Journal of Reliable Power - SEL

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Journal of Reliable Power 

Volume 1 Number 1 July 2010

Schweitzer Engineering Laboratories, Inc. 

2350 NE Hopkins Court 

Pullman, WA 99163 

Copyright ©2010 Schweitzer Engineering Laboratories, Inc. All rights reserved.

Journal of Reliable Power Volume 1 Number 1 July 2010 

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Introduction 

Distance Relay Element Design 

E. O. Schweitzer, III and J. B. Roberts (1993) 

Impedance-Based Fault Location Experience 

K. Zimmerman and D. Costello (2004) 

Digital Communications for Power System Protection: Security, Availability, and Speed 

E. O. Schweitzer, III, K. Behrendt, and T. Lee (1998) 

Transmission Line Protection System for Increasing Power System Requirements 

A. Guzmán, J. Mooney, G. Benmouyal, and N. Fischer (2001) 

Lessons Learned Analyzing Transmission Faults 

D. Costello (2007) 

Adaptive Phase and Ground Quadrilateral Distance Elements 

F. Calero, A. Guzmán, and G. Benmouyal (2009) 

Line Protection Bibliography 

SEL University 2010 Course Schedule 

July through December 

Modern Solutions for Protection, Control, and Monitoring of Electric Power Systems 

Ordering Information 

Issue Editors 

Bogdan Kasztenny is a principal systems engineer in the Research and Development Division of 

Schweitzer Engineering Laboratories, Inc. He has 20 years of experience in protection and control, 

including his ten-year academic career at Poland’s Wrocław University of Technology, Southern 

Illinois University, and Texas A&M University. He also has ten years of industrial experience with 

General Electric, where he developed, promoted, and supported many protection and control products. 

Bogdan is an IEEE Fellow, Senior Fulbright Fellow, Canadian member of CIGRE Study Committee 

B5, and an adjunct professor at the University of Western Ontario. He has authored about 200 technical 

papers and holds 16 patents. He is active in the IEEE Power System Relaying Committee and is a 

registered professional engineer in the province of Ontario. 

Karl Zimmerman is a senior power engineer with Schweitzer Engineering Laboratories, Inc. 

in Fairview Heights, Illinois. His work includes providing application and product support and 

technical training for protective relay users. He is an active member of the IEEE Power System 

Relaying Committee and chairman of the Working Group on Distance Element Response to 

Distorted Waveforms. Karl received his BSEE degree at the University of Illinois at Urbana- 

Champaign and has over 20 years of experience in system protection. He is a past speaker at many 

technical conferences and has authored over 20 papers and application guides on protective relaying.

Introduction 

With this inaugural issue, SEL introduces the 

Journal of Reliable Power. This regularly published 

journal will present a series of papers with lasting 

value that focuses on the fundamentals of power reliability. 

We believe that the concepts, case studies, technologies, 

and issues that the Journal covers will be applicable 

to power engineers working for utilities, industrial and 

commercial facilities, government, and academia. 

Each issue of the Journal will focus on a broad topic 

area or theme. The theme of this first issue, guest-edited 

by SEL Senior Power Engineer Karl Zimmerman and 

Principal Systems Engineer Bogdan Kasztenny, with the 

combined technical expertise of many SEL authors, is 

line distance protection, where SEL got its start. Future 

themes will include the application of digital communications 

in protection and control, distribution automation 

and protection (“smart grid”), communications for critical 

infrastructure, synchronous measurement and control, 

and advances in protection methods. The second issue, 

edited by SEL Senior Automation System Engineer Tim 

Tibbals, will focus on communications and protocols. We 

welcome your suggestions for topics as well. 

Several outstanding publications in the electric power 

industry today communicate important ideas, applications, 

successes, and trends through news articles, editorials, 

and success stories. Our goal is to complement 

these publications by sharing in-depth, conference-length 

papers in a journal format. 

The Journal is forward-looking. When we include an 

older paper, it will be a foundational classic, with concepts 

that are still applicable today. In many cases, these 

older papers will teach us new things as we read and apply 

them; the power system and the work we do have changed 

in ways that none of us could have anticipated. 

We hope that you find this first collection of papers 

centered around line protection relevant to you and the 

work you do to make electric power safer, more reliable, 

and more economical. 

*** 

Microprocessor-based relay technology became possible 

more than 25 years ago, owing to a perfect 

combination of available, suitable microprocessors and 

advancements in industrial electronics more generally; 

the opportunity to provide new functions far beyond what 

was possible within the electromechanical and static technologies; 

remarkable size and cost reductions; and the 

imagination, skills, and perseverance of early inventors in 

this new field. 

Early designs, although limited by available processing 

power, integrated a wealth of new functions, ranging 

from sequential events recording and fault location to 

metering, multiple settings groups, and communications. 

Once digital relays proved reliable in the eyes of the 

power system protection community, and as the dramatic 

cost reduction compared to previous technologies became 

evident, the digital relay revolution only accelerated. It 

became increasingly obvious that analog technology, in 

addition to being more expensive, could not provide new 

functions, self-monitoring, reliability, innovative operating 

principles, and other facets of protection performance 

made possible through microprocessor-based technology. 

Early microprocessor-based protective relays brought 

innovation in line protection principles as well as digital 

implementation of the existing art of distance protection. 

Constrained by the available processing power and 

facing the disadvantage of a nonzero processing latency, 

designers strived for increased response time of their 

algorithms while optimizing the computational power 

required. Applying the cosine filter and shaping distance 

characteristics via “m calculations” are good examples 

of smart design that delivered good performance under 

the limitations of early microprocessor-based relay platforms. 

“Distance Relay Element Design,” written in 1993 

and included in this issue of the Journal, is a foundational 

paper for SEL microprocessor-based distance protection. 

One cannot overlook the role that fault location played 

in the industry’s adoption of the new technology. This 

useful and “safer”—compared with the full protection 

package—function opened the door for new technology 

(SEL-21 and SEL-121 Distance Relay and Fault Locator 

products). In the 1980s, early applications of relays 

working as fault locators demonstrated hardware and software 

reliability and delivered solid, useful, and verifiable 

information to early adopters. “Impedance-Based Fault 

Location Experience” summarizes the almost 25 years of 

advancements in fault location at the time it was written 

in 2004. 

2 | Journal of Reliable Power

Capable of running protection calculations with latencies 

low enough for line protection, microprocessor-based 

relays allowed designers to take full advantage of the flexibility 

of digital implementations. Building protection elements 

by calculating signature signals and freely applying 

comparators, logic, and timers, designers were no longer 

constrained by analog means; they could truly innovate 

by going back to first principles and using these principles 

to devise new and powerful protection elements. Positivesequence 

voltage memory to maintain distance element 

security during close-in faults, advancements in digital filtering, 

a negative-sequence impedance ground directional 

element, load-encroachment logic, and fault identification 

selection logic are among the many innovations introduced 

in the early 1990s as part of the SEL-321 Relay. 

Ability to communicate was an inherent advantage 

of microprocessor-based relays from the very beginning. 

Communication started with users accessing and manipulating 

settings, records, and online measurements but 

quickly progressed into serving data to SCADA systems 

and peer-to-peer devices. Invention of Mirrored Bits ® 

communications—fast, reliable, and dependable protection-grade 

communications—opened a new chapter of 

digital teleprotection signaling for line protection. (See 

“Digital Communications for Power System Protection: 

Security, Availability, and Speed” in this issue.) 

The last decade brought considerable advances in 

distance protection. Higher sampling rates and increased 

processing power opened the door to sophisticated protection 

principles and enhancements. Improvements in security 

and speed of distance protection have been achieved 

through a combination of CVT transient detection under 

high SIR conditions and usage of incremental quantities 

while applying optimized, faster, short-window filters. 

Fault type identification logic now performs better under 

weak infeed conditions. Adaptive polarizing algorithms 

maintain the best possible choice of polarization while 

releasing the user from making tradeoffs and running 

detailed engineering studies to aid setting selection. Protection 

issues related to series compensation of transmission 

lines have been addressed as well. Frequency tracking 

of modern relays allows applications under stressed 

system conditions when frequency excursions and rate of 

change of frequency jeopardize some traditional concepts, 

such as memory polarization. “Transmission Line Protection 

System for Increasing Power System Requirements” 

gives an excellent overview of these advancements. 

The SEL-421 Protection, Automation, and Control 

System, developed in 2001, incorporates all of these 

enhancements while including a truly impressive set of 

functions that complement its core protection functionality. 

Examples are high-resolution digital fault recording, 

sequential events recording, and synchrophasor measurements, 

all with submicrosecond accuracy, a wealth of 

both peer-to-peer and SCADA communications protocols, 

metering functions, advanced programmable protection 

and automation logic, two CT sets of inputs for dualbreaker 

line terminals with associated protection, and 

automation functions. These are functions that we all take 

for granted today. 

Looking back, the ability to provide data for postevent 

analysis turned out to be one of the major benefits 

of microprocessor-based relays. “Lessons Learned Analyzing 

Transmission Line Faults” provides an overview of 

how data produced by modern relays aid troubleshooting 

and improve our understanding of the power system. 

Innovations in line protection are ongoing. Examples 

include improved power swing detection based on the rate 

of change of the swing center voltage and better resistive 

coverage of distance functions through an adaptive quadrilateral 

characteristic. (See “Adaptive Phase and Ground 

Quadrilateral Distance Elements” in this issue.) 

The journey that started a quarter of a century ago 

continues. Today, we use precise timing to align and timetag 

measurements. We use high-speed communications 

to share data in real time to improve protection and automation 

functions. And, we use more powerful processors 

to efficiently run increasingly more sophisticated algorithms. 

The opportunity that technology created 25 years 

ago is still here. It is only the laws of physics and our own 

imaginations that bound us today. 

If you have comments or suggestions, please e-mail 

journal@selinc.com or share your thoughts with our editors 

by phone at +1.509.332.1890. 

Introduction | 3

Distance Relay Element Design 

Edmund O. Schweitzer, III and Jeff B. Roberts, Schweitzer Engineering Laboratories, Inc. 

I. INTRODUCTION 

All distance relays compare voltages and currents to create 

impedance-plane and directional characteristics. Electromechanical 

relays do so by developing torques. Most staticanalog 

implementations use coincidence-timing techniques. 

Numerical techniques are the newest way to implement 

distance and directional relay elements. These relays use 

torque-like products and other methods to accomplish their 

operating characteristics. How do these new techniques relate 

to the classical electromechanical and static phase-angle 

comparators 

This paper presents basic distance and directional element 

design. A large emphasis is placed on relating the newer 

digital and numerical methods to the established electromechanical 

and static-analog methods of designing relay 

elements. 

In addition, we discuss: 

• A new method for characterizing distance elements; 

i.e., equations for mapping points on a relay 

characteristic onto a single point on a number line. 

• How multi-input comparators can be viewed as a 

family of two-input comparators. 

• Which characteristics result from various 

combinations of comparator inputs. 

• Classical element-security problems and remedies. 

• A new negative-sequence directional element. 

• A different approach to the load-encroachment 

problem. 

Finally, we point out a problem with fault-type selection 

logic which uses the angle between the negative- and zerosequence 

currents. It can select the wrong phase for certain 

resistive line-line-ground faults. We present a solution to this 

problem which compares ground and phase fault-resistance 

estimates. 

II. PHASE ANGLE COMPARATORS 

Phase angle comparators test the angle between various 

voltage and current combinations to produce directional, 

reactance, mho, and other characteristics. 

This section describes three technologies frequently used to 

compare phasors in relays: induction cylinders, coincidence 

timers, and digital multiplication. It also presents a new 

method: mapping of a characteristic (e.g., a mho circle) onto a 

point on a number line. 

A. Induction Cylinder Phase Comparator 

Figure 1 is a sketch of an induction cylinder comparator. 

Assume currents A and B flow in the windings as shown. The 

cup tends to rotate in the direction of the rotating flux 

established by the currents. For example, if B leads A, the cup 

rotates clockwise to close the contacts. If A and B are in 

phase, the net torque is zero and the cup does not move. This 

is the only external information available from the relay; 

either the contacts are open or closed. 

The equation for the cup torque, T, is: 

T = k •│A│•│B│• sin Θ, 

where Θ is the angle between A and B. External circuitry and 

the coils themselves can be used to modify the torque equation 

to test other phase relationships. 

Figure 1: 

Induction Cylinder Comparator 

B. Digital Product Phase Comparator 

We can easily emulate the behavior of the induction cup 

element using a computer as part of a digital relay. Given 

phasors A and B, consider the following complex product: 

S = A • B* 

= (Ax + j • Ay) • (Bx – j • By) 

= Ax • Bx + Ay • By + j • (Ay • Bx – Ax • By) 

( * = complex conjugate) 

The angle of the product A • B* is the same as the angle of 

A/B, and is the angle by which A leads B. 

Without loss of generality, assume our phase reference is 

B, and phasor A leads phasor B by angle Θ. In this frame of 

reference, 

Bx = │B│ By = 0 

Ax = │A│• cos Θ Ay = │A│• sin Θ 

and, 

S = │A│•│B│• cos Θ + j•│A│•│B│• sin Θ 

Separate the real and imaginary parts of S = P + j • Q = 

A • B*: 

P = │A│•│B│• cos Θ 

Q = │A│•│B│• sin Θ 


Both P and Q are two-input phase angle comparators. The 

P-comparator has a maximum “torque” when A and B are in 

phase. The Q-comparator has maximum torque when the two 

inputs are in quadrature. The Q-comparator is essentially the 

same as the induction cylinder with current inputs. 

In digital relays, it is easy to save the torques (P, Q). We 

can use the sign of the result (analogous to the cup rotation 

direction) as well as the magnitudes for tests involving fault 

type, sensitivity, etc. 

C. Coincidence-Timing Two-Input Phase Comparator 

To test the phase angle between sinusoids a and b, we can 

first convert a and b to square waves to derive signals A and 

B. The time coincidence of A and B is shown in Figure 2. 

We need to test the angle between δV and V p . When the 

angle is 90°, the relationship between δV and V p is any point 

on the circle, as shown in Figure 3. 

IX 

r • Z • I 

V = r • Z • I – V 

V 

Vpol 

a 

A 

Characteristic 

Timer, T 

IR 

AND 

T 

Output y 

b 

B 

Figure 3: Mho Element Derivation 

Figure 2: 

Coincidence-Timing Two-Input Comparator Logic 

One advantage of this comparator is the characteristic timer 

setting T controls the phase angle of coincidence required to 

obtain an output y, so we can easily synthesize mho, 

lenticular, and tomato characteristics. 

D. Application of Digital Product Phase Comparator 

A mho element tests the angle between a line-dropcompensated 

voltage and a polarizing or reference voltage. 

Let δV = (r • Z • I – V), where δV is the line-drop 

compensated voltage 

Z = replica line impedance 

r = per-unit reach in terms of the replica impedance 

I = measured current 

V = measured voltage 

V p = polarizing voltage. 

Let us test δV and V p using a digital product comparator. 

Which one should we use—sine or cosine Since balance (or 

zero torque) is at 90°, we need to use the cosine comparator, 

because cos 90° = 0. 

Let P = Re[δV • Vp*] 

Then: P > 0 represents the area inside the circle of reach 

r • Z 

P = 0 represents the circle itself 

P < 0 represents the area outside the circle of reach 

r • Z 

(Re = real portion) 

E. Characteristic-Mapping Approach 

Traditionally, one comparator is required for each zone, 

and for each voltage and current input combination. We can 

achieve significant economy in processing with no loss in 

performance by mapping the points on any mho circle of reach 

r onto a unique point on a number line. 

Recall the mho comparator, P: 

P = Re[δV • V p *] 

= Re[(r • Z • I – V) • V p *] 

For any V, I, V p combination on a circle of reach r, P is 

zero. This condition of balance is: 

0 = Re[(r • Z • I – V) • V p *] 

Solving for r yields in an equation which is the reach of the 

mho circle corresponding to the condition of balance: 

* 

Re ( V • Vp 

) 

r = 

(1) 

* 

Re ⎡Z • I • V ⎤ 

⎣ p ⎦ 

Distance Relay Element Design | 5

Observations: 

1. Equation 1 maps all the points on any mho circle 

of reach r onto a single point on the number line. If 

we need four mho circles, we no longer require 

four comparators. Instead, we simply need four 

tests of the calculated r. 

For example, a Zone 1 mho circle test might test r 

against 0.85, which represents a reach of 85%. 

Figure 4 illustrates mapping of mho circles into 

points for a four zone relay. 

2. Because V could be zero, we cannot rely on the 

sign of r to reliably indicate direction. Fortunately, 

the denominator of the r-equation is a directional 

element because it tests the angle between a 

voltage and a current. The sign of the denominator 

reliably indicates fault direction. 

The answer is simply the intersection of three two-input 

comparator characteristics, using pairs (X,Y), (Y,Z), and 

(Z,X). This arrangement is shown in the bottom of Figure 5. 

Refer to the coincidence timing diagram shown in the 

middle of Figure 5. Assume signals X and Y are slightly less 

than 90° apart, so we barely produce an output if X and Y 

were the only two inputs. Input Z does not interfere with the 

output as long as its leading edge is between the leading edges 

of X and Y. (Assuming all pulses are 180° wide, we need not 

make the parallel argument about the trailing edges.) 

The first condition is X and Y overlap by at least 90°. The 

two-input comparator XY represents this condition. The 

second condition is that the leading edge of Z lies between the 

leading edges of X and Y. The ZX condition ensures that Z is 

within ±90° of X. The YZ condition ensures that Z is within 

±90° of Y. 

If Z leads X, then we lose the YZ output. If Z lags Y then 

we lose the ZX output. Therefore Z must be between X and Y, 

which is the same condition we noted for the three-input 

comparator. 

X 

Y 

Z 

90° 

0° 

Output T 

X 

Y 

Z 

X 

Y 

90° 

90° 

Figure 4: 

Each Mho Circle Maps Onto a Point on the M-Line 

Y 

Z 

90° 

90° 

T 

III. MULTIPLE-INPUT COMPARATORS ARE REALLY A 

FAMILY OF TWO-INPUT COMPARATORS 

Multi-input comparators are widely used in distance relays. 

These comparators can be easily understood by representing 

them as several two-input comparators. 

The top of Figure 5 shows a three-input comparator. If 

inputs X, Y, and Z overlap by at least 90°, then output T 

asserts. 

What characteristic does a multiple-input comparator 

provide 

Z 

X 

90° 

90° 

Figure 5: Coincidence-Timing Multi-Input Logic 

IV. A QUICK REVIEW OF MHO ELEMENT 

POLARIZING CHOICES 

Mho elements compare the angle between (Z • I – V) and 

V p . There are many choices for the polarizing voltage, V p . 

Table 1 reviews some of them. 


TABLE 1: 

MHO ELEMENT POLARIZING CHOICES 

Operating Polarizing Characteristic General Comments 

(Z • I bc – V bc ) V bc 

(self pol.) 

• No expansion 

• Unreliable for zero-voltage faults. 

• Directionally insecure for reverse bus faults 

during high load. Requires additional 

directional element. 

(Z • I bc – V bc ) –j • V a 

(cross pol. 

w/o memory) 

• Good expansion for φ–φ faults. 

• Unreliable for zero-voltage 3φ faults. 

• Reverse bus fault security problems during 

high load periods. Requires additional 


(Z • I bc – V bc ) –j • V a,mem 

(cross pol. 

w/ memory) 

(Z • I bc – V bc ) –j • V a1mem 

(pos.-seq. 

mem. pol.) 

[Z • (I) –V a ] 

I = I a + k • I r 

V a 

(self pol.) 

• Good expansion for phase faults. 

• Reliable operation for zero-voltage 3φ faults. 

• Rev. φ–φ bus fault security problems during 



• Single-pole trip applications require study for 

pole-open security. 

• Greatest characteristic expansion for φ–φ and 

3φ faults. 

• Reliable operation for zero-voltage 3φ faults 

until pol. memory expires. 

• Rev. φ–φ bus fault security problems during 



• Best single-pole trip security. 

• No expansion. 

• Unreliable for zero voltage single-lineground 

faults. 

• Requires directional element. 

[Z • (I) –V a ] 

I = I a + k • I r 

j • V bc 

(cross pol.) 

• Good expansion. 

• Reliable operation reliable for zero-voltage 

single-line-ground faults. 

• Requires directional element. 

• Single-pole trip applications require study for 

pole-open security. 

[Z • (I) –V a ] 

I = I a + k • I r 

V a1mem 

(pos.-seq. 

mem. pol.) 

• Greatest expansion. 

• Reliable operation for zero-voltage ground 

faults. 

• Best single-pole trip security. 


The positive-sequence memory-polarized elements are 

generally preferred. The benefits include: 

• The greatest amount of expansion for improved 

resistive coverage. These elements always expand 

back to the source. 

• Memory action for all fault types. This is very 

important for close-in 3φ faults. 

• A common polarizing reference for all six distancemeasuring 

loops. This is important for single-pole 

tripping, during a pole-open period. 

V. CREATING QUADRILATERAL GROUND DISTANCE 

CHARACTERISTICS 

The quadrilateral characteristic requires four tests: 

• Reactance test (top line) 

• Positive and negative resistance tests (sides) 

• Directional test (bottom) 

A. Ground Distance Reactance Comparator 

A reactance element tests the angle between the line-drop 

compensated voltage and the polarizing current. 

Let δV = (r • Z • I – V), where δV is the line-drop 

compensated voltage 

Z1 = replica positive-sequence line impedance 

Z0 = replica zero-sequence line impedance 

r = per-unit reach in terms of the replica impedance 

I = phase current plus the residual current compensated 

by k = (Z0 – Z1)/3 • Z1 

V = measured voltage 

I p = polarizing current. 

We need to test the angle between δV and I p *. When the 

angle is 0°, the impedance is on the line shown in Figure 6. 

poor choices for the polarizing reference, because they make 

the reactance element severely under- or overreach, depending 

on the flow of load current. Negative-sequence or residual 

currents are appropriate polarizing choices. 

In some non-homogeneous system applications, the tip 

produced by I p may be insufficient to prevent overreach. To 

compensate, we can introduce an angle bias, or tip, to the 

reactance characteristic, or else reduce the reach of the Zone 1 

element. 

B. Ground Fault Directional Element 

Directional elements for ground fault must operate at fault 

current levels well-below the magnitude of load currents. 

Negative- and zero-sequence currents and voltages are mainly 

due to faults, and therefore are good choices for directional 

elements. 

System unbalance and measurement errors ultimately limit 

the sensitivity of directional elements based on negative- or 

zero-sequence components. 

Let V seq = measured sequence voltage (V 2 or V 0 ) 

I seq = measured sequence current (I 2 or I 0 ) 

Z = impedance whose angle adjusts I seq 

When the angle between –V seq and Z • I seq is 0°, the 

directional comparator has maximum torque. A basic 

negative-sequence implementation of this concept is shown in 

Figure 7. 

Figure 6: 

Ground Distance Reactance Element Derivation 

Again, using a digital product comparator, test the angle 

between δV and I p . The correct comparator to use is the sine 

comparator, since the balance point is 0°. 

Let Q = Im[δV • I p *]; (Im = imaginary portion) 

Then: Q < 0 represents the area above the line with reach 

r • X 

Q = 0 represents the line itself 

Q > 0 represents the area below the line of reach 

r • X 

This element must measure line reactance without adverse 

affects from fault resistance or load flow. Phase currents are 

Figure 7: Negative-Sequence Directional Element 

The cosine comparator gives a maximum output when the 

angle between the two inputs is zero degrees. 

Let P = Re[V seq • (Z • I seq )*]; 

Then: 

P < 0 represents the area above the zero-torque line 

(forward) 

P = 0 represents the zero torque line 

P > 0 represents the area below the zero-torque line 

(reverse) 

C. Resistance Tests 

Rather than using two separate comparators, we shall apply 

the digital-mapping method to calculate the apparent 

resistance and test it against left and right side resistance 

thresholds. 


For an Aφ-ground fault on the system in Figure 8, the Aφground 

voltage at Bus S is: 

V A = m • Z1L • (I AS + k 0 • I RS ) + R AF • I F (2) 

Where: 

V A = Aφ voltage measured at Bus S 

m = per-unit distance to the fault from Bus S 

R AF = Aφ fault resistance 

I F = total current flowing through R F 

I AS = Aφ current measured at Bus S 

I RS = residual current measured at Bus S (3I 0S ) 

Figure 8: 

System One-Line Diagram With SLG Fault 

The goal is to extract R AF from Equation 2. We must 

eliminate the line-drop voltage term, m • Z1L • (I AS + k 0 • I RS ), 

save the imaginary components, and solve for R AF . The result 

is: 

R 

Im ⎡ 

⎢ 

V • Z1L• I 

= 

⎣ 

( ( + k •I )) 

( ( + k •I )) 

A AS 0 RS 

AF * 

Im ⎡I F• Z1L• IAS 0 RS 

⎢⎣ 

The denominator contains I F , which includes fault and load 

current from both ends of the line. However, only Bus S 

currents are available to the relay at Bus S. We need to 

approximate I F in terms of Bus S current components. The 

approximation must be minimally system and load dependent. 

This last requirement permits setting the resistive thresholds 

with less concern that the resistive boundaries might be 

crossed under balanced load-flow conditions. 

Let I F = 3/2 • (I 2S + I 0S ), where I 2S and I 0S are the Bus S 

negative- and zero-sequence currents respectively. This 

current combination has all the available fault information, 

except the positive-sequence current (I 1 ). We specifically 

ignore I 1 because it is heavily influenced by load flow. 

Then: 

R 

= 

⎤ 

⎥⎦ 

⎤ 

⎥⎦ 

* 

⎡ 

A ( ( AS 

+ k 

0•I 

)) 

⎤ 

RS 

⎣⎢ 

⎥⎦ 

( + ) ( ( + )) 

Im V • Z1L• I 

AF 3 * 

Im ⎡ • I I • Z1L• I k •I 

2 2S 0S AS 0 RS 

⎢⎣ 

With this substitution, the fault resistance estimate of 

Equation 3 is independent of balanced load. The 3/2 scale 

factor accounts for the missing I 1 contribution and ensures R AF 

measures the true fault resistance on a radial system. Infeed 

from Bus R causes R AF to increase, because our substitution 

for I F does not include any measurement of current from 

Bus R. For example, if the impedances on either side of the 

fault are equal, R AF is half the actual fault resistance. 

This method provides an easy means of testing R AF for 

both the left and right sides of the quadrilateral element: 

calculate R and test the result against ±R thresholds for each 

zone. 

* 

⎤ 

⎥⎦ 

(3) 

For example, a Zone 1 resistive boundary might test R AF 

against ±2 Ω. If the result is 1 Ω, this satisfies the criteria set 

for the Zone 1 quadrilateral resistive checks. 

VI. MAINTAINING DIRECTIONAL SECURITY 

Directional security is paramount. At first glance, mho 

elements appear directional. However, some safeguards are 

required to ensure security. 

A. Ground Direction Security Concerns 

Reverse Ground Faults: The operating quantities for all 

ground distance elements include residual current. For 

example, the residual current produced by a reverse Aφ 

ground fault is also used in the phase-ground distance 

elements for B and C phases. The residual current can cause a 

forward-reaching Bφ or Cφ ground distance element to 

operate. We can avoid this problem by supervising the ground 

distance elements with a directional element, by a phaseselection 

comparator, or by introducing additional conditions 

in a multiple-input comparator. 

B. Selection of Directional Element Input Quantities 

Negative-sequence directional elements have notable 

advantages: 

• Insensitivity to zero-sequence mutual coupling. 

• There is generally more negative-sequence current 

than zero-sequence current for remote ground faults 

with high fault resistance. This allows higher 

sensitivity with reasonable and secure sensitivity 

thresholds. 

• Insensitivity to vt neutral shift, possibly caused by 

multiple grounds on the vt neutral. 

Perhaps the major disadvantage is negative-sequence 

elements are rendered useless when one or two poles of the 

breaker are open. 

C. Compensated Negative-Sequence Directional Element 

When the negative-sequence source behind the relay 

terminal is very strong, the negative-sequence voltage (V2) at 

the relay can be very low, especially for remote faults. 

To overcome low V2 magnitude, we can add a 

compensating quantity which boosts V2 by (α • ZL2 • I2). 

The constant α controls the amount of compensation. 

Equation 4 shows the torque equation for a compensated 

negative-sequence directional element. 

T32Q = Re[(V2 – α • ZL2 • I2) • (ZL2 • I2)*] (4) 

The term (α • ZL2 • I2) adds with V2 for forward faults, 

and subtracts for reverse faults. Setting α too large can make a 

reverse fault appear forward. This results when (α • ZL2 • I2) 

is greater but opposed to the measured V2 for reverse faults. 


D. Relationship of the Apparent Z2 to Fault Direction 

The sequence network for a ground fault at the relay bus is 

shown in Figure 9. The relay measures IS2 for forward faults, 

and –IR2 for reverse faults. 

ES 

Positive 

Sequence 

Negative 

Sequence 

Zero 

Sequence 

Figure 9: 

ZS1 

ES 

Relay 

ZL1 

ZS1 ZL1 ZR1 

ZR1 

IS2 

IR2 

V2 

ZS2 ZL2 ZR2 

ZS0 ZL0 ZR0 

RF 

Sequence Network for a Reverse Single-Line-Ground Fault 

From V2 and I2, calculate Z2: 

−V2 

Forward SLG Faults: Z2 = = − ZS2 

IS2 

−V2 

Reverse SLG Faults: Z2 = = ( ZL2 + ZR2) 

−IR2 

This relationship is shown in Figure 10 for a 90° system. 

S 

Reverse Fault 

ZS 

Reverse 

Forward 

RF 

Relay 

RF 

ZL 

Z2 Impedance Plane 

+X2 

Forward Fault 

ZS2 

ZR 

ZR2 + ZL2 

X2 = 0 

Figure 10: Measured Negative-Sequence Impedance Yields Direction 

For the system in Figure 10, the fault is forward if Z2 is 

negative, and reverse if Z2 is positive. 

ER 

R 

ER 

E. Negative-Sequence Directional Element Based on 

Calculating and Testing Z2 

The discussion above shows that calculated Z2 could be 

used to determine fault direction. 

Recall the compensated negative-sequence directional 

element equation, T32Q: 

T32Q = Re[(V2 – α • ZL2 • I2) • (ZL2 • I2)*] 

The forward/reverse balance condition for this element is 

zero torque. This is: 

0 = Re[(V2 – α • ZL2 • I2) • (ZL2 • I2)*] 

Let α = z2 

ZL2 = 1∠Θ where Θ is the angle of ZL2 

Substituting, 

0 = Re[(V2 – z2∠Θ I2) • (I2 • 1∠Θ)*] 

Solving for z2 results in an equation corresponding to the 

condition of zero-torque: 

Re[V2 • (I2 • I ∠Θ)*] 

z2 = 

Re[(I2 •1 ∠Θ) • (I2 •1 ∠Θ)*] 

Re[V2 • (I2 •1 ∠Θ)*] 

z2 = 

2 

I2 

Recall the (α • ZL2 • I2) term increases the amount of V2 

for directional calculations. This is equivalent to increasing 

the magnitude of the negative-sequence source behind the 

relay location. This same task is accomplished by increasing 

the forward z2 threshold. 

The criteria for declaring forward and reverse faults are 

then: 

If 

z2 < forward threshold, then the fault is forward 

z2 > reverse threshold, then the fault is reverse 

The forward threshold must be less than the reverse 

threshold to avoid any overlap. 

The z2 directional element has all of the benefits of both 

the traditional and compensated negative-sequence directional 

element. It also provides better visualization of how much 

compensation is secure and required. Set the for-ward and 

reverse impedance thresholds based upon the strongest source 

conditions. 

F. Phase-Phase Distance Element Security for Reverse 

Phase-Phase Faults 

Phase-phase distance elements use phase-phase currents. 

For example, a BC phase-phase distance element uses I BC or 

(I B – I C ). For a close-in reverse CA fault, the Cφ current can 

cause operation of the forward-reaching BC element. An easy 

way to avoid this risk is by supervising the phase-phase 

distance elements with the negative-sequence direction 

element just described. (The negative-sequence directional 

element is ignored for 3φ faults which pick up all three phasephase 

distance elements.) 

G. Phase-Phase Distance Element Security for Reverse 

Three-Phase Faults 

Phase distance elements require memory polarization to be 

secure and reliable for reverse three-phase (3φ) faults. 


The most onerous 3φ fault is one with the following 

qualifications: 

1. A small critical amount of fault resistance. 

2. Significant load flow into the bus from a weaker 

source. 

Three-phase faults are a concern to phase distance elements 

only after the memory expires. For bolted faults, each phase 

voltage is zero. Once the memory expires, the distance 

elements are disabled. However, with some resistance, the 

polarization voltage does not go to zero, and could move to an 

angle permitting tripping. 

Figure 11(a) illustrates a system with a reverse 3φ fault 

with fault resistance. Figure 11(b) shows the total Aφ fault 

current (I F,a ), the prefault memory voltage (V a,mem ), Aφ voltage 

and current seen by the relay (V af and I RLY,a respectively), and 

I RLY,a adjusted by the replica line impedance. 

Recall the denominator term of Equation 1 for a phase 

distance element. This denominator term is a directional 

element. It indicates how a phase distance element of infinite 

reach would perform for this same fault. If the angle between 

Z • I and V p is less than 90°, the phase distance element 

declares the fault forward. From Figure 11(b), the angle 

between I RLY,a • Z and V a is less than 90°. Thus, after the 

memory voltage (V a,mem ) becomes in step with V af , the 

directional security of the phase distance element is 

compromised. 

Figure 11(c) illustrates the same reverse 3φ fault with load 

flowing out from the relay terminal (from E S towards E R ). For 

this case, the phase distance relay is secure even after the 

memory voltage becomes in-step with the fault voltage. 

Solutions: 

1. Clear the 3φ fault before the memory expires. 

2. The apparent impedance for the reverse 3φ-G fault 

enters the tripping characteristic in the secondquadrant. 

Reducing the maximum torque angle 

reduces the amount of second-quadrant coverage. 

3. Require an increased torque magnitude output from 

the comparator (i.e., desensitize the element). As the 

apparent impedance enters the tripping characteristic 

very near the origin, forward direction 3φ faults 

produce greater torques than do the reverse 3φ faults. 

4. Add current offset in the positive direction to the 

polarizing reference. 

5. Test the angle between the positive-sequence current 

and voltage (i.e., use a positive-sequence directional 

element). This angular test limits the three-phase fault 

coverage to a 180° impedance angle sector of –120° to 

60°. 

VII. LOAD ENCROACHMENT 

The impedance of heavy loads can actually be less than the 

impedance of some faults. Yet, the protection must be made 

selective enough to discriminate between load and fault 

conditions. Unbalance aids selectivity for all faults except 

three-phase faults. 

Figure 12 shows the load-encroachment characteristics in 

the impedance plane. 

Figure 11: 

Reverse 3φ Fault Conditions and Mho Element Performance 

Figure 12: Load Encroachment on Mho Distance Element Characteristics 

When power flows out, the load impedance is in the 

wedge-shaped load-impedance area to the right of the X-axis. 

When power flows in, the load impedance is in the left-hand 

load-impedance area. 

There is overlap (shaded solid) between the mho circle and 

the load areas. Should the load impedance lie in the shaded 

area, the impedance relay will detect the under-impedance 

condition and trip the heavily-loaded line. Such protection 

unnecessarily limits the load-carrying capability of the line. 

For better load rejection, the mho circle can be squeezed 

into a lenticular or elliptical shape. Unfortunately, this also 

reduces the fault coverage. 


Alternatively, we could use additional comparators to make 

blinders parallel to the transmission line characteristic, to limit 

the impedance-plane coverage, and exclude load from the 

tripping characteristic. 

Or, we could build quadrilateral characteristics, which boxout 

load. 

All traditional solutions have the same common approach: 

shape the operating characteristic of the relay to avoid load. 

The traditional solutions have two major disadvantages: 

1. Reducing the size of the relay characteristic 

desensitizes the relay to faults with resistance. 

Avoiding a small area of load encroachment often 

requires sacrificing much larger areas of fault 

coverage. 

2. From a user's point of view, the more complex shapes 

become hard to define, and the relays are harder to set. 

A new approach does not modify the relay characteristic 

shape directly. Instead, it defines the load regions in the 

impedance plane, and blocks operation of distance elements if 

the impedance is in either of the load regions. 

Figure 13 shows the new approach applied to a four-zone 

mho relay. The mho characteristics are conventional, and are 

not modified to exclude load. 

Figure 13: 

Improved Load-Encroachment Method 

There are two load regions shown (load-in and load-out). 

The relay calculates the complex positive-sequence impedance 

and tests it against the boundaries of these load regions. If the 

impedance is inside either region, then the relay concludes the 

impedance represents load, and blocks the mho elements. If 

the impedance is outside both load regions, the mho elements 

are permitted to operate. 

The advantages of the new approach include: 

1. Greater coverage for faults is possible because only 

the overlap between the load characteristic and the 

relay characteristic is blocked. 

2. The load-encroachment characteristics are easy to set, 

because they can be directly related to the maximum 

load conditions. Once we have maximum load-in and 

load-out conditions, and the range of power factors of 

the load, the load-impedance areas can be found. No 

customization of relay characteristics is required to 

avoid load. 

3. Separate characteristics for load-in and load-out are 

easy to define. 

4. Since the characteristics for faults and loads are 

independent, there is less chance of setting errors. 

The logic applies to three-phase faults only. Loadencroachment 

blocking is not required or desired for 

unbalanced faults (e.g., AB, BC, CA, AG, BG, CG, ABG, 

BCG, CAG faults). 

VIII. FAULT-TYPE SELECTION CONSIDERATIONS 

For security, distance relay schemes must consider the 

behavior of the distance elements in all six fault loops (AG, 

BG, CG, AB, BC, and CA) under very broad and general 

system, load, and fault conditions. 

There are two major concerns: 

1. Ground distance elements can overreach for line-lineground 

(LLG) faults. 

2. Phase distance elements can operate for close-in lineground 

(LG) faults. 

The first concern is generally considered a problem in all 

applications. The second concern is a problem in single-poletrip 

schemes, and a targeting nuisance. 

How can we reliably prevent unwanted relay elements 

from interfering with the performance of the overall scheme 

If we know the fault is an AG fault, then we can block the 

AB and CA elements in order to avoid a three-pole trip for a 

LG fault. 

If we know the fault is a BCG fault, then we can block the 

BG and CG elements, avoiding possible overreach by the BG 

and CG elements. 

(The BG element tends to overreach for a BCG fault with 

resistance to ground. The CG element tends to overreach for a 

BCG fault with resistance between the phases.) 

A. Selection Using the Angle Between I 0 and I 2 

The angle between the negative-sequence current and the 

zero-sequence current is a frequently used and very useful 

indicator. 

Figure 14 shows the sequence networks for AG and BCG 

faults. The symmetrical component currents are referenced to 

phase A. That is, I 0 means I A0 , and I 2 means I A2 . For these two 

faults, the angle between I 2 and I 0 is zero degrees. Figure 15 

shows phasor diagrams for AG, BG, and CG faults. It also 

shows the phase relationships between I 0 and I 2 for the three 

faults. 


If the angle is near +120°, then the fault is CG or ABG. 

• Enable CG and AB elements only. 

• One approach is to assign 120° sectors to AG, BG and 

CG faults. For example, angles between ±60° belong 

to AG and BCG faults. 

B. Fault Resistance Can Affect This Scheme 

Figure 16 shows the effects of introducing fault resistance 

between the point where phases B and C are shorted together 

and ground. Rf appears in the zero-sequence net-work, and the 

angle of the I 0 leads the angle of I 2 , because the network zerosequence 

impedance angle is less than that of the negativesequence 

impedance angle. 

Figure 14: 

Resistance) 

I 0 and I 2 Relationship for AG and BCG Faults (Without Fault 

Figure 15: 

I 0 and I 2 Relationship for AG, BG, and CG Faults 

Given that the fault is a single-line-ground (SLG) fault, the 

angle between I 0 and I 2 in the fault is a very reliable indicator 

of the fault type: centered around zero degrees for AG, –120° 

for BG (I 2 lags I 0 by 120°), and +120° for CG (I 2 leads I 0 by 

120°). Fortunately, these angles do not change much over a 

broad range of system conditions. 

Thinking about Figures 14 and 15 at the same time, we 

conclude: 

If the angle is near zero, then the fault is AG or BCG. 

• If it is AG, then AB or CA could also pick up and 

three-pole trip for a single-line-ground fault. 

• If it is BCG, then the BG and CG ground distance 

elements may overreach. 

• THEREFORE: Enable AG, BC elements only. 

If the angle is near –120°, then the fault is BG or CAG. 

Enable BG and CA elements only. 

Figure 16: Effects of Increasing Rf for a BCG Fault 

When Rf is big enough, there may be confusion as to 

whether the fault is AG/BCG or BG/CAG, because the angle 

could be less than –60°, as shown in the bottom of the figure. 


1) Estimating and Comparing Fault Resistances Solves the 

Problem 

When the angle itself is not conclusive, e.g., when the 

angle is more than 30° from its expected value, we can 

compare phase and ground fault resistance estimates, and 

select the fault type associated with the minimum resistance. 

For example, and again referring to the bottom of Figure 16, a 

comparison of an estimate of Rbg against the minimum phaseto-phase 

fault resistance (in this case, Rbc), would reveal that 

Rbg is much larger than Rbc. Therefore, the logic concludes 

the fault mainly involves phases B and C, and the best 

measurement is made by the BC element. 

IX. SUMMARY 

Important points presented in this paper include: 

1. A review of several types of phase-angle comparators 

shows their similarities and differences. 

2. A multiple-input comparator can be viewed as a 

family of two-input comparators, which includes 

every pair of inputs. 

3. Writing the torque equation for a relay characteristic, 

setting it equal to zero, and solving for a scalar 

multiple of the element reach yields a result which 

maps points on the characteristic onto a single point 

on the number line. This makes for very efficient 

synthesis of a family of characteristics with different 

reaches. 

4. Positive-sequence memory potential is generally the 

most secure and reliable polarization method for mho 

characteristics. 

5. A negative-sequence element which calculates 

negative-sequence impedance, and tests it against 

thresholds is presented. It is easy to adapt to virtually 

any system conditions, because its two threshold 

settings relate to system impedances. 

6. We present ground-fault-resistance elements for 

quadrilateral characteristics, which estimate the fault 

resistance, and use the fault-current estimate 

1.5 • (I0 + I2). This estimate rejects the loadinfluenced 

positive-sequence current, but includes the 

rest of the fault current. 

7. A negative-sequence directional check is sufficient to 

overcome security problems with phase and ground 

distance elements for unbalanced faults. 

8. A positive-sequence directional element can be used 

to cut off part of the mho characteristics in the second 

quadrant of the impedance plane, to enhance security 

for three-phase faults. This element would normally be 

set with a maximum torque angle much less than that 

of the mho circle. 

9. Instead of shaping impedance-plane tripping 

characteristics to avoid load, we introduced a load 

characteristic. Impedances must leave the load 

characteristic, before tripping is permitted for threephase 

faults. The load characteristic looks like a bowtie 

without the knot, and therefore neatly surrounds 

load areas. It minimizes the area of the impedance 

plane eliminated for load considerations. 

10. We point out a potential problem with fault-type 

selectors based on the angle between I0 and I2. They 

may err for certain resistive LLG faults. The solution 

is a comparison of estimates of LL and LG fault 

resistances. 

X. REFERENCES 

[1] R.J. Martilla, “Directional Characteristics of Distance Relay Mho 

Elements: Part II - Results.” IEEE Trans-actions on Power Apparatus 

and Systems, Vol. PAS-100, No.1 January 1981. 

[2] Edmund O. Schweitzer III, “New Developments in Distance Relay 

Polarization and Fault Type Selection,” 16th Annual Western Protective 

Relay Conference, October 24 - 26, 1989, Spokane, WA. 

[3] A.R. Van C. Warrington, “Protective Relays: Their Theory and 

Practice.” Chapman and Hall, 1969, Volume I and II. 

XI. BIOGRAPHIES 

Edmund O. Schweitzer, III received BSEE and MSEE degrees from Purdue 

University in 1968 and 1971, respectively. He earned a PhD at Washington 

State University (WSU) in 1977.His professional experience includes 

electrical engineering work at Probe Systems in California and the National 

Security Agency in Maryland. He served as an assistant professor at Ohio 

University and as an assistant and an associate professor at WSU. Since 1983, 

he has directed the activities of Schweitzer Engineering Laboratories, Inc. 

(SEL), the company he founded in Pullman, Washington. SEL designs, 

manufactures, and markets digital protective relays for power system 

protection. 

Schweitzer started investigating digital relays during PhD studies at WSU in 

1976, which produced both his doctoral dissertation and SEL. His university 

research was supported by Bonneville Power Administration, Electric Power 

Research Institute, and various utilities. Although the company has grown 

significantly, Schweitzer is still involved in the development of new relays 

and auxiliary equipment. 

He is a Fellow of the Institute of Electrical and Electronic Engineers (IEEE), 

is a member of Eta Kappa Nu and Tau Beta Pi, and has authored or coauthored 

30 technical papers. 

Jeff B. Roberts received his BSEE from Washington State University in 

1985. He worked for Pacific Gas and Electric Company as a relay protection 

engineer for over three years. In November, 1988 he joined Schweitzer 

Engineering Laboratories, Inc. as an Application Engineer. He now serves as 

Application Engineering Supervisor. He has delivered papers at the Western 

Protective Relay Conference, Texas A&M University and the Southern 

African Conference on Power System Protection. He holds one patent on the 

SEL-121B relay and has other patents pending. 

Copyright © SEL 1992, 1993 

(All rights reserved.) 

Printed in USA 

Rev. 2 


Impedance-Based Fault Location Experience 

Karl Zimmerman and David Costello, Schweitzer Engineering Laboratories, Inc. 


Accurate fault location reduces operating costs by avoiding 

lengthy and expensive patrols. Accurate fault location 

expedites repairs and restoration of lines, ultimately reducing 

revenue loss caused by outages. 

In this paper, we describe one- and two-ended impedancebased 

fault location experiences. We define terms associated 

with fault location, and describe several impedance-based 

methods of fault location (simple reactance, Takagi, zerosequence 

current with angle correction, and two-ended 

negative-sequence). We examine several system faults and 

analyze the performance of the fault locators given possible 

sources of error (short fault window, nonhomogeneous 

system, incorrect fault type selection, etc.). 

Finally, we show the laboratory testing results of a twoended 

method, where we automatically extracted a two-ended 

fault location estimate from a single end. 

II. FAULT LOCATION METHODS AND DEFINITIONS 

Several methods of estimating fault location are presently 

used in the field: 

• DFR and short circuit data match 

• Traveling wave methods 

• Impedance-based methods 

− One-ended methods without using source 

impedance data (simple reactance, Takagi) 

− One-ended methods using source impedance data 

• Two-ended methods 

In this paper, we focus on certain impedance-based fault 

location methods and provide results from actual system 

faults. 

III. NOTABLE IEEE DEFINITIONS 

IEEE PC37.114, “Draft Guide for Determining Fault 

Location on AC Transmission and Distribution Lines”[1] was 

recently balloted and is in the approval process. One of the 

important contributions of the guide is the definitions section. 

Here are a few notable definitions found in the guide: 

Fault location error: Percentage error in fault location 

estimate based on the total line length: e (error) = (instrument 

reading – exact distance to the fault) / total line length. 

For example, suppose a line is 100 miles long and the 

actual fault is 90 miles from the local terminal. If the local 

fault locator provides a fault location of 94 miles, the fault 

location error is (94–90)/100 = 4%. If the remote fault locator 

indicates 8 miles, the fault location error is (8–10)/100 = 2%. 

Homogeneous line: A transmission line where impedance 

is distributed uniformly on the whole length. 

Examples of this are lines that use the same conductor size 

and construction throughout. Lines that are nonhomogeneous 

can be a source of error for one- or two-ended impedancebased 

fault location methods. 

Homogeneous system: A transmission system where the 

local and remote source impedances have the same system 

angle as the line impedance. A homogeneous system is shown 

in Figure 1. 

Z 

Z 

Figure 1 

1S 

0S 

Z 1S 

= 2∠80° 

= 3 • Z 

1S 

Relay 

mZ 2L 

Z 

Z 

1L 

0L 

R F 

(1-m)Z 2L 

= 8∠80° 

= 3• Z 

Example of a Homogeneous System 

1L 

Relay 

∠Z 

∠Z 

1R 

0R 

Z 1R 

= ∠Z 

1S 

= ∠Z 

Nomograph: A graph that plots measured fault location 

versus actual fault location by compensating for known 

system errors. 

Figure 2 shows a 69 kV line with 12.47 kV underbuild. 

Figure 2 

Relay 

Location 

N 

69 kV Line Configuration Sketch 

N 

69 kV 

0S 

12.47 kV 

Load 

How to build a nomograph: 

1. Calculate line constants. 

2. Determine which faults require a nomograph. 

3. Using short circuit program, apply faults along the 

length of line (10%, 20%, etc.). 

4. Plug resultant voltage and current values into fault 

location algorithms. 

5. Plot a short circuit (actual) vs. calculated (relay) 

fault location. 

Impedance-Based Fault Location Experience | 15

Without Underbuild 

With 50 Miles Underbuild 

R1 7.50 Ω 7.50 Ω 

X1 22.757 Ω 22.757 Ω 

R0 21.327 Ω 15.488 Ω 

X0 134.16 Ω 88.75 Ω 

Figure 3 shows a completed nomograph. 

Figure 3 

Printout Miles 

69 kV Nomograph 

Partial, Total, and No Underbuild 

60 

55 

50 

45 

40 

35 

30 

25 

20 

15 

10 

5 

0 

0 10 20 30 40 50 60 

Actual Miles 

10 Miles Underbuild No Underbuild 60 Miles Underbuild 

Completed Nomograph for 69 kV Line 

IV. IMPEDANCE-BASED FAULT LOCATION 

METHODS AND REQUIREMENTS 

Impedance-based methods require the following approach: 

1. Measure the voltage and current phasors. 

2. Extract the fundamental components. 

3. Determine the phasors and fault type. 

4. Apply impedance algorithm. 

One-ended impedance methods of fault location are a 

standard feature in most numerical relays. One-ended 

impedance methods use a simple algorithm, and 

communication channels and remote data are not required 

(except when a channel is required to bring the fault location 

estimate to an operator). 

Two-ended methods can be more accurate but require data 

from both terminals. Data must be captured from both ends 

before an algorithm can be applied. 

The most popular impedance-based fault location methods 

are discussed in this paper: 

• Simple reactance method (one-ended) 

• Takagi method (one-ended) 

• Modified Takagi method that corrects for source 

impedance angle differences (one-ended) 

• Two-ended negative-sequence method 

One-ended impedance-based fault locators calculate the 

fault location from the apparent impedance seen by looking 

into the line from one end. An example system one-line is 

shown in Figure 4. To locate all fault types, the phase-toground 

voltages and currents in each phase must be measured. 

(If only line-to-line voltages are available, it is possible to 

locate phase-to-phase faults; if the zero-sequence source 

impedance, Z 0 , is known, we can estimate the location for 

phase-to-ground faults). 

If the fault resistance is assumed to be zero, we can use one 

of the impedance calculations in Table 1 to estimate the fault 

location. 

Fault Type 

TABLE 1 

SIMPLE IMPEDANCE EQUATIONS 

Positive-Sequence Impedance 

Equation (mZ 1L =) 

A–ground Va ( Ia + k • 3 • I0 

) 

B–ground Vb ( Ib + k • 3 • I0 

) 

C–ground V ( I + k • 3 • I ) 

a–b or a–b–g 

b–c or b–c–g 

c–a or c–a–g 

c c 0 

a–b–c Any of the following: Vab I 

ab, Vbc I 

bc, Vca I 

ca 

Where: 

k is (Z 0L – Z 1L ) / 3Z 1L , 

Z 0L is the zero-sequence line impedance, 

Z 1L is the positive-sequence line impedance, 

m is the per unit distance to fault (for example: 

distance to fault in kilometers divided by the total 

line length in kilometers), 

is the zero-sequence current. 

I 0 

S 

Z S 

Figure 4 

VS 

VS 

I S 

m 

mZ L 

Z L 

V 

V 

V 

I S 

I R 

VR 

I F 

R F 

ab 

bc 

ca 

I 

I 

I 

1-m 

ab 

bc 

ca 

(1-m)Z L 

One-Line Diagram and Circuit Representation of Line Fault 

The challenges for accuracy of one-ended fault location are 

well known and are described in several sources [1] [2] [3] 

[4]. To summarize, the following conditions can cause errors 

for one-ended impedance-based fault location methods: 

• Combined effect of fault resistance and load 

• Zero-sequence mutual coupling 

• Zero-sequence modeling errors 

• System nonhomogeneity 

• System infeeds 

− Remote or third terminal infeed 

− Tapped load with zero-sequence source 

• Inaccurate relay measurement, instrument transformer 

or line parameters. 

I R 

VR 

R 

Z R 


A. Simple Reactance Method 

From Figure 4, the voltage drop from the S end of the line 

is: 

VS = m • Z1L • IS + R F • IF 

(1) 

For an A-phase to ground fault, Vs = V a−g and I S = Ia + k • 3• I0 

The goal is to minimize the effect of the R F • IF 

term. 

The simple reactance method divides all terms by I S (I 

measured at the fault locator) and ignores the (R F •I F / I S ) term. 

To do this, save the imaginary part, and solve for m: 

( ) 

Im V /I = Im(m • Z ) = m • X 

S S 1L 1L 

m = 

I 

m 

⎛ VS 

⎞ 

⎜ 

⎝ I ⎟ 

⎠ 

X 

1L 

Error is 0 if ∠ I = ∠ I or R = 0 

S 

S F F 

B. Takagi Method—One-Ended Impedance Method With No 

Source Data 

The Takagi method requires prefault and fault data. It 

improves upon the simple reactance method [2] by reducing 

the effect of load flow and minimizing the effect of fault 

resistance. 

VS = m • Z 1L • I + R F • IF 

(3) 

Use Superposition current (I sup ) to find a term in phase with 

I F : 

Isup 

= I − Ipre 

I = Fault Current 

(4) 

I = Pre-fault Current 

pre 

Voltage drop from Bus S: 

VS = m • Z 1L • IS + R F • IF 

Multiply both sides of equation (1) by the complex 

conjugate of I sup (I sup* ) and save the imaginary part. Then, 

solve for m: 

I m[VS • I sup* ] = m • I m (Z1L • IS • I sup* ) + R F • I m (IF • I sup* ) 

I m (VS • I sup* ) 

(5) 

m = I (Z • I • I ) 

m 1L S sup* 

The key to the success of the Takagi method is that the 

angle of I S is the same as the angle of I F . For an ideal 

homogeneous system, these angles are identical. As the angle 

between I S and I F increases, the error in the fault location 

estimate increases. 

(2) 

C. Modified Takagi—Zero-Sequence Current Method with 

Angle Correction 

Another method (modified Takagi) uses zero-sequence 

current (3 • I 0S ) for ground faults instead of the superposition 

current. Therefore, this method requires no prefault data. 

Modified Takagi also allows for angle correction. If the 

user knows the system source impedances, the zero-sequence 

current can be adjusted by angle T to improve the fault 

location estimate for a given line. 

* − jT 

( ( ) ) 

− 

( ) 

Im V S • 3• I 0S • e 

m = (6) 

I Z • I • 3• I • e 

* jT 

( ) 

m 1L S 0S 

The angle T selected will be valid for one fault location 

along the line. Figure 5 shows how to calculate T. 

Z 0S 

Figure 5 

known) 

3•I RS 

mZ 0L 

T 

3• I RS 

I F 

I F 

(1-m)Z 0L 

Zero-Sequence Current Angle Correction (if source impedances are 

IF 

Z0S + Z0L + Z0R 

= = A∠T 

3• I (1− m) • Z + Z 

RS 0L 0R 

D. Two-Ended Negative-Sequence Impedance Method 

A relatively new method, introduced in 1999, uses 

negative-sequence quantities from all line terminals for the 

location of unbalanced faults. By using negative-sequence 

quantities, we negate the effect of prefault load and fault 

resistance, zero-sequence mutual impedance, and zerosequence 

infeed from transmission line taps. Precise fault type 

selection is not necessary. Data alignment is not required 

because the algorithm employed at each line end uses the 

following quantities from the remote terminal (which do not 

require phase alignment). 

• Magnitude of negative-sequence current, I2 

• Calculated negative-sequence source impedance, 

Z ∠θ 

° 

2 

2 

Z 0R 

(7) 


An observation from Figure 6 is that the negative-sequence 

is the same when viewed from all ends of 

fault voltage ( V2F 

) 

the protected line. 

Source 

S 

Z 1S 

Z 2S 

Z 0S 

I 1S 

Relay S 

I 2S 

Relay S 

I 0S 

Relay S 

mZ 1L 

mZ 2L 

mZ 0L 

V 2F 

+ 

(1-m)Z 1L 

(1-m)Z 2L 

(1-m)Z 0L 

I 1R 

Relay R 

I 2R 

Relay R 

I 0R 

Relay R 

3RF 

Source 

R 

Z 1R 

Z 2R 

Z 0R 

I TOTAL 

Figure 6 Connection of Sequence Networks for a Single Line-to-Ground 

Fault at m 

At Relay S: 

At Relay R: 

( ) 

V = –I • Z + m • Z 

(8) 

2F 2S 2S 2L 

( ) 

V = − I • Z + (1− m) • Z 

(9) 

2F 2R 2R 2L 

Eliminate V 2F from Equations 8 and 9 and rearrange the 

resulting expression as follows: 

( Z2S 

+ m • Z2L 

) 

( 2R + ( − ) 2L ) 

I2R 

= I 2S • 

Z 1 m • Z 

(10) 

To avoid alignment of Relay S and R data sets, take the 

magnitude of both sides of Equation 10 as follows: 

( Z2S 

+ m • Z2L 

) 

( 2R + ( − ) 2L ) 

I2R 

= I 2S • 

Z 1 m • Z 

Equation 11 is then simplified to Equation 12 below. 

I 

2R 

= 

( I 2S • Z2S ) + m •( I 2S • Z2L 

) 

( Z + Z ) − m •( Z ) 

2R 2L 2L 

(11) 

(12) 

To further simply Equation 12, define the following 

variables: 

I • Z = a + jb 

2R 

2S 

2S 

2S 

I • Z = c + jd 

2L 

Z + Z = e + jf 

2L 

Z = g + jh 

2L 

Substituting these variables into Equation 12 produces: 

I 

2R 

= 

( a + jb) + m •( c + jd) 

( e + jf ) − m •( g + jh) 

(13) 

Taking the square of both terms of Equation 13, expanding 

and rearranging terms produces a quadratic equation of the 

form: 

2 

A • m + B• m + C = 0 

(14) 

Equation 14 is solved for m using a quadratic solution. The 

coefficients of Equation 14 are given below. 

( ) ( ) 

2 2 2 2 2 

2R 

A = I • g + h − c + d 

( ) ( ) 

2 

2R 

2 2 2 2 2 

2R 

B = − 2 • I • e • g + f • h − 2 • a • c + b • d 

( ) ( ) 

C = I • e + f − a + b 

(15) 

V. DISTRIBUTION SYSTEMS 

Fault location for distribution feeders uses the same basic 

principles as for transmission lines, but presents a great 

challenge for substation fault locators because of the diverse 

topology of the distribution system: laterals, spurs, and singlephase 

taps. On important feeders, some utilities model the line 

parameters to achieve a more precise fault location. 

One utility models a feeder using an Excel ® spreadsheet to 

show the line parameters. The spreadsheet includes node 

numbers, wire size, distance from the source, positive- and 

zero-sequence impedances, and fault currents. Figure 7 is an 

actual model of a feeder that is 5.47 miles long. 

Figure 7 

Spreadsheet Model (See Appendix for Enlarged View) 

A graphical representation of the feeder is shown in 

Figure 8. 

1 

Figure 8 

(distance in miles) 

2 

3 

4 

5 

Actual Fault 

(3 miles) 

Distribution Feeder Topology 

11 

6 7 8 9 10 

(1.41) (2.29) 

(3.29) 

12 

(3.06) 

21 

(5.39) 

13 

(3.27) 

14 15 16 17 18 

(3.66) (3.99) 

23 

(5.47) 

(2.56) 

20 19 

22 

(4.47) 


Figure 9 shows a screen capture of event report data from 

an actual fault. 

Figure 9 

Distribution Feeder Fault Event Screen Capture 

The event report indicates that a B-phase-to-ground fault 

occurred 3.02 miles from the station. From the feeder 

topology, there are two possible locations for the fault. As it 

turns out, line crews found a fast growing skinny tree growing 

close to the line, approximately three miles from the 

substation on the main line near Node 12. 

VI. USE OF FAULT INDICATORS 

Fault Indicators can be applied on lines to help locate 

faults. If a fault occurs beyond the location of the fault 

indicator, line crews observe an LED or flashing light, 

indicating that fault current was sensed. Reset can be done 

manually, electrostatically, or through a timer, depending on 

the design. Figure 10 is an example of how fault indicators 

can be placed to assist line crews in finding the fault location. 

VII. TRANSMISSION FAULT LOCATION EXAMPLES 

A. Example 1: 345 kV Automatic Spraying System 

Background: Repeated phase-phase faults had occurred on 

a 345 kV line. There was no inclement weather or lightning in 

the area. The number of faults caused voltage issues and a 

negative-sequence overcurrent element went into an alarm 

state at a regional nuclear plant. Nuclear plant personnel were 

concerned about the possibility of tripping the unit off line. 

The line data for the transmission line: 

• Circuit 345-LINE is a 28.16 mile long, 345 kV line 

between terminals G and H. 

• 345-LINE—“We had dispatched linemen to the area 

based on fault location. The lineman was patrolling 

the line in the area when he observed an automatic 

spraying system operating very near the line. He went 

to the property owner’s home and learned that the 

automatic system runs along a track and sprays 

liquefied manure onto the open fields. The landowner 

checked the mechanism that controls the sprinkler and 

found that it had failed, causing the sprinkler to run 

under the line.” 

Figure 11 shows a one-line and event report screen 

captures. 

G 

C-A 

17.28 mi 

Reported 

17.8 mi from G 

10.36 mi from H 

Actual 

345-Line 28.16 mi 

C-A 

10.00 mi 

Reported 

H 

Relay 

Figure 10 

Example Location for Fault Indicators on Distribution Feeder 

Figure 11 

Example 1: One-Line and Event Report Screen Captures 


As a way of confirming that the data was correct, we ran 

the two-ended negative-sequence impedance algorithm using 

the event reports from each end, as shown in Figure 12. 

A 

A-B-G 

-143.2 mi 

Reported 

6.8 mi from A 

Actual 

No event 

available 

B 

1.8 

115-Line 48.4 mi 

1.5 

m v 

ms v 

.633 

1 

0.5 

Calculated 

Two-Ended FL 

Actual FL 

0.1 

0 2 4 6 8 

0 v 

8 

RS 

Figure 12 Example 1: Mathcad Screen Capture—Actual Fault Location vs. 

Two-Ended Estimate 

The actual fault occurred where the sprinkler system was 

found, between 17.8 and 17.9 miles (m = .633) from 

Terminal G (based on patrol map tower locations). 

Conclusions for Example 1: 

1. The one-ended (17.28 and 10.00 miles, respectively) 

and two-ended (17.46 miles) fault locations yielded 

good results. All fault location estimates were within 

2%. 

2. Two-ended negative-sequence impedance-based 

method corroborates one-ended method. 

B. Example 2: Incorrect Fault Location Due to Incorrect 

Fault Type Identified 

Background: On this 115 kV Line, a relay tripped for an 

apparent fault. Targets indicated an A B-G fault that tripped 

on Zone 2. Upon analysis of the event report data, both ground 

directional overcurrent and ground distance elements tripped. 

All of the data indicated that the relay elements functioned 

properly. However, the relay produced a fault location 

estimate of –143 miles. This spawned an investigation to find 

the correct fault location. 


captures. 

Figure 13 


By inspecting the event data directly, we saw a depressed 

C-phase to ground voltage and relatively low fault current 

(under 400 A primary) on all three phases. Based on this, we 

suspected that the fault was C-phase to ground with a weak 

source behind the relay and that the relay selected the wrong 

fault type. 

The relay used in this application is for three-pole trip 

applications. Its fault identification logic compares the angular 

relationship between I 0 and I 2 [5]. For this fault, I 2 leads I 0 by 

about 120 degrees (using A-phase as reference,), as shown in 

Figure 14. This indicates that the fault is either C-phase to 

ground, or A-B-ground. 

Figure 14 

Symmetrical Components from Fault—I2 leads I0 by 120 degrees 


The relay then performs “torque” calculations to determine 

which fault appears to be “closer” to the relay to decide 

between the two loops (C-G or A-B-G). For this case, the 

“torque” calculation showed the A-B-G as being closest. Thus, 

the relay selected the wrong loop. 

Improved relay designs (intended for single-pole or threepole 

applications) have better fault-type selection. These 

designs measure the fault resistance between phases and 

phase-to-ground. These would have correctly identified the 

fault type. 

Still, this example demonstrates the need for correct fault 

type selection. Knowing that the fault was C-G or A-B-G, we 

calculated the actual fault location to be 6.8 miles for the C- 

phase-to-ground fault (calculations from the event report data 

using the one-ended modified Takagi method): 

Calculated Fault Locations: 

C-G: 6.8 A-B-G: –137 


1. Fault was C-phase-to-ground, one-ended location 

6.8 miles. (later confirmed from field reports). 

2. Weak source conditions challenge the one-ended 

fault locators for two reasons: nonhomogeneous 

system is more likely; fault type selection more 

difficult. 

3. Superior fault type selection would have provided 

the correct fault type and fault location. 

4. Two-ended negative-sequence impedance fault 

location would have correctly selected fault 

location for faults all along the line. (fault type 

selection not needed) 

C. Example 3: 345 kV Line Failed Insulator 

The line data for the transmission line: 

• Circuit 345-LINE is a 39.26 mile long, double-circuit 

345 kV line between terminals E and F. 

• 345-LINE circuit fault data: 

− 345-LINE E SUB SEL-311C 08-19-03.txt 

− 345-LINE F SUB SEL-311C 08-19-03.txt 

• 345-LINE – “A failed insulator strut was found on 

structure # 483, at about 6 miles from the F 

termination. Total line length is 39.26 miles.” Note – 

the line length setting in the relays is 39.30 miles. 


captures. 

IA IB IC 

VA VB VC 

Figure 15 

5000 

2500 

0 

-2500 

-5000 

200 

100 

0 

-100 

-200 

E 

15000 

10000 

5000 

0 

-5000 

-10000 

-15000 

200 

IA IB IC 

VA VB VC 

100 

B-G 

28.55 mi 

Reported 

33.26 mi from E 

6.0 mi from F 

Actual 

345-Line 39.26 mi 

B-G 

6.29 mi 

Reported 


In Figure 16, the horizontal axis is the number of cycles 

and the vertical axis is the two-ended fault location averaged 

over several cycles. The actual fault location (33.26 miles) is 

about 0.85 per unit from the E terminal (depicted by a 

horizontal line on the graph). Note that the calculated fault 

locations are close to but do not exactly match the actual. 

1.5 

1.5 

m v 

ms v 

.85 

0 

-100 

-200 

1 

0.5 

IA IB IC VA VB VC 

2.5 5.0 7.5 10.0 12.5 15.0 

Cycles 


2.5 5.0 7.5 10.0 12.5 15.0 

Cycles 

Actual FL 

Calculated 

Two-Ended FL 

F 

0.0 

0 

0 2 4 6 8 

0 v 

RS 

8 

Figure 16 Example 3: Mathcad Screen Capture—Actual Fault Location 

versus Two-Ended Estimate 


1. The system was slightly nonhomogeneous, which 

contributed to the poor local one-ended fault 

location estimate and the remote end being more 

accurate. 


2. The fault was a fast clearing fault (approximately 

two cycles). The fault was interrupted just as the 

relay filtering (one-cycle cosine filter) had 

processed the data. As a result, fault location 

results are based on data less accurate than that of a 

fault present for a longer time window. 

3. The only event reports collected were 4-sample per 

cycle event reports. Thus, our analysis was limited 

because of the limited number of data points. 

When possible, it is better to collect event data 

with more data points (16 or more samples-percycle). 

4. Two-ended negative-sequence impedance fault 

location provided the best estimate, mainly because 

it mitigated any effects of the nonhomogeneous 

system and smoothed out the short data window by 

averaging the fault location estimates over several 

samples. 

D. Example 4 - 345 kV Line – Fire Under Line Conductors 

Background: There was a fire on a long 345 kV line in a 

wooded area. The fire caused several faults to occur, on 

different phases. Several reclose attempts were momentarily 

successful, until the still burning fire caused other phases to 

flash over creating another fault. 

345-LINE – “Line crews found a fire burning under a 

transmission line approximately 90.7 miles from the G 

substation. Total line length is 160.63 miles.” 

G 

A-G 

93.64 mi 

Reported 

90.7 mi from G 

69.93 mi from H 

Actual 

345-Line 160.63 mi 

A-G 

67.01 mi 

Reported 

H 

m v 

1.0 

ms v 

.564 

0.0 

1 

0.5 

Actual FL 

0 

0 2 4 6 8 10 

0 v 

Calculated 

Two-Ended FL 

Figure 18 Example 4: MathCad Screen Capture—Actual Fault Location vs 



In Figure 18, the horizontal axis is the number of cycles 

and the vertical axis is the two-ended fault location averaged 

over several cycles. The actual fault location (90.7 miles) is 

0.564 per unit from the G terminal (depicted by a horizontal 

line on the graph). Even though the one-ended method 

produced good results, the two-ended negative-sequence 

impedance method is superior and allows operators to get 

much closer to the actual fault location. 

VIII. LAB TESTS TO OBTAIN TWO-ENDED FAULT 

LOCATION FROM ONE END 

The examples from the previous sections show how we can 

use the two-ended negative-sequence impedance method to 

get fault location data for operators. However, it takes time to 

collect the event reports and analyze the data. Is there any way 

we can get the two-ended data faster 

Many relays have the capability to send and receive the 

status of up to eight digital elements. In some newer designs, 

if less than 8 bits are used, we can use the unassigned bits to 

send additional information, such as remote time 

synchronization, virtual terminal sessions, and analog data. 

Via relay settings, we can send either measured or 

calculated analog quantities over a communication channel. 

Remembering that we need to exchange negative-sequence 

impedance and current information, we made an effort in the 

lab to calculate two-ended fault location from a single end 

with some promising results. 

Once analog values are sent, the remote relay receives the 

analog quantities. The received analog quantities can be used 

directly in logic or math equations and viewed using a 

software command. 

The relay receiving the remote data then processes the 

multi-ended fault location algorithm. To do this, the relay uses 

internal mathematical capabilities, such as trigonometric 

functions, multiplication, division, addition, subtraction, and 

square root, to solve the quadratic equation for the fault 

location. 

RS 

10 

Figure 17 



IX. LAB TEST SETUP 

Several line faults with known fault locations were used as 

test cases. Local and remote relays exchange and use fault 

data for the purpose of implementing the two-ended negativesequence 

impedance fault location algorithm. 

We created a time-aligned COMTRADE file from the two 

line-end event reports for each fault. This fault simulation file 

is replayed into two relays to simulate the faults as seen by the 

relays in the field. 

The relays measure phase currents and voltages, and 

calculate 3I2 and ZS2. The magnitude of 3I2, and the 

magnitude and angle of Z2S from the remote line terminal is 

needed by the local relay to calculate a two-ended fault 

location. Therefore, we have to first save the 3I2 and Z2 

values at an appropriate time during the fault, and then 

communicate those values to the remote line terminal for the 

purpose of the fault location calculation. 

The data from the two ends of the line does not have to be 

time-aligned. However, we do need to select a point during the 

fault when values have settled to a steady state. We arbitrarily 

chose a point 1.5 cycles after fault detection for our data 

capture. At that point in time, the local relays will lock and 

hold the present fault value of 3I2 and Z2S. These values are 

sent to the remote line terminal. The remote line terminal will 

then perform a two-ended fault algorithm. 

Once physical test connections are verified and data scaled 

properly, the fault is played back to the relays. We compared 

the actual event report data to the played back data to verify 

accuracy, as shown in Figure 19. 

1_IA 1_IB 1_IC 

1_VA 1_VB 1_VC 

2500 

0 

-2500 

-5000 

50 

0 

-50 

-100 

10000 

1_IA 1_IB 1_IC 1_VA 1_VB 1_VC 2_IA 2_IB 2_IC 2_VA 2_VB 2_VC 

.066667 sec 

1_IA(A) 1_IB(A) 1_IC(A) 

1_VA(kV) 1_VB(kV) 1_VC(kV) 

2_IA(A) 2_IB(A) 2_IC(A) 


2500 

0 

-2500 

50 

0 

-50 

10000 

0 

-10000 

50 

0 

-50 

Figure 19 

Data 

1_IA(A) 1_IB(A) 1_IC(A) 1_VA(kV) 1_VB(kV) 1_VC(kV) 

2_IA(A) 2_IB(A) 2_IC(A) 2_VA(kV) 2_VB(kV) 2_VC(kV) 

.075 sec 

30.650 30.675 30.700 30.725 30.750 30.775 30.800 30.825 30.850 

Event Time (Sec) 15:13:30.717666 

Screen Capture of Original Event Data and COMTRADE Event 

X. TEST RESULTS AND ANALYSIS 

Table 2 shows the results from the laboratory tests. 

The One-Ended Estimate is the fault location taken directly 

from the relays. 

The Two-Ended Mathcad Point Estimate is a fault location 

based on the two-ended negative-sequence impedance 

method, where two-ended event report data is manually 

entered from one point in time (selected by the user). 

The Two-Ended Mathcad Average Estimate is based on the 

two-ended negative-sequence impedance method that 

averages the fault location over several samples. These results 

are produced using four-samples-per-cycle event reports. 

The Two-Ended Relay Estimate is the two-ended negativesequence 

impedance fault location automatically estimated by 

a relay using local and remote data captured 1.25 or 1.5 cycles 

after fault inception. (This estimate is based on the Two- 

Ended Mathcad Point Estimate Method.) A detailed listing of 

the logic settings and calculated analog results are in the 

Appendix. 

2_IA 2_IB 2_IC 


0 

-10000 

100 

0 

-100 

2.50 2.55 2.60 2.65 2.70 

Event Time (Sec) 18:53:02.576166 

XI. CONCLUSIONS 

1. One-ended impedance-based fault location still 

produces very good results in most cases. 

2. If event data is available from both ends of the line, 

two-ended impedance fault location can improve fault 

location estimate. 

3. Off-line analytical tools are available to find the best 

fault location estimates. 

TABLE 2 

RESULTS FROM 345 KV LINE FAULT LOCATION LAB TESTS 

One-Ended Estimate 


Case Study Actual Location (Local) (Remote) Mathcad Point Mathcad Average Relay 

345-LINE Example 2 90.7 miles 93.64 miles 67.01 91.2 miles 90.7miles 91.25 miles 

Case Study Actual Location (Local) (Remote) Mathcad Point Mathcad Average Relay 


4. Improve results by collecting events with the highest 

sampling rate and by using the average of several fault 

location estimate samples instead of a single point 

estimate. 

5. Short events present a challenge. More analysis is 

often required to get a more accurate fault estimate 

because of the short data window. The longer an event 

lasts, the better the fault location estimate. 

6. Technology is available to automatically calculate a 

two-ended fault location from a single end. Lab testing 

confirmed the viability of the technology. Testing 

indicates that accuracy is good on stable, longer 

lasting events. 

7. Developments are needed to make automatic 

collection of two-ended fault location applicable for 

all lines and faults. 

XIII. BIOGRAPHIES 

David Costello graduated from Texas A&M University in 1991 with a BSEE. 

He worked as a System Protection Engineer for Central and Southwest, and 

served on the System Protection Task Force for the ERCOT. In 1996, David 

joined Schweitzer Engineering Laboratories, where he has served as a Field 

Application Engineer and Regional Service Manager. He presently holds the 

title of Senior Application Engineer and works in Boerne, Texas. He is a 

member of IEEE, and the Planning Committee for the Conference for 

Protective Relay Engineers at Texas A&M University. 

Karl Zimmerman is a Senior Application Engineer with Schweitzer 

Engineering Labs in Belleville, Illinois. His work includes providing 

application support and technical training for protective relays. He is an active 

member of the IEEE Power System Relaying Committee and is the Chairman 

of Working Group D-2 on fault locating. Karl received his BSEE degree at the 

University of Illinois at Urbana-Champaign and has over 20 years of 

experience in the area of system protection. He is a past speaker at many 

technical conferences and has authored several papers and application guides 

on protective relaying. 

XII. REFERENCES 

[1] IEEE Standard PC37.114, “Draft Guide For Determining Fault Location 

on AC Transmission and Distribution Lines,” 2004. 

[2] T. Takagi, Y. Yamakoshi, M. Yamaura, R. Kondou, and T. Matsushima, 

“Development of a New Type Fault Locator Using the One-Terminal 

Voltage and Current Data,” IEEE Transactions on Power Apparatus and 

Systems, Vol. PAS-101, No. 8, August 1982, pp. 2892-2898. 

[3] Edmund O. Schweitzer, III, “A Review of Impedance-Based Fault 

Locating Experience,” Proceedings of the 15th Annual Western 

Protective Relay Conference, Spokane, WA, October 24-27, 1988. 

[4] D.A. Tziouvaras, J.B. Roberts, G. Benmouyal, “New Multi-Ended Fault 

Location Design For Two- or Three-Terminal Lines,” presented at 

CIGRE Conference, 1999, http://www.selinc.com/techpprs/6089.pdf. 


APPENDIX 

The following are the relay logic settings to perform two-ended fault location from one end after receiving data from remote 

terminal. We based these settings on the two-ended negative-sequence impedance fault location method described in this paper. 

=>>SHO L 

Protection 1 

1: # 

2: # THESE SETTINGS ARE USED FOR TWO-ENDED FAULT LOCATION 

3: # 

4: # USE DEFINITE-TIME O/C DELAYS IN CONJUNCTION WITH 

5: # A COND TIMER TO MARK 1.5 CYCLES INTO FAULT 

6: # 

7: PCT10PU := 0.000000 

8: PCT10DO := 0.875000 #1.0 CYCLE DELAY INCLUDING PROCESSING TIME 

9: PCT10IN := R_TRIG 67P1T OR R_TRIG 67G1T 

10: # 

11: # USE A PROCESSING-INTERVAL WIDE PULSE TO MARK THE FAULT DATA 

12: # 

13: PSV02 := F_TRIG PCT10Q # 2 MSEC PULSE 1.5 CYCLES AFTER EVENT TRIGGER 

14: PSV03 := NOT PSV02 # THIS WILL BE ONE ALL TIMES EXCEPT DURING FAULT 

15: # 

16: # MEMORIZE FAULT DATA I2S MAG & ANG, Z2S MAG AND ANG, V2S MAG AND ANG 

17: # READ MEASURED VALUE TIMES PULSE BINARY ONE DURING FAULT, PLUS ZERO 

18: # NEXT TIME THRU, READ ZERO PLUS PREVIOUS STORED VALUE TIMES ONE 

19: # 

20: PMV01 := L3I2FIM * PSV02 + PMV01 * PSV03 

21: # PMV01 STORES THE LINE 3I2 MAGNITUDE AT 1.5 CYCLES AFTER EVENT TRIGGER 

22: # UNTIL A NEW EVENT OCCURS 

23: # 

24: PMV02 := L3I2FIA * PSV02 + PMV02 * PSV03 

25: # PMV02 STORES THE LINE 3I2 ANGLE AT 1.5 CYCLES AFTER EVENT TRIGGER 

26: # UNTIL A NEW EVENT OCCURS 

27: # 

28: PMV03 := 3V2FIM * PSV02 + PMV03 * PSV03 

29: # PMV03 STORES THE LOCAL 3V2 MAGNITUDE AT 1.5 CYCLES AFTER EVENT 

30: # TRIGGER UNTIL A NEW EVENT OCCURS 

31: # 

32: PMV04 := 3V2FIA * PSV02 + PMV04 * PSV03 

33: # PMV04 STORES THE LOCAL 3V2 ANGLE AT 1.5 CYCLES AFTER EVENT 

34: # TRIGGER UNTIL A NEW EVENT OCCURS 

35: # 

36: PMV05 := (3V2FIM / (L3I2FIM + 0.001000)) * PSV02 + PMV05 * PSV03 

37: # PMV05 STORES THE NEG SEQ SOURCE IMPEDANCE MAGNITUDE AT 1.5 CYCLES 

38: # AFTER EVENT TRIGGER UNTIL A NEW EVENT OCCURS 

39: # 

40: PMV06 := (3V2FIA - L3I2FIA) * PSV02 + PMV06 * PSV03 

41: # PMV06 STORES THE NEG SEQ SOURCE IMPEDANCE ANGLE AT 1.5 CYCLES AFTER 

42: # EVENT TRIGGER UNTIL A NEW EVENT OCCURS 

43: # 

44: # ANALOG MIRRORED BIT VALUES ARE 16-BIT SIGNED INTEGERS 

45: # SO WE MUST SCALE APPROPRIATELY BEFORE SENDING TO RETAIN ACCURACY 

46: # 

47: PMV07 := PMV01 * 100.000000 # SCALE 3I2 MAG BY MULTIPLYING BY 100 

48: PMV08 := PMV05 * 100.000000 # SCALE Z2S MAG BY MULTIPLYING BY 100 

49: PMV09 := PMV06 * 10.000000 # SCALE Z2S ANGLE BY MULTIPLYING BY 10 

50: # 

51: # SEND PMV07, PMV08, AND PMV09 AS MIRRORED BIT ANALOGS 

52: # AND REMEMBER TO DIVIDE BY SCALING VALUE AT OTHER END 

53: # 

54: PMV10 := 0.970000 # ENTER Z1MAG FROM RELAY SETTINGS HERE 

55: PMV11 := 79.000000 # ENTER Z1ANG FROM RELAY SETTINGS HERE 

56: PMV12 := 2.170000 # ENTER LINE LENGTH FROM RELAY SETTINGS HERE 

57: # 

58: # SCALE RECEIVED MIRRORED BIT ANALOG VALUES FROM REMOTE RELAY 

59: # 

60: PMV13 := MB1A / 100.000000 # REMOTE 3I2 MAG RECEIVED THRU MB A, SCALED 

61: PMV14 := MB2A / 100.000000 # REMOTE Z2S MAG RECEIVED THRU MB A, SCALED 

62: PMV15 := MB3A / 10.000000 # REMOTE Z2S ANGLE RECEIVED THRU MB A, SCALED 

63: # 

64: # CORRECTION MADE - CONVERT TO PRIMARY VALUES 

65: # 

66: # NEXT WE SOLVE THE QUADRATIC EQUATION AND DETERMINE FAULT LOCATION 

67: # REFER TO ROBERTS, TZIOUVARAS, BENMOUYAL "NEW MULTI-ENDED FAULT LOC" 

68: # REFER TO MOXLEY, WOODWARD "IMPROVE SUBSTATION CONTROL AND PROTECTION" 

69: # REFER TO ZIMMERMAN "TWO-ENDED FAULT LOCATION" MATHCAD FILE 

70: # 

71: PMV16 := (PMV03 * 600.000000 / 3.000000) * COS(PMV04) # A' 

72: PMV16 := (PMV03 * 600.000000 / 3.000000) * COS(PMV04) # A' 

73: PMV17 := (PMV03 * 600.000000 / 3.000000) * SIN(PMV04) # B' 

74: # 

75: PMV18 := (PMV01 * 400.000000 / 3.000000) * (PMV10 * 600.000000 / \ 

400.000000) 


76: PMV18 := PMV18 * COS(PMV02 + PMV11) # C' 

77: # 

78: PMV19 := (PMV01 * 400.000000 / 3.000000) * (PMV10 * 600.000000 / \ 

400.000000) 

79: PMV19 := PMV19 * SIN(PMV02 + PMV11) # D' 

80: # 

81: PMV20 := (PMV14 * 600.000000 / 400.000000) * COS(PMV15) 

82: PMV20 := PMV20 + (PMV10 * 600.000000 / 400.000000) * COS(PMV11) # E' 

83: # 

84: PMV21 := (PMV14 * 600.000000 / 400.000000) * SIN(PMV15) 

85: PMV21 := PMV21 + (PMV10 * 600.000000 / 400.000000) * SIN(PMV11) # F' 

86: # 

87: PMV22 := (PMV10 * 600.000000 / 400.000000) * COS(PMV11) # G' 

88: # 

89: PMV23 := (PMV10 * 600.000000 / 400.000000) * SIN(PMV11) # H' 

90: # 

91: PMV24 := (PMV13 * 400.000000 / 3.000000) * (PMV13 * 400.000000 / \ 

3.000000) * (PMV22 * PMV22 + PMV23 * PMV23) 

92: PMV24 := PMV24 - (PMV18 * PMV18 + PMV19 * PMV19) 

93: # PREVIOUS LINE IS A 

94: # 

95: PMV25 := -2.000000 * (PMV13 * 400.000000 / 3.000000) * (PMV13 * \ 

400.000000 / 3.000000) 

96: PMV25 := PMV25 * (PMV20 * PMV22 + PMV21 * PMV23) 

97: PMV37 := PMV25 - 2.000000 * (PMV16 * PMV18 + PMV17 * PMV19) 

98: # PREVIOUS LINE IS B - NOTE EQUATION STARTS WITH "-2" 

99: # CORRECTING A TYPOGRAPHICAL ERROR IN REFERENCES ABOVE 

100: # 

101: PMV26 := (PMV13 * 400.000000 / 3.000000) * (PMV13 * 400.000000 / \ 

3.000000) * (PMV20 * PMV20 + PMV21 * PMV21) 

102: PMV26 := PMV26 - (PMV16 * PMV16 + PMV17 * PMV17) 

103: # PREVIOUS LINE IS C 

104: # 

105: PMV27 := ABS(PMV37 * PMV37 - 4.000000 * PMV24 * PMV26) 

106: PMV27 := SQRT(PMV27) 

107: PMV27 := PMV27 - PMV37 

108: PMV28 := PMV27 * PMV12 / (2.000000 * (PMV24 + 0.001000)) 

109: # PREVIOUS LINE IS M1 FAULT LOC ESTIMATE 

110: # 

111: PMV29 := -PMV37 

112: PMV30 := (PMV37 * PMV37 - 4.000000 * PMV24 * PMV26) 

113: PMV30 := SQRT(PMV30) 

114: PMV31 := -PMV30 

115: PMV32 := PMV29 + PMV31 

116: PMV33 := PMV32 * PMV12 / (2.000000 * (PMV24 + 0.001000)) 

117: # PREVIOUS LINE IS M2 FAULT LOC ESTIMATE 

118: # 

119: # ONE ESTIMATE WILL BE "REASONABLE", WITHIN THE LINE, TRASH OTHER 

120: PMV34 := ABS(PMV28) 

121: PSV04 := PMV34 > PMV12 

122: PSV05 := NOT PSV04 # THIS WILL BE A LOGICAL ONE IF M1 IS OK 

123: PMV35 := ABS(PMV33) 

124: PSV06 := PMV35 > PMV12 

125: PSV07 := NOT PSV06 # THIS WILL BE A LOGICAL ONE IF M2 IS OK 

126: # 

127: PMV36 := PSV05 * PMV34 + PSV07 * PMV35 # THIS IS THE FAULT LOC ESTIMATE 

128: PMV64 := PMV36 # MOVE FAULT LOC TO AREA VISIBLE TO "METER PMV" 

129: # 


The following shows the analog math results from the relay logic. PMV64 is the two-ended fault location calculated from the 

relay. 

=>>MET PMV A 

4XX RELAY Date: 09/10/2004 Time: 17:49:07.559 

SUB C Serial Number: 2004104018 

Protection Analog Quantities 

PMV01 = 9.051 

PMV02 = -64.952 

PMV03 = 14.069 

PMV04 = -175.743 

PMV05 = 1.554 

PMV06 = -110.791 

PMV07 = 905.150 

PMV08 = 155.413 

PMV09 = -1107.905 

PMV10 = 3.960 

PMV11 = 84.000 

PMV12 = 160.630 

PMV13 = 11.590 

PMV14 = 1.080 

PMV15 = 255.700 

PMV16 = -14029.924 

PMV17 = -1044.396 

PMV18 = 33881.355 

PMV19 = 11697.921 

PMV20 = 3.679 

PMV21 = 72.294 

PMV22 = 10.348 

PMV23 = 98.458 

PMV24 = 8.217E+08 

PMV25 = -3.076E+09 

PMV26 = 9.283E+08 

PMV27 = 3.268E+09 

PMV28 = 319.442 

PMV29 = 2.101E+09 

PMV30 = 1.167E+09 

PMV31 = -1.167E+09 

PMV32 = 9.336E+08 

PMV33 = 91.249 

PMV34 = 319.442 

PMV35 = 91.249 

PMV36 = 91.249 

PMV37 = -2.101E+09 

PMV38 = 0.000 

PMV39 = 0.000 

PMV40 = 3000.000 

PMV41 = 120.000 

PMV42 = 0.000 

PMV43 = 0.000 

PMV44 = 0.000 

PMV45 = 0.000 

PMV46 = 0.000 

PMV47 = 0.000 

PMV48 = 0.000 

PMV49 = 0.000 

PMV50 = 0.000 

PMV51 = 0.000 

PMV52 = 0.000 

PMV53 = 0.000 

PMV54 = 0.000 

PMV55 = 0.000 

PMV56 = 0.000 

PMV57 = 0.000 

PMV58 = 0.000 

PMV59 = 0.000 

PMV60 = 0.000 

PMV61 = 0.000 

PMV62 = 0.000 

PMV63 = 0.000 

PMV64 = 91.249 


28 | Journal of Reliable Power 

Copyright © SEL 2004 

(All rights reserved) 

20041004 TP6180

Digital Communications for Power System 

Protection: Security, Availability, and Speed 

Edmund O. Schweitzer III, Ken Behrendt, and Tony Lee, Schweitzer Engineering Laboratories, Inc. 


New channels and digital techniques in communications 

provide opportunities to advance the speed, security, 

dependability, and sensitivity of protection—while 

simultaneously reducing the costs associated with using 

communications. Lower communication costs mean more 

opportunities to benefit from pilot protection. The net result is 

a higher quality of electric power delivered for each dollar 

invested. 

A classical pilot communication scheme is shown in 

Figure 1, and a direct digital-to-digital scheme is shown in 

Figure 2. Clearly, the direct digital system is simpler. In this 

paper, we will show that direct digital communications 

economically provide several bits in each direction—and these 

extra bits lead to simpler, more sensitive, and more flexible 

schemes. 

Figure 1 

Figure 2 

Frequency-Shift Audio Keying Over Voice Channel 

Direct Digital Signaling Over Asynchronous Channel 

II. WHAT IS THE CAPACITY OF A CHANNEL 

TO COMMUNICATE 

How much information can be sent, theoretically and 

practically, through a given channel while still maintaining 

acceptable reliability 

In 1948, Claude E. Shannon [1] mathematically formalized 

a theoretical limit. His theory was that information can be 

reliably transmitted over a noisy channel if the data 

transmission rate is sufficiently low. If the relative noise 

increases, the maximum reliable transmission rate decreases. 

For instance, a channel with bandwidth W and received noise 

power N, can transmit information at rate C with arbitrarily 

high dependability, as long as the average signal power P 

satisfies: 

⎛ P ⎞ 

C = W log2 

⎜ + 1⎟ 

⎝ N ⎠ 

The ratio P/N is the signal to noise ratio (SNR). The base 

of the logarithm depends on how we measure C. When C is 

measured in bits per second, the logarithm is base two. In 

general, the logarithm base is the number of symbols in the 

alphabet to be transmitted. 

Quieter channels lend themselves to faster data 

transmission. Conversely, faster data transmission requires a 

quieter channel. 

If SNR = P/N = 1, then the Shannon limit is C = W 

(bits/second), i.e., the channel capacity for reliable 

transmission is the channel bandwidth. 

If the SNR = 20dB = 100, then C = 6.7 W (bits/second). 

We can see that increasing the SNR gives us an opportunity to 

reliably transmit more data, faster. 

For example, contrast the channel requirements for two 

different transmission rates. A frequency shift keyed (FSK) 

audio tone transmission over a voice channel might carry a 

single bit of information, such as a permissive trip signal. 

Suppose we require transmission to occur reliably in 20 ms, so 

the required data transmission rate is 1 bit / 20 ms = 

50 bits/second. Also assume the receiver filter has a 

bandwidth of 300 Hz. According to Shannon, the received 

signal, after filtering, must have an SNR of greater than about 

0.1. Before filtering, the SNR on a 3 kHz channel must be 

greater than about 0.01, assuming white noise. 

A 9600 bits/second data stream transmitted over a 3 kHz 

channel requires an SNR of at least about 10, according to 

Shannon's work. Therefore, the voice grade channel must be 

about 10/0.01 or 1000 times quieter (assuming the same 

transmit power and modulation techniques) to reliably transfer 

data at 9600 baud. 

In practice, it is difficult to approach Shannon's limits. The 

two examples cited above, when implemented using present 

technology, both need about ten times better SNR than 

Shannon’s limit. 

Both Shannon’s prediction and practical experience show 

that when we have a better channel, we can send more 

information per unit bandwidth. The quality of many digital 

channels is excellent, and opens the door to new digital 

techniques in protection. 

The communications engineer uses encoding and 

modulation techniques to approach Shannon’s limit, and to 

balance data rate with reliability within the context of a given 

application. 

Digital Communications for Power System Protection: Security, Availability, and Speed | 29

III. ENCODING EIGHT BITS FOR DIGITAL TRANSMISSION 

We foresee a great future for sharing a handful of bits 

directly from one relay to another, over an array of digital 

channels of moderate capacity. Pilot protection, control, 

adaptive relaying, monitoring, and breaker-failure are some 

examples. 

Our starting point was eight bits of information in a 

message with enough redundancy to meet protection-security 

requirements, yet efficient enough to be useful at data rates 

from several kilobaud and up. 

A. Security 

Communications are secure when the receiving end 

reliably detects whether the received information differs from 

the transmitted information. 

The standard IEC 834-1 [2] contains recommendations for 

blocking, permissive, and direct tripping pilot schemes, in 

terms of their susceptibility to noise bursts. The short table 

below gives the expected minimum number of noise bursts 

required to produce an undesirable output. 

Scheme Type 

Security 

(bursts/undetected error) 

Blocking 10 4 

Permissive Tripping 10 7 

Direct Tripping 10 8 

To help detect noise bursts, we can add some redundant 

information to the transmitted message. Shannon gives a 

formal definition of redundancy: 

Redundancy = Total Bits Transmitted – Information 

For example, if we transmit a total of 10 bits, and there are 

eight bits of information, then the redundancy is 10 – 8 = 

2 bits. 

Redundancy is necessary, but not sufficient for security. 

One of the objectives of encoding is to make each of the 

distinct messages (e.g., for eight bits there are 256 different 

messages) as different as possible from the rest. The 

quantitative measure of this difference is the Hamming 

distance. It is defined as the minimum number of bits that 

could be corrupted in one distinct message, which would 

result in a different distinct valid message. 

The simplest form of redundancy that increases Hamming 

distance is repetition. Consider a single bit of information 

(permissive trip for instance) that must be received by the 

remote relay from the local relay. If the local relay transmits 

only that bit, the remote relay cannot detect whether the bit 

has been corrupted. The remote relay receives a one or a zero, 

and has no indication if the received value is the same as the 

transmitted value. 

Now assume that the local relay transmits the bit of 

information twice. The receiving relay compares the two bits. 

If they are the same, the receiving relay assumes they are 

correct and accepts the bit of information. But, if they differ, 

the receiving relay discards the information. 

When we inject noise bursts onto the channel, we generate 

messages almost at random, because the bit error rate is so 

high. There are two valid messages (00 and 11) and two 

invalid messages (10 and 01). Therefore, we expect that a 

randomly generated message will be accepted by the receiving 

relay half the time, or once per two noise bursts. Since that is a 

long way from 10 7 , add more redundancy. 

If the transmitting relay adds another bit of redundancy, 

then there are still only two valid messages (000 and 111), but 

there are now six invalid messages (001, 010, 011, 100 101, 

and 110). The receiving relay will accept a randomly 

generated message two out of eight times, or one out of four, 

on average. 

Every time we add a bit of redundancy, we cut the 

probability of accepting a randomly generated message by 

half. Thus, the expected number of randomly generated 

messages is 2 n per undetected error, where n is the number of 

redundant bits. 

We need log 2 (10 7 ), or about 23.3, bits of redundancy to get 

10 7 security. Our 1 bit of information, plus 24 redundant bits, 

yields a 25-bit message. 

This method does not make very good use of our channel 

however, because we must transmit 25 bits to securely 

communicate a single bit of information. Now that we have 

the required security, we can add more information bits with 

no loss of redundancy. 

Suppose we decide to repeat eight bits of information three 

times, and add some channel framing bits for 36 bits total. 

Four of these channel framing bits do not count as redundant 

bits, so there are 36 – 4 – 8 = 24 redundant bits. We have 

increased our information transmission capability by a factor 

of eight over the original single bit, decreased the rate of 

transmission by 1 – 36/25 = 44%, and maintained 2 24 = 1.7 x 

10 7 security to randomly generated messages. 

B. Dependability 

Suppose we want to transmit eight data bits with 10 7 

security as described above. We have shown that the message 

must consist of at least the eight data bits plus 24 redundant 

bits, plus some non-redundant channel framing bits (36 bits 

total). 

Assume that channel errors occur at some average random 

bit error rate (BER). The receiver rejects an entire message of 

36 bits even if just one bit is in error. In addition, after the 

receiver detects a bit error, it will probably require that two or 

more consecutive messages are received without error before 

using the received information. The probability that a message 

will not be accepted is about 2 • k • BER, where k is the 

number of bits in the message. This approximation holds for 

2 • k • BER < 0.1. Therefore, we expect the average 

unavailability to be about 72 times the channel bit error rate. 

By increasing the redundancy from one to 24 bits we have 

increased security from 2 to 10 7 . Simultaneously, we increased 

unavailability by a factor of 72. If we started with a channel 

with BER of 10 -6 the unavailability is now 72 x 10 -6 . This 

demonstrates a trade-off between security and dependability: 


increasing security by a factor of 10 6 decreased dependability 

by a factor of 72. 

C. Speed 

Again consider the 36-bit message developed earlier. 

Compared to the two-bit message with a single redundant bit, 

it takes 18 times as long to transmit/receive. At 

9600 bits/second, it takes about 3.6 ms to transmit/receive the 

36-bit message, compared to 0.2 ms for the 2 bit message. 

Therefore, increasing security decreases speed somewhat. 

D. Adaptability 

The 36-bit message developed above gives 10 7 security, 

and, when coupled with the proper digital channel, still yields 

high speed and excellent dependability. Suppose we use one 

of the eight data bits for a block-trip signal, and another of the 

bits for a remote-control direct-trip signal. The security 

afforded by the 36-bit protocol is sufficient for blocking 

schemes. However, IEC 834-1 recommends ten times better 

security for direct tripping. We want to increase the security of 

the direct trip signal without affecting the speed or availability 

of the blocking signal. 

This is easily accomplished with a pickup security counter 

on the direct trip bit. For example, a count of two requires 

reception of two successive 36-bit messages with the direct 

trip bit set before updating the direct trip bit in the receiving 

relay. If we return to the test prescribed by IEC 834-1, we 

would still expect to inject 10,000,000 bursts of noise, on 

average, to get one corrupted message that is incorrectly 

accepted by the receiving relay. However, to perturb the 

direct-trip bit qualified by a two-count security counter, the 

very next message must also be acceptable, and must have the 

same direct trip value. This also happens about one in 

10,000,000 times. So the probability of a false trip in response 

to noise bursts is about (10 7 ) 2 or 10 14 . This is six orders of 

magnitude more secure than the IEC 834-1 recommendation 

for direct tripping. 

Remember we must trade off speed and/or availability to 

gain security. Here, the direct trip signal is delayed by one 

additional message-time, and the unavailability is roughly 

doubled. 

E. Practical Implementation 

We implemented the 36-bit code described above. The 36- 

bit message is transmitted at 19,200 kbits/s in 36/19,200 = 

1.875 ms. Allowing for 2 ms of latency, plus 2 ms for 

processing time in the receiving relay, gives a total of about 

6 ms from the time the transmitting relay makes a decision to 

when the receiving relay has makes a decision influenced by 

the transmitting relay. 

The delays for a tone set between two relays are much 

longer: 

2 ms output contact + 12 ms tone set + 

2 ms latency + 2 ms processing = 18 ms. 

Thus, the direct digital communications gives us eight 

times the data with one-third the delay, at far less cost and 

complexity. 

To test the protocol security, we injected 200 ms long 

white noise bursts onto a direct copper connection between 

relays. We set the transmitting relay to transmit a known set of 

eight bits, and we set the receiving relay to trigger an event 

report upon reception of anything but that known pattern. 

The receiving relay triggered the first event report after 

7 million noise bursts. We terminated the test after 20 million 

noise bursts (and nearly 50 days) with still only one 

undetected error. 

F. Applicability 

Since the protocol described above is a simple serial bit 

stream, it is compatible with many channels and many types 

of data communications equipment. 

G. Channel Performance Monitoring 

Digital communications provide opportunities for 

performance monitoring, so the quality can be assessed, and 

problems can be quickly detected and remedied. 

One channel monitor tallies the time the received data are 

corrupted or absent, and normalizes that time to the total 

elapsed time. This directly measures the unavailability of the 

communications. Although unavailability is a useful long-term 

measurement, it hides long but infrequent channel 

disturbances. For example, suppose a channel monitor is set to 

alarm when the unavailability exceeds 500 x 10 -6 . If that 

channel is error-free for one year and then the channel is 

completely lost, the unavailability monitor will not alarm until 

four hours later. 

A second monitor can be used to alarm when the channel is 

not available for a certain continuous time, say one second. 

The unavailability alarm responds to gradual degradations 

in bit-error rate. The duration alarm responds more quickly to 

outright channel failures. 

A sample report from such a monitor follows. It reports the 

256 most-recent errors, the average unavailability for the time 

of the report, and the longest-duration channel outage. 


Summary for Channel A 

For 06/19/98 15:43:48.887 to 07/30/98 10:13:11.925 

Total failures 14 Last error Re-sync 

Relay disabled 1 

Data error 4 Longest failure 0 00:00:41.352 

Re-sync 4 

Underrun 1 Unavailability 0.000015 

Overrun 0 

Parity error 3 

Framing error 1 

START START END END 

# DATE TIME DATE TIME DURATION EVENT 

1 07/10/98 11:19:14.769 07/10/98 11:19:24.419 00:00:09.650 Re-sync 

2 07/09/98 11:48:13.572 07/09/98 11:48:14.126 00:00:00.554 Underrun 

3 07/09/98 11:48:12.710 07/09/98 11:48:13.481 00:00:00.770 Re-sync 

4 07/09/98 10:38:32.062 07/09/98 10:39:13.414 00:00:41.352 Parity error 

5 07/07/98 09:33:35.389 07/07/98 09:33:35.419 00:00:00.029 Re-sync 

6 07/07/98 09:21:44.183 07/07/98 09:21:44.229 00:00:00.045 Parity error 

7 07/07/98 09:21:44.087 07/07/98 09:21:44.154 00:00:00.066 Data error 

8 07/07/98 09:21:36.077 07/07/98 09:21:36.127 00:00:00.049 Data error 

9 07/07/98 09:21:33.727 07/07/98 09:21:33.777 00:00:00.050 Data error 

10 06/29/98 09:19:12.075 06/29/98 09:19:12.120 00:00:00.044 Framing error 

11 06/26/98 15:04:28.653 06/26/98 15:04:28.701 00:00:00.047 Data error 

12 06/26/98 15:01:40.209 06/26/98 15:01:40.243 00:00:00.033 Re-sync 

13 06/26/98 15:00:27.803 06/26/98 15:00:27.845 00:00:00.041 Parity error 

14 06/19/98 15:43:48.887 06/19/98 15:43:48.887 00:00:00.000 Relay disabled 

=> 

This specific channel is a digital leased line running at 

56 kbaud. The relay detected 14 total errors that resulted in an 

average unavailability of 15 x 10 -6 . The longest channel 

outage was 41.352 seconds. 

Notice that the errors are grouped in clumps. The report 

was cleared on 6/19, and the circuit experienced no errors 

until 6/26. On 6/26 there were three errors in four minutes. 

The circuit was then perfect for three days, until a single error 

occurred on 6/29. There were no more errors for over a week, 

then there were four errors in eleven seconds, followed by 

another error twelve minutes later. After two days without 

error, there was a span of 41 seconds where the relay did not 

receive an acceptable message. This underscores the 

additional value of a continuous outage monitor, because the 

unavailability monitor would not have alarmed for this outage 

unless it was set as low as 30 x 10 -6 . On the next day another 

extended outage of over nine seconds occurred. The channel 

was error-free for the next 20 days, from 7/10 to 7/30, when 

the report was downloaded from the relay. 

Later, we will discuss error-seconds per day as a measure 

of quality of the leased lines. Performance monitoring 

provides the quantitative feedback needed to maintain and 

improve the quality of communications. Relay event reporting 

provides an additional perspective on the performance of 

communications for every event, because the communicated 

bits are reported as additional I/O points. For example, 

communications disruptions during faults are easily observed, 

should they occur. 

IV. CHANNELS 

This section compares some communications channels that 

might be used in pilot and control schemes. 

A. Dedicated Fiber 

Perhaps the ultimate digital channel in terms of 

dependability, security, speed, and simplicity is dedicated 

fiber optics. Low-cost fiber-optic modems make dedicated 

fiber channels even more attractive. Often, the modems can be 

powered by the relay, eliminating the cost and loss of 

availability involved in separate power sources. Some 

modems also plug directly onto the digital relay [3], which 

eliminates a metallic cable. Eliminating the cable and the 

external power source removes “antennas” for possible EMI 

susceptibility. 

When the communications path is short, the cost of the 

fiber is not very significant. On longer paths, multiplexers 

may be considered, to increase the amount of data 

communicated over a fiber-pair. However, the relatively small 

incremental cost of adding and using one fiber-pair for 

protection alone is probably justified by the increase in 

simplicity and availability that a dedicated fiber scheme 

offers. Furthermore, the small incremental cost is partially 

offset by the very low cost of the simple direct-connected 

fiber-optic modems. 

Bit errors are extremely rare on most fiber-optic links. If 

the link is available, then it is near-perfect, because the fiber 

medium is unaffected by the RFI, EMI, ground-potential rise, 

weather, and so on. 


The receiver amplifier is the major source of noise in the 

system—and that noise source is very small compared to the 

large signals used in simple, practical systems. The received 

signal strength is the transmit power minus attenuation. 

Attenuation in decibels is proportional to fiber length plus 

some loss for each connection or splice. A system designer 

usually fixes the transmit power at some level, specifies a 

power margin, and then guarantees some allowable fiber 

length at some maximum bit-error-rate or BER. If we use less 

fiber or fewer connections, there is more signal power at the 

receiver, and the BER decreases. 

Suppose the system designer chose a maximum allowable 

BER of 10 -9 at some maximum allowable fiber length. 

Figure 3 was adapted from [4]. It shows that decreasing the 

fiber length by 40% in such a system (to 0.6 per unit), 

decreased the BER from 10 -9 to about 10 -23 , a decrease of 14 

orders of magnitude! Random bit errors cease to be an 

important source of unavailability. 

Unavailability then becomes dominated by other factors 

such as fiber breaks, misapplications, etc. Therefore, welldesigned 

fiber-optic communications systems will result in 

long periods of error-free performance separated by complete 

outages caused by human factors or equipment failure. 

BER 

Figure 3 

Bit Error Rate vs. Normalized Fiber Length 

10 -10 

10 -15 

10 

-25 

10 

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 

10 -5 Fiber Length (1.0 at BER=1.0E-9) 

Conservative Designs Yield Near-Zero BER on Fiber Links 

Does this mean we can ignore communications security 

No. Consider what happens to a fiber-optic receiver when a 

user disconnects one end of the fiber while the link is in 

service. The disconnection process is slow compared to most 

fiber-optic data transfer rates. As the user draws the fiber 

away from the receiver, attenuation increases and ambient 

light begins to flood the receiver. This causes the bit error rate 

to increase until the received bit stream is essentially all noise. 

The receiving device must recognize this noise and reject the 

corrupted data, or a misoperation may result. The security 

built into the 36-bit message described earlier is sufficient to 

ensure less than a 10 -7 chance that disconnecting the fiber 

could cause an undetected error. A security counter of just two 

virtually eliminates the risk, even for direct tripping. 

Can direct fiber channels be affected by faults There is 

some risk that the physical event which breaks the fiber could 

cause the fault, such as a tower collapse or static wire failure 

where the fibers are in the static wire. Tornadoes, ice loading, 

or an airplane collision are also possibilities. Even then, there 

is some chance the message will get through to permit the 

scheme to work, after the fault occurs and before the channel 

is destroyed. 

When a dedicated fiber is closely associated with the power 

line right-of-way, the probability that an external fault will 

cause a communications disturbance is negligible. 

B. Multiplexed Fiber 

Fiber-optic multiplexers combine many relatively slow 

digital and analog channels into one wideband light signal. 

The multiplexer, therefore, makes efficient use of bandwidth 

in the fiber. A direct digital connection between the relay and 

the multiplexer is more reliable and economical than 

interfacing through conventional relay contacts, then a tone 

set, and into an analog channel on the multiplexer. The 

multiplexer adds a level of complexity, which can be avoided 

by the simple dedicated fiber approach discussed earlier. 

C. Fiber-Optic Networks 

Wide-area networks, such as SONET, move large 

quantities of data at high speed. Many such networks consist 

of self-healing rings. 

Since the self-heal time is long compared to expected 

protective relay tripping times, we must still be concerned 

with correlation between faults and communications 

problems. 

There is a tradeoff between long-term availability and 

short-term dependability. The ring self-heals so that 

communications are rarely totally lost. However, a failure 

anywhere in the network results in a short communications 

loss. Power Networking [5] describes a cascaded ring 

topology that reduces the exposure to these short interruptions. 

While the ring is self-healing, the terminal equipment is 

generally not. Thus the terminal equipment, and possibly other 

points, must be considered as possible single points of 

failure—even though we have a self-healing ring. 

D. Multiplexed Microwave 

Microwave systems have gone digital, too—opening new 

opportunities for direct relay-to-relay communications. (Later 

we describe a low-delay modem, which can be used to transfer 

digital information through analog microwave channels, with 

the quality required for pilot protection.) 

Microwave equipment failures include multiplexers, radio 

gear, antenna pointing errors, cabling, etc. Microwave 

communications are fairly immune to power system faults. In 

general, the likelihood of a communication failure for an 

internal fault is not much different from the likelihood of a 

failure for an external fault. 

E. Narrow-Band UHF Radio 

Dedicated radios have been used for pilot channels. 

Reference 1 describes how a 960 MHz radio link was used in 

a POTT scheme. The radio was purchased with a single onoff-keyed 

tone interface between the radio and the relay 


contact I/O. The security of this scheme comes from the 

inherent security of POTT schemes. 

Narrow-band digital radios permit the use of direct digital 

communications. The performance would be similar to that of 

the microwave system given earlier, but may be more reliable 

than a channel in a microwave system, because of lower 

complexity. 

Radio channels are relatively immune to interference from 

faults. One possible source of interference is the power wiring 

to the radio. Radio channels might also be disrupted by 

antenna-pointing errors and severe weather. 

Radio and fiber channels can be highly complementary. 

Mechanical damage that might disrupt a fiber channel is 

generally unlikely to interfere with a radio channel, and vice 

versa. However, it is possible to conceive of events that would 

destroy both communications channels and cause a fault. For 

example, suppose a radio tower collapses during an 

earthquake or windstorm, and falls through the static wire 

with the fiber in it, and then causes a line fault! 

F. Spread-Spectrum Radio 

Spread-spectrum techniques have been broadly applied in 

radar systems to increase the energy in a radar pulse, while 

maintaining and enhancing target resolution. Spread-spectrum 

communications are used in military applications for the 

advantages of communications security, interference 

immunity, low probability of detection, and difficulty in 

jamming. Commercial uses of spread-spectrum radio have 

been growing, ever since the Federal Communications 

Commission permitted license-free operation under certain 

conditions. For power system protection, the advantages of 

spread-spectrum radio channels are immunity to interference, 

freedom from licensing requirements, and low cost. 

Signals may be spread in the frequency domain by several 

methods. For example, frequency hopping, either slow or fast 

compared to the information rate, spreads the signal over the 

spectrum covered by dozens of discrete frequencies occupied 

sequentially in time, in a pseudo-random sequence. Directsequence 

spread spectrum systems, on the other hand, 

multiply the information bit stream by a much faster pseudorandom 

binary sequence. The bandwidth is expanded by the 

fast rate of the pseudo-random sequence. 

The processes of spreading, despreading, synchronization, 

and forward error correction (FEC) take some time, and, 

depending on the scheme, may be too slow for teleprotection. 

Most presently available radios also rely on the data terminal 

equipment (DTE) to negotiate a half-duplex channel. 

However, at least one model automatically switches its halfduplex 

channel rapidly enough to simulate full-duplex 

transmission at speeds as high as 19,200 baud. This same 

radio performs no FEC, and so has a very reasonable roundtrip 

delay of about 2.5 power system cycles. The cost, power 

requirements, and performance are promising for applications 

all the way down to distribution voltages [7]. 

G. Digital Telephone Circuits 

Telephone companies offer leased digital lines for several 

hundred dollars per month, and these can be used for pilot 

protection schemes. A CSU/DSU interfaces the protective 

relay to the leased line. It receives timing information from the 

telephone company equipment via the leased line, and passes 

that timing information on to the relay (for synchronous data) 

or synchronizes the asynchronous data stream from the relay 

(for asynchronous data). It also converts the serial data 

received from the relay to the proper electrical levels and 

format. 

The digital data are not modulated on the twisted pair in the 

traditional sense; they remain binary (actually ternary) while 

on the leased line. Such communications are characterized by 

long periods between short bursts of errors. For example, the 

standard AT&T Technical Reference TR 62310 [8] defines 

acceptable performance of a 56kbps using the concept of an 

error-second (ES) and a severe-error-second (SES). At 

56 kbps, an ES has between one and 56 bit-errors. A SES has 

more than 56 bit-errors. That standard allows 20 error-seconds 

and six severe-error-seconds per day. 

If we assume each ES results in 1 second of protection 

scheme unavailability, then communications-assisted 

protection might not be available for 26 seconds per day. This 

is a very extreme upper limit. 

Like fiber-optic links, digital leased lines are distancesensitive. 

Far from the distance limit, the actual performance 

is significantly better than the worst-case prediction above. 

Never accept anything close to the worst-case scenario 

depicted above. We have experience with digital leased lines 

that produced less than one error every three days. Earlier in 

this paper, we presented data from a digital line that was 

unavailable for approximately 1 minute during a 40 day 

period. This is 17 times better than the worst-case scenario. 

Another factor affecting error rates on digital leased lines is 

transmit power. In AT&T Data Communications TR 62310 

transmit power is restricted at 9,600 and 12,400 bits per 

second to 1/4 of the power allowed at other rates. At least one 

CSU/DSU manufacturer takes advantage of the higher 

allowed transmit power at data rates other than 9,600 and 

12,400 bits per second. As with fiber optics, increasing the 

transmit power by a factor of four on a twisted pair can have a 

profound impact on random bit errors. Assuming a leased line 

takes advantage of the higher permitted power, then rates 

other than 9,600 are greatly preferred. 

Any leased line must be galvanically isolated between the 

substation and the central office. This isolation prevents 

damage and danger when ground faults produce high voltages 

between the substation ground and the telephone exchange 

[9]. However, isolation does not guarantee that the leased line 

will remain operational during the fault. Ground potential rise 

or noise coupled from the faulted power line to the twisted 

pair can produce enough noise on the circuit to cause bit errors 

or a complete loss of signal. The analysis required to 

determine if a circuit will remain operational would be 

difficult. 


Noise from faults or other sources that might not corrupt 

signaling by audio tones over a given twisted pair still might 

interfere with fast digital signaling over that same channel. 

(Recall that faster signaling requires a higher SNR, given the 

same bandwidth.) 

H. Analog Voice-Grade Channels 

Figure 4 shows a low-delay modem interface between the 

direct digital data from the protective relay, and a voice 

channel. The voice channel may be analog microwave, a 

leased circuit from the telephone company, a dedicated 

twisted pair, or something similar. Analog channels on 

microwave should not suffer the same degradation during 

power system faults as analog channels on a twisted pair or 

some other conductor. The challenge becomes modulating the 

9600 bit per second data stream so it will be compatible with 

the 300 to 3,000 Hz audio band channel. 

Relay 

U 

A 

R 

T 

Figure 4 

Asynchronous 

Serial Bit 

Stream 

Power 

Low-Delay Modem 

Quadrature 

Amplitude 

Modulated 

Direct Digital Signaling Over Voice Channel 

Voice Channel 

Computer modems generally are unsuitable for protection. 

They are optimized for throughput, at the expense of delay. 

Therefore a special low-delay modem was developed. It also 

takes a very short time to adapt to changes in the channel 

(retraining), compared to computer modems [10]. 

V. PILOT PROTECTION APPLICATIONS 

Direct underreaching transfer trip schemes require 

extremely secure communications, because there is no local 

confirmation that a fault exists. DUTT is very simple. The 

digital communications described in this paper provide much 

greater security than that required by IEC 834-1 for direct 

tripping, when the protection scheme uses a security count of 

two or greater. It is inherently secure from current reversals. 

Permissive underreaching transfer trip does not require as 

secure a level of communications, because the received 

underreaching element is qualified by a local overreaching 

element. The scheme is also quite simple, and requires no 

current-reversal logic. Sensitivity is very similar to DUTT. 

Permissive overreaching transfer trip schemes provide 

greater sensitivity, and have the same channel dependency as 

PUTT. In most cases, POTT schemes must be protected 

against current reversals. POTT schemes handle weak 

terminals, when the schemes include echo logic. If internal 

faults cause channel failures, then POTT schemes may not 

operate. 

Directional comparison blocking schemes provide very 

similar speed and sensitivity to POTT with echo logic, yet 

DCB schemes do not require echo logic. DCB schemes must 

also be protected against current reversals. If external faults 

cause channel failures, then DCB schemes will overtrip. The 

security and practicality of DCB schemes depend on known 

and reasonable upper limits on element pickup times and 

channel delays. 

Directional comparison unblocking schemes attempt to 

give the best of POTT and DCB. DCUB schemes only make 

sense when we can definitely associate a much greater 

likelihood of channel failures with internal faults, than with 

external faults. For example, DCUB might be sensible for a 

power-line carrier channel, or an optical-fiber in the shield 

wire of the protected line. 

Consider some pilot-scheme possibilities, given different 

channels. 

A. Fiber-Optic Ring 

A good approach is POTT, with weak-infeed and openbreaker 

echo. DCB should not be used because: security 

depends directly on availability of the communications, we 

cannot associate channel failures with internal faults, and 

communication delays may depend on routing. DCUB should 

not be used, because we cannot associate channel failures with 

internal faults. 

B. Leased Digital Line 

As with the ring, it is not generally possible to associate 

channel failures with either internal or external faults, and 

delays may be variable. Therefore DCB and DCUB should be 

avoided. 

C. Dedicated Fiber Optics 

If the fiber and the power line share the same path, then 

DCUB might be used to gain some availability, with little loss 

in security. This is because channel failures simultaneous with 

faults might reasonably be associated with internal faults. 

Sending multiple bits in each direction opens up some new 

possibilities in pilot protection. 

D. Cross-Country Faults 

Consider a double-circuit line from S to R, as shown in 

Figure 5. An AG fault on Line 1 simultaneously exists with a 

BG fault on Line 2. In a single-pole-tripping scheme, the 

desired action is for Line 1 to trip phase A, and Line 2 to trip 

phase B, so service is essentially uninterrupted between S and 

R. If the relays at R communicate the observed fault types, 

then the relays at S can trip single-pole and avoid the 

undesired three-pole trips for this situation. The fault type is 

easily communicated on three bits, or on just two, with some 

encoding. 

Figure 5 Communicate Fault Type for Secure Single-Pole Tripping 


E. Remote-End Open Keying 

Given a line from S to R, assume the breaker at R is open. 

A POTT scheme needs to inform S that R is open. 

Traditionally, there are two ways. One is for S to send 

permission to R and for R to “echo” the permission back to S 

based on the open-breaker status. This status is sensed by 

monitoring an auxiliary contact at R. Breaker S trips after two 

communications delays, plus possibly an echo time-delay in 

terminal R. Given 16 ms for the protective relay element at S, 

12 ms for each communications delay, and no echo time-delay 

in R, we have a total time of 40 ms from fault inception until S 

trips. (Another timer is used to limit the echo duration to a few 

cycles, so the channel does not lock up.) 

A second method is for terminal R to send S a standing 

permission whenever the breaker at R is open. Both 

communications delays are eliminated, so tripping can occur 

in just relay-element time, e.g., 16 ms. With conventional 

channels, this method makes a compromise with security 

because guard-before-trip cannot be used. However, with 

direct digital communications, the security is built into the 

message so no loss of security occurs with hard-keying. 

An alternative is shown in Figure 6, where the remote end 

transmits its breaker status and breaker control commands to 

the local end. Overreaching elements trip the local breaker, as 

long as the remote end is open. The philosophy here is for the 

remote end to send the local end the state of the breaker so 

that the local end can directly observe it and use it as desired, 

in this scheme and possibly others. If the local end receives 

notice of close commands from the remote end, then this 

scheme can be briefly delayed to avoid risk of misoperation by 

very sensitive elements due to pole scatter. Other advantages 

are that this scheme is never encumbered by current-reversal 

timers, and it is possible to use different overreaching 

elements when the breaker is open than when it is closed. 

Figure 7 Avoid Lockup With Simple POTT Scheme 

G. Control and Balance of Speed, Sensitivity, and Security 

With multiple bits of information to transfer, we can 

consider schemes that simultaneously coexist and provide the 

advantages of each, while minimizing the risk of their 

individual disadvantages. Figure 8 and Figure 9 illustrate the 

concept for ground faults. The design uses an individual bit 

(channel) for each relay element that is desired at the remote 

end—instead of combining them into one. Then each terminal 

uses the set of local and remote elements to make its 

decisions, as desired or required by the immediate operating 

conditions. 

1 

2 

Remote 

Elements 

Zone 1 

Zone 1.5 

Local 

Elements 

Zone 1 

C 

0 

C Security Counts 

Zone 1.5 

Direct Trip 

Direct Transfer Trip 

PUTT or Short-POTT 

3 

Zone 2 

Zone 2 

POTT 

4 

Zone 3 

0 

T 

Figure 6 

Line Protection for Open-Remote-End 

Zone 3 

0 

T 

F. Simplify Pilot Logic 

When a single bit is available, say in a POTT scheme, a 

timer and additional logic are necessary to avoid latching the 

channels on during echo. The logic is simpler if we elect to 

use individual bits to transmit the status of individual relay 

elements, and of the breaker. Each terminal builds up its trip 

outputs from the locally-observed and remotely-reported relay 

elements without the need for feedback paths that lead to 

channel lock-up or other surprises. Figure 7a shows how a 

traditional POTT scheme avoids channel lock-up with extra 

logic and a timer. Figure 7b shows a simpler scheme, which 

does not have the risk of lock-up because there is no feedback 

path. 

5 

6 

50N 

ROK 

50N 

Figure 8 Balance Sensitivity, Speed, and Security 

T 

T 

0 

0 

S Not Blocked 

R Not Blocked 


80 

60 

40 

20 

R F 

100 

3 3 

S 

2 

5 6 

4 

1.5 1.5 

4 4 

1 3 

1 

2 

1 

2 

Figure 9 Fault Resistance Regions Covered by the Schemes in Figure 8 

The standard IEC 834-1 suggests that the user should 

decide the states of communicated bits, given a loss of 

communications. For example, during a loss of 

communications, should the received bit maintain (hold) its 

previous state, or default to a 1, or to a 0 As we apply bits in 

various schemes below, we will also determine the desired 

action of the bits given communication loss. 

A local Zone 1 element, such as a ground quadrilateral 

element, trips the breaker directly. Non-pilot tripping 

covers the area of overlap of the zones 1, marked by the 

circled 1 in the house-shaped characteristic in Figure 9. 

We must rely on the channel, or wait for zone timers 

for all other faults. Appendix A gives some guidelines 

for setting the resistance and reactance reaches, taking 

into consideration some of the angle errors that might 

be expected. 

The remote Zone 1 element state is communicated on 

one bit and passes through a local security counter to 

provide a Direct Transfer Trip. The additional regions 

covered are marked by the circled 2s. Given a channel 

failure, the received bit should default to a ‘0’. (A 

default of ‘1’ would trip the remote breaker for 

communications failures; a default of ‘hold’ defeats the 

receive security counter.) 

PUTT and short-POTT schemes follow: 

In a PUTT scheme (not shown in Figure 8), the local 

Zone 2 element would be set to reach beyond the 

remote end. The remote Zone 1 element is an 

underreaching element. The scheme is fast and 

simple—and is not encumbered by current-reversal 

timers or logic, which might delay tripping for faults 

that evolve to the healthy line. 

A short-POTT scheme can also be considered here, and 

is illustrated in the figures. The Zone 1.5 elements at 

2 

R F 

R 

each terminal would be set to cover the entire line, but 

would have their reaches limited sufficiently to avoid 

current-reversals on parallel paths. This improves faultresistance 

coverage and speed over PUTT, but does not 

involve current-reversal timing. 

Elements for a short-POTT scheme are labeled 1.5, and 

cover the additional area marked with the circled 3. 

The received bits should default to ‘0’ for 

communications failures. There is no benefit to 

holding—only risk. 

A POTT scheme based on directional overcurrent 

elements, labeled Zone 2, can provide some more 

sensitivity, but must be guarded against current 

reversals. Reverse-looking elements (Zone 3 directional 

overcurrent elements) and timers provide blocking for a 

short time after current reverses. The delay that would 

result if a fault evolved from one line to the other is not 

important, because of the coverage by the PUTT or 

short-POTT schemes. A timer could be added after the 

AND-gate, to gain some security against system 

unbalances produced by switching, for example. The 

additional coverage from the POTT scheme is labeled 

with the circled 4. 

Received bits for Zone 2 should default to ‘0’ on loss of 

channel. A ‘hold’ or ‘1’ would significantly risk 

misoperation, with little or no benefit in dependability. 

The Zone 3 received bits should default to a ‘0,’ if 

communications are lost. A default to a ‘1’ would 

defeat the protection for T seconds for every bit error. 

A high-resistance fault close to S could be in region 5, 

which is not covered by the POTT scheme. After some 

time delay, and if no reverse elements pick up at the 

remote end, we can trip for such a fault, with the 

sensitivity we are accustomed to with DCB schemes. 

However, this scheme enjoys much greater security 

than DCB. 

Conventional blocking schemes assume the fault is 

internal if the blocking message is not received. (The 

truth might be that the channel or relay equipment 

failed to deliver the message to block. Put another way, 

in traditional DCB schemes, the block signal means 

“reverse.” No block signal means “forward,” “not 

detected,” or “bad channel.”) 

Here, the local terminal knows with near certainty the 

states of the remote forward and reverse elements, or it 

knows the channel is down. There is no confusing a lost 

channel with an internal fault. The fact that we are 

receiving messages from the remote end reassures us 

that the remote relay is functioning, and ready to 

produce blocking signals when appropriate. 

In addition, the security can be enhanced somewhat by 

an undercurrent element, 50N. This element would 

block tripping, if enough residual current is produced 

by an open CT, for instance. 


The received-OK signal (ROK) ensures this part of 

the logic is active only if the remote end is 

successfully communicating, and therefore in a 

position to block the local end should an external 

fault occur. 

If the source behind R is very weak, then Zone 2 at R 

might not be able to see all the way back to S. This is 

the only scheme described here that is capable of 

detecting the fault. 

A high-resistance fault near R can be cleared in a 

complementary way, as compared to above. The 

ROK signal is not necessary, assuming the Zone-2- 

received signal defaults to a zero on communications 

loss. 

Protection speeds can be impressive, as the following quick 

look at a POTT scheme reveals. Consider a direct digital link 

at 19,200, and allow 6 ms for the message and processing 

time. Assume the overreaching elements operate in under 

12 ms, and the relays use instantaneous trip contacts, such as 

transistors. Both terminals trip their breakers in less than one 

cycle. With a 1.5-cycle breaker, the fault is cleared in under 

2.5 cycles, at both ends. Given such fast tripping, and also 

given that the channel could be used for breaker failure, we 

should investigate shorter breaker-failure times and faster 

time-step backup. 

In summary, the direct tripping Zone 1 elements cover very 

little of the line when the channel is not available. The 

coverage is limited to the small region of overlap near the 

middle of the line. The direct transfer trip path depends on 

secure measurements from one end, but involves a short 

security delay of about 4 ms. Because it depends on 

information from the remote end alone, it can trip the local 

breaker even if there is a problem at the local terminal such as 

a loss-of-potential (LOP) condition. The short-POTT path 

approximately doubles the fault resistance coverage as 

compared to the DT and DTT paths, but could be disabled by 

a LOP condition at either end. The POTT scheme adds 

sensitivity and speed (which might be sacrificed with an extra 

timer, if temporary unbalances could pick up the sensitive 

overreaching elements). Again, both ends must determine the 

fault to be internal. The last two schemes cover faults in the 

“bow-tie” regions labeled with the circled 5 and 6. Some time 

delay is required to wait for the possible block from the other 

end. Overcurrent elements can block these two regions, to 

ensure they are only active for low-level currents, thereby 

reducing the risk of misoperation should a current transformer 

fail at either end. 

It should be noted that the schemes above are presented as 

a concept, to show how communicating multiple bits of 

information end-to-end can produce an adaptive and balanced 

protection scheme. 

VI. CONCLUSIONS 

1. The high quality of many digital communications 

channels permits more information to be sent in less 

time, as predicted by Shannon and demonstrated in 

practice. 

2. Direct-digital communications between relays can be 

designed with the security, speed, dependability, and 

adaptability needed for blocking, permissive, and 

direct-tripping applications—as well as for control. 

3. Eight bits can be securely communicated every 2 ms, 

with a worst-case end-to-end delay of 6 ms, including 

processing latency, over a 19,200 bit/second channel. 

4. Extremely secure direct transfer tripping can occur in 

less than 6 ms, when a two-message sequence is 

employed over a 19,200 bit/second channel. 

5. Direct communications using a simple serial 

asynchronous bit stream ensures compatibility with a 

wide variety of communications channels, systems, 

and test equipment. 

6. Channel performance monitoring, including sequence 

of events, outage duration, and unavailability provides 

the measurements of performance required to maintain 

and improve communications—without periodic 

testing. System operation is a continuous test of the 

channel. 

7. Relay event reports closely relate the performance of 

the protection and the communications, during faults 

and other events. 

8. Fiber-optic networks and links, digital microwave 

systems, and point-to-point radio (narrow-band and 

spread-spectrum) are excellent channels to consider 

for direct digital-to-digital applications. The 

combination of lower-cost channels with direct relayto-relay 

communications opens up applications at 

lower voltages, including distribution feeders. 

9. Although metallic circuits have demonstrated 

satisfactory performance in the field, we must consider 

ground potential rise, isolation, and induced 

interference during faults. Channel and event 

monitoring can quickly point out difficulties, should 

they appear, and lead us to their resolution. 

10. High-quality analog channels, such as analog 

microwave, can be used for digital communications at 

protection speeds with the help of a limited-delay 

modem. 

11. As always, the channel characteristics, including 

signal routing, must be considered in selecting and 

designing protection schemes. 

12. Because channels fail in different ways, using 

different channel types can provide redundancy 

against failures produced by faults. 

13. Communicating eight bits end-to-end opens 

opportunities for new protection schemes, and for 

combining traditional schemes for enhanced 

performance. 

14. Schemes can be simpler, and some problems, such as 

channel lockup, can be avoided or solved more simply 

when more than one bit is available end-to-end. 


15. A POTT scheme implemented over a 

19,200 bit/second channel can clear at both ends in 

less than one cycle, plus breaker times. 

VII. REFERENCES 

[1] Shannon, C.E., 1948, “A Mathematical Theory of Communication,” The 

Bell System Technical Journal, Volume XXVII, July. 

[2] IEC 834-1, Performance and Testing of Teleprotection Equipment of 

Power Systems. Part 1: Command Systems, May 1996. 

[3] OSD 136L, Optical Systems Design Pty Ltd 7/1 Vuko Place, 

Warriewood 2102, NSW Australia; http://www.optsysdesign.com 

[4] Haus, Robert J., 1980, Fiber Optics Communications Design Handbook 

pg 158. Inglewood Cliffs, New Jersey: Prentice Hall. 

[5] Gardner, Terry N., 1998, “Power Networking”, Transmission & 

Distribution World, February. 

[6] Kahler, J. Kraig, “Installation of 930-960 MHz Low Density Point-To- 

Point Radios and Solid State Relays for Primary Transmission Relay 

Protection on 69 kV Transmission Lines,” 21st Annual Western 

Protective Relay Conference, Spokane, Washington, October 18–20, 

1994. 

[7] Roberts, J. and Zimmerman, K, “Trip and Restore Distribution Circuits 

at Transmission Speeds,” 25th Annual Western Protective Relay 

Conference, Spokane, Washington, October 13–15, 1998. 

[8] AT&T Technical Reference TR 63210, “DS0 Digital Local Channel, 

Description and Interface Specification,” August 1993. 

[9] IEEE Std 487-1992, IEEE Recommended Practice for the Protection of 

Wire-Line Communication Facilities Serving Electric Power Stations, 

November 4, 1992. 

[10] MBT 9600, Pulsar Technologies, Inc., 4050 NW 121st Ave, Coral 

Springs, FL 33065; http://www.pulsartech.com. 

[11] Schweitzer, E.O. III and Roberts, J, “Distance Relay Element Design,” 

19th Annual Western Protective Relay Conference, Spokane, 

Washington, October 20–22, 1992. 

VIII. APPENDIX A: QUADRILATERAL REACTIVE REACH 

VERSUS RESISTIVE REACH SETTING GUIDELINE 

A. Quadrilateral Element Review 

To pick up a forward-reaching zone of quadrilateral ground 

distance protection, the relay must determine that the fault 

presented to the relay passes the following four measurement 

test criteria: 

• Reactance < set reactance (top line) 

• Apparent fault resistance (RF) < positive-resistance 

(right-side) blinder 

• RF > negative-resistance (left-side) blinder 

• Fault direction is forward as measured by a negative- or 

zero-sequence polarized ground directional element 

Equations 1 and 2 repeat the equations shown in [11] for 

the Zone 1 A-Phase reactance and resistance tests. 

R 

X 

AF 

AG1 

jT 

∗ 

( A 

⋅( R 

⋅ ) ) 

jT 

( ) ( ) 

Im V I e 

= 

Im Z I k I I e 

∗ 

( 1L 

⋅ 

A 

+ 

0 

⋅ 

R 

⋅ 

R 

⋅ ) 

∗ 

( A 

⋅( 1L 

⋅ ( A 

+ 

0 

⋅ 

R )) 

) 

Im V Z I k I 

= 

⎛ 3 

Im ⎜ ⋅ I 

⎝ 2 

+ I ⋅ Z ⋅ I + k ⋅ I 

( A2 0 ) ( 1L ( A 0 R )) 

∗ 

⎞ 

⎟ 

⎠ 

(1) 

(2) 

Where: 

Im = Imaginary portion 

V A = A-Phase voltage, [V] 

I A = A-Phase current, [A] 

I R = Residual Current (I A + I B + I C ), [A] 

Z 1L = Positive-sequence replica line impedance, [Ω] 

Z 0L = Zero-sequence replica line impedance, [Ω] 

k 0 = (Z 0L - Z 1L )/(3• Z 1L ), [unitless] 

I A2 = Neg.-sequence current (I A + a 2 •I B + a•I C ), [A] 

I 0 = Zero-sequence current (I R /3), [A] 

T = Nonhomogeneous system factor, [degrees] 

* = Complex conjugate operator 

B. Calculating Reactance Reach As a Function of Resistive 

Reach 

The elements described by Equations (1) and (2) are phase 

angle comparators. For the reactance element described by (1), 

when the angle between the polarizing quantity (I R ) and the 

line drop compensated voltage (Z 1L •(I A + k 0 •I R ) – V) is 0°, the 

impedance is on the reactance element boundary. This element 

must measure line reactance without under- or overreaching 

from the effects of load flow or fault resistance. Hence, the 

element must use an appropriate polarizing current: negativeand 

zero-sequence currents are suitable choices. In some 

nonhomogeneous systems, the tip produced by the polarizing 

current may be insufficient to prevent overreach. To 

compensate for this nonhomogeneity, we introduce polarizing 

current angle bias (tip), or reduce the reach of the Zone 1 

element. 

Reducing the Zone 1 reach restricts that portion of the line 

protected by overlapping instantaneous Zone 1 protection. 

This overlapping “zone” is realized for low-resistance faults. 

As we show next, a large resistive reach can limit the 

reactance element reach when we consider instrumentation 

angle errors. If the quadrilateral ground distance elements are 

the only Zone 1 protection, then we strike a balance between 

overlapping zone for mid-line faults, and large resistive 

coverage by one terminal for close-in faults. 

Specifically, the instrumentation angle errors we consider 

are those due to current transformers (CTs), voltage 

transformers (VTs), and the measuring relay. For our example, 

the values of these angles are: CT = 1°, VT = 2°, Relay 

Measurement = 0.2° 


Let us consider Relay R shown in Figure A.1. 

Figure A.1 System-Single Line and First Quadrant of the Quadrilateral 

Distance Characteristic at Source S Terminal 

For a ground fault outside of the protected zone with a 

reach m [XAG1 of Equation (1)], what is the maximum secure 

reactive reach for a given resistive reach coverage [RAG1 of 

Equation (2)] 

XL 

m⋅ 

XL 

From Figure A.1: tan θ 1 = and tan θ2 

= 

R 

R 

Solve for m: 

m ⋅ X 

R 

∴ 

L 

= tan 

( θ − ε) 

L 

1 

= 

⎛ 

tan⎜ 

tan 

⎝ 

⎛ 

⎜ 

⎝ 

−1 

R ⎛ 

−1 

⎛ XL 

⎞ ⎞ 

m = ⋅ tan tan ε 

X ⎜ ⎜ − 

⎝ ⎝ R 

⎟ 

⎠ ⎟ 

⎠ 

X 

R 

L 

⎞ ⎞ 

⎟ − ε⎟ 

⎠ ⎠ 

For R >> X L , tan -1 (X L /R) and tan(X L /R) ≅ X L /R. (Note: this 

approximation nets an error less than 5% for R/X L > 2.5). If 

we assume the protected system is homogeneous (i.e., the only 

angular errors we must account for are those of the CT, VT, 

and relay), ε = 3°≅ 1/20 radians. Given these simplifications: 

R ⎛⎛ 

XL 

⎞ ⎞ 

m = ε 

X ⎜⎜ 

− 

L ⎝⎝ 

R 

⎟ 

⎠ ⎟ 

⎠ = R ⋅ε 

1− = 

X 

1 R 

− 

(3) 

X 20 

L 

L 

⋅ 

Equation 3 shows us that the lower the resistive reach, the 

greater the permissible reactance reach. Figure A.2 shows a 

graph of allowable resistive to reactive reach ratio for ε = 1/20 

radians (3°). The dashed line in this figure shows an example 

where an R/X L ratio = 8 (for a 1 ohm line and an 8-ohm 

resistive reach) permits setting m = 0.6 per-unit of the line. 

Figure A.2 

ε ≠ 0) 

Increase Reactance Reach By Decreasing Resistive Reach (for 

Copyright © SEL 1998, 2004 



20040126 


Transmission Line Protection System for 

Increasing Power System Requirements 

Armando Guzmán, Joe Mooney, Gabriel Benmouyal, Normann Fischer, 

Schweitzer Engineering Laboratories, Inc. 

Abstract—This paper describes a protective relay for fast and 

reliable transmission line protection that combines elements that 

respond only to transient conditions with elements that respond 

to transient and steady state conditions. In this paper, we also 

present an algorithm that prevents Zone 1 distance element 

overreach in series-compensated line applications and show how 

to prevent corruption of the distance element polarization during 

pole-open conditions. We also introduce an efficient frequency 

estimation logic for single-pole-tripping (SPT) applications with 

line-side potentials. This logic prevents distance element 

misoperation during a system frequency excursion when one pole 

is open. We also discuss an algorithm and logic to prevent singlepole 

reclosing while the fault is present, avoiding additional 

power system damage and minimizing system disturbance. 

Applying these algorithms and logics results in a protective 

system suitable for increasing power system requirements such 

as heavy loading, SPT, series line compensation, and shunt line 

compensation. 


Right-of-way restrictions and limitations on building new 

transmission lines necessitate optimization of transmission 

networks. This optimization imposes challenges on distance 

relay-based transmission line protection. Network 

optimization increases transmission line loading and requires 

fast fault clearing times because of reduced stability margins. 

In many cases, series compensation, SPT, or the 

combination of both is necessary to optimize transmission 

network investment. Series compensation generates 

subharmonics that can cause distance element overreach. SPT 

adds complexity to the ability of the distance element to track 

the power system frequency during single-pole open (SPO) 

conditions when the line protection uses line-side potentials. 

Shunt compensation can corrupt the distance element 

polarization because of the presence of transient voltages 

during three-pole open conditions when the line protection 

uses line-side potentials. 

SPT applications without arc extinction methods can 

jeopardize power system operation if the fault condition has 

not disappeared before the reclosing attempt; that is, the 

breaker closes under fault condition, making the power system 

prone to instability. 

Combining elements that respond only to transient 

conditions with elements that respond to transient and steady 

state conditions results in dependable, high-speed protection. 

Dedicated logic for series compensation applications adds 

security to the distance elements in the presence of 

subharmonics. Flexible polarizing quantities and frequency 

tracking algorithms adapt to different breaker and system 

operating conditions. Secondary arc extinction detection 

optimizes the single-pole open interval and minimizes power 

system damage in SPT applications. 

In this paper, we present solutions to the above issues that 

result in improved transmission line protection suitable for the 

most challenging power system requirements. 

II. RELIABLE HIGH-SPEED TRIPPING 

A significant reduction in operating time is one trend in 

recently developed digital transmission line relays. A number 

of new techniques allow secure sub-cycle tripping of 

transmission line distance relays. One of the first proposed 

methods uses variable-length data-window filtering with 

adaptive zone reach [1]. Developments described in Reference 

[2] introduced the concept of multiple data-window filters (a 

total of four) with corresponding fixed reach (the smaller the 

data-window, the smaller the reach). Line protective relays not 

only need to pick up fast for incipient faults but also to 

provide proper and fast fault type selection in SPT 

applications. 

A. High-Speed Distance Element Operating Principles 

Based on the principle of multiple data-window filters 

mentioned above [2], we developed the concept of the dualfilter 

scheme. This scheme combines voltage and current data 

from half-cycle and one-cycle windows (Figure 1) to obtain 

Zone 1 distance element detection and achieve fast tripping 

times. 

V, I 

One-cycle 

Filter 

Half-cycle 

Filter 

One-cycle 

mho Calc. 

Half-cycle 

mho Calc. 

Zone 1 

Reach 

Reduced 

Zone 1 

Reach 

_ 

+ 

_ 

+ 

Zone 1 

Detection 

Figure 1 Concept of a Zone 1 Distance Element Using Dual-Filter Scheme 

The mho calculation in Figure 1 uses operating (S OP ) and 

polarizing (S POL ) vector quantities defined as follows to 

implement mho distance element calculations [3]: 

S OP = r ⋅ ZL1 ⋅ IR − VR 

(1) 

S POL = V POL 

(2) 

Where: 

V R = line voltage of the corresponding impedance loop 

I R = line current of the corresponding impedance loop 

Z L1 = positive-sequence line impedance 

r = per-unit mho element reach 

V POL = polarizing voltage 

Transmission Line Protection System for Increasing Power System Requirements | 41

V R and I R are the relay voltage and current phasors 

particular to an impedance loop (six loops are necessary to 

detect all faults), and V POL is the polarizing voltage, consisting 

of the memorized positive-sequence phasor [3]. A mho 

element with reach r detects the fault when the scalar product 

between the two vectors is positive (i.e., the angle difference 

between S OP and S POL is less than 90 degrees). We can 

represent this condition mathematically as: 

( ) 

* 

Re al ⎡ r ZL1 IR VR V ⎤ 

⎣ 

⋅ ⋅ − ⋅ 

POL ⎦ 

≥ 0 (3) 

In this expression, “Real” stands for “real part of” and “*” 

for “complex conjugate of.” 

For a forward fault, this expression becomes equivalent to 

the reach r being greater than a distance m computed in 

Equation 4 [3]: 

* 

Re al ⎡VR 

V ⎤ 

⎣ 

⋅ 

POL ⎦ 

r ⋅ ZL1 

≥ m⋅ ZL1 

= 

Re al ⎡ 

⎣( 1∠θ 

) ⋅ I ⋅V 

* 

L1 R POL 

Where: 

∠θ L1 = phasor with unity magnitude and an angle equal 

to the positive-sequence line impedance angle 

m = per-unit distance to fault 

As Figure 1 shows, we use two sets of filtering systems to 

achieve speed in fault detection: one fast (data window of one 

half-cycle) and one conventional (data window of one-cycle) 

to compute the line voltage and current phasors. For each 

loop, we implement two mho-type detectors, each of which 

uses the fast or the conventional phasors. We achieve the final 

detection logic simply by “ORing” the outputs from the two 

mho-type detectors. We apply this principle for Zone 1 

detection and for zones (normally 2 and 3) used in 

communications-assisted schemes (POTT, DCB, etc.). In the 

case of Zone 1, the half-cycle detector has a reach less than 

the one-cycle detector reach. For Zones 2 and 3, the reach 

remains the same. We do not apply the principle in timedelayed 

stepped distance schemes because high-speed 

detection offers no benefit with the delayed outputs of these 

schemes. For each zone and the corresponding six impedance 

loops, using the two sets of phasors to implement two 

calculations for the distance m leads necessarily to a faster 

result with the phasors derived from the half-cycle window 

than with phasors derived from the one-cycle window. 

Mho-type detectors are inherently directional but are not 

useful for fault type selection because multiple elements pick 

up for single-phase-to-ground faults. Furthermore, phasors 

derived from the half-cycle data window are less stable than 

the ones derived with a one-cycle data window. Therefore, in 

order to achieve security for high-speed tripping, we 

supplement the fast mho-type fault detectors with an 

algorithm called High-Speed Directional and Fault Type 

Selection, HSD-FTS [4][5]. This algorithm calculates three 

incremental torques (Equation 5) to determine the faulted 

phases and the fault direction. 

⎤ 

⎦ 

(4) 

( θ ) 

Δ T = Re al ⎡ΔV ⎣ 

⋅ 1∠ ⋅ΔI 


⋅ 1∠ ⋅ ΔI 


⋅ 1∠ ⋅ ΔI 

AB AB L1 AB 

( θ ) 

BC BC L1 BC 

( θ ) 

CA CA L1 CA 

Where: 

ΔV AB = two-cycle window incremental A-phase-to-Bphase 

voltage 

ΔI AB = two-cycle window incremental A-phase-to-Bphase 

current 

The relay uses the sign of the torques to establish direction 

and the relative values of these torques to select fault type. 

The high-speed directional element, HSD, provides a 

combined directional and fault type selection signal for a total 

of seven outputs in each direction; Table 1 shows the elements 

for forward faults (equivalent elements are derived for reverse 

faults). As shown in Table 1, we use a logical “AND” to 

combine each fast mho element with the corresponding HSD- 

FTS output. The result of this combination has two objectives: 

• Provide a single output when a fault detection occurs, 

allowing then reliable fault type selection for SPT 

applications. 

• Provide fast and reliable fault detection, allowing fast 

tripping times. 

TABLE 1 

COMBINING THE HSD-FTS AND FAST MHO ELEMENT LOGIC 

HSD-FTS 

Output 

Fault Type Selection 

* 

* 

⎤ 

⎦ 

⎤ 

⎦ 

⎤ 

⎦ 

* 

“ANDed” With 

HSD-AGF Forward A-phase-to-ground MHO-AGH 

HSD-BGF Forward B-phase-to-ground MHO-BGH 

HSD-CGF Forward C-phase-to-ground MHO-CGH 

HSD-ABF Forward phases A-B MHO-ABH 

HSD-BCF Forward phases B-C MHO-BCH 

HSD-CAF Forward phases C-A MHO-CAH 

HSD-ABCF Forward phases A-B-C MHO-ABH, MHO- 

BCH, MHO-CAH 

As shown in Figure 2 in the case of the A-phase-to-ground 

impedance loop, we simply “OR” signals from the one-cycle 

and half-cycle data-window fault detectors to get the final 

loop logic signal. We apply similar logic for the five other 

impedance loops. Note that we also supplement the 

conventional one-cycle mho element with a directional 

element [6] derived from the one-cycle data window and with 

a fault type selection logic [3]. 

The result of this technique is that reliable high-speed fault 

detection occurs before conventional one-cycle fault detection. 

The amount of time advance varies and depends primarily 

upon the network (particularly the source-impedance ratio, 

SIR) and the fault location. Extensive testing revealed that 

fault detection occurs in practically all cases within a subcycle 

time frame. 

(5) 


One-Cycle Directional Element 

Figure 2 

A-Phase One-Cycle 

Fault Selection 

A-Phase-to-Ground 

One-Cycle Mho Element 

High-Speed Directional 

HSD-AGF 


Half-Cycle Mho Element 


Fault Detector-MAG 

A-Phase Impedance Loop Half- and One-Cycle Combination Logic 

B. High-Speed Distance Element Performance 

As an example, Figure 3 shows the two calculations of the 

distance m for a long line (in a 50 Hz system), Zone 2 A- 

phase-to-ground fault occurring at 0.1 s in a system with an 

SIR = 0.2. In this case, the half-cycle signal detects the fault at 

0.111 s and the one-cycle signal detects the fault at 0.123 s. 

The half-cycle element detects the fault 12 ms faster than the 

one-cycle element. 

m calculation (pu) 

2 

1.5 

1 

0.5 

Figure 3 

m half-cycle 

detection 

Zone 2 reach = r 

m one-cycle 

detection 

Fault 

inception 

0 

0.05 0.1 0.15 0.2 

Time (Seconds) 

m Calculations for a Zone 2 A-Phase-to-Ground Fault 

For the same example as the Zone 2 A-phase-to-ground 

fault shown in Figure 3, the timing of the different half-cycle 

and one-cycle signals is shown in Figure 4. The HSD-FTS 

signal (HSD-AGF in this case) occurs first (this signal has a 

duration of two cycles because it is based on superimposed 

quantities). After a few milliseconds, the half-cycle mho 

element (MHO-AGH) follows. More than a half-cycle later, 

we have the one-cycle mho (MHO-AGF) detection. 

Because the mho-detector signals are “ORed”, the time 

occurrence of the final fault detection MHO-AG corresponds 

to the fast detection MHO-AGH. In this case, we achieve an 

improvement, typical in practically all cases, of about one 

half-cycle. Two cycles after the fault inception, the detection 

depends only upon the one-cycle derived signals. 

HSD-AGF 

MHO-AGH 

MHO-AGF 

MHO-AG 

0 0.05 0.1 0.15 0.2 


Figure 4 

A-Phase-to-Ground Zone 2 Fault Signals 

III. SERIES COMPENSATION OVERREACHING 

PROBLEMS AND SOLUTION 

Series capacitors applied on transmission systems improve 

system stability and increase power transfer capability. The 

application of a series capacitor reduces the inductive 

reactance of the given transmission line, making the line 

appear electrically shorter. Although series capacitors may 

improve power system operation, using these capacitors 

results in a challenging problem for impedance-based line 

protection. 

Adding series capacitors on a transmission line causes 

subharmonic transients to occur following faults or switching 

of the series capacitor. These subharmonics can cause 

underreaching Zone 1 distance elements to overreach for 

external faults. There are other problems associated with 

subsynchronous resonance in generators. In this paper, we 

focus on problems associated with distance relays. 

All series capacitors come equipped with protective 

elements that reduce or eliminate over-voltages across the 

capacitor. The protection may be as simple as a spark gap set 

to flashover at a given voltage or as elaborate as metal-oxide 

varistors (MOV) using complex energy monitoring schemes. 

In any case, operation of the series capacitor protection 

elements can either remove the series capacitor completely or 

change capacitive reactance in a nonlinear fashion. 

The simplest series capacitor protection scheme removes 

the series capacitor when the series capacitor voltage exceeds 

a set threshold. The use of a spark gap protection scheme can 

simplify use of underreaching distance relays on seriescompensated 

lines. Firing of the spark gap for external faults 

may prevent Zone 1 overreach, so it is then possible to ignore 

the series capacitor. In most applications, however, the spark 

gap firing voltage threshold is high enough that the spark gap 

does not fire for external faults. 

MOVs present an interesting challenge because this type of 

protection scheme does not fully remove the series capacitor. 

In fact, the capacitive reactance can be very nonlinear. We can 

use an iterative model [16] to approximate the effective 

reactance of the MOV-protected bank. However, this model 

does not provide insight about the transient response. Some 

MOV-protected capacitor banks include energy monitoring of 

the MOVs. Bypassing of the capacitor bank occurs when the 

energy level exceeds a specified threshold. This can work to 

our advantage when we use impedance-based schemes. 

In either case, we need careful analysis and study before 

applying any impedance-based protection scheme on seriescompensated 

lines. 

A. Distance Relay Overreaching Problems 

The series connection of the capacitor, the transmission 

line, and the system source create a resonant RLC circuit. The 

natural frequency of the circuit is a function of the level of 

compensation and the equivalent power system source. The 

level of compensation can change according to the switching 

in and out of series capacitor “segments.” The source 

impedance can change because of switching operations 

external to the protected line section. 


Figure 5 illustrates a transmission line with a 50 percent 

series-compensated system (e.g., the series capacitor reactance 

equals 50 percent of the positive-sequence line reactance). For 

the fault location shown, the underreaching distance element 

at the remote terminal (Station S) should not operate. 

Intuitively, we would expect that setting the reach to 

80 percent of the compensated impedance (Z L1 – jX C ) would 

be an appropriate reach setting. However, the series capacitor 

and the system inductance generate subharmonic oscillations 

that can cause severe overreach of the distance element. 

Figure 6 shows the impedance plane plot for the fault location 

shown in Figure 5 (where the series capacitor remains in 

service). 

S 

Relay 

Figure 5 System With Series Capacitors at One End With a Fault at the End 

of the Line 

R 

Ignoring variables such as mutual coupling and fault 

resistance, we can see that the calculated voltage equals the 

measured voltage. Determining the ratio of the measured 

voltage to the calculated voltage would result in unity or one. 

When the fault moves to the other side of the series 

capacitor (line-side), the measured voltage increases and the 

calculated voltage decreases. The measured voltage increases 

because the series capacitor is no longer between the relay and 

the fault, and the line appears to be electrically longer. The 

calculated voltage decreases because the calculated voltage 

always includes the series capacitor. The ratio of the measured 

voltage to the calculated voltage is greater than one for a fault 

at this location. 

As the fault nears the relay location, the measured voltage 

decreases and the calculated voltage increases. The ratio of the 

measured voltage to the calculated voltage approaches zero as 

the fault location nears the relay location. Figure 7 is a plot of 

the measured voltage, V MEAS , calculated voltage, V CALC , and 

the ratio of the measured to the calculated voltage. Note that 

the scale is arbitrary; the purpose of this figure is to illustrate 

how the voltage magnitudes and the voltage ratio change with 

respect to fault location. 

Imaginary (Sec. ) 

Relay 

Ratio 

1 

V MEAS 

V CALC 

Figure 6 

Apparent Impedance for a Fault at the End of the Line 

As we can see from the impedance plot, the apparent 

impedance magnitude decreases to a value as low as 2 ohms 

secondary. This value is close to half of the compensated line 

impedance! Note that in Figure 6 the capacitor is modeled 

with no overvoltage protection. This condition is common for 

most external faults, because the overvoltage protection is 

typically sized to accommodate external faults (e.g., the 

overvoltage protection does not operate for external faults). 

B. Scheme to Prevent Distance Element Overreach (Patent 

Pending) 

From Figure 5, we can calculate the voltage drop for a 

bolted A-phase-to-ground fault at the line end as follows: 

( ) ( ) 

VCALC = ⎣⎡ IA + k0 ⋅ IG ⋅ ZL1 ⎤⎦ + ⎡⎣ IA ⋅ − jXC 

⎤⎦ (6) 

Where: 

I A = A-phase current at the relay location 

I G = residual or ground current at the relay location 

k 0 = zero-sequence compensation factor 

Z L1 = positive-sequence line impedance 

X C = capacitive reactance that the relay “sees” 

Figure 7 Measured and Calculated Voltages and Voltage Ratio for Faults 

Along the Line 

We can use the ratio we described earlier to supervise 

underreaching Zone 1 distance elements to prevent overreach 

for external faults. When the ratio of the measured to 

calculated voltage is less than a pre-defined threshold, the 

Zone 1 distance element can operate. Otherwise, the Zone 1 

element is blocked. The only additional information that the 

relay needs to calculate this ratio is the capacitive reactance 

that the relay “sees.” With the ratio supervision, you can set 

the Zone 1 reach based on the uncompensated line impedance. 

IV. DISTANCE ELEMENT POLARIZATION DURING 

POLE-OPEN CONDITIONS 

V POL is the polarizing voltage for calculating the distance to 

fault, m, as Equation 4 illustrates. The most popular polarizing 

quantity for distance protection is positive-sequence voltage 

with memory [2]. During pole-open conditions in applications 

with line-side potentials, eventual corruption of the polarizing 

quantity can occur if the input voltage to the memory circuit is 

corrupted. Invalid memory polarization may cause distance 


element misoperation. Shunt reactor switching generates 

damped oscillations with signals that have frequencies 

different from the actual system frequency. Let us look at an 

example of these signals and the logic that prevents the 

memory polarization from using unhealthy voltages. 

A. Shunt Reactor Switching 

Shunt reactors compensate the line charging currents and 

reduce overvoltages in long transmission lines. Figure 8 shows 

a 735 kV transmission line with shunt compensation at both 

ends of the line, 200 MVARs at each line end. The figure also 

shows line capacitance that generates 546 MVARs of reactive 

power. After the circuit breakers open at both line ends, the 

remaining circuit is basically an RLC circuit with a natural 

frequency of about 51.36 Hz; the circuit has stored energy in 

the reactor and in the line capacitance. Note that the circuit 

natural frequency is close to the nominal system frequency of 

60 Hz. After the three poles of each line breaker open, the 

shunt reactors interact with the line capacitance and maintain 

line voltages for several cycles. The circuit applies these 

voltages to the potential transformers (PTs) or capacitive 

voltage transformers (CVTs). These voltages corrupt the 

distance protection polarization and frequency estimation. 

Figure 9 shows the A-phase voltage at the relay location after 

deenergization of the line (in Figure 8). There is no need to 

feed this distorted voltage to the distance protection 

polarization and frequency estimation algorithm, as we 

explain later. 

zeros to the memory filter after the relay detects voltage 

ringing or undervoltage conditions. 

Figure 10 The Relay Inputs Zeros to the Memory Filter When Input 

Voltages are Corrupted 

V. EFFICIENT FREQUENCY ESTIMATION DURING 

POLE-OPEN CONDITIONS 

Figure 11 shows a two-source system with line protection 

using line-side potentials in an SPT application. This figure 

also shows Breaker 1 (BK1) and Breaker 2 (BK2) A-phase 

open, indicating a single-pole open condition for both 

breakers. The distance element can misoperate during 

frequency excursions and single-pole open conditions if it 

does not track the system frequency correctly [2]. To prevent 

relay misoperations, the distance element needs a reliable 

frequency estimation algorithm for proper frequency tracking 

during breaker pole-open conditions. 

S 

L2 

R2 

R 

Relay 

L1 

C1 

C1 

L1 

C1 = 1341 nF 

L1 = 7.162 H 

L2 = 0.1736 H 

R2 = 2.33 Ω 

QC1 = 273 MVARS 

QL1 = 200 MVARS 

Figure 8 735 kV Transmission Line With Shunt Compensation at Both Ends 

of the Line 

Figure 9 

A-Phase Line Voltage After Line Deenergization 

We need to eliminate the positive voltage input (V 1 ) to the 

polarizing memory when the voltage is distorted. Figure 9 

illustrates a voltage ringing condition after the circuit breakers 

open at both line ends. The relay detects this ringing condition 

and eliminates the corrupted voltage from the memory filter 

input. On a phase-by-phase basis, the relay inputs zeros to the 

memory filter during pole-open conditions to prevent distance 

element misoperation. Figure 10 shows the logic for inputting 

Figure 11 Line Protection Using Line-Side Potential Transformers in a 

Single-Pole Tripping Application 

Traditionally, relays that calculate frequency must have 

circuitry that detects zero-crossings of the voltage signals to 

determine the signal period. The inverse of the signal period is 

the frequency. Normally, this circuitry monitors a single-phase 

voltage; the relay cannot measure frequency if the monitored 

phase is deenergized during the pole-open condition. Some 

numerical relays use zero-crossing detection [7] or rate-ofchange 

of angle algorithms to calculate frequency [8]. Some 

of these relays use positive-sequence voltage to include 

voltage information from the three phases [8]. These relays 

calculate frequency reliably as long as the voltages are present 

and healthy. 

Parallel line mutual coupling [12][13] or line resonance 

because of shunt reactor compensation can cause voltage 

distortion during the pole-open condition; this distortion 

introduces frequency estimation errors. This section describes 

logic to correctly estimate the system frequency during poleopen 

conditions and unhealthy voltage conditions. 


A. Frequency Estimation Sources of Error 

The following are power system conditions that the 

frequency estimation logic evaluates to prevent distance 

element misoperation. First, we show a frequency excursion 

during a pole-open condition. Second, we show the frequency 

of the voltage signal after a transmission line deenergization. 

1) Frequency Excursion During Pole-Open Condition 

During pole-open conditions, the power system is prone to 

instability. Particularly in weak source systems, the frequency 

changes when one phase is open because of the sudden 

increase in the impedance between the two line terminals. The 

distance relay needs to track this frequency to minimize 

distance element overreach. Figure 12 shows a 600 MVA 

generator connected to a 275 kV network through two 

transmission lines. The frequency changes, as illustrated in 

Figure 13, when Line 2 opens A-phase to clear an A phase-toground 

fault located 50 km from Station S while Line 1 is 

open. The frequency varies from 60.2 to 59.8 Hz during the 

pole-open condition. 

voltage in Figure 9; the frequency of the voltage signal 

oscillates between 44.6 and 54.4 Hz after the line 

deenergization (Figure 15). These corrupted voltages must be 

removed from the frequency estimation logic to prevent errors 

in the estimation, as we see later. 

S-275 

= 250 KM 

Line 1 

R-275 

Figure 15 Frequency Estimation Using A-Phase Voltage After Line 

De-energization 

600 MVA 

600 MVA 

22/275 

Relay 

ØA-G 

Line 2 

Figure 12 275 kV Network With 600 MVA Generator 

System 

Equivalent 

B. Frequency Estimation Logic (Patent Pending) 

Figure 16 shows the logic for frequency estimation that 

increases distance element reliability. The figure also shows 

alternate methods for determining the power system 

frequency, FREQ, for normal system operating conditions, 

pole-open conditions, and unhealthy voltage conditions. The 

relay uses FREQ to obtain the relay tracking frequency and to 

adapt the line protection to power system changes. 

Figure 13 

Frequency at the Terminal Close to the 600 MVA Generator 

If the relay in Figure 12 does not track the system 

frequency, the apparent impedance begins to appear as a fault 

condition, as shown in Figure 14. The relay must use voltage 

information from the unfaulted phases to track the system 

frequency and minimize distance element overreach. 

mBC Calculation (Pri. Ω) 

400 

300 

200 

100 

0 

Zone 2 Reach 

0.5 1 1.5 2 2.5 


Figure 14 Distance Element Apparent Impedance During Pole-Open 

Conditions 

2) Shunt Reactor Compensation 

We saw earlier the line voltages resulting from the 

deenergization of a line with shunt reactor compensation. 

Figure 15 shows the frequency estimation for the A-phase 

Σ 

Figure 16 Frequency Estimation Logic for Transmission Line Protection 

Applications 

The relay uses the V A , V B , and V C voltages to calculate the 

frequency, FREQ. Depending on breaker pole status and 

voltage source health, switches SW1, SW2, and SW3 select 

the V A , V B , and V C voltages, respectively, or zero. Switches 

SW1, SW2, and SW3 have two positions. Position 2 is the 

normal state; the switches are in this position if the 

corresponding pole is closed. The relay applies the source 

voltages when SW1, SW2, and SW3 are in Position 2. The 

relay selects Position 1 for SW1, SW2, and SW3 according to 

the following: 

• SW1 is in Position 1 when there is an A-phase poleopen, 

SPOA, condition; a three-pole open, 3PO, 

condition; or a loss-of-potential (LOP), condition. 

When SW1 is in Position 1, V1 is zero. Otherwise, 

V1 = V A . 


• SW2 is in Position 1 when there is a B-phase poleopen, 

SPOB, condition; a 3PO condition; or an LOP 

condition. When SW2 is in Position 1, V2 is zero. 

Otherwise, V2 = V B . 

• SW3 is in Position 1 when there is a C-phase poleopen, 

SPOC, condition; a 3PO condition; or an LOP 

condition. When SW3 is in Position 1, V3 is zero. 

Otherwise, V3 = V C . 

V1, V2, and V3 are the voltages after SW1, SW2, and SW3 

switch selection. The relay uses these voltages to calculate the 

composite signal, V α [14]. Equation 7 shows the V α 

calculation. 

⎛ V2 V3⎞ 

Vα 

= ⎜ V1 − − ⎟ ⋅ K 

(7) 

⎝ 2 2 ⎠ 

Where the constant K depends on the SW1, SW2, and SW3 

switch positions as shown in Table 2. 

TABLE 2 

K CONSTANT TO CALCULATE THE COMPOSITE VOLTAGE, V α, 

DEPENDS ON BREAKER POLE CONDITION 

Breaker Pole Condition SW1 SW2 SW3 

K 

A Pole B Pole C Pole Position Position Position 

Closed Closed Closed 2 2 2 2/3 

Open Closed Closed 1 2 2 2 

Closed Open Closed 2 1 2 2 

7 

Closed Closed Open 2 2 1 2 

Closed Open Open 2 1 1 1 

Open Closed Open 1 2 1 2 

Open Open Closed 1 1 2 2 

Open Open Open 1 1 1 2/3 

The digital band-pass filter, DBPF, extracts the 

fundamental component signal (60 Hz or 50 Hz) from the 

composite voltage, V α , to obtain V α_FUND . The relay uses the 

fundamental quantity, V α_FUND , to calculate the frequency, 

FREQ. As stated before, there are several methods for 

calculating frequency [7][8][9][10]. In this case, the frequency 

estimation algorithm uses the zero-crossing detection method. 

To prevent erroneous frequency estimation during power 

system transients (faults), the relay freezes the output of the 

frequency estimator if the relay detects a transient or a tripping 

condition. The output of the logic is the power system 

frequency, FREQ. The relay uses this frequency to determine 

the tracking frequency. 

The frequency estimation logic removes the voltage signal 

from the open phase to prevent using corrupted signals during 

pole-open conditions or LOP conditions. The composite 

signal, V α , allows the relay to combine information from three 

phases without additional signal manipulation with the “a” 

operator [15], as in the case of positive-sequence quantity. 

This composite signal does not require additional filtering for 

7 

implementation and has improved transient response. The 

relay uses the composite signal, V α , to track the system 

frequency during pole-open conditions. The constant K (see 

Table 2) modifies the gain of the composite signal, V α , to 

provide a constant signal amplitude to the frequency estimator 

for different line operating conditions. 

VI. SECONDARY ARC EXTINCTION DETECTION AND 

ADAPTIVE RECLOSING 

One of the challenges in SPT applications is to prevent the 

breaker pole from reclosing before the fault extinguishes. 

Reclosing under fault provides added power system damage 

and compromises system stability. There are several 

approaches to prevent these damaging conditions. One of the 

most common approaches is to add shunt and neutral reactors 

[17] to suppress the secondary arc present during the poleopen 

condition and have a dead time (open phase interval) 

long enough to allow for arc suppression and air de-ionization. 

Another approach is to increase the dead time and expect the 

secondary arc to be self-extinguished. None of these 

approaches verify expiration of the arc before the breaker pole 

recloses. 

As soon as the arc extinguishes, recovery voltage appears 

across the secondary arc path. This recovery voltage may 

initiate a restrike and create a reclose-onto-fault condition. 

Ideally, we want the breaker to close if and only if there is no 

fault on the line. Detection of the secondary arc extinction 

prevents reclosing under fault conditions and optimizes the 

dead time. 

A. The Secondary Arc Phenomenon 

In a three-phase circuit, there is electromagnetic and 

electrostatic coupling between the phase conductors [11]. A 

phase-to-ground fault results in formation of a primary arc 

between the faulted phase and ground. A protective system 

isolates the faulted phase from the power system in SPT 

applications; the other two healthy phases remain in service, 

thereby isolating the primary arc. Because two of the three 

phases are still at approximately nominal voltage and the 

faulted phase is coupled capacitively and inductively to the 

healthy phases, a secondary arc is maintained. The air is 

already ionized from the primary fault, so the two healthy 

phases need little current to maintain this secondary arc. 

Figure 17 Transmission Line Π Equivalent Circuit 

Figure 17 shows an equivalent Π circuit representing a 

transmission line section. If a trans-mission line lacks shunt 

reactors, we can simplify the equivalent circuit by considering 

only the electrostatic coupling of the phase conductors. 


Figure 18 represents a simplified, single, symmetrical, and 

fully transposed transmission line. The capacitances between 

phases are identical, i.e., C ab = C bc = C ca = C m and the 

capacitances to ground for each phase are identical, i.e., C ag = 

C bg = C cg = C g . 

Figure 18 

Equivalent Circuit Considering Only the Line Capacitances 

If this system now experiences an A-phase-to-ground fault, 

we can represent the system during the pole-open condition as 

illustrated in Figure 19. This figure also shows the vector 

diagram while the secondary arc is present. 

V 

REC 

= V ⋅ 

LN 

C 

m 

( 2Cm 

+ Cg 

) 

(10) 

If the transmission line has shunt reactors, one must 

consider the electromagnetic coupling from the healthy 

phases; a portion of the secondary arc current becomes 

inductive. In this case, the secondary arc current is the vector 

sum of the electrostatic (I ARC-C ) and electromagnetic ( IARC-M ) 

currents. Calculation of the electromagnetic current is a nontrivial 

task; you would need the assistance of a transient 

analysis software package such as EMTP. 

B. Secondary Arc Extinction Detectors, SAEDs 

A secondary arc extinction detector can be added to 

supervise the closing signal to the breaker and prevent 

reclosing under fault. This supervision blocks the closing 

signal to the breaker when the secondary arc is present and 

minimizes the possibility of unsuccessful reclosures. 

Figure 20 shows the close supervision logic using secondary 

arc extinction detection (SAED) for close supervision. The 

SAED can minimize the dead time by initiating the reclose 

after the secondary arc extinguishes. The SAEDD time delay 

provides time for the air formerly occupied by the arc to 

regain dielectric capabilities. 

Secondary Arc 

Extinction Detection 

(SAED) 

SAEDD 

DO 

Reclosing 

Relay 

Supervision 

SAED 

Close 

Enable 

Figure 19 

Equivalent Circuit While the Secondary Arc is Present 

The magnitude of the secondary arc current resulting from 

the electrostatic coupling is a function of the line voltage and 

the line length. The line capacitance is a function of the 

distance between phase conductors and the height of these 

conductors above ground. If we represent the transmission line 

as a series of Π circuits, we can see that all these capacitances 

are effectively in parallel; the capacitance increases 

proportionally with the line length. From the equivalent circuit 

in Figure 19, we can calculate the secondary arc current, 

disregarding fault resistance, as follows: 

IARC− C = VDR−C 

⋅ j⋅ 

ϖ ⋅ 2Cm 

(8) 

Where the voltage V DR-C for an A-phase-to-ground fault 

equals (V B + V C )/2 = V LN /2. We can therefore rewrite 

Equation 8 as follows: 

IARC− C = VLN 

⋅ j⋅ 

ϖ ⋅ Cm 

(9) 

For a typical 400 kV line, I ARC-C has an approximate value 

of 0.1085 A/km, or 10.85 A/ 100 km. Once the secondary arc 

extinguishes, a voltage known as the recovery voltage appears 

across the ground capacitance, C g . The magnitude and/or rate 

of rise of the recovery voltage can initiate a restrike. We can 

calculate the recovery voltage as follows: 

Figure 20 Reclosing Relay Close Supervision Using Secondary Arc 

Extinction Detection 

Figure 21 shows the A-phase voltage after the line relay 

clears an A-phase-to-ground fault in an SPT application. After 

one pole opens, the voltage to ground, V ARC , exists in the 

faulted phase until the secondary arc extinguishes. When the 

secondary arc extinguishes, a phase-to-ground voltage, V A , 

results from the mutual coupling between the sound phases 

and the faulted phase. This voltage provides information to 

detect secondary arc extinction [18]. 

V C 

V A 

V B 

V Arc 

Figure 21 Line Voltages During the Pole-Open Condition 


Complete reclosing relay supervision requires three 

secondary arc extinction detectors, one per phase. These 

detectors measure the angle, φ, between the phase-to-ground 

voltage of the faulted phase (V γ ) and the sum of the sound 

phases phase-to-ground voltages (V Σ ). For -β ≤ φ ≤ β, and |V γ | 

> V thre , the detector determines the secondary arc extinction 

and asserts the SAED bit. β and V thre determine the region that 

detects the secondary arc extinction. Table 3 shows the V γ and 

V Σ voltages for A-, B-, and C-phase SAEDs. 

TABLE 3 

V γ AND V Σ VOLTAGES FOR A-PHASE, B-PHASE, AND C-PHASE SAEDS 

Detector V γ V Σ 

A-phase V A V B + V C 

C. SAED Performance in Transmission Lines With Shunt 

Compensation 

SAED is suitable for lines with or without shunt reactor 

compensation. We will look at the performance of the SAED 

for an A-phase-to-ground fault at the middle of the line in the 

power system shown in Figure 8. In this case, we assume that 

both breakers at the line ends open A phase poles to create an 

A-phase open condition. Figure 24 shows the A-phase voltage 

and the fault current through the arc at the fault location. The 

fault occurs at cycle eight (133 ms) and the poles open at 

cycle 14 (233 ms). The figure also illustrates the presence of 

arc; primary arc exists before the breaker poles open, and 

secondary arc exists after the breakers clear the fault. The 

secondary arc extinguishes at cycle 23.5 (392 ms). 

B-phase V B V C + V A 

C-phase V C V A + V B 

The angle φ = 180° and V γ is outside of the SAED region 

when the line is energized under normal conditions as shown 

in Figure 22. 

During single-pole open conditions, after the secondary arc 

extinguishes, the angle φ = 0° and V γ is inside the SAED 

region (Figure 23). The A-phase detector asserts the SAED bit 

for this condition, allowing the reclosing sequence to 

continue. 

V C 

φ 

β 

V Σ 

= V B 

+ V C 

V γ 

= V A 

β 

V thre 

V B 

Figure 22 The Angle φ = 180° and V γ is Outside of the SAED Region for 

Normal Conditions 

V C 

V γ 

= V A 

V Σ 

= V B 

+ V C 

Figure 23 V γ is Inside the SAED Region After the Arc Extinguishes 

V B 

Figure 24 A-Phase Voltage, Arc Current, and Arc Presence Indication for an 

A-Phase-to-Ground Fault at the Middle of the Line 

The A-phase voltage undergoes three significant changes 

during fault and pole-open conditions: 

• Voltage reduction because of the fault presence. The 

voltage changes from normal to fault conditions. 

• Additional voltage reduction after the breakers clear 

the fault. Reduced voltage exists during the pole-open 

condition while the secondary arc is present. 

• Voltage increase during the pole-open condition. The 

voltage increases after the secondary arc extinguishes. 

Figure 25 shows the A-phase voltage changes in magnitude 

and angle, and the SAED boundaries. During the pole-open 

condition before extinction of the secondary arc, the voltage 

magnitude is less than the voltage threshold, V thre , and the 

voltage angle is outside the 2β angle limits. After the 

secondary arc extinguishes, the voltage magnitude exceeds the 

voltage threshold, V thre , and the voltage angle is within the 2β 

angle limits of the SAED characteristic. You can see the A- 

phase voltage better in the polar plot of Figure 26. V A = 1∠0° 

(in per unit) before the fault occurs; V A = 0.7∠0° during the 

fault condition; V A = 0.1∠254° while the secondary arc is 

present; and V A = 0.8∠191° after the secondary arc 

extinguishes. The A-phase voltage operating point enters the 

A-phase SAED region after the secondary arc extinguishes. 


phases without additional signal manipulation, as in 

the case of positive-sequence quantity. 

5. Secondary arc extinction detection prevents singlepole 

reclosing while the fault is present and optimizes 

the single pole-open interval, avoiding additional 

power system damage and minimizing system 

disturbance. 

Figure 25 A-Phase Voltage Magnitude and Angle for an A-Phase-to-Ground 

Fault With the SAED Boundaries 

150 

210 

120 

Secondary Arc 

Extinguishes 

240 

90 

180 0 

2 70 

1 

0 .5 

1.5 

Secondary Arc 

Present 

Fault 

60 

30 0 

Prefault 

Figure 26 A-Phase Voltage Phasor Enters the SAED Characteristic After the 

Secondary Arc Extinguishes 

VII. CONCLUSIONS 

1. The result of using the dual-filter scheme technique is 

reliable high-speed transmission line protection 

compared to conventional one-cycle only filtering 

schemes. 

2. The ratio of the measured voltage, V MEAS , to the 

calculated voltage, V CAL , in series compensation 

applications provides information to block Zone 1 

distance elements and prevent distance element 

overreach. 

3. The ability to remove the open phase voltage prevents 

using corrupted signals for distance element 

polarization and frequency tracking during pole-open 

conditions or loss-of-potential conditions. 

4. Using the composite signal, V α , allows relays to track 

system frequency during pole-open conditions. The 

composite signal combines information from the three 

30 

330 

VIII. REFERENCES 

[1] M. A. Adamiak, G. Alexander, and W. Premerlani “Advancements in 

Adaptive Algorithms for Secure High-Speed Protection,” 23rd Annual 

Western Protective Relay Conference, Spokane, Washington, October 

15–17, 1996. 

[2] D. Hou, A. Guzman, and J. Roberts, “Inovative Solutions Improve 

Transmission Line Protection,” 24th Western Protective Relay 

Conference, Spokane, WA, October 21–23, 1997. 

[3] E. O. Schweitzer III and J. Roberts, “Distance Relay Element Design,” 

19th Annual Western Protective Relay Conference, Spokane, 

Washington, October 20–22, 1992. 

[4] G. Benmouyal and J. Roberts, “Superimposed Quantities: Their True 

Nature and Their Application in Relays,” Proceedings of the 26th 

Annual Western Protective Relay Conference, Spokane, WA, October 

26–28, 1999. 

[5] G. Benmouyal and J. Mahzeredjian, “A Combined Directional and 

Faulted Type Selector Element Based on Incremental Quantities,” IEEE 

PES Summer Meeting 2001, Vancouver, Canada. 

[6] A. Guzman, J. Roberts, and D. Hou, “New Ground Directional Elements 

Operate Reliably for Changing System Conditions,” 23rd Annual 

Western Protective Relay Conference, Spokane, Washington, October 

15–17, 1996. 

[7] Instruction Manual for Digital Frequency Relay Model BE1-81 O/U, 

Basler Electric, Highland, Illinois. Publication: 9 1373 00 990. Revision: 

E. December 1992. 

[8] A. G. Phadke and J. S. Thorp, “Computer Relaying for Power Systems,” 

Research Studies Press Ltd. 1988. 

[9] A. G. Phadke, J. S. Thorp, and M. G. Adamiak, “A New Measurement 

Technique for Tracking Voltage Phasors, Local System Frequency, and 

Rate of Change of Frequency,” IEEE Transactions on Power Apparatus 

and Systems, Vol. PAS-102, No. 5, May 1983. 

[10] P. J. Moore, J. H. Allmeling, and A. T. Johns, “Frequency Relaying 

Based on Instantaneous Frequency Measurement,” IEEE/PES Winter 

Meeting, January 21–25, 1996, Baltimore, MD. 

[11] IEEE PSRC Working Group: J. Esztergalyos et al. “Single-Phase 

Tripping and Auto Reclosing of Transmission Lines IEEE Committee 

Report.” 

[12] M. J. Pickett, H. L. Manning, and H. N. V. Geem, “Near Resonant 

Coupling on EHV Circuits: I-Field Investigations,” IEEE Transactions 

on Power Systems, Vol. PAS-87, No. 2, February 1968. 

[13] M. H. Hesse and D. D. Wilson, “Near Resonant Coupling on EHV 

Circuits: II-Method of Analysis,” IEEE Transactions on Power Systems, 

Vol. PAS-87, No. 2, February 1968. 

[14] E. Clarke, “Circuit Analysis of A-C Power Systems,” General Electric, 

Schenectady, N.Y., 1950. 

[15] C. F. Wagner and R. D. Evans, “Symmetrical Components as Applied to 

the Analysis of Unbalanced Electrical Circuits,” McGraw-Hill, New 

York, 1933. 

[16] D. L. Goldsworthy, “A Linearized Model for MOV-Protected Series 

Capacitors,” IEEE Transactions on Power Systems, Vol. PWRS-2, No 4, 

Nov 1987, pp 953–958. 

[17] E. N. Kimbark, “Suppression of Ground-Fault Arcs on Singe-Pole 

Switched EHV Lines by Shunt Reactors,” IEEE Transactions on Power 

Apparatus and Systems, Vol. 83, March 1964. 

[18] CFE-, LAPEM, UIE, ATN, “Secondary Arc Extinction Detection 

Project.” 


IX. BIOGRAPHIES 

Armando Guzmán, P.E. received his BSEE with honors from Guadalajara 

Autonomous University (UAG), Mexico, in 1979. He received a diploma in 

Fiber-Optics Engineering from Monterrey Institute of Technology and 

Advanced Studies (ITESM), Mexico, in 1990. He served as Regional 

Supervisor of the Protection Department in the Western Transmission Region 

of the Federal Electricity Commission (the electrical utility company of 

Mexico) for 13 years. He lectured at UAG in power system protection. Since 

1993, he has been with Schweitzer Engineering Laboratories, Pullman, 

Washington, where he is presently a Research Engineer. He holds several 

patents in power system protection. He is a registered professional engineer in 

Mexico, is a senior member of IEEE, and has authored and coauthored several 

technical papers. 

Joseph B. Mooney, P.E. received his B.Sc. in Electrical Engineering from 

Washington State University in 1985. He joined Pacific Gas and Electric 

Company upon graduation as a System Protection Engineer. In 1989, he left 

Pacific Gas and Electric and was employed by Bonneville Power 

Administration as a System Protection Maintenance District Supervisor. In 

1991, he left Bonneville Power Administration and joined Schweitzer 

Engineering Laboratories as an Application Engineer. Shortly after starting 

with SEL, he was promoted to Application Engineering Manager. In 1999, he 

became Manager of the Power Engineering Group of the Research and 

Development department at Schweitzer Engineering Laboratories. He is a 

registered professional engineer in the states of California and Washington. 

Gabriel Benmouyal, P.E. received his B.A.Sc. in Electrical Engineering and 

his M.A.Sc. in Control Engineering from Ecole Polytechnique, Université de 

Montréal, Canada in 1968 and 1970, respectively. In 1969, he joined Hydro- 

Québec as an Instrumentation And Control Specialist. He worked on different 

projects in the field of substation control systems and dispatching centers. In 

1978, he joined IREQ, where his main field of activity was the application of 

microprocessors and digital techniques to substation and generating-station 

control and protection systems. In 1997, he joined Schweitzer Engineering 

Laboratories in the position of Research Engineer. He is a registered 

professional engineer in the Province of Québec, is an IEEE member, and has 

served on the Power System Relaying Committee since May 1989. 

Normann Fischer joined Eskom as a Protection Technician in 1984. He 

received a Higher Diploma in Technology, with honors, from the 

Witwatersrand Technikon, Johannesburg, in 1988 and a B.Sc. in Electrical 

Engineering, with honors, from the University of Cape Town in 1993. He was 

a Senior Design Engineer in Eskom’s Protection Design Department for three 

years, then joined IST Energy as a Senior Design Engineer in 1996. In 1999, 

he joined Schweitzer Engineering Laboratories as a Power Engineer in the 

Research and Development Division. He was a registered professional 

engineer in South Africa and a member of the South Africa Institute of 

Electrical Engineers. 

Copyright © SEL 2001 



20020401 


1 

Lessons Learned Analyzing Transmission Faults 

David Costello, Schweitzer Engineering Laboratories, Inc. 

Abstract—Transmission line relays record interesting power 

system phenomena and misoperations due to a variety of 

problems. By analyzing event records, some common setting 

mistakes and misapplications have become evident. Setting and 

testing recommendations can be made to avoid these problems. 

In the interest of reducing transmission line relay misoperations, 

this technical paper shares practical lessons learned through 

experience analyzing transmission line relay event reports. 

I. FAULT LOCATION ERROR 

In December 2006, a single-line-to-ground fault occurred 

on a two-terminal 69 kV transmission line. The distance relay 

at the local terminal produced a fault location estimate, trip 

targets, and an event report. The actual fault location was 

found to be 3.6 miles from the local terminal, but the relay 

reported 7.31 miles. In addition, the relay targets included 

Zone 1 and time indication, which is contradictory because 

Zone 1 elements were set with no intentional time delay. 

Event data from the local relay are shown in Fig. 1. 

Ground current (3I0) reached a maximum magnitude of 3600 

amperes. The actual fault location was validated using this 

information and an ASPEN OneLiner power system model. In 

OneLiner, a line-to-ground fault was simulated and slid along 

the line until the 3I0 current matched the maximum value 

from the event data. The estimated location of this simulated 

fault matched the actual fault location from the field. 

IA IB IC IGMag 

VA(kV) VB(kV) VC(kV) VB(kV)Mag 

Digitals 

2500 

0 

-2500 

50 

25 

0 

-25 

-50 

Fig. 1. 

52A 

TRIP 

67G1 

51G 

IA IB IC IGMag 

VA(kV) VB(kV) VC(kV) VB(kV)Mag 

6.75 cycles 

0 1 2 3 4 5 6 7 8 9 10 

Cycles 

Event Data From 69 kV Transmission Line Relay 

The event data capture was triggered at Cycle 2 by an 

inverse-time ground overcurrent element (51G). The 3I0 

current is small (200 amperes 3I0) at the fault inception 

because of arcing or fault impedance. In the fifth cycle, the 

ground fault evolves into a bolted fault (3600 amperes 3I0). 

The instantaneous ground overcurrent element (67G1) asserts 

and calls for a trip, and the breaker opens 3 cycles later. 

An event record typically contains prefault, fault, and 

postfault data. After the event record is stored, the relay 

executes the fault location algorithm. This algorithm must first 

extract voltage and current phasor information from a point 

within the event data. What is the best point in the event data 

to choose 

A typical fault location algorithm will determine the 

contiguous fault data, which are defined by the window of 

time in which the element that triggered the event remains 

asserted. In Fig. 1, this window of time is 6.75 cycles long. 

The algorithm assumes that the contiguous data midpoint is a 

reasonably stable point at which to estimate the fault location. 

In this case, the fault data midpoint is just before the ground 

current magnitude increased to a larger value. The dramatic 

evolution of the fault and its unlikely timing led to the fault 

location error. 

An offline analysis of this event is required so one can 

manipulate where in the event data the fault algorithm extracts 

voltages and currents. In Fig. 2, a relay fault location algorithm 

is plotted using a MathCad simulation. At Cycle 6.75, 

the midpoint of the bolted fault data, the fault location 

estimate matches the actual fault location. 

m 

15 

10 

5 

Fig. 2. 

0 

0 1 2 3 4 5 6 7 8 9 10 

Cycles 

Fault Location MathCad Simulation 

We must now explain why a trip caused by an 

instantaneous ground element produced a time target. How 

fast is an instantaneous trip versus a time-delayed trip In this 

particular relay, the time target asserts when elements selected 

by the user have been asserted for longer than 3 cycles before 

a trip occurs. If the trip occurs before 3 cycles, we label the 

trip as instantaneous [1]. The same element that triggered the 

event data capture, 51G, was also set to signify that a fault is 

present. The dramatic evolution of the fault and its unlikely 

timing led to the confusing targets as well. 

Single-ended fault location estimates from relays are 

accurate in most cases. Offline tools, such as MathCad 

worksheets, can improve fault location accuracy for challenging 

cases. These tools offer the ability to vary the location at 

which the fault location estimate is calculated and can include 

data from both ends of the transmission line for even better 

results [2]. 


2 

II. COMMON ZONE TIMING 

In June 2006, a fault occurred just past the remote terminal 

on a two-terminal 138 kV transmission line. The directional 

comparison blocking (DCB) scheme was disabled at the time 

of the fault. Because the fault was within the Zone 2 reach, we 

expected a trip within the Zone 2 delay of 25 cycles. 

Event data from the local relay are shown in Fig. 3. The 

event data capture was triggered at Cycle 4 by the Zone 2 

phase distance element (M2P). The relay tripped and reported 

Zone 2 and time targets 0.5 cycles later. 

IA IB IC 

IGMag 

VA(kV) VB(kV) VC(kV) 

Digitals 

2000 

0 

-2000 

750 

500 

250 

0 

100 

0 

-100 

Fig. 3. 

IN105 

IN106 

TRIP 

52A 

Z2T 

Z2GT 

Z2G 

M2PT 

M2P 

IA IB IC IGMag VA(kV) VB(kV) VC(kV) 

.5 cycles 

0 1 2 3 4 5 6 7 8 

Cycles 

Event Data From 138 kV Transmission Line Relay 

Unlike the ground fault in Section I, which evolved into a 

larger magnitude fault of the same type, this fault evolved 

from a single-line-to-ground fault to a phase-phase-ground 

fault. 

Distance relays support two philosophies of zone timing: 

independent or common timing (see Fig. 4). For the independent 

timing mode, the phase and ground distance elements for 

each zone initiate independent timers. For the common mode, 

the phase and ground distance elements for each zone drive a 

common timer. The common zone timer is suspended for 

1 cycle if the timer input drops out. This feature prevents timer 

reset when a fault evolves [3]. 

Suspend Timing 

during the fault transition period, and the common zone timer 

was suspended. The M2P element then asserted, the common 

zone timer resumed timing, and a trip was issued 0.5 cycles 

later. In this example, the benefit of common zone timing was 

a total relay response time of 25.5 cycles instead of the 

expected 50.5 cycles if we had chosen to use independent 

timing. 

In this event, the fault location estimate from the relay was 

accurate despite the evolving fault data. The contiguous fault 

data were roughly from Cycle 4 to 7, which was the window 

of time the triggering element M2P was asserted. During that 

time, the fault had already evolved, and the fault data were 

stable. 

In Fig. 5, the fault location estimate is plotted for the two 

different fault types experienced. Both estimates produce 

roughly the same fault location when data are stable. But from 

Cycle 2.5 to 3.5 you can see where both estimates veer wildly 

from the actual location because of the fault type evolution. 

The reported location from the relay would have been in error 

if it had selected data from that time. 

m 

m 

3.5 

2 

Single-Line-to-Ground Faults (BG) 

0 

0 1 2 3 4 5 6 7 8 

Cycles 

2 

Phase-to-Phase Faults (BC) 

0 

0 1 2 3 4 5 6 7 8 

Cycles 

Fig. 5. MathCad Fault Location Estimates for BG and BC Fault Types 

Event data can be replayed as IEEE COMTRADE files 

through test equipment into relays. Unique or challenging 

fault cases should be archived as IEEE COMTRADE files and 

used to test new relays, challenge standard schemes, and 

understand relay responses. 

M2P 

Z2G 

Fig. 4. 

Z2D 

Z2PD 

Z2GD 

Independent and Common Zone Timing Schemes 

0 

0 

0 

Z2T 

M2PT 

Z2GT 

We can deduce from the data in Fig. 3 that the initial fault 

had been present, and the Zone 2 ground distance element 

(Z2G) had been timing for 24.5 cycles before the fault 

evolved. All distance elements dropped out for 0.5 cycles 

III. RECLOSE FAILURE 

In May 2006, a 34.5 kV line feeding a hospital failed to 

reclose for a line fault. The relay was set for two reclose 

attempts. 

Event data from the relay are shown in Fig. 6. The event 

started as an A-phase-to-ground (AG) fault and evolved to a 

B-phase-to-ground (BG) fault. This was most likely caused by 

a slapping conductor or tree contact. At fault inception, an instantaneous 

ground overcurrent element (67G1) asserts and 

produces a trip output. At this same time, the relay enters the 

reclosing cycle state (79CY), indicating that reclosing openinterval 

timing has been initiated. However, we can see that as 

the AG fault progresses to a BG fault, the 67G1 element drops 

out for 0.75 cycles before reasserting. When the 67G1 element 

Lessons Learned Analyzing Transmission Faults | 53

3 

reasserts, the relay advances to lockout (79LO). The root 

cause can be found in the relay operation and user settings [1]. 

A programmable logic equation (79RI) defines the 

conditions that initiate reclose. 79RI is set equal to the rising 

edge of 67G1 plus a number of other conditions logically 

ORed together. Once 79RI asserts, the relay enters its cycle 

state (79CY) and begins to time to reclose. However, the 

reclose timer is interrupted when 79RI reasserts. The relay 

immediately assumes something has gone awry, such as a 

flashover during a breaker opening, and the relay immediately 

goes to lockout (79LO) to prevent further trouble. 

just after the fault transitioned from AG to BG; therefore, we 

are suspicious that the relay used corrupt data for its fault 

location estimate. 

A fault location algorithm MathCad simulation is shown in 

Fig. 7. We can see the fault location error during the fault type 

change, but before and after that transition the location estimate 

is consistent. 

m 

12 

9 

6 

Single-Line-to-Ground Faults (BG) 

IA IB IC 

2500 

0 

-2500 

IA IB IC IGMag VA(kV) VB(kV) VC(kV) 

5.25 cycles 

3 

0 

7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 

Cycles 

IGMag 


Digitals 

2000 

1000 

0 

25 

0 

-25 

FSB 

FSA 

52A 

79LO 

79CY 

79RS 

67G1T 

51G 

TRIP 

5.0 7.5 10.0 12.5 15.0 17.5 

Cycles 

Fig. 6. Reclosing Interrupted by Evolving Fault 

To prevent this from happening in the future, reclosing 

must not be reinitiated before reclose open-interval timing is 

complete and the breaker has been reclosed. Use the trip 

element to initiate reclose. Relays have a minimum trip 

duration time, so trip outputs remain asserted throughout 

evolving faults. 

It is also common to stall open-interval timing while the 

trip condition is still present. Additionally, there are likely 

conditions included in the trip logic for which we do not want 

to reclose. These conditions can be specified in a programmable 

drive-to-lockout equation (79DTL). Such conditions may 

include remote or manual OPEN commands, relay trips for 

three-phase faults, or time-delayed trips. 

An interesting breaker problem is also evident by the data 

in Fig. 6. Notice that the breaker status contact (52A) changes 

state shortly after the main breaker interrupts current. This is 

consistent with breaker operations in the previous two 

examples. However, we see that while the main breaker 

contacts remain open, the breaker auxiliary status contact 

bounces closed after 0.75 cycles and remains closed for 3.5 

cycles before opening again. Bouncy auxiliary contacts can 

cause reclosing failures. If 52A asserts before the relay calls 

for a close, relay logic assumes a manual or remote CLOSE 

command asserted. The auxiliary contacts of this breaker need 

maintenance to prevent future problems. 

The relay reported a fault location of 3.22 miles and a BG 

fault type. The contiguous fault data are roughly from Cycle 8 

to 13, which was the window of time the triggering element 

51G was asserted. The midpoint of that data corresponds to 

Fig. 7. MathCad Fault Location Estimates for AG and BG Fault Types 

The relay fault location algorithm selected data just prior to 

Cycle 10.5, where the B-phase current is still increasing to its 

maximum value. Therefore, its estimate is slightly further 

away from the local terminal because of the lower current 

magnitude used. The actual fault location is closer to 3.0 

miles. 

IV. COMMUNICATIONS PROBLEM 

In June 2007, a fault occurred beyond the remote terminal 

of a 115 kV line protected by a DCB scheme. DCB schemes 

use a high-speed on/off carrier signal to block high-speed 

tripping at the remote terminal for out-of-section faults. 

Therefore, we expected the remote terminal to send a blocking 

signal to the local relay to prevent it from tripping at a high 

speed. 

The event data recorded from the local relay are shown in 

Fig. 8. The received blocking signal was wired to a programmable 

input on the relay (IN5) and appears to have been 

asserted at the time of the trip. 

IA IB IC 

IRMag 

VA VB VC 

Digitals 

100 

0 

-100 

75 

50 

25 

0 

50 

0 

-50 

Fig. 8. 

IA IB IC IRMag VA VB VC 

OUT 1&2 

B 

IN 5&6 5 5 

67N 2 

-1 0 1 2 3 4 5 6 7 8 9 10 11 

Cycles 

Four Samples-per-Cycle Data From a DCB Scheme Trip 

The relay is set so that overreaching phase and ground 

elements are allowed to trip after a one-cycle carrier 

coordination delay if no block is received. However, the relay 

tripped by overreaching ground directional overcurrent ele- 


4 

ment 67N2 after a 1-cycle carrier coordination delay. 

Apparently, a blocking signal was being received. 

Higher resolution data from the same relay for the same 

event are shown in Fig. 9. The better resolution illuminates a 

0.25-cycle carrier hole that allowed the local relay to trip. 

IA IB IC 

IRMag 

VA VB VC 

Digitals 

100 

0 

-100 

75 

50 

25 

0 

50 

0 

-50 

Fig. 9. 

BTX 

OUT1 

IN5 

67N2T 

67N2 

IA IB IC IRMag VA VB VC 

.25 cycles 

-1 0 1 2 3 4 5 6 7 8 9 10 11 

Cycles 

Sixteen Samples-per-Cycle Raw Data From a DCB Scheme Trip 

The received blocking input must remain asserted to block 

the forward-looking elements after the coordination timer 

expires. If the blocking signal drops out momentarily because 

of noise or other channel-related problems, the local relay will 

trip for out-of-section faults. 

Relays include an extension timer to delay the control 

input dropout assigned to receive the blocking signal. The 

output of this timer (BTX) ensures unwanted tripping does not 

occur during momentary lapses of the blocking signal (carrier 

holes). A typical setting is 0.5 to 1.5 cycles. 

One drawback of using the block trip (BT) extension timer 

is that tripping would be delayed anytime the BT input is 

asserted. This can cause unnecessary delays for internal faults 

in applications using a nondirectional carrier start. That is, the 

BT input asserts momentarily when nondirectional elements 

assert then deasserts when the forward elements detect the 

fault. BTX would remain asserted and delay tripping until the 

extension timer expired. 

To avoid this delay, use programmable logic in the relay to 

extend the blocking signal (see Fig. 10). 

IN10x 

1.0 cyc 

Set pickup to longer than 

remote carrier assertion 

Fig. 10. 

1 cyc 

Set dropout to longer than 

expected carrier hole time 

BT 

0 cyc 

BTXD 

Set BTXD to zero (0) 

BT Extension for Nondirectional Carrier Start Applications 

In this logic, we extend the BT only if the carrier has been 

initially picked up longer than the remote carrier assertion. 

The typical BT extension timer setting can then be set equal to 

0 cycles [4]. 

BTX 

V. SENSITIVITY MISCOORDINATION 

In January 2001, two parallel 138 kV lines connecting a 

utility to a petrochemical plant tripped for an out-of-section 

fault. The simultaneous outages left the plant’s local 

generation and load electrically isolated from the utility. Both 

lines use identical permissive overreaching transfer trip 

(POTT) schemes with identical relay types at local and remote 

terminals. 

A simplified system one-line diagram with fault location is 

shown in Fig. 11. The tie line that is in parallel with Line 3–4 

and other infeeds to the petrochemical plant and utility bus are 

not shown. The utility is designated 1, and the petrochemical 

plant is designated 2. The actual fault location was behind the 

utility terminal (reverse to Terminal 1 and forward to Terminal 

2). 

2 – Petrochem 1 – Utility 

Fig. 11. 

1 2 3 4 5 6 

Zone 3 Zone 2 

Zone 2 Zone 3 

Simplified One-line Diagram of System With Relay Sensitivities 

Event data from both ends of one tie line are shown 

simultaneously in Fig. 12. The event data match the designations 

above, i.e., the utility data are designated 1, and the 

petrochemical plant data are designated 2. 

1_IA 1_IRMag 

2_IA 2_IRMag 

2_VA 1_VA 

Digitals 

1000 

500 

0 

-500 

1000 

500 

0 

-500 

50 

0 

-50 

Fig. 12. 

1_IA 1_IRMag 2_IA 2_IRMag 2_VA 1_VA 

.054167 sec 

2_OUT 3&4 3 3 

B 

2_OUT 1&2 

2_67N 1 

2_32 Q 

1_OUT 3&4 3 3 

1_OUT 1&2 2 2 

1_IN 1&2 1 

1_67N 

1_32 q 

34.725 34.750 34.775 34.800 34.825 34.850 34.875 34.900 34.925 

Event Time (Sec) 05:05:34.856396 

Utility and Plant Relay Data for Fault 

Terminal 2 responds to the forward AG fault by asserting 

its forward directional element (2_32Q) and its overreaching 

forward directional ground overcurrent element (2_67N2). 

The digital trace in Fig. 12 is identified with a 2_67N1, which 

is correct. Settings for the level one (67N1) and level two 

(67N2) ground elements are set to the same value, and the 

relay reports the assertion of the nearest zone. Terminal 2 keys 

a permission-to-trip (PTT) signal to the remote utility relay 

(2_OUT3). 


5 

MTCS 

Z3RB 

67N3 

67Q3 

Z3G 

M3P 

3P0 

OR 1 

AND 2 

0 

Z3RBD 

(Setting) 

AND 5 

OR 4 

Key 

EBLKD = OFF 

(Setting) 

ETDPU = OFF 

(Setting) 

PT 

(Input) 

AND 1 

0 

EBLKD 

(Setting) 

AND 3 

(Setting) 

ETDPU 

0 

0 

EDURD 

(Setting) 

AND 6 

EKey 

Fig. 13. 

Partial Relay POTT Scheme Logic Diagram 

Terminal 1 correctly sees the fault as reverse according to 

its directional element (1_32q). The PTT signal sent by 

Terminal 2 is received 10 ms later by Terminal 1 (1_OUT2). 

OUT2 is programmed to follow the local PT logic bit (PTT 

received). 

A portion of the relay POTT scheme logic diagram is 

shown in Fig. 13. The relays include logic that permits rapid 

clearing of end-of-line faults when one line terminal is open or 

has a very weak source. This is referred to as “echo” logic [5]. 

The open breaker or weak source terminal is allowed to echo 

the received permission signal as long as two main conditions 

are met: 

1. A reverse fault must not have been detected by the 

reverse-looking elements (67N3, 67Q3, Z3G, M3P). 

2. The PTT input must be received for a settable length of 

time. 

At Terminal 1, no reverse-looking elements are asserted. 

After 2 cycles, Terminal 1 echos the received PTT signal back 

to Terminal 2 as a four-cycle pulse. Why did Terminal 1 not 

have a reverse-looking element asserted The Zone 3 reverse 

ground distance element (Z3G) was desensitized by infeed 

from other lines at the utility bus. Reverse ground overcurrent 

(67N3) was not enabled at this relay. 

Meanwhile, the fault is still visible and on the system, and 

3 cycles after Terminal 2 originally sent PTT, it receives its 

own echoed signal back. This is received by Terminal 2 as 

PTT, and a local high-speed trip is asserted (2_OUT1&2). 

In Fig. 11, note the fault between Breakers 5 and 6; the 

67N2 ground overcurrent element at Breaker 3 is sensitive 

enough to see this fault, and Breaker 3 sends a PTT signal to 

the relay at Breaker 4. At Breaker 4, no reverse 67N3 ground 

overcurrent element is enabled. The ground distance element, 

Z3G, at Breaker 4 is not sensitive enough to see this reverse 

fault, so the Breaker 4 echo logic returns the received PTT 

signal. The result is that Breaker 3 trips for an out-of-section 

fault. The parallel line tripped in identical fashion. 

The root cause of this misoperation was dissimilar 

sensitivities in the local and remote relays. This difference was 

not because of differences in design, make, or model. The 

difference was because of different settings and elements 

enabled at each end of the line by different engineers. This 

was not discovered in the engineering review or by 

commissioning tests. 

Engineers and technicians continue to perform detailed 

element tests during commissioning. Testing the overall 

protection system, including installed settings, is more 

important. End-to-end testing in the lab before installation or 

end-to-end satellite-synchronized testing during commissioning 

may have found this setting problem. In order to do so, the 

test voltages and currents for each line terminal would have to 

be provided from a model of the power system for faults at the 

end of element reaches. 

When installing a POTT scheme, the need for echo logic 

should be considered carefully. Do you even have the 

possibility of a weak infeed condition If you enable echo 

logic, it is critical that reverse-looking Zone 3 elements are 

enabled so that they can supervise the echo decision. Local 

and remote line relay sensitivities should be coordinated, i.e., 

if ground overcurrent elements are enabled at the local end 

(forward 67N2, reverse 67N3), they should be enabled at the 

remote end as well [6]. 

In this event, we also notice that once an echo key 

condition was established, it continued indefinitely until 

stopped by personnel intervention. In Fig. 13, if echo pulse 

duration EDURD is set longer than pickup ETDPU, the local 

and remote relays will establish a permanent echo key 

condition. To prevent this from occurring, set ETDPU to 2 

cycles and EDURD to 1 cycle. Limiting the echo duration to 

less than the echo time-delay pickup ensures that a permanent 

echo key condition will not occur. A one-cycle duration is 

more than adequate for recognition by modern relays. The 

traditional criteria that the echo signal be longer than the 

remote breaker tripping time is not required if relays include 

an appropriate minimum trip duration time. The echo signal 

only needs to be long enough to initiate the high-speed trip, 

after which the trip duration delay determines how long a local 

trip signal is maintained to the breaker. A typical trip duration 

setting is 9 cycles. 


6 

VI. ZONE 1 OVERREACH DUE TO CVT 

In July 2002, a 230 kV transmission line experienced a 

C-phase-to-ground (CG) fault. The local relay tripped by 

Zone 1 ground distance element for a fault that was physically 

located beyond the Zone 1 reach setting. A capacitive voltage 

transformer (CVT) supplies secondary voltage for the relay. 

The unfiltered event data from this misoperation are shown 

in Fig. 14. The event shows a severe transient in the C-phase 

voltage just before the Zone 1 CG distance element operation. 

This transient makes the C-phase voltage magnitude appear 

smaller to the relay than the actual voltage value. The apparent 

impedance calculated by the relay is smaller (or closer to the 

terminal) than actual. The CG distance element asserted in less 

than 1 cycle. When the fault clears, the C-phase voltage has 

another transient that makes it appear higher in magnitude 

than the other nonfault-affected phases. 

IA IB IC IRMag 

VA VB VC 

3V1 3I1 

VCMag 

Digitals 

1000 

0 

-1000 

100 

0 

-100 

1000 

0 

-1000 

IA IB IC IRMag VA 

VB VC 3V1 3I1 VCMag 

.75 cycles 

150 

100 

50 

0 

OUT 1&2 1 . 

32 Q 

ZCG 1 

Fig. 14. 

2 3 4 5 6 7 8 9 10 11 

Cycles 

CG Fault Produces CVT Transient 

Equation (1) and the data from the event allow us to 

calculate the source impedance ratio (SIR) for this application. 

CVTs with an active ferroresonance-suppression circuit (FSC) 

and applications with a high SIR limit secure Zone 1 reach 

settings [7]. The positive-sequence source impedance for this 

application is 11 ohms secondary and the line impedance is 

0.59 ohms secondary, giving an SIR of over 18. 

V1FAULT 

– V1PREFAULT 

SIR = (1) 

(I1 FAULT – I1PREFAULT) 

• Z1 LINE 

For an SIR of 18 and an active FSC, the maximum 

recommended Zone 1 reach is 0.07 pu of the line. With such a 

short line (small impedance), this results in a secondary 

setting below the minimum value allowed by the relay 

(0.05 ohms secondary). In this application, the Zone 1 element 

needs to be completely disabled or time-delayed by at least 

1.5 cycles. In some applications, another option is to split 

Zone 1 into two zones; one zone with reduced reach and set to 

trip instantaneously, and the other zone set to the desired or 

normal reach with time delay. This is a more complex 

solution, but it gives faster tripping for close-in faults and 

takes advantage of the multiple zones available in relays. 

Modern relays now include CVT transient detection logic. 

This logic detects SIRs greater than 5 during a fault and 

blocks the Zone 1 distance tripping for up to 1.5 cycles or 

until the distance calculation “smoothes,” indicating the 

transient has subsided. This logic is ideal for preventing 

distance element overreach for CVT transients. The raw event 

data in Fig. 14 were converted to IEEE COMTRADE files and 

replayed into a relay with CVT transient detection logic. With 

CVT transient detection logic turned off, the relay 

overreached for every simulation. With CVT transient 

detection logic turned on, the logic correctly blocked the 

Zone 1 tripping for the entire 1.5-cycle duration and 

successfully prevented misoperation for all simulations. 

VII. CVT CAUSES RECLOSE FAILURE 

In June 2005, a 161 kV line experienced a BG fault. Both 

line ends use line-side CVTs. Fault data from the remote 

terminal are shown in Fig. 15, and fault data from the local 

terminal are shown in Fig. 16. Both terminals report balanced 

voltages and appropriate load currents flowing from the local 

to remote end before the fault occurs. 

For a BG fault that is forward to both terminals, we would 

expect the phase angle relationships shown in Fig. 15. However, 

voltage during the fault at the local end does not match 

that at the remote terminal. 

Fig. 15. 

Fig. 16. 

180 

135 

225 

VA 

VC 

90 

270 

IC 

VB 

IA 

IB 

45 

315 

Forward BG Fault as Viewed by Remote Line Relay 

180 

135 

225 

IC 

90 

VA 

IA 

270 

IB 

VC 

45 

VB 

315 

Forward BG Fault as Viewed by Local Line Relay 

Multiple CVT secondary grounds were suspected because 

the local prefault voltages were balanced and the fault voltages 

were corrupt. Technicians found two grounds, one at the 

CVT secondary wiring in the yard and another in the control 

building at the relay panel. 

Despite the CVT grounding problem, both terminals tripped 

correctly by a forward ground directional overcurrent element. 

0 

0 


7 

After the remote terminal tripped, a reclose was expected after 

approximately 0.5 seconds. The fault was not permanent, but 

the reclose attempt failed. 

Oscillography from the local relay is shown in Fig. 17. The 

relay’s polarizing voltage has a memory of about one second. 

The CVT transient response and long-time decay are evident. 

This decaying voltage continues to feed the relay positivesequence 

(V1) memory and corrupts V1 magnitude and angle. 

When the line terminal attempts a reclose, the V1 memory has 

not reset, and inrush current from a tapped transformer load is 

present (see Fig. 18). The high current combined with the 

memory voltage error produces a Zone 1 distance element trip. 

IA IB IC 

VA VB VC 

Digitals 

2000 

1000 

0 

-1000 

-2000 

100 

50 

0 

-50 

-100 

ZAB 


VA VB VC 

V1Mag 

V1Ang 

100 

0 

-100 

100 

75 

50 

25 

0 

100 

0 

-100 

Fig. 17. 

IA IB IC 

2500 

0 

-2500 

VA VB VC V1Mag V1Ang 

1 2 3 4 5 6 7 8 9 10 11 

Cycles 

Forward BG Fault as Viewed by Local Line Relay (Filtered Data) 

IA IB IC IAMag IBMag 

ICMag VA VB VC 

Fig. 19. 

0 1 2 3 4 5 6 7 8 9 10 11 12 

Cycles 

COMTRADE Replay of Event Data With V1 Memory Reset 

VIII. BLOWN PT FUSE 

In June 2000, both primary and backup relays at a 69 kV 

line terminal tripped for a potential transformer (PT) fuse 

problem. There was no system fault at the time of trip. The 

relays were different models but both provided distance and 

directional overcurrent functions. The primary relay was used 

in a DCB scheme and the backup relay provided step-distance 

protection and tripped instantaneously for Zone 1 faults. 

The false apparent impedance created by abnormal voltages 

and load currents caused the apparent impedance to 

encroach on the reach of the distance relays (see Fig. 20). The 

same bus potentials serve both relays. 

A B C 

Fuses 

IAMag IBMag ICMag 

2000 

1000 

0 

100 

To Relay 

VA VB VC 

Digitals 

0 

-100 

ZAB 3 1 1 1 1 1 1 1 

PT 

Loose 

Fig. 18. 

0 1 2 3 4 5 6 7 8 9 10 11 12 

Cycles 

Raw Data From Local Relay During Reclose 

Event data from the reclose were converted to IEEE 

COMTRADE format and replayed into a similar relay in the 

lab. With no influence from corrupted V1 memory as in the 

real event in the field, the Zone 1 distance element (ZAB_1) 

did not trip (see Fig. 19). This was because the V1 memory 

was reset at the time the test was started and a fast recharge 

circuit instructed the relay to use actual measured V1. 

The CVT transient coupled with a fast reclose attempt 

caused the reclose failure. Fault detectors that supervise 

distance elements should be set above transformer inrush 

currents [8]. Reclose-open intervals must take into account 

CVT transient response and decay and V1 memory in relays. 

Fig. 20. 

PT Fuse Problem 

Because a blown fuse results in a loss of polarizing inputs 

to the relays, detection of this condition is desirable and was 

enabled in both relays (see Fig. 21). The event data show that 

the loss-of-potential (LOP) detection asserts after the phase 

distance element trips. In both relays, there is a three-cycle 

delay before the LOP element asserts for unbalanced conditions 

to ensure LOP does not block protective elements during 

a fault. 


8 




25 

0 

-25 

0 

-50 

25 

0 

-25 

1_VA 1_VB 1_VC 2_VA 2_VB 

2_VC 3_VA(kV) 3_VB(kV) 3_VC(kV) 

.020833 sec 

Digitals 

3_LOP 

2_OUT TP * 

2_LOP * * 

2_IN 52A * 

L 

2_50P 

2_21P 1 

1_ZBC 4 2 

1_OUT 1&2 1 

1_LOP * * 

1_IN 1&2 B 2 

1_50P 

L 

1_32 Q Q 

50.50 50.55 50.60 50.65 50.70 50.75 

Event Time (Sec) 23:31:50.588677 

Fig. 21. Response of Primary (1), Backup (2), and Relay With Improved LOP 

Logic (3) to PT Fuse Problem 

In the primary relay, an LOP is detected when negativesequence 

voltage (V2) is greater than 14 volts secondary and 

negative-sequence current (3I2) is less than 0.5 amperes 

secondary [9]. In the backup relay, an LOP is detected when 

zero-sequence voltage (V0) is greater than 14 volts secondary 

and zero-sequence current (I0) is less than 0.083 amperes 

secondary [10]. Once asserted, LOP will block distance and 

directional elements that rely on healthy voltage signals. 

This event emphasizes that early LOP logic was designed 

to protect distance elements from misoperating for system 

faults that occurred some time after an initial LOP condition 

was detected. Overcurrent fault detectors, set above load, were 

used to prevent distance element misoperation when the LOP 

condition first occurred. In this event, the fault detector (50L) 

was picked up during balanced load flow. Ideally, fault 

detectors should be set above expected load currents and 

below minimum fault levels to ensure correct distance relay 

operation. 

Newer relays have LOP logic that operates based on the V1 

rate of change versus the rate of change of currents. The new 

logic operates in less than 0.5 cycles, so distance element 

security is less dependent on the fault detector settings [11]. 

In Fig. 21, the response of the original relays are shown 

with that of a relay with improved LOP logic. The new relay 

LOP logic operates more than 1 cycle before any distance 

elements assert, ensuring this misoperation would not happen 

again. 

IX. DIRECTIONAL ELEMENT CHALLENGE 

In June 2007, 80 MW of generation was tripped offline 

because of an unknown cause (at that time). The generator 

stepup transformer was fed radially from a 138 kV tie line to a 

local utility for several seconds. The line was protected by a 

DCB scheme. 

A BG fault then occurred on the line. The relay at the 

generator end of the line saw this fault as reverse and sent a 

blocking signal to the utility terminal, delaying fault clearing. 

Event data from the relay at the generator end of the line are 

shown in Fig. 22. The phase currents are all in phase. 

Fig. 22. 

Fault Data From Relay 

A one-line and symmetrical-components diagram for the 

fault is shown in Fig. 23. With the generator breaker open, 

there is a pure zero-sequence source behind the relay. 

S 

– 

+ 

Fig. 23. 

T 

Relay 

Z1S Z1T m • Z1L (1–m)Z1L Z1R 

Relay 


Relay 


Relay 

L 

3R F 

Symmetrical Components Diagram for BG Line Fault 

R 

– 

+ 


9 

The relay’s directional element can use negative-sequence 

voltage polarization (Q), zero-sequence voltage polarization 

(V), or current polarization (I) [10]. Only one element can be 

used at any one time. The user selected the negative-sequence 

element; its torque equation is shown as (2). 

32Q = V I cos ∠−V 

– ∠I 

+ MTA (2) 

( ( ) 

T ∠ 

2 2 

2 2 

With the local generation connected, negative-sequence 

polarization would have been dependable. However, with the 

generation isolated, the negative-sequence polarized element 

does not correctly determine the fault direction. This is 

because of the lack of negative-sequence current from the pure 

zero-sequence source (wye-grounded transformer) behind the 

relay. By replaying the event data into a relay, we prove that 

zero-sequence voltage polarization correctly determines this to 

be a forward fault. The event data indicate that zero-sequence 

current polarization would have also correctly declared a 

forward fault for this event; I POL and 3I0 are in phase. 

The user can choose to change the polarization quantity. 

This decision, however, sacrifices a more reliable directional 

element in order to trip faster during a rare operating condition. 

A practical improvement would be to wire a 52b contact 

from the generator breaker in parallel with the carrier squelch 

contact from the relay. This would allow high-speed clearing 

from the utility source for faults that occur when the 

generation is offline. 

The directional elements in newer relays offer the ability to 

choose the best choice for the current system configuration 

and fault without requiring settings changes [3]. Multiple 

elements with different polarizing quantities are processed 

simultaneously. One setting allows the user to determine 

which polarizing source to use first, second, and third. If the 

first-choice element does not have adequate quantities, then 

the second choice will be evaluated. If the second choice does 

not have adequate signal, then the third and final choice is 

evaluated. 

Event data were replayed into a newer relay with best 

choice ground directional element logic (see Fig. 24). 32VE 

is the zero-sequence polarizing enable element, and F32V and 

32GF are the forward ground fault directional declaration bits. 

32IE is the current polarizing enable element, and F32I and 

32GF are the forward ground fault directional declaration bits. 

32QGE and 32QE are the negative-sequence element enables, 

and 32QF and 32GF are the forward ground fault directional 

declaration bits. 

In the simulation, we chose an order that always gives 

preference to negative-sequence polarization (Q, V, I). In this 

case, there is little negative-sequence, so the relay checks 

zero-sequence and makes the proper forward directional 

declaration. This secure operation comes at the expense of a 

slight processing delay. Overall, this directional logic results 

in faster operating times for all system states. When the 

generation is online, the negative-sequence directional element 

operates most reliably, and when generation is offline, 

the zero-sequence element operates correctly. 

IA IB IC 


Digitals 

1000 

0 

-1000 

50 

0 

-50 

Fig. 24. 

32QF 

F32I 

32GF 

F32V 

32GR 

R32V 

32IE 

32VE 

32QE 

32QGE 

IA IB IC VA(kV) VB(kV) VC(kV) 

.125 cycles 

0.0 2.5 5.0 7.5 10.0 12.5 15.0 

Cycles 

Best Choice Ground Directional Element Logic for BG Fault 

If none of the directional element enables (32QGE, 32VE, 

and 32IE) assert, then the relay defaults to the negativesequence 

element (as long as Q is listed in the order setting). 

When the relay defaults in this manner, it also bypasses a ratio 

check of negative-sequence to zero-sequence. It was this ratio 

check, |I2| > k2 • |I0|, that prevented the negative-sequence 

element from operating in the simulation. 

X. WHEN STANDARD SETTINGS DO NOT WORK 

In August 2006, a 230 kV line terminal tripped incorrectly 

for a reverse CG fault. The line is a three-terminal DCB 

scheme. There is no positive-sequence source behind the 

relay, but there are two ground sources—an autotransformer 

with a delta tertiary and a wye-grounded high-side, delta lowside 

power transformer. 

The fault data from the event are shown in Fig. 25. During 

the fault, V2 leads I2 by 83 degrees and has a magnitude of 

15 volts secondary. The fault current magnitude is 

3700 amperes primary. The forward directional element 

(32QF) asserts incorrectly and allows a trip by the directional 

ground overcurrent element (67N2dcb). 

IA IB IC IRMag 

VA VB VC 

V2Ang I2Ang 

Digitals 

2500 

0 

-2500 

100 

0 

-100 

100 

0 

-100 

Fig. 25. 

32QF 

3PT 

67N2pu 

67N2dcb 

IA IB IC IRMag VA 

VB VC V2Ang I2Ang 

2 3 4 5 6 7 8 9 10 11 

Cycles 

Forward Fault Declaration for Reverse CG Fault 


10 

The phasors during the fault are shown in Fig. 26. C-phase 

fault current leads a reduced-magnitude C-phase voltage as 

expected for a reverse fault. The expected operation would 

have been for the relay to see this fault as reverse and send a 

blocking signal to the remote terminals. 

Fig. 26. 

180 

135 

225 

IC 

VB 

CG Reverse Fault Phasors 

VA 

90 

270 

IA 

IB 

VC 

45 

315 

Fig. 27 shows a MathCad simulation of the directional 

element. The directional element measures the negativesequence 

impedance (Z2) during the fault and compares it to 

settings to determine the fault direction. 

0.9 

m 0.4 

–0.1 

Fig. 27. 

3 4 5 6 7 8 9 10 11 

Cycles 

Directional Element Response With As-Set Settings 

For forward faults, Z2 is equal to the source impedance 

behind the relay (a negative value). For reverse faults, Z2 is 

equal to the remote source impedance plus the line impedance 

(a positive value). In Fig. 27, Z2 plots below the forward 

threshold, so the relay declares this a forward fault. 

The initial root cause theory blamed the forward and 

reverse threshold settings for the misoperation. The original 

forward threshold (Z2F) was set at one-half Z1MAG 

(positive-sequence line impedance in secondary ohms). The 

original reverse threshold (Z2R) was set at Z2F plus 0.1 ohms 

secondary. This is typical and is used by some relays that 

calculate thresholds automatically. 

There are four reasons this theory seemed credible. First, 

the directional decision made by the relay was incorrect. 

Second, by modifying the Z2F and Z2R settings the 

directional decision made by the relay would have been 

correct (reverse). Fig. 28 shows a MathCad simulation of the 

directional element with Z2F set to –0.1 ohms and Z2R set to 

+0.1 ohms secondary. Third, the engineers experienced a few 

cases where the standard settings did not work. Lastly, a 

subsequent reverse fault operated correctly with the modified 

settings. 

0 

m 

1 

0.5 

0 

–0.5 

–1 

3 4 5 6 7 8 9 10 11 

Cycles 

Fig. 28. Directional Element Response With Z2F = –0.1 Ohms and 

Z2R = +0.1 Ohms 

Standard settings offer convenience but should not be 

applied blindly. Directional element performance is critical 

and should be checked, especially for extreme conditions. Run 

fault studies for very strong or very weak sources, and check 

Z2 against thresholds Z2F and Z2R for proper operation. 

Consider a three-terminal line where one terminal has a 

very weak source (i.e., a large transformer). If the line is 

protected by a DCB scheme, any terminal will trip if an 

internal fault is seen without receiving a block. If the line is 

energized from two ends and the weak source breaker is 

closed to energize the large transformer, the relay at that 

terminal may be subjected to nearly balanced voltages (low 

V2) but unbalanced currents. Standard directional settings 

based on line parameters default to a forward decision for very 

low V2 values. Therefore, the weak terminal could trip 

because of unbalanced current (3I0) and an incorrect 

directional decision (forward for reverse infeed). For 

transformer applications, it is more secure to set Z2F to –0.1 

to –0.5 ohms and Z2R to +0.1 to +0.5 ohms, respectively [12]. 

Upon closer inspection of these event data, however, it 

appears that the Z2F and Z2R thresholds may not be the 

culprits at all. Several data anomalies are present. Standard 

settings tend to give us problems when V2 is small, such as in 

the transformer inrush example above. In this event, however, 

we have plenty of V2 (15 volts secondary). The line impedance 

and line length settings in the relay give us an estimate 

of 1.6 ohms per mile for a 230 kV line, which appears too 

large (half that value would be more reasonable). Z2 measured 

during a reverse fault should equal at least the line impedance; 

the data show a Z2 measurement of 0.5 ohms, less than half of 

the line impedance setting. This led to an alternative theory. 

Perhaps the standard thresholds were just fine, but the 

measured impedance was wrong. An incorrect CT ratio (CTR) 

setting or an incorrect CT tap could do just that. The CTR 

setting in the relay is 40 (200:5) for a 230 kV line. Assume 

that the CT is tapped at 100:5, while the relay settings expect 

200:5. If we leave directional thresholds at their original 

standard settings, we get a correct reverse decision for the 

original fault (see Fig. 29). 


11 

m 

2 

1.5 

1 

0.5 

0 

3 4 5 6 7 8 9 10 11 

Cycles 

Fig. 29. Directional Element Response With CT Tap Lower Than CTR 

Setting 

It is suspected that the CTR setting in the relay does not 

match the actual CT tap in the field. However, this is part of 

an ongoing investigation and, at the time of publication, root 

cause is yet to be determined. 

XI. DIRECTIONAL ELEMENT AFFECTS CARRIER EXTENSION 

In June 2006, a 161 kV line tripped incorrectly for a 

reverse AG fault. The line was protected by a DCB scheme. 

The ground directional element used the best choice logic 

described in Section IX. The element used ground current 

polarization first (I), followed by zero-sequence voltage 

polarization (V), and then by negative-sequence voltage 

polarization (Q). 

The event data from the misoperation are shown in Fig. 30. 

For a reverse fault, we expect the polarizing current (IP) and 

the terminal ground current (IG) to be 180 degrees out of 

phase. In the event data, however, IP and IG were in phase. A 

wiring error was found; the polarizing current CT was 

connected reverse polarity. This allowed the local breaker to 

trip. 

IA IB IC 


IP IG 

Digitals 

1000 

0 

-1000 

100 

0 

-100 

5000 

0 

-5000 

DSTRT 

Z3XT 

50G3 

32QR 

F32I 

67G1T 

IA IB IC VA(kV) VB(kV) VC(kV) IP IG 

2 3 4 5 6 7 8 

Cycles 

Fig. 30. Directional Element Misoperation due to IP Wiring Mistake 

The remote breakers were allowed to trip because of the 

carrier-blocking signal dropout as the breaker was interrupting 

the fault. In Fig. 31, directional carrier blocking (DSTRT) was 

asserted due to a negative-sequence element (50Q3) and a 

negative-sequence directional element (R32Q). At the end of 

the event, the DSTRT element chattered then dropped out. 

This was because of the phase angle error introduced by 

arcing during interruption. Carrier blocking extension is 

enabled in this relay but requires Zone 3 elements to be 

asserted for 2 cycles; they were only asserted for 1.5 cycles. 

During the investigation, it was noted that the directional 

element processing order of IVQ was not typically used by 

this utility; an order setting of QV was more common. Would 

carrier extension have asserted if we had used the typical 

order 

In Fig. 31, the ground-polarized directional elements (F32I 

and 32GF) assert because of the directional logic order and 

wiring error. The phase angle of the faulted phase current 

varies wildly during the beginning of the fault because of the 

fault arcing and evolution. This delays the voltage-based 

directional elements but has little effect on the current-based 

directional element. Also in Fig. 31, negative-sequence 

directional elements (32QR and R32Q) asserted later in the 

fault. 32QR and R32Q supervise phase distance and negativesequence 

overcurrent elements. Their ground logic equivalent 

(R32QG) is controlled by best choice logic. R32QG did not 

assert because the IP-based element has priority, but the 

directional decision it would make would match that of 32QR 

and R32Q when enabled. From this, we realize that the order 

and best choice logic processing did not delay the R32QG 

element; the evolving fault did. 

IA IB IC 


Digitals 

1000 

0 

-1000 

100 

0 

-100 

50Q3 

50G3 

NSTRT 

DSTRT 

Z3XT 

R32V 

F32V 

R32QG 

F32QG 

R32Q 

F32Q 

R32I 

F32I 

32QE 

32IE 

32QGE 

32VE 

32GR 

32GF 

32QR 

IA IB IC VA(kV) VB(kV) VC(kV) 

0.0 2.5 5.0 7.5 10.0 12.5 15.0 

Cycles 

Fig. 31. Detailed Relay Response to Fault 

The evolving fault should delay a directional decision for 

all the relays. Remote relays additionally include a carrier 

coordination delay for tripping. How fast the directional 

element sent blocking is not the real issue in this fault; it is 

how fast we enable carrier extension. Setting the carrier 

extension pickup delay (Z3XPU) to a lower value, even zero, 

is recommended [13]. 

XII. COMPARING PRIMARY AND BACKUP METERING 

In November 2005, a 138 kV transmission line experienced 

an AG fault. The backup relay correctly saw the fault as 

forward and tripped by the directional ground overcurrent 

element (67G1). The primary relay, however, declared a 

reverse fault and did not operate. 


12 

The prefault data from the backup relay are shown in 

Fig. 32, and the prefault data from the primary relay are 

shown in Fig. 33. The phase voltages seen by the primary 

relay in the prefault state did not look normal or balanced, and 

a significant standing zero-sequence voltage was present. The 

backup relay, on the contrary, reported normal prefault 

voltages. 

180 

135 

225 

135 

90 

VC (kV) 

IB 

IA 

VB (kV) 

270 

90 

IC 

45 

VA (kV) 

0 

315 

45 

The neutral bus of the primary relay three-phase voltage 

connections should have been connected at a terminal block to 

station ground; this wire was missing. The result was that the 

primary relay voltages were floating, and this distorted phaseto-neutral 

magnitudes, angles, and sequence components both 

before the fault and during the fault. The backup relay had 

properly terminated voltages and, therefore, its zero-sequence 

voltage polarized directional element performed correctly. 

The fault data collected from the backup relay are shown 

in Fig. 34. The zero-sequence current leads the zero-sequence 

voltage by about 120 degrees, as expected for a forward AG 

fault. Negative-sequence relationships are similar. The relay is 

set by the user to enable only zero-sequence quantities for 

directional decisions. However, the data show that the zerosequence 

directional element used (F32V) and the disabled 

negative-sequence directional element (F32Q) both made the 

correct directional decision. 

IA IB IC 


V0Ang I0Ang 

Digitals 

10000 

0 

-10000 

50 

0 

-50 

100 

0 

-100 

F32V 

F32Q 

67G1 

IA IB IC VA(kV) VB(kV) VC(kV) V0Ang I0Ang 

0.0 2.5 5.0 7.5 10.0 12.5 15.0 

Cycles 

Fig. 32. 

180 

225 

Prefault Data From Backup Relay 

135 

180 

225 

135 

180 

270 

90 

VC (kV) 

IB (A) 

IC (A) 

IA (A) 

VB (kV) 

270 

90 

V0 

V1 

0 

315 

45 

VA (kV) 

0 

315 

45 

V1 

0 

Fig. 34. 

Fault Data From Backup Relay 

The fault data collected from the primary relay are shown 

in Fig. 35. The zero-sequence current leads the zero-sequence 

voltage by about 210 degrees, which causes the zero-sequence 

directional element misoperation. Negative-sequence relationships 

match those reported by the backup relay and are 

correct. The relay is set by the user to enable only zerosequence 

quantities for directional decisions. However, the 

data show that the disabled negative-sequence directional 

element (F32Q) made the correct directional decision. 

IA(A) IB(A) IC(A) 


V0Ang I0Ang 

10000 

0 

-10000 

100 

0 

-100 

200 

0 

-200 

IA(A) IB(A) IC(A) VA(kV) VB(kV) VC(kV) V0Ang I0Ang 

225 

270 

315 

Digitals 

67G1 

F32V 

F32Q 

TRIP 

IN105 

Fig. 33. 

Prefault Data From Primary Relay 

Fig. 35. 

0.0 2.5 5.0 7.5 10.0 12.5 15.0 

Cycles 

Fault Data From Primary Relay 

Synchronized phasor measurement during commissioning 

is a useful tool for finding mistakes like these before they 

cause misoperations. When relays are connected to a common 

voltage or current source, automation systems can be easily 

designed to periodically retrieve metering data, compare them, 

and alarm when differences are discovered. Troubleshooting 

and repair can then be performed to fix problems before they 

are discovered by misoperations. 


13 

XIII. CONCLUSIONS 

• Evolving faults can challenge fault location and 

targeting algorithms; offline tools can improve fault 

location accuracy. 

• Evolving faults can delay distance element tripping; 

common zone timing allows faster fault clearing. 

• Evolving faults can create reclosing problems; use trip 

elements to initiate reclosing and nonreclosing elements 

in drive-to-lockout logic. 

• Carrier holes cause DCB scheme problems; BT 

extension logic adds security. 

• Sensitivities of local and remote line relays should be 

matched. 

• Commissioning tests should concentrate on proving the 

overall protection system. 

• Unique event reports should be archived as 

COMTRADE files and used to test new schemes. 

• CVT transients can cause Zone 1 overreach; CVT 

transient detection logic adds security. 

• Extend reclosing open intervals beyond CVT transient 

response and set fault detectors above inrush on lines 

with tapped loads. 

• Older LOP logic relied on fault detectors set above 

normal load currents; improved LOP logic operates 

faster and is less dependent on fault detector settings 

for security. 

• Relays that include multiple polarization schemes and 

choose the appropriate element for the system and fault 

offer the best sensitivity and security. 

• Do not apply standard settings blindly; directional 

element performance is critical and should be checked, 

especially for extreme conditions. 

• Set carrier extension pickup delay to zero in DCB 

schemes. 

• Missing or multiple ground wires in instrument 

transformer circuits cause directional element 

misoperations; thorough commissioning tests and 

automated meter data comparisons should find these 

errors before misoperations occur. 

[4] G. Alexander, K. Zimmerman, and J. Mooney, “Setting the SEL-421 

Relay With Sub-Cycle Elements in a Directional Comparison Blocking 

Scheme,” Schweitzer Engineering Laboratories, Inc. Application Guide 

2007-10. [Online] Available: http://www.selinc.com/aglist.htm. 

[5] A. Guzman, J. Roberts, and K. Zimmerman, “Applying the SEL-321 

Relay to Permissive Overreaching Transfer Trip (POTT) Schemes,” 

Schweitzer Engineering Laboratories, Inc. Application Guide 95-29. 

[Online] Available: http://www.selinc.com/aglist.htm. 

[6] J. Roberts, E. O. Schweitzer III, R. Arora, and E. Poggi, “Limits to the 

Sensitivity of Ground Directional and Distance Protection,” presented at 

the 1997 Spring Meeting of the Pennsylvania Electric Association Relay 

Committee. [Online] Available: http://www.selinc.com/techpprs.htm. 

[7] D. Hou and J. Roberts, “Capacitive Voltage Transformers: Transient 

Overreach Concerns and Solutions for Distance Relaying,” presented at 

the 22nd Annual Western Protective Relay Conference in Spokane, WA, 

October 1995. [Online] Available: http://www.selinc.com/techpprs.htm. 

[8] J. Mooney and S. Samineni, “Distance Relay Response to Transformer 

Energization: Problems and Solutions,” presented at the Texas A&M 

Conference for Protective Relay Engineers, College Station, TX, 

March 2007. [Online] Available: http://www.selinc.com/techpprs.htm. 

[9] SEL-321 Instruction Manual, Schweitzer Engineering Laboratories, Inc., 

Pullman, WA. 

[Online] Available: http://www.selinc.com/instruction_manual.htm. 

[10] SEL-221G5 Instruction Manual, Schweitzer Engineering Laboratories, 

Inc., Pullman, WA. 


[11] J. Roberts and R. Folkers, “Improvements to the Loss-of-Potential 

(LOP) Function in the SEL-321,” Schweitzer Engineering Laboratories, 

Inc. Application Guide 2000-05. 


[12] K. Zimmerman, “Negative-Sequence Directional Element Revisited,” 

presented at the 21st Annual SEL Technical Seminar at the Western 

Protective Relay Conference in Spokane, WA, October 2005. 

[13] G. Alexander, K. Zimmerman, and J. Mooney, Schweitzer Engineering 

Laboratories, Inc. Application Guide 2007-10. 


XVI. BIOGRAPHY 

David Costello graduated from Texas A&M University in 1991 with a BSEE. 

He worked as a system protection engineer at Central Power and Light and 

Central and Southwest Services in Texas and Oklahoma. He has served on the 

System Protection Task Force for ERCOT. In 1996, David joined Schweitzer 

Engineering Laboratories, Inc., where he has served as a field application 

engineer and regional service manager. He presently holds the title of senior 

application engineer and works in Boerne, Texas. He is a senior member of 

IEEE, and a member of the planning committee for the Conference for 

Protective Relay Engineers at Texas A&M University. 

XIV. ACKNOWLEDGMENT 

The author gratefully acknowledges Normann Fischer, 

Karl Zimmerman, Bill Fleming, Joe Mooney, and Matt Leoni 

for their contributions to the original event analyses. 

XV. REFERENCES 

[1] SEL-311B Instruction Manual, Schweitzer Engineering Laboratories, 



[2] K. Zimmerman and D. Costello, “Impedance-Based Fault Location 

Experience,” presented at the 31st Annual Western Protective Relay 

Conference in Spokane, WA, October 2004. 

[Online] Available: http://www.selinc.com/techpprs.htm. 

[3] SEL-311C Instruction Manual, Schweitzer Engineering Laboratories, 



© 2007 Schweitzer Engineering Laboratories, Inc. 

All rights reserved. 

20070913 • TP6280-01 


1 

Adaptive Phase and Ground 

Quadrilateral Distance Elements 

Fernando Calero, Armando Guzmán, and Gabriel Benmouyal, Schweitzer Engineering Laboratories, Inc. 

Abstract—Quadrilateral distance elements can provide 

significantly more fault resistance coverage than mho distance 

elements for short line applications. Quadrilateral phase and 

ground distance element characteristics result from the 

combination of several distance elements. Directional elements 

discriminate between forward and reverse faults, while reactance 

and resistance elements are fundamental to the proper 

performance of the quadrilateral characteristic. Load flow 

considerations determine the choice of the polarizing quantity for 

these elements. Reactance elements must accommodate load flow 

and adapt to it. Resistive blinders should detect as much fault 

resistance as possible without causing excessive overreach or 

underreach of the quadrilateral distance element. In this paper, 

we discuss an adaptive quadrilateral distance scheme that can 

detect greater fault resistance than a previous implementation. 

We also discuss application considerations for quadrilateral 

distance elements. 

Phase B are shown), the tower structure, the insulator chains, 

the ground wire, and the different impedances to the flow of 

fault current. These impedances are simplified to be resistive 

values only [4][5]. 

I. OVERVIEW 

Whereas the literature debates the differences and benefits 

of mho and quadrilateral ground distance elements [1], this 

paper describes the theory, application, and characteristics of a 

particular implementation of phase and ground quadrilateral 

distance elements. 

It is well accepted that a quadrilateral characteristic is 

beneficial when protecting short transmission lines [1][2]. It is 

also accepted that sensitive pilot protection schemes do not 

rely on distance elements only; these schemes also rely on 

ground directional overcurrent (67G), a unit that provides 

higher fault resistance (Rf) detecting capabilities than ground 

distance elements of any shape [3]. 

Generally, high Rf faults have been associated with singleline-to-ground 

faults (AG, BG, CG). For these faults, the 

associated Rf is considerable. On the other hand, phase faults 

are less susceptible to high Rf values. However, because short 

transmission lines are much more affected by high Rf values, 

the element with the most fault detecting capabilities should 

be used [1][2][3]. 

A. Fault Resistance 

Short circuits along the transmission line will have some 

degree of additional impedance. If this additional impedance 

is negligible, the line impedance is prevalent, and the apparent 

impedance measured will reflect it by reporting an impedance 

with the same angle as the line impedance. On the other hand, 

if this additional impedance is not negligible, the measured 

apparent impedance no longer appears at the line angle. 

Fig. 1 shows the different components of fault resistance 

for transmission line faults. Although extremely simplified, 

the figure shows the phase conductors (only Phase A and 

Fig. 1. Visualizing the Rf component 

The Rtower resistance is generally called the “footing 

resistance.” It is a critical parameter regarding the design and 

construction of transmission lines [6]. For an insulation 

flashover fault, the return path is through the tower itself. 

When a foreign object touches the conductors, the current 

distributes between adjacent towers but returns through the 

footing resistance. Ideally, the smaller the footing resistance, 

the better the transmission line ground fault detection 

performance will be. However, even though smaller values 

exist, practical values range from 5 to 20 ohms; and in rocky 

terrain, the resistance could be 100 ohms or more [1]. 

In Fig. 1, Raφg represents the arc resistance for an insulator 

flashover for a phase-to-ground fault. This is in the path of the 

ground fault flashover current Igffo. Raφφ is the arc resistance 

for a phase-to-phase fault. 

The arc resistance value is dependent on the arc length and 

the current flowing through the arc. A well-accepted formula 

is the one empirically derived by A. Van Warrington, 

expressed in (1). Other equations yield similar results [7]. In 

(1), the arc length is expressed in meters. 

Rarc length 

= 28688.5 Ω (1) 

I 1.4 

The arc initially presents a few ohms of impedance. Over 

time, it could develop into 50 or more ohms [1]. Importantly, 

its value is dependent on the arc length and the current 

Adaptive Phase and Ground Quadrilateral Distance Elements | 65

2 

flowing through the arc. In Fig. 1, the arc length is denoted as 

dφg for ground faults and dφφ for phase faults. 

Rstruc is the tower structure resistance. Although 

insignificant for a metallic structure, this resistance may carry 

a significant value if built from a nonconductive material like 

wood. 

Rtreeg and Rtreep are the resistances of foreign objects that 

could be causing a power system fault. A tree is chosen as an 

example. These resistance values could be a few hundred 

ohms. 

1) Phase-to-Ground Faults 

Phase-to-ground faults are the most common type of faults 

in the power system. They involve a single phase that 

conducts fault current to ground. There are two possible 

single-phase-to-ground fault scenarios: insulator flashover and 

an object creating a path to ground. 

a) Insulator Flashover 

An insulator flashover (arc resistance Raφg), which may be 

due to a lightning strike or any other event that would stress 

the insulator, conducts fault current from the phase conductor 

to the tower structure (Igffo) and then to ground through the 

“tower footing resistance” (Rtower). The arc forms on the dφg 

length. This length is the “creepage distance” of the insulator 

string, which is the shortest electrical distance between the 

conductor and the tower measured along the insulator string 

structure. 

b) Ground Fault Through an Object 

Another possible phase-to-ground fault may occur when 

the phase conductor contacts an object, such as a tree (Rtree), 

which is in contact with ground (see Fig. 1). The contact is 

most likely not at the tower location. It could occur any place 

along the span from one tower to another tower. The fault 

current distributes to ground through the tower resistances, 

with a larger percentage of current flowing to the footing 

resistance of the closer tower. Conservatively, we can assume 

that current is only flowing through a single tower footing 

resistance. This simple assumption contrasts with other 

advanced and accurate analysis techniques [8]. 

Regardless of the two possible scenarios, the path to 

ground involves the equivalent Rtower, which is the resistance 

of the composite path from earth to system ground. For an 

insulator flashover, Rf is the sum of Raφg and Rtower, 

ignoring the tower resistance (Rstruc). For a ground fault 

occurring because of contact with an object to ground, Rf is 

the sum of Rtreeg and Rtower. The Rf component for this type 

of fault can be significant. 

The presence of ground wires in the tower distributes the 

fault current differently. A portion of the fault current will 

return to ground (Igw) through these wires. The ground wires 

are part of the zero-sequence impedance and therefore not 

associated to Rf. 

2) Phase-to-Phase Faults 

Phase-to-phase faults, as Fig. 1 illustrates, do not involve 

the ground return path. As with phase-to-ground faults, an 

insulator flashover or phase-to-phase connection through an 

object could be the cause of the fault. 

If the fault is due to insulation flashover, Rf is expressed by 

(1), and the arc length could be a straight line or a path around 

the tower (dφφ). The important factor is that Rf is fully due to 

the arc resistance. 

Because of the spacing between phases in high-voltage 

(HV) and extra-high-voltage (EHV) transmission networks 

and even in subtransmission levels, it is highly improbable 

that an object could produce a phase-to-phase fault because of 

contact. However, in distribution networks, phase-to-phase 

faults have a higher probability of occurrence because the 

conductor can have contact with different objects, like tree 

branches, flying debris, etc. 

B. The Need for a Quadrilateral Element in Transmission 

Networks 

The following three conclusions can be made based on 

Fig. 1: 

• The arc component of the fault, Raφg or Raφφ, has a 

value that can be estimated. Equation (1) indicates that 

the value may not be significant for transmission 

levels. 

• Ground faults may have significant values of Rf. The 

tower footing resistances or foreign object resistances 

can have large values. 

• Phase faults in transmission networks will most likely 

have a small arc resistance. 

When discussing protective distance relaying for 

transmission lines, it is of interest to understand the relay 

impedance characteristics and schemes used. Per the 

discussion above, ground distance relaying for short lines, 

which can be complicated, benefits from the use of a 

quadrilateral characteristic because ground faults involve more 

than the arc resistance. Phase distance relaying, on the other 

hand, detects faults where only the arc resistance is involved, 

and therefore the complications of a quadrilateral element are 

not generally required. For these reasons, protective relaying 

distance schemes that implement mho phase distance 

algorithms to detect phase faults and a combination of mho 

and quadrilateral ground distance elements to detect ground 

faults are justified. 

For the majority of transmission line applications, from 

subtransmission to EHV voltage levels, the mho phase 

element and mho quadrilateral ground distance scheme have 

proven to be adequate. Extremely short lines may be a 

challenge to this scheme. Zero-sequence and negativesequence 

directional overcurrent elements have proven to be 

the solution for distance element limitations for short lines. 


3 

C. Short Line Applications 

A short transmission line will generally have lowimpedance 

and short length values. On an R-X diagram, like 

the one shown in Fig. 2, the line impedance is electrically very 

far from the expected maximum load. For some applications, 

the line impedance reach (Zset) values challenge the 

measurement accuracies of the relay itself. 

Even for a ground fault with no arc resistance (Raφg equals 

zero), the Rf component will have the value of the tower 

footing resistance, as discussed previously. Mho ground 

elements have an intrinsic ability to expand and accommodate 

more Rf. This expansion is proportional to the source 

impedance (Zs), as shown in Fig. 2 [9]. However, if the tower 

footing resistances are in the range of the line impedances, 

which add to Rf, the mho element will have difficulty 

detecting faults even with no arc resistance. The situation is 

negatively amplified if the source behind the relay is very 

strong—implying a very small Zs. 

D. Directional Overcurrent 

Directional overcurrent protection is a more sensitive fault 

detecting technique than any type of distance element [1][10]. 

The reach of these elements varies with the source impedance 

of a transmission network. Ground directional elements are 

polarized with zero-sequence or negative-sequence voltage. 

Negative-sequence polarization is also used for phase 

directional overcurrent protection. Other phase directional 

schemes are also possible. 

In line protection schemes, directional overcurrent is used 

as a backup scheme for pilot channel loss. 

Directional comparison pilot relaying schemes compare the 

direction to the fault between two or more terminals. It is 

recommended to include directional overcurrent elements (67) 

to complement the traditional distance elements (21), as 

illustrated in Fig. 3. 

jX 

Load 

Zset 

Rf 

Fig. 3. 

Directional comparison with directional overcurrent elements 

Zs 

R 

Pilot schemes for ground directional overcurrent, as shown 

in Fig. 3, will make up for any lack of sensitivity of mho 

elements for short lines. In fact, greater sensitivity is achieved 

by using directional overcurrent elements in the scheme, 

regardless of the types of line and distance elements. 

Fig. 2. 

Short line apparent impedance 

Quadrilateral ground distance elements can provide a larger 

margin to accommodate Rf. These elements are better suited to 

protect short lines. There are some limitations in the amount 

of Rf that they can accommodate (see Section IV). 

Nevertheless, their performance is better than that of a mho 

circle. 

The situation for phase fault detection is similar to that of 

ground fault detection in short line applications. If the 

expected arc resistance is approximately the same magnitude 

as the transmission line impedance, the mho phase circle will 

experience problems detecting the fault. In significantly short 

line applications, quadrilateral phase distance elements 

provide notably better coverage than a mho phase element. 

Nevertheless, it is accepted that directional overcurrent 

elements are the most sensitive fault detecting elements and 

should be included in pilot relaying schemes [1][3]. 

E. Fault Resistance on the Apparent Impedance Plane 

Relay engineers use the apparent impedance plane to 

analyze distance element performance during load, fault, and 

power oscillation conditions, either with mho or quadrilateral 

elements. In this plane, we can represent the apparent 

impedance for line faults with different values of Rf and line 

loading conditions. Fig. 4 shows the system that we used to 

calculate the apparent impedance for phase-to-ground faults at 

85 percent from the sending end. 

Fig. 4. Power system parameters and operating conditions to analyze the 

performance of distance elements 


4 

Fig. 5 shows the apparent impedance locus for different 

loading conditions (δ equal to –20, –10, 0, 10, and 20 degrees) 

and all possible values of Rf. 

forward direction, ZLOAD is on the right side (positive values 

of resistance) of the plane. As Rf starts decreasing, the 

apparent impedance describes the locus that Fig. 7 shows. 

Notice that with Rf equal to 0, the apparent impedance is 

exactly equal to 85 percent of the line impedance. 

200 

4 

Reactance (ohms) 

100 

0 

-10 

-20 

20 

-100 0 100 

Resistance (ohms) 

Fig. 5. Apparent impedance for δ equal to –20, –10, 0, 10, and 20 degrees 

while Rf varies from 0 to ∞ 

Fig. 6 shows that the apparent impedance can cause 

distance elements with fixed characteristics over- and 

underreach and have limited Rf coverage if the distance 

element does not have an adaptive characteristic [11]. 

20 

10 

0 


2 

0 

-2 

-4 

Rf = 0 

Rf = ∞ 

ZLOAD 

0 10 20 30 40 


Fig. 7. Apparent impedance locus for load in the forward direction (δ equal 

to 10 degrees) 

Fig. 8 shows the impedance locus for incoming load flow 

(δ equal to –10 degrees). This apparent impedance makes it a 

challenge for the distance elements to detect large values of Rf 

and avoid element underreach. 

150 

10 


0 


100 

50 

Rf = ∞ 

-10 

-10 0 10 20 

Resistance (ohms)} 

Fig. 6. Apparent impedance can cause distance element over- and 

underreach and have limited Rf coverage 

Fig. 7 shows the impedance locus for load flow in the 

forward direction (δ equal to 10 degrees). In this case, the 

remote-end voltage VR equals 0.98 pu. Regardless of the 

impedance loop measurement (ground fault loop or phase fault 

loop), the apparent impedance starts at a load value, ZLOAD, 

that corresponds to Rf equals ∞. For active power flow in the 

0 

ZLOAD 

Rf = 0 

-50 

-100 -80 -60 -40 -20 0 20 40 60 80 100 


Fig. 8. Apparent impedance locus for incoming load flow (δ equal to 

–10 degrees) 


5 

II. QUADRILATERAL DISTANCE ELEMENTS 

Mho distance elements describe a natural and smooth 

curvature on the impedance plane. The shape is the result of a 

phase comparison of two quantities that yield the familiar 

circle on the apparent impedance plane [9]. Quadrilateral 

distance elements are not as straightforward. Combining 

distance elements has allowed designers to create all types of 

shapes and polygonal characteristics. 

An impedance function with a quadrilateral characteristic 

requires the implementation of the following: 

• A directional element 

• A reactance element 

• Two left and right blinder resistance calculations 

Fig. 9 illustrates a typical quadrilateral element composed 

of three distance elements. The element that determines the 

impedance reach is the reactance element X. The element that 

determines the resistive coverage for faults is the right 

resistance element Rright. The element that limits the 

coverage for reverse flowing load is the left resistance element 

Rleft. A directional check keeps the unit detecting faults in the 

forward direction only. 

Fig. 9. 

Components of a quadrilateral distance element 

The setting of the reach on the line impedance angle locus 

is denoted by Zset in Fig. 9. It is not a setting on the X axis but 

is the reach on the line impedance. We will show that this 

setting is the pivot point of the line impedance reach. The Rset 

setting is the resistive offset from the origin. A line parallel to 

the line impedance is shown in Fig. 9. 

The impedance lines in Fig. 9 are straight lines for practical 

purposes. The theory, however, shows that these lines are 

infinite radius circles [9]. The polarizing quantity for creating 

these large circles is the measured current at the relay location. 

A. Adaptive Reactance Element 

Several protective relaying publications report that serious 

overreach problems are experienced by nonadaptive reactance 

elements because of forward load flow and Rf [1][2][11]. If 

the reactance element in a quadrilateral characteristic is not 

designed to accommodate the situation shown in Fig. 10, an 

external fault with Rf may enter the operating area. The 

intrinsic curvature and beneficial shift of the mho circle are 

sufficient to overcome this problem. However, reactance lines 

need to be designed to accommodate this issue. 

Fig. 10. 

jX 

The reactance and mho elements adapt to load conditions 

Fig. 10 shows the desired behavior of the reactance line for 

forward load flow. A tilt in the shown direction is required. 

Several techniques have been proposed for this purpose, 

including a fixed characteristic tilt and the use of prefault load. 

Interestingly, an infinite diameter mho circle provides the 

same tilt as a regular mho circle, and the reactive line becomes 

adaptive [9]. The proper polarizing current is the negativesequence 

component [12]. The homogeneity of the negativesequence 

network and the closer proximity of the I2 angle to 

the fault current (If) angle makes the I2 current an ideal 

polarizing quantity. 

To obtain the desired reactance characteristic for the AG 

loop, the following two quantities can be compared with a 

90-degree phase comparator: 

S1 = VRA − Zset(IRA + k0 3I0) 

(2) 

( ) jT 

S2 = j IR2 e 

(3) 

Equations (4) and (5) define the resulting a and b vectors 

used to plot the reactance element characteristic [9]. 

a = Zset 

(4) 

⎡ 

o ⎛ IA1 IA0 Zset0 ⎞⎤ 

− j ⎢90 − T+ ang ⎜1+ + 

⎟⎥ 

⎣ ⎝ IA2 IA2 Zset ⎠⎦ 

b = ∞ e 

(5) 

Zset0 − Zset1 

k0 = (6) 

3• Zset1 

where: 

k0 is the zero-sequence compensating factor. 

Zset0 is the zero-sequence impedance reach derived from 

k0 and Zset. 

R 


6 

Fig. 11 shows the adaptive behavior of the reactance line 

derived from (4) and (5). Calculating a proper homogeneity 

angle tilt (denoted by T in the equation), the unit ensures 

correct reach regardless of the direction of the load flow. 

Similarly, Equations (13) and (14) define the adaptive 

phase resistance element for phase faults. 

S1 = (VRB − VRC) − Rset(IRB − IRC) (13) 

j L1 

S2 = (IRB2 − IRC2) e θ 

(14) 

jX 

ZL 

Fig. 11. 

Adaptive ground reactance element characteristic 

For ground distance elements, I0 is another choice for 

polarizing the reactance element. This option is acceptable if 

the homogeneity factor, T, for the zero-sequence impedances 

is known. 

For phase distance elements, using the negative-sequence 

current is also an option. 

S1 = (VRB − VRC) − Zset(IRB − IRC) (7) 

jT 

S2 = j(IRB2 − IRC2)e 

(8) 

The resulting a and b vectors are shown in (9) and (10). 

a = Zset 

(9) 

⎛ ⎛ IB1− IC1 ⎞⎞ 

− j ⎜90− T+ ang ⎜1+ 

⎟⎟ 

⎝ ⎝ IB2 − IC2 ⎠⎠ 

b = ∞ e 

(10) 

As described in [9], vector b defines the infinite diameter 

and the tilt angle, both of which are expressed in (5) for the 

ground reactance line and (10) for the phase reactance line. 

The resulting line is adaptive to the load flow direction, as 

shown in Fig. 11. The reactance line adapts properly to load 

flow and Rf. 

B. Adaptive Resistance Element 

Fig. 9 shows that the right resistance element is responsible 

for the resistive coverage in a quadrilateral distance element. 

This component of the quadrilateral distance element should 

accommodate and detect as much Rf as possible. 

In proposing an adaptive resistance line, it is possible to 

make the line static or adaptive as the reactance line. An 

adaptive resistive blinder is obtained by defining Rset in (2) 

and shifting (3) by (θL1 – 90°), where θL1 is the angle of the 

positive-sequence line impedance. The benefit shown in 

Fig. 12 is a shift of the resistance element to the right, which 

accommodates faults with forward load flow. Equations (11) 

and (12) implement the adaptive ground resistance element. 

S1 = VRA − Rset(IRA + k0 3I0) (11) 

j L1 

S2 = IR2 e θ 

(12) 

Rset 

Fig. 12. Adaptive ground resistance element characteristic 

While the use of negative-sequence current yields a 

beneficial tilt of the resistance element for load in the forward 

direction, as shown in Fig. 12, the tilt is in the opposite 

direction for load in the reverse direction. Therefore, the tilt is 

not beneficial under this condition. 

Additional polarizing options, like that the alpha 

component (I1 + I2) for ground and I1 for phase distance 

elements, yield satisfactory tilt behavior for reverse load flow. 

The reverse load flow behavior is the same. 

C. Left Resistance Element 

The left resistive line in Fig. 9 is responsible for limiting 

the operation of the quadrilateral element for reverse load 

flow. It does not need to be adaptive. Care has been taken not 

to include the origin to ensure satisfactory operation for very 

reactive lines. 

D. High-Speed Implementation 

In many transmission line protection applications, subcycle 

operation is required for distance elements. In many relays, 

distance elements with mho or quadrilateral characteristics are 

available. When the distance elements selected have 

quadrilateral characteristics only, the same high-speed 

requirement is applicable for faults with low-resistance value. 

In order to obtain subcycle operation with quadrilateral 

elements, the same dual-filter concept presented in [14] for 

mho elements is used here. The basic principle is to process 

the same distance function twice, using two types of voltage 

and current phasors: the function is processed first using halfcycle 

(high-speed) filter phasors and a second time with fullcycle 

(conventional) filter phasors. The final function state is 

obtained by the logical OR operation from the two processes. 

For single-pole tripping applications, these three ground 

distance elements (AG, BG, and CG) need to be supervised 

with a faulted phase selection function. 

R 


7 

For the purpose of implementing the directional element 

and the faulted phase selection for the high-speed part of the 

quadrilateral function, the algorithm described in [14] and [15] 

uses a function known as high-speed directional and fault type 

selection (HSD-FTS). It processes signals using half-cycle 

filters and superimposed quantities to provide the 

14 directional signals listed in Table I. 

TABLE I 

HIGH-SPEED DIRECTIONAL SIGNALS 

Signal 

HSD-AGF, HSD-AGR 

HSD-BGF, HSD-BGR 

HSD-CGF, HSD-CGR 

HSD-ABF, HSD-ABR 

HSD-BCF, HSD-BCR 

HSD-CAF, HSD-CAR 

HSD-ABCF, HSD-ABCR 

Fault Description 

Forward, reverse AG 

Forward, reverse BG 

Forward, reverse CG 

Forward, reverse AB 

Forward, reverse BC 

Forward, reverse CA 

Forward, reverse ABC 

Because the HSD-FTS signals are derived from 

incremental currents and voltages, they will be available only 

for 2 cycles following the inception of a fault. Consequently, 

the high-speed quadrilateral signals are available for the same 

interval of time following the detection of a fault. 

For the reactance element, the high-speed part of the 

quadrilateral characteristic implementation uses the same 

equations for the ground elements as the conventional 

counterpart uses with polarization based on negative- or zerosequence 

current. During a pole open, the polarization by the 

sequence current (negative or zero) is replaced by the 

incremental impedance loop current so that the ground 

elements remain operational for single-pole tripping 

applications. 

For the phase elements, polarization is based on the loopimpedance 

incremental current so that phase faults and singlepole 

tripping applications are automatically covered. 

For the two resistance blinder calculations, the equations 

are identical to their conventional counterpart so that the 

steady-state resistance reach will be identical. 

With the high-speed quadrilateral elements, reactance and 

resistance blinder calculations use a half-cycle filtering system 

to obtain fast operation. 

The logic for an A-phase-to-ground fault is presented in 

Fig. 13. Similar logic is used for the two other ground fault 

elements and the phase elements. 

Fig. 13. 

faults 

High-speed quadrilateral characteristic logic for A-phase-to-ground 

To illustrate the parallel operation of the high-speed and 

conventional quadrilateral elements, an A-phase-to-ground 

fault is staged at 33 percent of the line length of the highvoltage 

transmission line in the power network of Fig. 4. The 

impedance reach is set to 85 percent of ZL1. The fault is 

staged at 100 milliseconds of the EMTP (Electromagnetic 

Transients Program) simulation. 

Fig. 14 shows the distance to the fault calculations of the 

two reactance elements (high-speed and conventional) for Rf 

equal to 0 ohms. The high-speed element operates in 

12.5 milliseconds, and the conventional element operates in 

21 milliseconds. 

Distance to Fault (pu) 

Fig. 14. High-speed and conventional distance element calculations for a 

0-ohm, A-phase-to-ground fault at 33 percent of the line length 


8 

Fig. 15 depicts the same experiment but with a primary Rf 

equal to 50 ohms. The high-speed element has an operating 

time of 14.5 milliseconds, whereas the conventional element 

has an operating time of 25 milliseconds. 

1 

0.8 

High-speed distance calculation 

Fig. 16 illustrates the negative-sequence network of a 

simple transmission line and the respective source impedances 

at both terminals. If possible, this two-source network should 

be evaluated. If the system is slightly more complex (e.g., 

parallel lines), a short-circuit program can provide the IF2 and 

IR2 currents. The calculation should be done for a fault at the 

reach of the Zone 1, where m is approximately 80 percent. 

Distance to Fault (pu) 

0.6 

0.4 

Conventional distance calculation 

0.2 

Conventional trip 

High-speed trip 

0 

0.1 0.11 0.12 0.13 0.14 0.15 0.16 

Time (s) 

Fig. 15. High-speed and conventional distance element calculations for a 

50-ohm, A-phase-to-ground fault at 33 percent of the line length 

As a general rule, the quadrilateral high-speed logic will 

send an output signal a half cycle before the conventional 

logic. This corresponds most of the time to an overall subcycle 

operation for low Rf values. As illustrated in the two examples 

above, as Rf increases, both the fault current and the voltage 

dip will be reduced. Under these circumstances, the operation 

times of the high-speed and conventional quadrilateral 

elements will increase so that overall operation times close to 

or above 1 cycle will be more typical for high-resistance 

faults. 

III. QUADRILATERAL DISTANCE ELEMENT APPLICATION 

A. Homogeneity Calculation 

The reactive line in a quadrilateral distance element can be 

polarized with either negative-sequence (IR2) or zerosequence 

(IR0) current to properly adapt to load flow, as 

shown in Fig. 11. Polarizing with these currents makes the 

line adaptive and less susceptible to overreach. A check is 

needed, however, to ensure effective Zone 1 quadrilateral 

ground and phase distance element behavior [13]. This check 

is for the homogeneity of the negative-sequence impedances 

(or zero-sequence impedances, if zero-sequence polarization 

has been used). 

In a ground fault or asymmetrical phase fault, the total fault 

current always lags the source voltages. This fault current, IF, 

is the perfect polarizing current. It is in the same direction 

regardless of the type of fault (same angle but with different 

magnitude). Because the IF current is not measurable, the 

measured currents at the relay location are the only ones 

available. The negative-sequence current is an option for 

polarizing the reactance line of the quadrilateral element. The 

protective relay is measuring the local IR2 (negative-sequence 

current). The IF2 current is the proper current to use. 

Fig. 16. 

Two-source negative-sequence network 

The variable T is the homogeneity factor, and it is the angle 

difference between the fault current and the current measured 

at the relay location. Reference [12] illustrates the evaluation 

of this factor, which is the following current divider 

expression: 

⎛ IF2 ⎞ ⎡ ZS1 + ZL1 + ZR1 ⎤ 

T = arg ⎜ ⎟ = arg ⎢ ⎥ (15) 

⎝ IR2 ⎠ ⎣ ZR1 + (1 − m) ZL1 ⎦ 

The angle T in (15) adjusts the measured IR2 current to the 

angle of the fault current IF2. It is used in (3) and (8) to 

properly polarize the reactance line of the quadrilateral 

element. 

When the ground quadrilateral element is polarized with 

zero-sequence current (IR0), use a similar expression to 

calculate T (15), except that the currents and impedances are 

zero sequence. 

Equation (15) also provides some extra information 

regarding the homogeneity of the sequence network. For most 

transmission networks, the impedance angles in the negativesequence 

network are very similar. Evaluating (15) yields a 

small angle, usually in the range of ±5 degrees. On the other 

hand, in the zero-sequence network, the homogeneity angle 

varies considerably more. 

In (3) and (8), the reactance line is effectively tilted by the 

T angle. 

B. Load Encroachment 

The quadrilateral distance elements discussed in this paper 

are inherently immune to load encroachment. The reactive line 

that defines the reach is polarized with negative-sequence 

currents, as shown in (3) and (8). The phase and ground 

reactive lines start their computation when there is a fault 

condition that implies an unbalance of (I2/I1) or (I0/I1) greater 

than the natural unbalance of the system, which is less than 

10 percent. 

In a full protection scheme, however, there should be 

provisions to detect three-phase faults. Although rare, this 

type of fault is possible. It usually is a fault with almost no Rf. 


9 

The three-phase fault detection element is obtained by 

using current self-polarization. For example, the BC loop 

would be polarized with: 

predict the impedance trajectory, and stability studies may be 

required. 

S2 = j(IRB − IRC)e − jT 

(16) 

To avoid overreach because of forward flowing load, the 

setting T in degrees is a tilt, most likely downward, for the 

reactive line. The resistive reach is polarized with positivesequence 

current. 

The three-phase quadrilateral element just described is set 

with the same reach as the phase-to-phase distance elements. 

It does require certain load considerations to avoid load 

encroachment. 

If the transmission line is long and the resistive setting 

chosen conflicts with load, a load encroachment element is 

required. This element should clearly define the load area in 

the forward load flow direction. Fig. 17 illustrates a traditional 

and already widely used load-encroachment logic 

characteristic. The operating point of the load impedance in 

this region will clearly identify load conditions and prevent 

the three-phase fault detection algorithm from operating. 

Fig. 17. 

jX 

Load 

Load encroachment for quadrilateral three-phase distance elements 

C. Out of Step 

Much of the theory and discussion in literature on out-ofstep 

detection can be applied to quadrilateral distance 

elements [16][17]. When power flows are oscillating in a 

power system, the apparent impedances measured by the 

distance elements describe a trajectory on the R-X plane. 

These oscillations can be caused by angular instability or 

simply switching lines in or out [17]. If the oscillations are 

contained within a maximum oscillation envelope and are 

damped over time, the power swings are considered stable. On 

the other hand, if the power swings are not damped over time, 

the power swings are said to be unstable. 

On the R-X diagram shown in Fig. 18, a stable power 

swing impedance trajectory is contained on the right side (or 

the left side for reverse power flow) and eventually rests on a 

new load-impedance operating point. An unstable power 

swing, in contrast, will show a trajectory that crosses the plane 

from left to right (or right to left). Theoretically, and assuming 

the simple two-source network shown in Fig. 18, the unstable 

power swing will cross the electrical center of the system 

when the angle’s difference between the two source voltages 

is close to 180 degrees apart. Unless the power system can be 

reduced to a two-source model, it is not a simple matter to 

R 

Fig. 18. 

Traditional dual-zone out-of-step characteristic 

During power system oscillations, stability requirements 

demand that transmission lines remain in the power system. 

Tripping transmission lines unnecessarily jeopardizes the 

stability of the power system. It is therefore necessary to 

ensure that unstable trajectories on the R-X diagram entering 

distance element characteristics (shown in Fig. 18) do not 

unnecessarily trip the transmission line. However, some 

applications require tripping transmission lines in a controlled 

manner. 

Out-of-step detection techniques traditionally take 

advantage of the slower speed of the apparent impedance 

trajectory on the R-X diagram for power swing conditions. 

The trajectory of the operating point changes from load to 

fault almost instantaneously for fault conditions. 

Fig. 18 illustrates a traditional scheme comprised of two 

zones. If the inner zone operates after a set time delay (2 to 

5 cycles), an out-of-step condition is detected. If the trajectory 

is due to a power system fault, both zones will operate within 

a short time window. 

There are several philosophies to follow when setting the 

parameters of this scheme [17]. Some of the most important 

considerations are: 

• The inner zone should not operate for stable swings. 

As shown in Fig. 18, a stable swing eventually returns 

to the load impedance. 

• The outer zone should not include any possible load 

impedance. If load is included by the outer zone, there 

is a risk of incorrectly declaring a power swing 

condition. 

• The distance from the inner to the outer zone on the 

impedance plane should be made as wide as possible 

to allow the detection of the power swing condition. 

• The inner zone should not include any distance 

element zone that is to be blocked. For long line 

applications, achieving this goal for all distance zones 

may not be possible. We can place the inner zone 

across part of the distance element characteristic. This 

will effectively cut part of the characteristic. 


10 

Fig. 18 illustrates some of the these considerations. Short 

lines present sufficient margin to accommodate the inner and 

outer zones together with any type of distance element, such 

as a quadrilateral distance unit, following the above 

guidelines. Long transmission lines, however, may not allow 

sufficient margin. Engineering judgment should be used to set 

the inner and outer zones, as well as the resistive reach of the 

quadrilateral element. 

When determining the setting parameters, it may be very 

difficult to cover all possible scenarios of instability with a 

simple two-source model. Therefore, transient studies will be 

needed to understand the effectiveness of the scheme in 

Fig. 18. 

Recently, a power swing detection algorithm was proposed 

that requires little information from the user [18]. This 

algorithm will detect and declare a power swing based on the 

estimation of the swing center voltage (SCV), which is the 

voltage at the electrical center of a two-source model. This 

voltage can be estimated with local measurements and its 

behavior used to detect an out-of-step condition. The 

advantage of this methodology is that no network information 

is required. 

D. Series Capacitor Applications 

It is common to apply directional comparison relaying 

systems in the protection of series-compensated transmission 

lines. Protective relays intended to protect these lines should 

be designed to accommodate the changing measured 

impedance (because of the MOVs [metal oxide varistors] and 

spark gaps in parallel with the capacitor bank) and 

subsynchronous voltages and currents that are characteristic of 

series capacitor-compensated systems [19]. Moreover, 

protective relaying systems located in adjacent lines should 

reliably determine the direction to a fault. 

For distance elements that are polarized with voltage, like 

mho distance elements, the voltage inversion because of the 

series capacitor is properly handled with memory voltage 

[19][20]. Moreover, directional elements determine the correct 

direction to the fault [21]. 

Identifying the fault direction is important to keep the 

reactance and resistance lines of the quadrilateral distance 

element from operating improperly. An impedance-based 

negative-sequence polarized directional element (or an 

alternate zero-sequence polarized element for ground faults) 

will properly determine the direction to the fault, unless a 

current inversion is present. Depending on the location of the 

capacitor bank and the location of the voltage transformers 

(VTs), suggested settings for the directional thresholds (Z2F 

and Z2R) can be found in [20] and [21]. For the impedances 

of the compensated system in Fig. 19, the directional element 

threshold Z2F should be set to: 

(ZL1 − XC) 

Z2F ≤ (17) 

2 

Setting this threshold as close to the origin as possible will 

ensure proper directional determination, unless a current 

reversal is possible in the power system. 

jX 

–jXC 

ZL1 

Fig. 19. Series capacitor applications 

Uncompensated 

Compensated 

In Fig. 19, the perspective of a long line is shown. Seriescompensated 

lines are long lines that require compensation to 

transfer more power. There are no short lines compensated 

with series capacitors. Also, in the vicinity of a series 

capacitor installation, subsynchronous oscillations of the 

voltages and currents are possible [19][20][21]. While the 

filtering in protective relays is very good at eliminating highfrequency 

components, the filtering is not efficient at 

eliminating lower frequencies. These subsynchronous 

transients, shown as impedance oscillations on the apparent 

impedance plane, eventually converge on the true apparent 

impedance, as illustrated in Fig. 20. This figure also shows 

that distance element overreach is a possibility. 

jX 

Z1L 

–jXc 

Fig. 20. Subharmonic frequency transients can cause distance elements to 

overreach 

R 

R 


11 

Zone 1 distance elements should account for the above 

phenomena by reducing the reach [20][21]. A good suggestion 

is to set the reach of the reactive line to half of the 

compensated line impedance [20]. On the other hand, 

protective relays can have an automatic reach adjustment 

based on a measured apparent impedance compared to a 

theoretically calculated value [14][21]. This way, the reach is 

automatically reduced to half of the compensated line 

impedance when transients are detected. The resistive reach 

should follow the recommendations for a long line (e.g., Rset 

equal to one-half Zset). 

The presence of the series capacitor in the power system 

modifies the homogeneity of the negative- and zero-sequence 

impedances. Therefore, when adjusting the homogeneity 

factor T, described in (18) and (19), the capacitor impedance 

should be considered. When using a negative-sequence current 

polarized reactance element: 

⎛ IF2 ⎞ ⎡ ZS1 + ZL1 − XC + ZR1 ⎤ 

T = arg⎜ ⎟ = arg 

IR2 

⎢ 

ZR1 + (1 − m)(ZL1 − XC) 

⎥ (18) 

⎝ ⎠ ⎣ ⎦ 

And when using a zero-sequence polarized reactance line: 

⎛ IF0 ⎞ ⎡ ZS0 + ZL0 − XC + ZR0 ⎤ 

T = arg ⎜ ⎟ = arg 

IR0 

⎢ 

ZR0 + (1 − m)(ZL0 − XC) 

⎥ (19) 

⎝ ⎠ ⎣ ⎦ 

Notice that the zero- and negative-sequence impedance of a 

series capacitor are the same as the positive-sequence 

impedance. 

Equation (18) for the uncompensated line should also be 

evaluated. The minimum calculated T value (most negative) 

should be used. 

When applying any protective relaying scheme to seriescompensated 

lines, transient simulation and testing are 

recommended [19][21]. This step ensures dependability and 

confirms proposed settings. 

E. Single-Pole Trip Applications 

In transmission line protection, it is common to use singlepole 

trip schemes. The scheme trips the faulted phase only for 

a single-line-to-ground fault. Once the pole is open, the other 

two phases are still conducting power, and the system is 

capable of remaining synchronized. During the open-pole 

interval, it is expected that the arc deionizes. After the openpole 

interval, a reclosing command is sent to the breaker. 

Current polarization with negative-sequence current (I2) or 

zero-sequence current (I0) is not reliable during the open-pole 

interval. The open pole makes the power system unbalanced, 

causing negative- and zero-sequence currents to flow. The 

consequence to distance elements polarized with sequence 

component currents, as in (3) and (8), is that the polarization 

becomes unreliable. Depending on the load flow direction, I2 

and I0 will have different directions. Fortunately, there are 

other distance elements that will reliably operate during an 

open-pole condition [14]. The positive-sequence voltagepolarized 

mho element is stable during open-pole intervals and 

will reliably detect power system faults during this condition. 

In a practical scheme, the phase and ground quadrilateral 

elements should be disabled when an open-pole condition is 

detected. The high-speed quadrilateral distance element is 

implemented with incremental quantities and does not need to 

be disabled during the open-pole interval. 

IV. SETTING THE QUADRILATERAL DISTANCE ELEMENT 

Consider the A-phase-to-ground fault circuit of Fig. 4. 

Equation (20) determines the apparent impedance (Zapp) that 

the relay installed at the left side of the line measures as a 

function of fault voltages and currents. Equation (21) 

determines Zapp as a function of Rf and fault location m. 

VA 

Zapp = 

IA + k0 • IR 

(20) 

Zapp = m • ZL1 + KR • Rf 

(21) 

In (21), KR is a factor that depends upon the positive- and 

zero-sequence current distribution factors (C1 and C0) and is 

equal to: 

KR 3 

= 

(22) 

2 • C1 + C0(1 + 3• k0) 

C1 and C0 are equal to: 

(1 − m) • ZL1 + ZR1 

C1 = 

(23) 

ZS1 + ZL1 + ZR1 

(1 − m) • ZL0 + ZR0 

C0 = 

(24) 

ZS0 + ZL0 + ZR0 

k0 is the zero-sequence compensation factor equal to: 

ZL0 − ZL1 

k0 = (25) 

3• ZL1 

For no-load conditions (δ equal to 0) and homogeneous 

systems, the resistive blinder of the adaptive quadrilateral 

element will assert for an Rf that satisfies this condition: 

Rapp < Rset 

(26) 

Rapp = Real(KR) • Rf 

(27) 

where Rset is the resistive reach setting. Alternatively, we can 

calculate Rapp using relay voltage and currents for a fault at m 

according to (28). 

Rapp = Real( Zapp) − m • Real( ZL1) 

(28) 


12 

For the system in Fig. 4, Fig. 21 represents the values of 

Real(KR) as a function of m with a constant value of Rset. The 

increasing values of Real(KR) indicate that the maximum 

detectable Rf at no load decreases as the distance to the fault 

increases. 

10 

9 

8 

7 

Real (KR) 

6 

5 

4 

Fig. 22. CT and VT error evaluation for Zone 1 

Fig. 23 shows the Rmax pu as a function of Zset for θL1 

equal to 40, 55, 70, and 75 degrees and θε equal to 2 degrees. 

30 

3 

2 

1 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 

Fault Location (pu) 

Fig. 21. Factor Real(KR) for the system of Fig. 4 

Another consideration in determining the setting of the 

resistive coverage involves VT and CT (current transformer) 

errors. Reference [22] indicates that a composite angle error in 

the measurement θε can be assumed. 

A. Zone 1 

For a Zone 1 application, the requirement is that Zone 1 

never overreaches for any fault at the end of the line. 

Assuming that for resistive faults at the end of the line there is 

an angle error θε, the effective path for increasing Rf will tilt 

down an extra θε degrees, as shown in Fig. 22. For increasing 

Rf, the intersection with the Zone 1 reactive line is the 

indication of the maximum Rset or Rmax. Using the law of 

sines and trigonometry, Rmax can be expressed as: 

sin ( θε + θ L1) 

Rmax = • ( 1− Zset _ pu ) • ZL1 (29) 

sin θε 

( ) 

Equation (29) defines Rmax, the maximum secure resistive 

reach setting for Zone 1, taking into account CT, VT, relay 

measurement errors, and θε. Rmax is a function of the 

impedance reach setting Zset, the positive-sequence line 

impedance magnitude |ZL1| and angle θL1, and the total 

angular error in radians θε [22]. 

Maximum Resistive Reach Setting Rmax (pu) 

25 

20 

15 

10 

5 

0 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 

Impedance Reach Setting Zset (pu) 

Fig. 23. Maximum resistive reach setting as a function of the impedance 

reach due to measurement errors 

A typical Zone 1 impedance reach setting for short lines is 

70 percent. For the system in Fig. 4, Zset_zone1 is equal to 

1.4 ohms secondary. 

With Zset, |ZL1|, θL1, and θε, we can calculate Rmax using 

(29) or obtain the pu value Rmax_pu with respect to the total 

positive-sequence line impedance from Fig. 23. In this case, 

Rmax equals 17.17 ohms secondary, or Rmax_pu equals 

8.58 pu. 

Additionally, we need to verify that the fault current is 

above the maximum relay sensitivity. In this case, the residual 

current is 3.0 A secondary, and the relay sensitivity is 0.25 A. 

Therefore, the relay can see the fault at 70 percent of the line 

with Rf equal to 25 ohms primary. 

40 

55 

70 

85 


13 

Fig. 24 shows the apparent resistance for different Rf 

values for a fault at 70 percent of the line. Note that with 

Rset_zone1 equal to 11.52 ohms, the quadrilateral element can 

see 3 ohms secondary or 25 ohms primary. 

8 

7 

—— Rapp (ohms) 

Fault Resistance (ohms) 

6 

5 

4 

3 

2 

Rset = 11.52 ohms 

δ = 0 degrees 

1 

Fig. 24. 

Apparent resistance for a fault at 70 percent of the line 

Fig. 25 shows the margin of the selected Rset with respect 

to Rmax for the selected Zset. 

Fig. 25. 

Margin of Rset at Zset_zone1 equal to 0.7 pu 

Fig. 26 shows that the quadrilateral distance element can 

see up to 3 ohms for faults at 70 percent of the line for Rset 

equal to 11.52 ohms. 

0 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 


Fig. 26. Maximum Rf coverage with Rset equal to 11.5 ohms for faults 

along the line 

The analysis carried out for a phase-to-ground fault can 

also be applied for phase-to-phase faults. In these cases, the 

factor KR is equal to: 

1 

KR = (30) 

2 • C1 

For no-load conditions (δ equal to 0) and homogeneous 

systems, the resistive blinder of the phase quadrilateral 

element will assert for an Rf that satisfies (31) or (32). 

Rf 

( ) 

Rset 

2 • Real C1 < (31) 

⎛ Vϕϕ 

⎞ 

Rapp = Real⎜ 

⎟ − m • Real ZL1 

⎝ Iϕϕ 

⎠ 

( ) 

(32) 

B. Zone 2 

When considering overreaching zones, it is important to 

determine the maximum underreach and verify that the zone 

covers at least the expected Rf. For example, in a Zone 2 

application, it is expected that all faults on the line and those 

at the remote terminal will be detected. It is a common 

practice to set the Zone 2 reach to 120 percent of the line 

length. However, in certain circumstances, this impedance 

reach would not guarantee coverage for faults with Rf, and a 

longer reach would be required. 


14 

Following is a conservative approach to set Zone 2 that 

guarantees that the overreaching element sees all faults with 

specific Rf coverage. Fig. 27 shows the apparent resistance for 

a homogeneous system and no-load conditions. 

Fig. 28 shows Rset_zone2_pu for θL1 equal to 40, 55, 70, 

and 85 degrees and for θε equal to –2 degrees. 

Resistive Reach Setting Rset Zone 2 (pu) 

15 

10 

5 

40 

55 

70 

85 

Fig. 27. Apparent impedance for an end-of-line fault considering 

measurement errors 

From Fig. 27, we can estimate the required resistive reach 

Rset_zone2 and impedance reach Zset_zone2 settings 

according to (33) and (34) for a desired Rf coverage. 

( θL1 

+ θε ) 

( θL1) 

sin ( θε ) 

sin( θL1 

+ θε ) 

sin 

− j⋅θε 

Rset _ zone2 = • Real(KR) • Rf • e (33) 

sin 

Zset _ zone2 = ZL1 − 

• R set _ zone2 

(34) 

We can represent Rset_zone2_pu as a function of Ppu 

according to (35). These values are the normalized values of 

Rset_zone2 and P (see Fig. 27) with respect to |ZL1|. 

( θL1 

+ θε ) 

sin ( θε ) 

sin 

Rset _ zone2 _ pu = − • Ppu (35) 

0 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 

P (pu) 

Fig. 28. The resistive reach setting as a function of the impedance reach 

setting for several values of θL1 

For the relay in Fig. 4, we calculate Rset_zone2 for a 

desired Rf equal to 3 ohms secondary. Using (33) with θε 

equal to –2 degrees and a fault at the end of the line, we obtain 

Rset_zone2 equal to 28.69 ohms secondary and 

Rset_zone2_pu equal to 14.35 pu. From Fig. 28, we obtain the 

required value of Ppu and the Zone 2 impedance reach 

Zset_zone2_pu equal to 1.5 or 150 percent of |ZL1|. 

V. DISTANCE ELEMENT PERFORMANCE 

A. Traditional Distance Element Characteristics 

Adaptive quadrilateral phase and ground distance elements 

were designed to improve Rf coverage in short line 

applications. A previous distance relay included a ground 

quadrilateral distance element characteristic with an adaptive 

reactance element and two resistance elements that calculate 

Rf according to (36) and a ground mho distance characteristic 

with an adaptive mho element that calculates the distance to 

the fault according to (37) [12] 

j⋅θ 

L1 

( ) 

* 

Im 

⎡ 

V • I • e 

⎤ 

⎢ 

⎥ 

R relay1 = 

⎣ 

⎦ 

⎡ 3 

Im 

⎢ 

• I2 I0 • I e 

⎣ 2 

j⋅θ 

L1 

( + ) ( ⋅ ) 

( ) 

* 

Re ⎡V • V1_ mem ⎤ 

m relay1 = 

⎣ 

⎦ 

j L1 

Re ⎡ ⋅θ 

I • e • V1_ mem 

⎣ 

( ) 

* 

* 

⎤ 

⎥ 

⎦ 

⎤ 

⎦ 

(36) 

(37) 


15 

B. Adaptive Resistance Element 

Fig. 29 shows the quadrilateral distance element 

characteristic that uses the adaptive reactance element of the 

previous design with an adaptive resistive element. 

X 

Adaptive Reactance Element 

setting of 11.52 ohms and an impedance reach (Zset) setting of 

120 percent of ZL1. The mho distance element has a reach of 

120 percent of ZL1. The sensitivity of all the distance 

elements is 0.05 • Inom. 

Fig. 30, Fig. 31, and Fig. 32 show the Rf coverage of mho 

and quadrilateral distance elements. We observe that the Rf 

coverage is severely reduced as the fault approaches the end of 

the line. As expected, the mho element is the one with less Rf 

coverage, and the adaptive resistance element has the greatest 

Rf coverage, especially for power flow in the forward 

direction, δ equal to 10 degrees. 

20 

18 

Mho Distance Element 

Quadrilateral Distance Element 

Adaptive Resistive Element 

Z LINE 

Adaptive 

Resistive 

Element 

16 

14 


δ = -10 degrees 

R 


12 

10 

8 

6 

Fig. 29. Quadrilateral distance element characteristic with adaptive 

resistance element 

The adaptive resistive element calculates Rf according to 

(38) and (39), and compares the minimum of the two 

calculation results against the resistive setting. 

j⋅θ 

L1 

( ) 

j⋅θ 

L1 

* 

( ) 

Im 

⎡ 

V • I2 • e 

⎢ 

R2 = 

⎣ 

Im 

⎡ 

I • I2 • e 

⎢⎣ 

Im 

⎡ 

V • I 

⎢ 

Rα 

= 

⎣ 

Im 

⎡ 

I • I 

⎢⎣ 

⎤ 

⎥⎦ 

⎤ 

⎥⎦ 

* 

j⋅θ 

L1 

( α • e ) 

j⋅θ 

L1 

* 

( α • e ) 

⎤ 

⎥⎦ 

⎤ 

⎥⎦ 

* 

(38) 

(39) 

Equation (38) is equivalent to (11) and (12). It uses a 

different form of phase comparator equation. Equation (39) 

uses the alpha component (Iα = I1 + I2). 

C. Resistive Coverage 

To compare the resistive coverage of the traditional 

distance elements with the adaptive resistive element, we use 

the system in Fig. 4 and perform the tests discussed in the 

following sections. 

1) Faults at Multiple Locations 

We calculate the maximum Rf that the distance elements 

can detect for an A-phase-to-ground fault for m values from 0 

to 1 and load angles of δ equal to –10, 0, and 10 degrees. The 

quadrilateral distance elements have a resistive reach (Rset) 

4 

2 

0 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 


Fig. 30. Rf coverage of mho and quadrilateral distance elements for 

δ equal to –10 degrees 


8 

7 

6 

5 

4 

3 

2 

1 






0 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 


Fig. 31. Rf coverage of mho and quadrilateral distance elements for δ equal 

to 0 degrees 


16 


12 

10 

8 

6 

4 






D. Adaptive Behavior 

A carefully designed quadrilateral characteristic should 

have an adaptive reactance line to avoid overreach because of 

load in the forward direction and Rf. Moreover, this paper has 

presented the concept of an adaptive resistive line that 

beneficially tilts to detect more Rf. 

Two figures will be used to illustrate the adaptive behavior 

of the reactive line. Fig. 34 illustrates a ground fault detected 

from the terminal with forward load flow. Fig. 35 shows the 

same fault, with the same Rf, detected from the other terminal 

(i.e., the terminal with reverse direction load flow). 

2 

0 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 


Fig. 32. Rf coverage of mho and quadrilateral distance elements for δ equal 

to 10 degrees 

2) Faults at m Equal to 0.7 for Multiple Load Angles 

We calculate the Rf coverage for a fault at 70 percent of the 

line and different load angles (see Fig. 33). The adaptive 

resistance element has the highest Rf coverage, while the mho 

element has the lowest Rf coverage. 

12 

10 





m = 0.7 


8 

6 

4 

Fig. 34. Example of a ground fault detected from the forward load flow 

direction terminal 

2 

0 

-10 -5 0 5 10 

Load Angle (degrees) 

Fig. 33. 

angles 

Rf coverage for faults at 70 percent of the line with different load 

Fig. 35. Example of a ground fault detected from the reverse load flow 

direction terminal 


17 

Fig. 34 and Fig. 35 illustrate the adaptive behavior of the 

quadrilateral distance element. Because these figures are for 

illustrative purposes, the power system impedances, fault 

location, and/or Rf value are not relevant to the discussion. 

These two figures simply illustrate the adaptive behavior of 

the reactance and resistive lines. 

The fault type is a ground fault; and the ground 

quadrilateral element is formed with a reactance line polarized 

with negative-sequence current (the preferred polarization). 

The two resistance elements are polarized with negative 

sequence (I2) and with the alpha component (I1 + I2). The 

polarization is what makes the lines adaptive, as explained in 

the previous sections. 

Fig. 34 and Fig. 35 provide a wealth of information about 

the behavior of these impedance lines, including the 

following: 

• The reactance element pivots on the line impedance 

reach, and that point is fixed. The resistance elements 

pivot on the resistive reach, which is a setting. 

• The degree at which these lines tilt is determined by 

the power system parameters and operating 

conditions. These include line impedances, load flow, 

and Rf. 

• The mho circle and reactance line tilt at the same time 

and in the same direction. 

• The resistance element trip decision is the OR 

combination of either resistive line. Their behavior is 

dependent on the direction of the load flow, and their 

operation is complementary to each other. 

For the forward load flow terminal in Fig. 34, we conclude: 

• The reactance element tilts beneficially in a clockwise 

direction. This behavior prevents overreaching 

because of high-resistance load flow. 

• The resistance element polarized with negativesequence 

current will adapt to provide better resistive 

reach coverage. This resistive line will make the 

decision for faults with load in the forward direction. 

• The resistance element polarized with the alpha 

component current tilts in the opposite direction. The 

resistive coverage of this characteristic is less effective 

compared to the other resistive line. 

For the reverse load flow terminal in Fig. 35, we conclude: 

• The reactance element moves in the direction that the 

apparent impedance locus moves, as shown in Fig. 10. 

• The resistance element polarized with negativesequence 

current moves in the opposite direction and 

with less resistive coverage. 

• The resistance element polarized with the alpha 

component provides more effective coverage and will 

detect the fault. 

VI. CONCLUSIONS 

Power system faults present different values of Rf. Ground 

faults present a larger value of Rf because of the arc resistance 

and tower footing resistance. 

Short line protection applications with distance elements 

favor the use of quadrilateral distance elements for phase and 

ground fault protection. The expected Rf for short lines can be 

in the same order of magnitude as the impedance of the 

transmission line. 

Rf and power flow have the effect of modifying the 

apparent impedance measured by the distance element. The 

description of the Rf influence was plotted for different Rf 

values and load flows. 

Especially for short lines, quadrilateral distance elements 

can detect faults with higher Rf than mho distance elements. 

Instrument transformers and relay measurement errors limit 

the Rf coverage in short line applications. 

An adaptive characteristic for ground and phase 

quadrilateral distance elements was presented. The reactance 

element, polarized with negative-sequence current, adapts 

based on the direction of the load flow and prevents 

overreaching issues associated with load flow in the forward 

direction. Resistance elements are polarized with two 

quantities simultaneously. The negative-sequence polarization 

has a better Rf coverage for forward load flow. Using ground 

distance (alpha component) and phase distance (positivesequence 

component) provides better coverage for faults with 

reverse load flow. For the resistance elements, running two 

polarizations at the same time helps to detect as much Rf as 

possible. 

A high-speed version of the quadrilateral elements 

typically improves the speed of operation by half a cycle. 

These elements are required in applications where high-speed 

tripping times are required. These elements provide subcycle 

operating speeds and operate reliably during open-pole 

conditions. 

The paper presented an improved distance element with an 

adaptive quadrilateral characteristic that can be part of a line 

protection relay. 

The performance of the adaptive quadrilateral distance 

element was compared to a previous quadrilateral 

implementation, showing the benefits. A graphical illustration 

of the performance expected from the reactance and resistive 

lines was presented with an example in Fig. 34 and Fig. 35. 

The Rf coverage of the adaptive quadrilateral element 

increases for terminals with forward direction load flow. 

The phase quadrilateral distance elements presented in this 

paper are suitable for any transmission line application, but 

because of their nature, they fit better in short line 

applications. No distance element, however, can provide better 

sensitivity and Rf coverage than directional overcurrent 

elements in a pilot scheme. 


18 

VII. REFERENCES 

[1] S. Ward, “Comparison of Quadrilateral and Mho Distance 

Characteristic,” proceedings of the 26th Annual Western Protective 

Relay Conference, Spokane, WA, October 1999. 

[2] J. Holbach, V. Vadlamani, and Y. Lu, “Issues and Solutions in Setting a 

Quadrilateral Distance Characteristic,” proceedings of the 61st Annual 

Conference for Protective Relay Engineers, College Station, TX, April 

2008. 

[3] J. Mooney and J. Peer, “Application Guidelines for Ground Fault 

Protection,” proceedings of the 24th Annual Western Protective Relay 

Conference, Spokane, WA, October 1997. 

[4] S. Sebo, “Zero-Sequence Current Distribution Along Transmission 

Lines,” IEEE Transactions on Apparatus and Systems, PAS-88, Issue 6, 

June 1969. 

[5] G. Swift, D. Fedirchuk, and T. Ernst, “Arcing Fault ‘Resistance’ (It 

Isn’t),” proceedings of the Georgia Tech Fault and Disturbance Analysis 

Conference, Atlanta, GA, May 2003. 

[6] H. Khodr, A. Menacho e Moura, and V. Miranda, “Optimal Design of 

Grounding System in Transmission Line,” proceedings of the 

International Conference on Intelligent Systems Applications to Power 

Systems, November 2007. 

[7] V. Terzija and H. Koglin, “New Approach to Arc Resistance 

Calculation,” IEEE PES Winter Meeting, Vol. 2, 2001. 

[8] L. Popovic, “A Digital Fault-Location Algorithm Taking Into Account 

the Imaginary Part of the Grounding Impedance at the Fault Place,” 

IEEE Transactions on Power Delivery, Vol. 18, Issue 4, October 2003. 

[9] F. Calero, “Distance Elements: Linking Theory With Testing,” 

proceedings of the 35th Annual Western Protective Relay Conference, 

Spokane, WA, October 2008. 

[10] J. Roberts, E. O. Schweitzer, III, R. Arora, and E. Poggi, “Limits to the 

Sensitivity of Ground Directional and Distance Protection,” proceedings 

of the 1997 Spring Meeting of the Pennsylvania Electric Association 

Relay Committee, Allentown, PA, May 1997. 

[11] J. Roberts, A. Guzmán, and E. O. Schweitzer, III, “Z = V/I Does Not 

Make a Distance Relay,” proceedings of the 20th Annual Western 

Protective Relay Conference, Spokane, WA, October 1993. 

[12] E. O Schweitzer, III and J. Roberts, “Distance Relay Element Design,” 

proceedings of the 46th Annual Conference for Protective Relay 

Engineers, College Station, TX, April 1993. 

[13] SEL-421 Instruction Manual. Available: http://www.selinc.com. 

[14] A. Guzmán, J. Mooney, G. Benmouyal, and N. Fischer, “Transmission 

Line Protection System for Increasing Power System Requirements,” 

proceedings of the 55th Annual Conference for Protective Relay 

Engineers, College Station, TX, April 2002. 

[15] G. Benmouyal and J. Roberts, “Superimposed Quantities: Their True 

Nature and Application in Relays,” proceedings of the 26th Annual 

Western Protective Relay Conference, Spokane, WA, October 1999. 

[16] D. Tziouvaras and D. Hou, “Out-of-Step Protection Fundamentals and 

Advancements,” proceedings of the 30th Annual Western Protective 

Relay Conference, Spokane, WA, October 2003. 

[17] J. Mooney and N. Fischer, “Application Guidelines for Power Swing 

Detection on Transmission Systems,” proceedings of the 32nd Annual 

Western Protective Relay Conference, Spokane, WA, October 2005. 

[18] G. Benmouyal, D. Tziouvaras, and D. Hou, “Zero-Setting Power-Swing 

Blocking Protection,” proceedings of the 31st Annual Western 


[19] H. Altuve, J. Mooney, and G. Alexander, “Advances in Series- 

Compensated Line Protection,” proceedings of the 35th Annual Western 


[20] J. Mooney and G. Alexander, “Applying the SEL-321 Relay on Series- 

Compensated Systems,” SEL Application Guide AG2000-11. Available: 

http://www.selinc.com. 

[21] F. Plumptre, M. Nagpal, X. Chen, and M. Thompson, “Protection of 

EHV Transmission Lines With Series Compensation: BC Hydro’s 

Lessons Learned,” proceedings of the 62nd Annual Conference for 

Protective Relay Engineers, College Station, TX, March 2009. 

[22] E. O. Schweitzer, III, K. Behrendt, and T. Lee, “Digital 

Communications for Power System Protection: Security, Availability 

and Speed,” proceedings of the 25th Annual Western Protective Relay 

Conference, Spokane, WA, October 1998. 

VIII. BIOGRAPHIES 

Fernando Calero received his BSEE in 1986 from the University of Kansas, 

his MSEE in 1987 from the University of Illinois (Urbana-Champaign), and 

his MSEPE in 1989 from the Rensselaer Polytechnic Institute. From 1990 to 

1996, he worked in Coral Springs, Florida, for the ABB relay division in the 

support, training, testing, and design of protective relays. Between 1997 and 

2000, he worked for Itec Engineering, Florida Power and Light, and Siemens. 

Since 2000, Fernando has been an application engineer in international sales 

and marketing for Schweitzer Engineering Laboratories, Inc., providing 

training and technical assistance. 

Armando Guzmán received his BSEE with honors from Guadalajara 

Autonomous University (UAG), Mexico. He received a diploma in fiberoptics 

engineering from Monterrey Institute of Technology and Advanced 

Studies (ITESM), Mexico, and his MSEE from the University of Idaho, USA. 

He lectured at UAG and University of Idaho in power system protection and 

power system stability. Since 1993, Armando has been with Schweitzer 

Engineering Laboratories, Inc. in Pullman, Washington, where he is research 

engineering manager. He holds several patents in power system protection 

and metering. He is a senior member of IEEE. 

Gabriel Benmouyal, P.E. received his BASc in Electrical Engineering and 

his MASc in Control Engineering from Ecole Polytechnique, Université de 

Montréal, Canada, in 1968 and 1970. In 1969, he joined Hydro-Québec as an 

instrumentation and control specialist. He worked on different projects in the 

fields of substation control systems and dispatching centers. In 1978, he 

joined IREQ, where his main field of activity was the application of 

microprocessors and digital techniques for substation and generating station 

control and protection systems. In 1997, he joined Schweitzer Engineering 

Laboratories, Inc. in the position of principal research engineer. Gabriel is an 

IEEE Senior Member, a registered professional engineer in the Province of 

Québec, and has served on the Power System Relaying Committee since May 

1989. He holds over six patents and is the author or coauthor of several papers 

in the fields of signal processing and power networks protection and control. 

© 2009 by Schweitzer Engineering Laboratories, Inc. 

All rights reserved. 

20091214 • TP6378-01 


Line Protection Bibliography 

Issue I of the Journal of Reliable Power 

Costello, David, and Karl Zimmerman. “Determining the 

Faulted Phase.” March 2010. 

Stevens, Ian, Normann Fischer, and Bogdan Kasztenny. 

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Blocking Schemes.” March 2010. 

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Miller, Hank, John Burger, Normann Fischer, and 

Bogdan Kasztenny. “Modern Line Current Differential 

Protection Solutions.” January 2010. 

Calero, Fernando, Armando Guzmán, and Gabriel 

Benmouyal. “Adaptive Phase and Ground Quadrilateral 

Distance Elements.” December 2009. 

Calero, Fernando. “Distance Elements: Linking Theory 

With Testing.” August 2009. 

Plumptre, Frank, Mukesh Nagpal, Xing Chen, and 

Michael Thompson. “Protection of EHV Transmission 

Lines With Series Compensation: BC Hydro’s Lessons 

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Calero, Fernando. “Rebirth of Negative-Sequence 

Quantities in Protective Relaying With Microprocessor- 

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Calero, Fernando. “Mutual Impedance in Parallel 

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Maezono, Paulo Koiti, Enrique Altman, Kennio Brito, 

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Altuve, Héctor, Joseph Mooney, and George Alexander. 

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October 2008. 

Costello, David, and Karl Zimmerman. “Distance 

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Schweitzer III, Edmund O., and Stanley E. Zocholl. 

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December 2007. 

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Hubertus, James, Joe Mooney, and George Alexander. 

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Lines: Field Experience in Mexico.” September 2007. 

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Araujo, Chris, Fred Horvath, and Jim Mack. “A 

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Line Protection Bibliography | 83

Benmouyal, Gabriel, and Joe Mooney. “Advanced 

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Tziouvaras, Demetrios. “Relay Performance During 

Major System Disturbances.” September 2006. 

Roberts, Jeff, and Armando Guzmán. “Directional 

Element Design and Evaluation.” August 2006. 

Tziouvaras, Demetrios. “Protection of High-Voltage AC 

Cables.” January 2006. 

Abboud, Ricardo, Walmer Ferreira Soares, and Fernando 

Goldman. “Challenges and Solutions in the Protection of 

a Long Line in the Furnas System.” November 2005. 

Zimmerman, Karl, and Dan Roth. “Evaluation of 

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Power Transformers or Open-Delta VTs.” September 

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Benmouyal, Gabriel. “The Trajectories of Line Current 

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Zhou, Zexin, Xiaofan Shen, Daqing Hou, and Shaojun 

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Designs to Today’s Stringent Protection Requirements.” 


Mooney, Joe, and Normann Fischer. “Application 

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Systems.” September 2005. 

Zimmerman, Karl, and David Costello. “Impedance- 

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Benmouyal, Gabriel, Daqing Hou, and Demetrios 

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Tziouvaras, Demetrios, Jeff Roberts, and Gabriel 

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for Two- or Three-Terminal Lines.” November 2004. 

Topham, Graeme, and Edmund Stokes-Waller. “Steady- 

State Protection Study for the Application of Series 

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Calero, Fernando, and Daqing Hou. “Practical 

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Schemes.” September 2004. 

Benmouyal, Gabriel, and Tony Lee. “Securing Sequence- 

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Fodero, Ken, and Girolamo Rosselli. “Applying Digital 

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Service.” September 2004. 

Moxley, Roy. “Analyze Relay Fault Data to Improve 

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Schweitzer III, Edmund O., Ken Behrendt and Tony Lee. 

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December 2003. 

Henville, Charlie, Ralph Folkers, Allen Hiebert, and Rudi 

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A Case History.” September 2002. 

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System for Increasing Power System Requirements.” 

April 2001. 

Alexander, George, Joe Mooney, and William Tyska. 

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and Hector J. Altuve. “The Effect of Multiprinciple Line 

Protection on Dependability and Security.” February 

2001. 

Costello, David. “Understanding and Analyzing Event 

Report Information.” October 2000. 


Hou, Daqing, and Jeff Roberts. “Capacitive Voltage 

Transformers: Transient Overreach Concerns and 

Solutions for Distance Relaying.” July 2000. 

Benmouyal, Gabriel, and Jeff Roberts. “Superimposed 

Quantities: Their True Nature and Application in Relays.” 

October 1999. 

Zocholl, Stanley E. “Symmetrical Components: Line 

Transposition.” March 1999. 

Behrendt, Kenneth. “Relay-to-Relay Digital Logic 

Communication for Line Protection, Monitoring, and 

Control.” November 1998. 

Fleming, Bill. “Negative-Sequence Impedance 

Directional Element.” February 1998. 

Schweitzer III, Edmund O., Bill Fleming, Tony Lee, and 

Paul Anderson. “Reliability Analysis of Transmission 

Protection Using Fault Tree Methods.” October 1997. 

Hou, Daqing, Armando Guzmán, and Jeff Roberts. 

“Innovative Solutions Improve Transmission Line 

Protection.” October 1997. 

Mooney, Joe, and Jackie Peer. “Application Guidelines 

for Ground Fault Protection.” October 1997. 

Schweitzer III, Edmund O., and John Kumm. “Statistical 

Comparison and Evaluation of Pilot Protection 

Schemes.” October 1996. 

Guzmán, Armando, Jeff Roberts, and Daqing Hou. 

“New Ground Directional Elements Operate Reliably for 

Changing System Conditions.” September 1996. 

Mooney, Joe. “Microprocessor-Based Transmission Line 

Relay Applications.” March 1996. 

Roberts, Jeff, Edmund O. Schweitzer III, Renu Arora, 

and Ernie Poggi. “Limits to the Sensitivity of Ground 

Directional and Distance Protection.” October 1995. 

Zocholl, Stanley E. “Three-Phase Circuit Analysis and 

the Mysterious k 0 

Factor.” September 1995. 

Roberts, Jeff, Armando Guzmán, and Edmund O. 

Schweitzer III. “Z = V/I Does Not Make a Distance 

Relay.” April 1994. 

Schweitzer III, Edmund O. “A Review of Impedance- 

Based Fault Locating Experience.” June 1993. 

Schweitzer III, Edmund O., and Jeff Roberts. “Distance 

Relay Element Design.” April 1993. 

Zimmerman, Karl, and Joe Mooney. “Comparing Ground 

Directional Element Performance Using Field Data.” 

April 1993. 

Schweitzer III, Edmund O., and Daqing Hou. “Filtering 

for Protective Relays.” April 1993. 

Roberts, Jeff, and Edmund O. Schweitzer III. “Analysis 

of Event Reports.” April 1991. 

Schweitzer III, Edmund O. “New Developments in 

Distance Relay Polarization and Fault Type Selection.” 

October 1989. 

Line Protection Bibliography | 85

SEL University 2010 Course Schedule 

Course No. Course Name July August September October November December 

Fundamentals 

PWRS 400 

Power System Fundamentals for Engineers 

Pullman, WA 

3—6 

PROT 401 

Protecting Power Systems for Engineers 

Chicago, IL 

19—23 

Pullman, WA 

9—13 

Los Angeles, CA 

6—10 

PROT 403 

Distribution System Protection 

Dothan, AL 

19—21 

PROT 405 

Industrial Power System Protection 

Pullman, WA 

21—24 

PROT 407 

Transmission Line Protection 

Pullman, WA 

23—25 

PROT 409 

Generation System Protection 

Pullman, WA 

13—15 

PROT 411 

Substation Equipment Protection 

Folsom, CA 

12—14 

Applications 

APP 87 

SEL-387 and SEL-587 Percentage-Restrained Differential Relays 

Folsom, CA 

15—16 

APP 300G 

SEL-300G Generator Relay 

Pullman, WA 

16—17 

APP 311L 

SEL-311L Line Current Differential Relay 

Pullman, WA 

26—27 

Folsom, CA 

16—17 

APP 351 

SEL-351 Directional Overcurrent and Reclosing Relay 

Chicago, IL 

3—4 

Folsom, CA 

28—29 

Orlando, FL 

14—15 

APP 351R 

SEL-351R Recloser Control 

Charlotte, NC 

9—10 

APP 403 

Enhancing Distribution Protection Using the SEL-351S 

Dothan, AL 

22—23 

APP 405 

Protecting Induction Motors Using the SEL-710, SEL-701 

Charlotte, NC 

13—15 

Pullman, WA 

28—30 

Dallas, TX 

7—9 

APP 421 

SEL-421 Protection, Automation, and Control System 

Orlando, FL 

16—18 

APP 487B 

SEL-487B Bus Protection Relay 

Raleigh, NC 

5—6 

APP 651R 

SEL-651R Advanced Recloser Control 

Atlanta, GA 

26—27 

APP 751A Feeder Protection Using the SEL-751A Relay NEW in 2010 

APP 3530 SEL-3530 Real-Time Automation Control NEW in 2010 

Pullman, WA 

13—14 

Philadelphia, PA 

14—15 

Testing 

TST 101 

SEL Relay Testing Basics 

Chicago, IL 

5—6 

Nashville, TN 

16—17 

TST 107 

SEL Transmission Substation Relay Testing 

Denver, CO 

14—16 

Web-Based Training 

WBT 351 

SEL-351 Relay Coordination Techniques 

Online 

2 & 4 

WBT 421 

Applying Dual-Breaker Reclosing With the SEL-421 Relay 

Online 

6 & 8 

WBT 2411S RTU Replacement Using IEC 61850 

Online 

31 

Online 

2 

WBT 3332 

Configuring Logical Expressions Using the SEL-3332 Intelligent 

Server and SEL-3351 System Computing Platform 

Online 

14 & 16 

Since its inception, SEL University has had one clear mission—to provide the education and training needed to make electric power safer, more reliable, 

and more economical. We’ve developed programs that help you meet the technical challenges and complexities of integrating digitally based technologies 

into your expanding power system infrastructure. 

For the most up-to-date course descriptions, dates, and locations, visit www.selinc.com/selu • Phone: +1.509.338.4026 • selu@selinc.com 


©2010 Schweitzer Engineering Laboratories, Inc. 

20100616

Journal of Reliable Power - SEL

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