Chapter Seven cross watt meter verification. Cross watt meter verification is a tool used to check or verify graphically current phasor relationships to voltage phasers. This is done with the aid of a watt meter, and you can also use an amp meter and volt meter in the mix. The basis for this verification is the use of the formula power is equal to voltage times the current times the cosine of the angle between them. Which graphically tells us that given a known voltage phasor say voltage phasor be rotating counterclockwise in a circuit. The current phasor I in the same circuit with a displacement angle of theta When measured by a watt meter, the result is by virtue of the cosine rule, the projection of that current onto the voltage phasor.

I'm going to repeat that the basis of the verification is the use of the power formula, which is equal to b times i times cosine of theta, where theta is the angle between the voltage and the current. What this tells us is, if we have a known voltage phasor, the it's rotating counterclockwise in this circuit and there is a current generated by that voltage in the same circuit with a displacement angle of theta when measured by a watt meter. The result is by virtue of the cosine rule, the projection of the current onto the voltage phasor. If that unknown current is part of a three phase circuit, and the voltages are balanced and counterclockwise and rotation, a power reading taken with a watt meter using that unknown current and the voltage V read to neutral is by virtue of the rule of cosines the projection of that current on the voltage phasor the AR n and a second power reading then taken this time using the white to neutral voltage is the projection of that same current on Voltage vector or voltage phasor v white to neutral.

And a third power reading taken using this time, the voltage blue to neutral is the projection of that current on the blue to neutral. And those three projection lines intersect at one and only one point at the tip of the current phaser. So, if we wanted to plot an unknown current relative to a known set of voltages, we would connect that current to our watt meter and using the red to neutral voltage, while taking that watt meter would record the walk reading, scaling it and marking it on the red to neutral phaser. We know that that point is On a projection of that current onto the voltage vector such that the tip or the head of the phaser arrow would be somewhere on a 90 degree projection line. Next, using the white to neutral voltage, we would record a watt reading, using the same scaling as before marketing marking it on white to neutral voltage phasor.

And we know that that point is on a projection of the current onto that voltage vector such that the tip or the head of the phasor arrow would be somewhere on a 90 degree projection line. Those two projection lines intersect at only one point and that point would be at the tip of the unknown current are the head of the phaser arrow repeating the process you Using the Bluetooth neutral voltage would simply verify our previous readings and plot. Notice that the scaled watt meter plot is on blue to neutral negative. In this case the watt meter reading will be negative indicating that the scaled plot is negative and the projection line would be on the negative blue to neutral voltage phasor. This is the process of crosswalk meter verification, and it is worth repeating. So, let's do it again.

So, if we wanted to plot an unknown current relative to a known set of voltages, we would connect that current to our watt meter and using the red to neutral voltage, while taking that watt meter would record the water Reading, scaling it and marking it on the red to neutral phasor. We know that that point is on a projection of that current onto the voltage vector such that the tip or the head of the phaser arrow would be somewhere on a 90 degree projection line. Next, using the light to neutral voltage, we would record a watt reading, using the same scaling as before marketing marking it on the white to neutral voltage phasor. And we know that that point is on a projection of the current onto that voltage vector such that the tip or the head of the phasor arrow would be somewhere on a 90 degree projection line.

Those two projection lines intersect at only one point Not point would be at the tip of the unknown current or the head of the phaser arrow. repeating the process, using the blue to neutral voltage would simply verify our previous readings and plot. Notice that the scaled watt meter plot is on the blue to neutral negative. In this case the watt meter reading will be negative indicating that the scaled plot is negative and the projection line would be on the negative blue to neutral voltage phasor. Let's walk through the process with a mirroring reeling. Protection circuits such as the one shown here are known set of voltages would be accessible on a set of fuses similar to the ones shown here.

And our unknown set of currents would be accessible on these FPS switches similar to the ones shown here, the voltages would be connected one at a time to our walk meter for each current and there are three of them here, a test plug would be inserted in the appropriate switch, and the switch would then be up opened to allow the current to flow through the watt meter. schematically, this is what our setup would look like. The voltages and currents would be connected to the CTS and vt s at the bottom of the fuses and the FT switches, the meters and or relays would be connected to the tops of the fuses and ft switches. It is required that we verify for correctness the currents flowing into the mirroring and relaying protection circuits via the FT switches We call these the CT links I one I two and i three a voltage reference source is first established in this case a Nolan three phase star connected voltage transformer, secondary source is available at the VTX links here showing red white, blue and neutral.

The star connection provides for both phase to neutral and phase to phase reference voltages, the reference voltages is positioned facing the panel, red white and blue and neutral from left to right as shown. The test circuit is constructed using a portable volt meter a meter and watt meter as shown here. First, the voltage leads are connected to our known potential sources The red or marked lead is clipped to the top of the red fuse, and the black or unmarked lead to the neutral or the dummy fuse, then the current leaves are connected to our current links. The red or marked lead is connected to the bottom of I one current link via the bottom of a test plug and the black or unmarked lead to the top of the current link via the top of the test plug. We then open the current link or ft switch which would allow the current end to flow through our watt meter.

We should now have an indication of on all three test meters and upscale reading on the watt meter with the connection as described would indicate a positive reading. If the watt meter deflection is down scale, this would indicate a negative reading and the voltage leads may be reversed to obtain an upscale reading. This watt meter reading would then be recorded as a negative value. Some electronic watt meters are equipped with a reading switch that you can switch back and forth to allow a negative reading upscale. Record then on all these meter readings for these connections Now move the read or Mark lead clip to the top of the red face to use and connected to the top of the white face cues. record all meter readings.

Now move the red or Mark lead clip on the top of the white face to use and connected to the top of the blue face to use and record all the readings. We are now finished with current One, so close the eye one switch. Care must be taken to ensure that there is a current path at all times. Now move the red or Mark lead back to the top of the red face pews. Remove the test plug and move it to I to such that the red or marked lead is at the bottom of it to link and the black or unmarked lead is on the top. Now open that current link we should have an indication on all three test meters.

Record all meter readings. Now move the red or Mark lead clipped on the top of the red face hues and connected to the white face use and record all all the readings. Now move that over to The blue phase fuse and record all readings. We are now finished with current i two, so close I to switch care. As I said before care must be taken to maintain a path for the current at all times. Repeat the procedure for i three recording all meter readings, opening a switch and recording the readings for the read to neutral voltage for the white to neutral voltage and for the blue to neutral voltage, closing the switch, then removing all the leads.

So, when taking cross what meter verification readings it's handy to have a chart like this laid out ahead of time and you can just fill in the blanks. This is the sequence of meter readings. For current i one, we would read a one and four the three voltages v1, v2 and v3, which would yield what readings of W one w two and W three. Then for the current itu we would get an ampere you'd say a two yielding watt readings of W for W five and W six. And lastly, I three current of a three would yield watt meter reading, say W, seven w, and w nine, completing our chart, and then we can proceed with the plotting process. Let's look at some real numbers.

In doing this plotting process, the voltage readings are As you can see are recorded there, they aren't necessarily absolutely equal. In fact, it's very likely they won't be equal, but they they must be close if you find them way out of whack then something might be wrong, but closeness is is good enough for our purposes here. We can start plotting the verification results using these cross reading templates which are three sets of intersecting lines positive and negative 120 degrees apart. Note these template lines are used to plot the scaled watt readings along the direction of the no on voltages. They are not used to plot the magnitudes of the voltages are known voltages are 120 degrees apart. So they can be marked on the template lines as such, to read to neutral voltage and the minus read to neutral voltage The white to neutral voltage and the minus y to neutral voltage, the blue the neutral voltage and the minus blue the neutral voltage which we also know is rotating in a counterclockwise direction when we measure the current i one which is 4.75 amps, then take its watt meter reading with respect to the read to neutral voltage, which is 315 scale it and then plot it on the red to neutral voltage factor line.

The projection of the current i one on the voltage phasor voltage read to neutral is shown here. Since we know it is the projection from the current phaser I one I one must lie somewhere along this projected line And we now take the watt meter reading with respect to the white to neutral voltage which is minus 91 scale it then plotted on the white to neutral voltage line the projection of the current i one on the voltage phasor b w n or white to neutral voltage is showing here. Since we know is the projection from the current phaser then I one must lie somewhere along this projected line. These two projection lines intersect at only one point therefore, this is where the current phasor is one must be taking the watt meter reading with respect to the blue to neutral voltage which is minus 224 the projection of the current i one The voltage phaser v blue to neutral verifies this as its projection line must also intersect where the current phaser I, one is this plot is not necessary to define the current i one but it serves as a verification.

This process is repeated for I two and i three currents using the second and third row watt meter readings respectively. Upon completion of the phasor diagram plot it is observed that our current phasers lag their corresponding phase voltages by an angle of theta one, theta two and theta three these angles are should be very close to each other. In reality, they should be identical, but that's not always the case. So, that If we want to find the power factor angle, we average these three angles by summing them and dividing by three. Hence the corresponding power factor is calculated by taking the cosine of this average value of the three angles. So far, we have been using red to neutral light to neutral and blue the neutral voltages because they tend to be the easiest to deal with however, taking cross what meter readings using any known voltage will give you the same currents and angles that you would get as long as they are known voltages.

For example, as you can see in this process, we are going to use red the white white to blue and blue to read voltages. You can see where the red to white voltages phaser lines up here, the white to blue voltage phasor lines up like this and the blue the red voltage lines up like this. I've left the red to neutral, white to neutral and blue, the neutral phasers locations on the diagram. And you can see from these readings which were done with the face to face voltages that they do correspond to the same currents the same current phasers are plotted using these vectors. We're going to go through a couple of what I call classroom exercises now and seen as this is a video which you have control over. I'm going to state the problem and I'm getting I will get you to then to pause the video so you can work on the solution you can return to the video started up and the next slide and or the next series of slides will have the solution.

And you'll see how you did. The first problem is a cross what meter exercise that involves the fact that we took these readings using known voltages which were the face neutral voltages, took the current readings and the watt meter readings which you see here in this chart. The first step is to plot the current phasers I one I two and three, then find the power factor angle and then calculate the power factor. So now you can pause this video and work on the problem when you feel you've worked hard enough on the problem or you've come to the conclusion. Start the video up and the next series of slides will will show the solution So the solution here happens to be fairly easy. And I'm going to take a couple of shortcuts which I'll explain, you can follow the steps that we did before, which essentially, we're going to do now, but we're going to do it in a little bit different fashion.

The first thing you might notice is that our red to neutral voltage phasor is horizontal rather than vertical. That does not matter as long as we position the blue to neutral and the white to neutral voltage phasers, such that they are subsequently 120 to 40 degrees displaced from the red to neutral voltage, which we've done in this diagram. We've marked the positive red to neutral voltage going from the origin to the right, the negative red to neutral voltage going from the origin to the left and the white to neutral Voltage 120 degrees displaced from the red to neutral voltage and then the minus y to neutral voltage in the opposite direction. And then the blue to neutral voltage 240 degrees displaced from the red to neutral voltage, and it's minus sine going in the opposite direction. They've all been marked here so you can see what you know how they operate.

Now, one of the things that you will notice if you look at the table, that basically we we are dealing as far as the watt meter readings are concerned. And if we're talking about the absolute watt meter readings, that is without a sign attached to them, well, that means we're going to ignore the fact that they're either positive or negative. For the moment, we will see or you can see that there are only three values 200 240, and 40. These values are going distances from the origin. Depending on whether you're dealing with the plot along any of the voltage lines, they still are going to be that scaled distance from the origin. So if you look at our diagram I've drawn or I count or circled, I've performed three circles, one at 40 watts, one scaled at 200 watts and one scale at 240 watts.

They cross all of the voltage phasers at some point. And now all we have to do or plotting our, our projections, we only have to deal with where they are crossing the particular phasor that we're dealing with at that particular time. So if we look at the red to neutral voltage, and we look at the projection line of the first reading for I one, it's 200 So you can see where 200 crosses the red to neutral voltage, we just draw a perpendicular there and and, and all of the projections and currents associated with the red face current or AI one is colored in red, so you can see it fairly easy. So the projection line going from the red to neutral voltage, you can see is quite obvious. The next thing we can look at is the light to neutral voltage plot for the for the watts and it is plus 40 along the white to neutral voltage vector, and that's where our circle crosses the voltage of phaser white to neutral and we draw her perpendicular there which is in red, and it perfectly intersects the line for the one we had just previously drawn for the voltage read to neutral.

And that indeed is where our red face current lies. You can verify that by picking up the minus 240 watt reading that we get when we use the blue to neutral voltage and draw perpendicular there. And that verifies our answer. So you can see the three red lines intersect where the current is, and those are our three Voltage Readings across the top of our chart. Now if we look at the white to neutral, or I two, you will see that the green line the green line projections are crossing at the particular point where the green phase current is and it's just a repeat of the process that we did for the red phase current. And then if we deal with i three or the blue phase current, you will see that we have plus Minus 240 plus 200.

And we can again can use our intersecting circles with the voltage Phasers to mark our projection lines project are our perpendicular lines and they will intersect where the blue phase current is and hence that is the plot of our of our current phasers. Now we know that the red face current is and you can see it from the diagram it's and we've read it 3.55 amps and it's at a lag of 39 degrees from the red phase voltage. The white phase current is 3.54 amps and it is at 159 degrees lagging from the face to neutral or sorry fate, the red to neutral voltage which is 39 degrees displaced from the lighting control voltage and blue phase current at 3.55 amps is at 279 degrees from our red phase voltage, but it is only 39 degrees from the blue to neutral voltage. So the the angles that they are that each of the currents are displaced from their associated Neutra paste a neutral voltage is 39 plus 39 plus 39 divided by three is 39 degrees, so our power factor angle is 39 degrees and the power factor is just the cosine of that angle which works out to 0.777.

The next problem involves trying to solve a suspected problem The fuses and current links Shown here are used to feed a three phase three element watt meter, the meter is suspected of being wrong. In other words, it's reading the wrong values. The voltages have been verified as being correct. That is, the red, white and blue to neutral voltages are all equal in 120 degrees apart, and you can see the voltage readings on our chart. When plotted, they definitely point out the air. So our task is to plot the voltages with respect to the currents.

In other words, do the crosswalk meter verification and see just where the error occurs? Now, you can stop the video, work on the problem. Come up with the answer and then we Start the video and see if you're correct. Okay, so if we plotted out the currents using our crosswalk meter verification process, the first thing you do is you plot out your known voltages in this time I'm taking the red to neutral voltages being vertically pointing up so it's negative value will be pointing down and the white to neutral voltage will be 120 degrees displaced from the red to neutral, which means it's kind of going in a southeast direction on our on our chart here. And the blue the neutral voltage is 120 degrees lagging that and is kind of heading in the southwest direction. So we have our plotted voltages there as we plot our current So you can see that I one, which is the red face current is lagging the red to neutral voltage like it should.

The I two is lagging the white to neutral voltage, which is the white phase current and it seems pretty normal. However, I three is actually going in a direction that we're not suspected. So it really should be theoretically 180 degrees in a different direction from what it's pointing in right now. So yes, indeed, it looks like they've got the white face current going. Or sorry, the blue phase current going through the watt meter in the opposite direction, which would give us our error. This is what the current should look like.

It should be going in this direction. So this would give us an indication Or who would actually tell us that our blue phase current or i three is connected wrong and we want to get into the back of the wiring of that panel and make the correction or find the problem by eyeballing it and then making the correction. So this ends chapter seven