1. Ground-Distance Concepts for Relay Technicians
Steve Laslo
System Protection and Control Specialist
Bonneville Power Administration

2. Special Thanks Quintin ‘Jun’ Verzosa Jr. Doble Engineering Company
Schweitzer Engineering Laboratories, Inc.
Some information in this presentation comes from three excellent sources:
A paper from Doble’s Quintin ‘Jun’ Verzosa: Ground Distance Relays – Understanding the
Various Methods of Residual Compensation, Setting the Resistive Reach of Polygon Characteristics, and Ways of Modeling and Testing the Relay (2005)
SEL’s 321 Relay Manual: _IM_
SEL White Paper: Application Guidelines for Ground Fault Protection, by Joe Mooney and Jackie Peer (1997)

3. Presentation Information
Our Objectives for this presentation are to enhance attendee knowledge by:
Reviewing Ground-Distance relay fundamentals that affect relay settings and relay decision-making.
Review calculations for test quantities for testing basic Ground-Mho and Ground-Quad characteristics.
Explore testing of basic Ground-Mho and Ground-Quad characteristics.
Note that we will use a ‘representative’ relay in our presentation / discussion: the SEL-321 relay.
This presentation is intended to be vendor neutral, and the concepts discussed should apply to ground-distance relays from any vendor. There are many outstanding ground-distance relays available and used by many different utilities.

4. Some Background
Historically, ground-distance relays were not commonly used in the era of electro-mechanical relaying.
In that ‘era’ protection was commonly:
Phase-distance
Directional Ground-overcurrent
With the advent of solid-state and now microprocessor relays, the ground-distance functions are more easily accomplished and have become more commonly applied.

5. Some Background
Training Programs for Relay Technicians have historically educated new technicians well in how to test and work on phase-distance relays because they have been around for so long.
Not all training programs have done as well when it comes to ground-distance concepts and practical application.
This presentation will attempt to fill in some of the conceptual gaps that might be present between phase-distance and ground-distance relaying.

6. Protection Key Concept
Relays make impedance calculations based on the values of voltage and current at the relay location.
The location of Voltage Transformers and Current Transformers are important factors in the ability of a relay to make these decisions.

7. Phase-Distance Decisions
Fault current is limited by the line impedance.
Relays ‘see’ the correct impedance to the fault location.
Note that this is for an ideal fault with zero fault/arc resistance. We are ignoring their possible impacts for this discussion. Protection Engineers deal with them in the real world but Relay Technicians rarely have to deal with them as they generally do not impact relay testing.
One scenario for this type of fault is if Line workers inadvertently left personal protective grounds in place or if the line at Station 2 was inadvertently energized with protective grounds in place.
Impedances in diagram are in Secondary Ohms.

8. Phase-Distance Decisions
Test values are relatively easy to calculate:
Assume test voltage = 40.4V
I = E / Z = 40.4V / 9.36Ω = 4.32A
Test Quantities:
VA = 40.40°V, VB = 40.4-120°V, VC = 40.4120°V
IA = 4.32-83.97°A, IB = 4.32 °A, IC = 4.3236.03°A
Remember that fault current lags the fault voltage by the angle determined by the characteristics of the transmission line and that the ratio of reactance to resistance is (for the most part) a constant along the length of the line. So while the fault current changes based on the fault location the fault angle is fairly constant >> in this case lagging by an angle of degrees.

9. Relay Settings for our example
- Positive and Zero-Sequence impedance of the protected line (magnitude and angle) in Secondary Ohms.
- Reach of Zone 1, Zone 2, and Zone 3 for Phase Mho Characteristic in Secondary Ohms.
- Overcurrent Supervision settings; ignored for our discussion.
- Reach of Zone 1, Zone 2, and Zone 3 for Ground Mho Characteristic in Secondary Ohms.
- Reactive* Reach of Zone 1, Zone 2, and Zone 3 for Ground-Quadrilateral Characteristic in Secondary Ohms.
Note that some manufacturers give all settings ‘per-phase’, while others give some ‘per-phase’ and some in ‘loop’ impedance. Settings Engineers and Relay Technicians need to keep this in mind in order to properly set and test the relay for correct operation in-service.
In our example settings, Zone 3 is reversed. The actual setting for this is not shown here (DIR3 = R).
*In our example relay, the XGx settings are actually at the line angle even they it is somewhat implied that they are a reactive reach. For many vendors this type of setting is true reactive reach at 90 degrees; in this relay it is not. Knowing some of these details can clearly be very important in proper setting and operation of the relay.
- Resistive Reach of Zone 1, Zone 2, and Zone 3 for Ground-Quadrilateral Characteristic in Secondary Ohms.
- Zero-Sequence Compensation Factor Settings; magnitude and angle. ‘T’ is a correction factor we will ignore in our discussion.
Note that all settings above (for this manufacturer) are ‘Per-Phase’ Values…

10. While you don’t need to be an expert Protection Engineer familiar with sequence networks to follow this discussion, a very fundamental knowledge of symmetrical components is extremely useful. Let’s spend a few minutes with a very basic discussion.
Symmetrical Components are used to analyze unbalanced 3-phase systems. For balanced systems (like when everything is normal) our basic electrical theory provides us all we need. But faults almost always unbalance the system and that is where Symmetrical Components are extremely useful.
They function by taking something complicated and simplifying it: 3 unbalanced phasors become 3 sets of ‘components’, each of which is uniform and balanced. It is not much different from taking a voltage and current out of phase, calculating power, then breaking down the power phasor into Watts and VARS. Watts and VARS make up a single Power Flow yet their effects are quite different. The effects are much easier to analyze using the components than the resultant phasor.
In this picture we have an unbalanced system broken down into its 3 sets of symmetrical components. Note how each ‘set’ is balanced and symmetrical.
Positive Sequence Set: All same magnitude, 120 degrees apart, positive sequence.
Negative Sequence Set: All same magnitude, 120 degrees apart, negative sequence.
Zero Sequence Set: All same magnitude, exactly in-phase, rotate together.

11. Note here how the components still add up back to the original phasors
Note here how the components still add up back to the original phasors. It is somewhat ‘magical’ how 3 sets of symmetrical components can represent any 3-phase unbalanced system (note this happens by the ‘components’ being different for different cases, just like how Watts and VARS are different for different conditions).
Here we can see the common descriptors for the sequence sets as well:
‘1’ for positive sequence component
‘2’ for negative sequence component
‘0’ for zero-sequence component.
Symmetrical Components courtesy of Charles ‘Chuck’ Fortescue (1918)…

12. The descriptions are quite simplified, and there are classes and books devoted entirely to this subject so a few slides is only enough time for the barest of introductions.
People new to the field should focus on just the ‘big picture’ view and more understanding will come with time and exposure.
In the context of this presentation, having a general grasp of these last few slides should suffice to help us get a fundamental grasp of ground-distance relaying.
Associated with ‘Normal’ conditions where we only have positive sequence. This diminishes when things go wrong.
Associated with ‘unbalance’, in any form. Does not exist when we are under ideal normal conditions.
Associated with ‘ground’, as in ground-faults. Does not exist when we are under ideal normal conditions.

13. Zone 2 Settings
If the impedance to the fault is 9.3683.97° Ohms secondary, and the reach of our relay based on our setting is the same value, then our relay is reaching right up to the fault and should operate.

14. ‘Per-Phase’ Values
Are just what they sound like: In this case, they are the values of impedance ‘per-phase’, as shown in the picture below.
Note that our Zone 1 reach is 80% of the line length and Zone 2 is 120% of the line length, and in our example relay, 100% of the line length is 7.8 ohms secondary (Z1MAG Setting).
If you need a reminder about converting ohms primary to secondary, or the converse, remember that Z = E/I and this also applies to the PTR and CTR to form an ‘impedance’ ratio. If the PTR=2000 and CTR=200, then Z = E/I = 2000/200 = 10. Thus, primary-secondary conversions for this position are a factor of 10; If Z > 1 then the primary impedance is greater than the secondary impedance. If the secondary impedance is 7.80 ohms, then the primary impedance is 78 ohms.
For advanced learners we should note on this slide that the ‘per-phase’ positive sequence impedance is a ‘three-phase’ value; if one were to measure the resistance and reactance of a single line conductor you would not get the results in our drawing. But when the line is energized and operated as a three-phase system and the phases are allowed to interact with each other you get the values reflected in our drawing above.

15. Ground-Distance Decisions
Fault current is limited by conductor impedance + ground impedance.
Relays ‘see’ an ‘incorrect’* ‘loop’ impedance to the fault location.
*Note that this statement is being made in regards to how the relay is set and is only partially true. This will become more clear as we move forward.
In this case, the voltage at Bus 1 and current through PCB-1 calculate to a ‘Z’ at the relay location of 16.1582.42° Ω.
Note that the distance to the fault is exactly the same as the fault is in the same location on the transmission line as it was before. But here we have a single-line-to-ground fault instead of a 3-phase fault. Also note that the Zone 2 Ground-Mho and Ground-Quadrilateral settings are exactly the same as the Zone 2 Phase-Mho setting: 9.3683.97° Ω.
We now also have some background for the term ‘loop impedance’.
It should be noted for the more advanced learners that the ‘ground impedance’ shown in drawings in this presentation is a simplified description used to promote a useful visual image. In reality, the ground return path does not include large amounts of reactance – that comes from the zero sequence impedance of the transmission line itself.

16. Ground-Distance Decisions
If the relay ‘sees’ an impedance of 16.1582.42°Ω, then the fault appears to be much farther away than it actually is on the transmission line.
How does the relay properly locate the fault?
Again, note that the fault location is in the exact same location on the transmission line. In our example, without some extra logic of some sort, the relay will miss the fault as it is seen as well beyond Zone 2.
It is also worth noting that relays are generally set based on the positive sequence line impedance because that directly translates to physical location(s) on the protected transmission line.

17. Zero Sequence Compensation
We factor out the ‘ground impedance’ using a ‘compensation factor’: KN
What does KN do for us?
First remember that for a ground fault a relay sees a combination of line impedance + ground impedance.
Compensation factors allow a relay to factor out the portion of impedance seen at the relay location that is the ground impedance.
This allows the relay to estimate the transmission line impedance to the fault location.
KN: sometimes called: Residual Compensation Factor, Current Compensation Factor, or variations of these.
Factoring out the portion of impedance seen at the relay location that is ground impedance leaves us (hopefully) with the positive sequence line impedance; this allows the relay to make logic decisions based on where the fault is at on the protected transmission line.

18. Ground-Distance Decisions
How does the relay properly locate the fault?
Relay ‘sees’ an impedance of 16.1582.42°Ω
Relay uses KN to factor out 6.8080.28°Ω of ground impedance.
Relay knows impedance to fault is 9.3683.97°Ω
Relay takes proper logical actions
Note that modern relays know when to use the compensation factor based on the type of fault. The compensation factor is not used when it is not needed (i.e. when the fault is not a ground fault). This is commonly done with some form of fault identification logic.

19. This table from Jun’s paper helps illustrate that compensation is not universally used in a single form.
The compensation formula varies – but fundamentally the formulas are fairly equivalent; notice they all have factors that compare zero sequence impedances to positive sequence impedances (Z0/Z1, etc.)
The exact names of the compensation factors also vary; since impedance is Z = E/I compensation can be in the current variable, the voltage variable, or made directly to Z. The end result is always to Z so we basically get to the same place regardless of how we get there.
The variables used to describe the compensation also vary; KN is just the most common.
Compensation factors are generally vectors (magnitude and direction) but in some cases are scalars (magnitude only).
Note that Jun also has a table (Table 2) that shows how to convert from one form of compensation to another.

20. How does this relay properly locate the fault?
This relay uses the settings highlighted on the right to make compensation calculations.
The first two are used for Zone 1 while the second two are used for other Zones.
From the SEL-321 Manual:
Here, we can see how Protection Engineers use electrical data about the transmission line (Z0 and Z1) to calculate the K0M/K0A settings. We can tell by the fact that compensation in this relay has a magnitude and angle that it is a vector.
Note that in this relay the ‘T’ setting is also used for ground impedance relaying but for our discussion it can be ignored and it is not important.

21. Ground-Mho Where did this test current come from?
Since relay manufacturers vary in their exact form of compensation we need the form specifically used by this relay:
ZAG = (VA / IA) / (1+k0)
ZPer-Phase = ZLoop / (1+k0)
Let’s look at how to use the compensation factor to test the ground-mho element in this relay. We’ll use Zone 2 again for our test point as well as an assumed test voltage of 40.4V; note that this principle works regardless of what test voltage is assumed.
Note that Equation 7.13 is a form of current compensation since the base formula Z=E/I has the current term modified by ‘1+k0’.
If we look modify Equation 7.13 we can see that the relay calculates Z (per-phase impedance) by taking the loop impedance (VA/IA) and dividing by the compensation factor ‘1+k0’. This knowledge is extremely useful in that we essentially have a conversion factor from per-phase impedance to loop impedance: 1+k0.

22. Ground-Mho How do we use this?
Using our knowledge that the loop impedance is the per-phase impedance times the compensation factor we can take the Zone 2 settings, multiply the compensation factor and our result is the relay reach for Zone 2. Let’s do it:
Zone 2 per-phase setting/reach is Z2MGZ1ANG°Ω
Z=9.3683.97°Ω
The compensation factor=1+k0 where k0=k0mk0A°
KN = -3.69° = 1.725-1.552°
ZLoop= 9.3683.97°Ω * 1.725-1.552° = 16.1582.42°Ω
Look familiar?
For testing impedance elements we typically use a given test voltage, apply current, and verify the value of current when the relay outputs an appropriate trip (Zone 2 Trip in this case). In this case our test voltage is 40.4V, so if we know the impedance the relay will pick up for we can calculate the current: I = E/Z.
This is a good time to note that for ground faults the relay essentially always ‘sees’ the loop impedance so relay technicians will always be interested in the loop impedance because that impedance dictates the raw values of voltage and current that the relay will respond to…

23. Ground-Distance Decisions
How does the relay properly locate the fault?
Relay ‘sees’ an impedance of 16.1582.42°Ω
Zloop / KN = Zper-phase
16.1582.42°Ω / ( -3.69° ) = 9.3683.97°Ω
Relay knows impedance to fault is 9.3683.97°Ω
Relay takes proper logical actions
- Relay uses KN to factor out 6.8080.28°Ω of zero sequence impedance
Back to this slide if we replace the bullet that previously said: Relay uses Kn to factor out 6.8080.28°Ω of ground impedance with the actual calculation above things should be looking clearer…
Note that we’ve slightly altered some of our descriptive text on our drawing to increase accuracy now that we are cementing our fundamental ideas.

24. Ground-Distance Graphical Analysis
Here we see:
ZPh = the per-phase impedance:
Z=9.3683.97°Ω
ZKN = the compensated impedance:
Z=6.8080.28°Ω
KN = -3.69° = 1.725-1.552°
ZLp = the loop impedance:
Z=16.1582.42°Ω
Note that the relay response is defined by the Loop impedance…
Let’s replace our drawing of line and ground impedance on our last slide with a great visual depiction. In our example we were looking at a Ground-Mho characteristic.
Note that the angle differences in this drawing have been exaggerated to enhance the concept. Also note that KN is a ‘factor’, not a straight impedance.

25. Ground-Distance Graphical Analysis
Any point on the per-phase characteristic can be translated to an equivalent point on the loop characteristic.
Any per-phase impedance multiplied by the compensation factor gives the equivalent loop impedance.
Here we’ve added a graphic from Jun’s paper that is very informative.
In this particular relay and this vendor’s implementation the ground-mho is fairly straightforward.
We’ll see next that the ground-quadrilateral characteristic is slightly more complex…

26. Ground Quadrilateral Key Ground-Quadrilateral Settings:
XG2 = ‘Reactive’* reach of the quadrilateral element.
Z=9.3683.97°Ω
RG2 = Resistive reach of the quadrilateral element.
Z=5.000°Ω
*Note that in this relay one might assume that the ‘XGx’ setting is truly reactive – a magnitude at 90 degrees. In actuality, for this vendor the setting is at the line angle. It is this type of detail that Protection Engineers and Relay Technicians must be aware of for proper relay performance.
The picture on this slide is from SEL’s Application Guidelines for Ground Fault Protection, by Joe Mooney and Jackie Peer.

27. Ground Quadrilateral XG2 RG2
This slide comes from Jun’s paper, and shows how the quadrilateral element has similar per-phase and loop impedance characteristics.
The big difference for this particular vendor/characteristic is that the resistive reach is constant. For this relay the left resistive blinder is also equal to RG2. The bottom of the characteristic for this vendor is defined by a directional element.
RG2

28. Ground Quadrilateral XG2 RG2
This slide also comes from Jun’s paper, and shows how translating between per-phase and loop impedance planes must be done (for this specific relay).
With no resistance our fundamental rule we used on them Mho element also applies here. But when resistance is added we must modify our translation for this specific relay; we must subtract any per-phase resistance until we ‘hit’ the per-phase impedance at the line angle, then multiply by our compensation factor, then add the resistance back into the loop plane.
It is also worth noting that at zero degrees the loop and per-phase resistances are the same: the reach is 5 ohms.
For those wondering about the ‘T’ setting still it is a setting that tilts the reactive (top) line of this relay when source impedances at each of the line ends have different impedance angles.
What this mainly means to relay technicians who might have to test this relay is that some additional math/trig is involved when calculating test points to account for the top line not being parallel with the x-axis. But a tester needs to have good trig skills to test ‘polygon’ characteristics from most vendors.
For those who might think it looks like you should not have to do all the addition/subtraction with the resistance and should be able to just go back and forth between the two characteristics by just using the compensation factor, one point makes it clear that won’t work: the reach at 0° is the same for both characteristics. Using the method above shows they come to the same value. Using the compensation factor alone gives two different points.
RG2

29. Ground Quadrilateral Z2MG XG2 RG2
Before we move on to testing, it is worth considering that in this relay, with the settings we have for our example, the relay reach at the line angle is exactly the same for both the mho and quadrilateral ground characteristics in both the per-phase and loop impedance planes respectively…
We should also pause to note a given utility may opt to use either or both of these characteristics if they choose to enable ground-impedance relaying.
When both are enabled, they essentially run in parallel; we can see areas that one covers that the other does not; the end result is a combined characteristic where tripping will occur when the impedance seen by the relay enters either characteristic.
RG2

30. Testing Ground-Distance Relays
Review:
Relays must make decisions based on the voltage and current at the relay location.
Raw relay response to ground-impedance functions happens in the loop-impedance plane.
The relay has to factor out the zero-sequence impedance to calculate a fault position on the protected line.
Testing:
Essentially happens in the loop-impedance plane.
Once a test voltage is determined, one divides the loop impedance to calculate the test current for the impedance point being tested.

31. Calculating Test Quantities
Ground-Mho Characteristic:
Test voltage = 300°V
What is our test current at:
The Line Angle?
Line Angle = 16.1582.42°Ω
I = E / Z = 300°V / 16.1582.42°Ω
I = 1.86-82.42°A
At 45°?
= 16.15Ω * COS(82.42°-45°) = 12.83Ω
I = E/Z = 300°V / 12.8345°Ω
I = 2.34-45°A
At 90°?
= 16.15Ω * COS(82.42°-90°) = 16.01Ω
I = E/Z = 300°V / 16.0190°Ω
I = 1.87-90°A
Hint: ZR = ZMAX * COS(MTA-θ)
Given our example settings, let’s calculate a few test points:
Note on hint: when converting between points on a mho circle we use this formula: ZR = ZMAX * COS(MTA-θ)
Reach is equal to the maximum reach of the circle (its diameter from the origin) * the Cosine of the angle you are interested in subtracted from the maximum torque angle, which is still the diameter of the circle from the origin.
This roughly translates to taking the farthest point on the circle, which is always its diameter, and multiplying by an appropriate number that is always less than one; our reach is always less at any point not the MTA/Diameter and the cosine function gives us that ratio.

32. Interpreting Test Results
Examine how your results are reported:
Note here how the test results appear to have an inconsistency:
The fault voltage is 45.03V, and if we look at the test current where the relay picked up we see a value of 5.52A.
Z = E / I = 45.03V / 5.52A = 8.16Ω
But if we look at the results, we see that the test software reports the pickup as 4.393Ω and the expected value as 4.345Ω…???
You can probably guess at this point in our discussion that the relay is actually responding to the loop impedance. But the expected results are in per-phase values. This can be confusing to someone testing the relay because the values the relay are responding to do not align with the numbers being reported…
Let’s see on the next slide some more detail…

33. Interpreting Test Results
Note here how this test program has a worksheet function that lets the user select the compensation factor. Also note that it has a pulldown field that lets the user select from multiple compensation factors so multiple vendors are covered.
What we want to take away here is that the test software has been programmed to report results in per-phase values.
Why? Because those values directly relate to the settings on the relay.
Some test software just reports the results and compares them to an expected current value. This is fine but it makes it harder to interpret the test result aligns with the relay settings. It is worth a ‘spot check’ here and there when time allows to confirm the results are correct, especially if you are given test software setup by someone else…

34. Calculating Test Quantities
Ground-Quad Characteristic:
Test voltage = 300°V
What is our test current at:
The Line Angle?
Line Angle = 16.1582.42°Ω
I = E / Z = 300°V / 16.1582.42°Ω
I = 1.86-82.42°A
At 90°?
= ‘y’ component of: 16.1582.42°Ω
16.1582.42°Ω = ( j16.01)Ω; y = 16.01Ω
I = E/Z = 300°V / 16.0190°Ω
I = 1.87-90°A
Given our example settings, let’s calculate a few test points on the quadrilateral characteristic:
Graphic from Jun’s paper.

35. Calculating Test Quantities
Ground-Quad Characteristic:
Test voltage = 300°V
What is our test current at:
At 0°?
= 5Ω
I = E/Z = 300°V / 50°Ω
I = 60°A
At Top Right Corner of Quad?
= 16.1582.42°Ω + 50°Ω = 17.5265.99°Ω
I = E/Z = 300°V / 17.5265.99°Ω
I = 1.71-65.99°A
Basic geometry and trig functions help us find the major edges/corners of our quadrilateral element.

36. Calculating Test Quantities
Ground-Quad Characteristic:
Test voltage = 300°V
What is our test current at:
A point in the per-phase plane:
ZP1 = 4.6260°Ω?
ZP1 = 4.6260°Ω = j4.00Ω
Z1´X = Tan( )°*4.00 = 0.422Ω
Z1´ = j4.00Ω = 4.02283.97°Ω
Z1´´ = Z1´*KN = 83.97°Ω * 1.725-1.552°
KN = -3.69° = 1.725-1.552°
Z1´´ = 6.9482.42°Ω = j6.88Ω
ZL1 = Z1 ´´+ ( j0)Ω = j6.88Ω = 7.4367.82°Ω
I = E/Z = 300°V / 7.4367.82°Ω
I = 4.04-67.82°A
Brain Teaser, time permitting… This is fairly complicated and if you can handle this problem then you have a solid understanding of this topic.
In Summary:
Find ‘y’ or ‘j’ component of point in question (ZP1).
Find this point on the per-phase Z1 setting impedance. Solve for the ‘x’ component of this phasor at the line angle (Z1’X).
Subtract the original phasor in question ‘x’ component from the per-phase setting ‘x’ component to determine the amount to add back in after finding the equivalent loop impedance ( =1.89Ω)
Multiply the per-phase setting impedance (Z1’) by KN to get equivalent loop impedance (Z1’’)
Add the calculated ‘x’ component back into the calculated loop impedance to get the final loop impedance equivalent (Z1’’+(1.89+j0)Ω)
Test voltage divided by final loop impedance determines expected current.

37. Some Test Considerations
When testing ground-impedance elements one should consider how variances in test quantities and relay performance can affect test results.
Consider the red arrow above, where we are testing the relay reach at the line angle with a static test voltage. If the relay and/or test set angle are off by a small amount in either direction the current (and associated impedance) where the relay picks up varies by an extremely small (practically unnoticeable) amount.
If look at the green arrow, we can see the difference in a few degrees presents more potential error; slightly left and we get a higher impedance, while slightly right we get a lower impedance.
Base graphic from SEL paper by Joe Mooney / Jackie Peer (Figure 5).

38. Some Test Considerations
The Quadrilateral characteristic can present even more challenges.
With the red arrow above, testing the relay reach at the line angle gives similar results to the Ground-Mho characteristic if the relay/test equipment are slightly off.
The green arrow at the top right corner of the quadrilateral element presents more room for error if angles are slightly off since on either side of the corner the impedance lines rapidly recede from the corner point. To truly catch the corner one suggested method is to set test voltage and current, then ‘swing’ the impedance phasor around the corner. Repeat with slightly varying impedances (usually alter the current slightly) and at some point you will determine your maximum reach when you no longer ‘hit’ the corner as you swing the impedance around the corner angle.
The orange line in the fourth quadrant presents special challenges. A tester might want to test for the corner point, or verify the directional angle of the characteristic boundary. If the relay and/or test set angle are off by a small amount in the direction of the teal line a tester might get great results.
But consider if the test set or relay are off in the direction of the purple line. This test will almost certainly fail if a tester has set test angles and is ramping voltage or current magnitude. The test impedance can be greatly reduced and still not hit the characteristic.
This is an inherent problem in testing any characteristic boundary that passes through (or originates from) the origin.
For this test, one could just alter the angle slightly to ensure you do not end up ‘outside’ the characteristic line, or purposefully start outside the line and again ‘swing’ into the line. A combination of angle rotation and varying impedance can still determine the exact corner of the characteristic if desired.
Base graphic from SEL paper by Joe Mooney / Jackie Peer (Figure 4).

39. Synopsis - Fundamentals
Relays make decisions based on voltage and current at the relay location.
Relays are generally set in terms of ‘per-phase’ impedance.
For ground faults relays respond to ‘loop’ impedance.
Relays are tested in the loop impedance plane.
A Compensation Factor (KN) is used to factor out zero sequence impedance to allow a relay to make a fault location decision based on the per-phase settings.
Relay manufacturers use a variety of forms of compensation but their fundamental application is the same.
Relay test software may need interpretation to resolve discrepancies between raw values of voltage and current and per-phase settings.
Based on location of PT’s and CT’s.
Note some manufacturers have some settings in per-phase but others in loop values. Look for descriptors that show this.
Based on raw values of voltage and current at the relay location that the relay responds to.
It is extremely important that for a given relay the exact form of compensation is found and understood.
Technicians should strive to understand the details of automated test routines to avoid falling into the ‘pass/fail’ trap. This is especially important when things do not go as planned. Manual testing fundamentals can help one make a quick determination of whether a failed test is due to an actual relay failure (generally low likelihood) or a test routine/hookup problem (generally high likelihood).

40. Thanks for your time!
Please provide feedback to the school on this presentation and its content. 