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Ground-Distance Concepts
for Relay Technicians
Steve Laslo
System Protection and Control Specialist
Bonneville Power Administration
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Special Thanks
Quintin ‘Jun’ Verzosa Jr.
Doble Engineering Company
Schweitzer Engineering Laboratories, Inc.
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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.
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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.
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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.
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Protection Key Concept
• Relays make impedance calculations based on the
values of voltage and current at the relay location.
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Phase-Distance Decisions
• Fault current is limited by the line impedance.
• Relays ‘see’ the correct impedance to the fault
location.
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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∠-203.97°A, IC = 4.32∠36.03°A
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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.
- 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…
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Associated with ‘Normal’
conditions where we only
have positive sequence.
This diminishes when
things go wrong.
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Associated with
‘unbalance’, in any form.
Does not exist when we
are under ideal normal
conditions.
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Associated with ‘ground’,
as in ground-faults. Does
not exist when we are
under ideal normal
conditions.
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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.
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‘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.
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Ground-Distance Decisions
• Fault current is limited by conductor
impedance + ground impedance.
• Relays ‘see’ an ‘incorrect’* ‘loop’ impedance
to the fault location.
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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?
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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.
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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
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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:
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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)
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Ground-Mho
• How do we use this?
– Using our knowledge that the loop impedance is the perphase 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 = 1 + 0.726∠-3.69° = 1.725∠-1.552°
• ZLoop= 9.36∠83.97°Ω * 1.725∠-1.552° = 16.15∠82.42°Ω
• Look familiar?
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Ground-Distance Decisions
• How does the relay properly locate the fault?
– Relay ‘sees’ an impedance of 16.15∠82.42°Ω
factor out 6.80∠80.28°Ω of zero
–- Relay
Zloop /uses
KN =KNZto
per-phase
• 16.15∠82.42°Ω
sequence
impedance/ (1+ 0.726∠-3.69° ) = 9.36∠83.97°Ω
– Relay knows impedance to fault is 9.36∠83.97°Ω
– Relay takes proper logical actions
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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 = 1 + 0.726∠-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…
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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.
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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
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Ground Quadrilateral
XG2
RG2
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Ground Quadrilateral
XG2
RG2
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Ground Quadrilateral
Z2MG
XG2
RG2
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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.
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Calculating Test Quantities
• Ground-Mho Characteristic:
– Test voltage = 30∠0°V
• What is our test current at:
– The Line Angle?
• Z@ 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°?
• Z@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°?
• Z@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)
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Interpreting Test Results
• Examine how your results are reported:
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Interpreting Test Results
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Calculating Test Quantities
• Ground-Quad Characteristic:
– Test voltage = 30∠0°V
• What is our test current at:
– The Line Angle?
• Z@ 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°?
• Z@90° = ‘y’ component of: 16.15∠82.42°Ω
– 16.15∠82.42°Ω = (2.13 + j16.01)Ω; y = 16.01Ω
• I = E/Z = 30∠0°V / 16.01∠90°Ω
• I = 1.87∠-90°A
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Calculating Test Quantities
• Ground-Quad Characteristic:
– Test voltage = 30∠0°V
• What is our test current at:
– At 0°?
• Z@0° = 5Ω
• I = E/Z = 30∠0°V / 5∠0°Ω
• I = 6∠0°A
– At Top Right Corner of Quad?
• Z@TRC = 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
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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 = 2.31 + j4.00Ω
Z1´X = Tan(90-83.97)°*4.00 = 0.422Ω
Z1´ = 0.422 + j4.00Ω = 4.022∠83.97°Ω
Z1´´ = Z1´*KN = 4.022∠83.97°Ω * 1.725∠-1.552°
– KN = 1 + 0.726∠-3.69° = 1.725∠-1.552°
– Z1´´ = 6.94∠82.42°Ω = 0.915 + j6.88Ω
• ZL1 = Z1 ´´+ (1.89 + j0)Ω = 2.80 + j6.88Ω = 7.43∠67.82°Ω
• I = E/Z = 30∠0°V / 7.43∠67.82°Ω
• I = 4.04∠-67.82°A
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Some Test Considerations
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Some Test Considerations
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Synopsis - Fundamentals
1. Relays make decisions based on voltage and current at the
relay location.
2. Relays are generally set in terms of ‘per-phase’ impedance.
3. For ground faults relays respond to ‘loop’ impedance.
–
Relays are tested in the loop impedance plane.
4. 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.
5. Relay test software may need interpretation to resolve
discrepancies between raw values of voltage and current and
per-phase settings.
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Thanks for your time!
Please provide feedback to the school
on this presentation and its content.
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