# Drawing Phasor Diagrams for Relay Testers

Waveform diagrams contain every detail of an electrical system, but that information can be difficult to understand without a lot of effort. Phasor drawings take the complex information embedded in waveform drawings and convert it into phasor diagrams so that you can see the most important information about an electrical system at a glance. Understanding phasor drawings is probably one of the most important skills that a relay tester must have to be successful!

This video will introduce you to phasor diagrams, show you how to create a phasor diagram from a waveform drawing, and demonstrate the different kinds of phasor diagrams used by the most popular equipment used in the relay testing world.

This video is an introduction to our latest online training course Course 1-2: Phasor Diagrams for Relay Testers.  Click the button below for more information about the course.

### Here’s a transcript of the “Drawing Phasor Diagrams for Relay Testers” video:

“Electrical signals in an AC world can be displayed as waveform drawings that show the magnitudes of each signal, and how they relate to each other in time. You can get an amazing amount of information from a waveform diagram, but it takes a lot of time and effort that most electrical workers don’t have.  The electrical industry needed a way to understand the electrical system at a glance, so phasor diagrams were born.

Some people use the term vectors to describe phasors, but you should never confuse the two terms in front of an electrical purist. A vector describes the distance and direction between two fixed objects like the directions you get from your GPS. This simple map shows three vectors that will get you to your car. You can turn right and then left with the horizontal and vertical vectors, or you can walk directly to your car with the resultant vector.

Phasors are like vectors except all phasors on a phasor diagram are rotating at the same frequency.  Each phasor on the drawing has a magnitude and an angle. Phasor diagrams are often referred to as vectors because they look the same on a piece of paper, but phasors are really vectors with a rotation.

Phasors are direct representations of waveforms and are constantly moving as shown here where the waveform is on the left-hand side, and the corresponding phasor is on the right-hand side.

Moving phasors can be drawn to look like vectors because all of the phasors are moving at the same speed relative to each other, in the same way that a strobe light can make moving objects look like they’re standing still. If we choose the same reference point in every cycle, we can simulate a strobe light to make moving phasors appear to stop like a two-dimensional phasor drawing.

There are several different ways to convert waveform drawings into phasor diagrams.

You can choose a single reference and plot the phasors at that moment in time. We’ve chosen the peak of the red waveform as a reference and drew a vertical line through all of the waveforms in this example.

We can create a phasor by drawing a line from the waveform peak to the phasor diagram and plotting a circle.  That circle defines the magnitude of the phasor, which could be drawn at any angle on the phasor drawing depending on what we chose as a reference.

We determine the direction of the phasor by drawing a line from the point where the red waveform touches the vertical reference. The phasor is drawn where our new line touches the circle, and we finish the phasor with an arrowhead to indicate its direction.

We can draw the black waveform using the same method. We start by determining the magnitude of the phasor using the peaks, and then find the direction by drawing a line from the point where the waveform crosses the reference over to the circle. There are two possible angles to draw the black phasor at, and choosing the right angle requires a little imagination.

If we let the waveform and final phasor drawing move, you can see that the red waveform crosses the line first, followed by the black waveform, which is then followed by the blue waveform.  We want to maintain that phase rotation, so the black waveform is plotted at the right-side dot.

We can repeat the same steps for the blue phasor which also has two possible locations on the phasor diagram.  The black and blue waveforms are not drawn on top of each other, so the blue phasor must be drawn at the empty dot.

The second method for plotting phasors from waveforms takes the guesswork out of the phasor positions.

If we simplify the waveform and start it moving again, you can see that one full cycle is equal to one full revolution of the phasor. Therefore, one cycle is 360 degrees. If we draw the three-phase waveform again, we can create scales on the waveform and phasor drawings that match one full cycle.

Scientists and low-voltage people tend to look at waveform peaks when relating to electrical signals, but high-voltage technicians almost always look at the rms, or root mean square of the waveform. The rms of a waveform calculates the area under the peaks, which can be considered the usable energy in an AC system. We can calculate the rms of a perfect sine wave by dividing the peak by the square root of two, or multiplying the peak by 0.707. We will use the rms to determine the magnitude of the red phasor and draw our circle. We can find the direction of the red phasor by looking for the red zero crossing to positive peak, which in our case is zero degrees. The red phasor is drawn from the origin to zero degrees and finished with an arrowhead.

The black and blue waveforms are drawn using the same procedure.

The most confusing aspect of phasor diagrams is that it seems that nobody can agree on what phasor angles to use. Different parts of the world use different color codes, different standard voltages, different CT secondaries, different phase rotations, and different phasor angles to describe the same system. The only thing that the industry seems to agree on is that ALL phasors rotate counter-clockwise.

The previous examples showed the system used by Megger test-sets, Enoserv/RTS software, and GE SR relays.

Here’s how you would draw the same phasor using test-sets from Manta Test Systems and Doble. Notice that the angles have the same zero to 360 degree reference, but they’re drawn in the opposite direction.

If you generated the following voltages into a GE SR relay with a Doble test-set, your test-set would report these angles, but your relay would report these angles:

It looks like you are generating A-B-C rotation from your test-set, but the relay is receiving A-C-B, or vice-versa depending on your background. If you look at the correct angle system used by each device, you can see that the phasors don’t move, it’s the angles that are relabeled in each device.

Two different angle systems aren’t enough for the world, apparently, so GE UR relays use a negative angle system. In this system, the angles are plotted from zero to negative 360 degrees in the clockwise direction. If you generated the same signals into a GE UR relay, it would report these angles:

Nothing seems to match until you get a picture of the phasors where you can see that the phasors are in the same place, but the angles have different labels.

There is a fourth angle system that combines the positive system from Doble and Manta test-sets from zero to 180 degrees on the top half of the phasor diagram, and the negative system from GE UR relays on the bottom half.  This combined angle system is probably the most popular system in the world because it simplifies any math equation that uses angles. It is possible, or even likely, to get results greater than 360 degrees when using the other angle systems, which means you always have to be watching for it, and modify your answers accordingly.  This rarely happens with a combined angle system which is used in S E L relays and Omicron test-sets.  An S E L relay would report these angles:

When we get a picture of the phasors from each device, you can see that the phasors are in the same place, but the angles have different labels.

Phasor diagrams usually include three voltage phasors and three current phasors, which are plotted in groups with different scales. The procedure for plotting multiple groups on a phasor diagram is the same once you choose the angle system you want to use, but we use different arrowheads to indicate which signal group each phasor is in.  Voltage phasors are typically plotted with open arrowheads, and current phasors are typically plotted with closed arrowheads.

You should always have some visual cue when different types of phasors are plotted on the same diagram.

It is important that relay testers understand how to create and interpret phasor diagrams using all of the systems we’ve described here because you can’t properly test a relay without understanding the correct references.

Our protective relay online training course for phasor diagrams covers all of these topics in detail to help you understand and interpret phasor diagrams.  If you take this course, you will be able to draw phasor diagrams from waveforms or reports, and be able to convert between different angle systems.

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Valence Electrical Training Services is the independent source for protective relay training for relay testers. We offer: • Online Training Courses that can be completed at any location at any time • The Relay Testing Handbook series of books written for relay testers by a relay tester • Hands-On Training Classes where you come to us, or we come to your organization