to inject current or measure current in in a metering circuit and you can even do that with without disconnecting the meter or the power source to the from to and from the meter.

Although it is recommended to remove the power and and then do your connections and then reconnect the power. However, these plugs are made to bring the power connections to your test equipment. And you can see here a side view of the, the test block where the switches open, but the connection to the meter is still maintained through spring loaded connections. And as the test plug is inserted, it makes connection with the bottom and the top of the plug and our bottom and the top of the switch and the current will then flow through our test plug connection. Once the Flexi test switches are mounted, they are wired to a standard which is also found on the measurement Canada standard connections. This figure shows a typical installation of a two element meter with the hydro one Delta Connection.

Notice the indicated current flow through the CP and meter coil and the labeled currents at the test block. Also note that the neutral potential is shown having a solid or dummy fuse. This is the required connection tracing the potential current flow you'll see that it flows from line a to neutral and from line C to neutral in the left and right elements, if the neutral potential link was a normal fuse and it opened the potential coils would be placed in series and potential e AC and ECA would be applied to the potential coils. This would definitely cause errors in the measurement. This figure shows a typical installation of a two element meter with a Schlumberger Delta Connection And this figure shows a typical installation of a two element meter with the measurement Canada Delta Connection. Now these connections basically read the same to the meter or the meter reads the same current.

It's just that the wiring on the test switches themselves are are different. blondell dows theorem states that if energy is supplied to any system of conductors through n wires, that's n the number of wires. The total power in this system is given by the algebraic sum of the readings of n watt meters. Solar range that each of the N wires contains one current coil, the corresponding voltage coil being connected between that wire and some common point. If this common point is on one of the N wires, the measurement may be made by the use of n minus one watt meters. Looking at our example of a three phase four wire system, the number of wires in that system is four and the common point is the neutral.

So we can measure the total power to that load with n minus one or three watt meters. Now this is a sounds like a pretty complex and long theorem. However, it can simply be stated that in a system of n wires, the number of watt meters required to measure the total power is minus one, or the total power is measured with one less watt meter than the number of wires, certainly a lot better or a lot easier to understand than a long paragraph that we've just read. A single phase two wire requires one watt meter. A single phase three wire system requires two meters or two elements. a three phase three wire system requires two meters or two elements.

And a three phase four wire system requires three watt meters or a watt meter with three elements. If a meter is wired correctly, and the right number of metering components or elements are present for metering a system of in wires than meters that meet the requirement of Minus one elements for in wire service are said to be blondell compliant. And it's it's usually accepted that there are no errors in this type of a metering system that are incurred by the connections there may be errors due to the PTS or the CTS themselves. But as far as the connections are required, it should be reading 100% accurate when we did an example of 100%, blonde blonde compliant metering in our example of a three element meter using measurement Canada standard 3418 as seen here, you can see that there are four wires and we are using the three elements which is it meets the requirement of n minus one elements for wires.

When a metering system is non compliant and meets the meet, that means the meters do not meet the requirement of n minus one elements for an N wire service. Now, this doesn't mean that the metering is in error. Because some of the assumptions that are made are within the accuracy rating that we're looking for. It just means that if the system was pushed, it is a there is a possibility that we would land outside the metering accuracy that wouldn't be required. However, there's plenty of meters out there that are non blondell compliant. And they were basically put in the system because of economic reasons as we stated before, where we can reduce the number of elements and reduce the number of PTs and CTS that are connected to the system in order to save money over the long run meters that do not have blown Dell combined to provide stability and accuracy of measurement.

The reasons are needed one have fewer, fewer elements as I said and lower costs, especially true for electromechanical meters. There's an avoidance of interference between two elements driving a single disc in an induction meter. There would be fewer CTS and PTs and in very high voltage systems, CTS and pts can introduce a significant significant cost into the metering system. Of course there's less wire wiring and there's fewer things that can go wrong if there's fewer wires, as well as some savings in not buying the wire. Some of the assumptions that are made that are used and we've looked at those already, some of the assumptions are that the voltages are balanced and equal and 120 degrees apart. Here's Here are some examples of meters that are not blonde out compliant.

And they can either be in this case going from left to right, left to right, there's three wires in this system, but they're only using one element to meter the system. And in the middle one, there's four wires and they're only using two elements to me to the system. And in the case of measurement, Canada standard 3407 they so making that assumption Doesn't introduce a great deal of inaccuracy into the metering system. As long as you can sum the currents which they can do here in the case of using CTS, so they can get away with using a two element meter and they do it quite often. And this ends chapter six