One-Terminal Traveling Wave-Based Protection for HVAC and
HVDC Transmission Lines
vorgelegt von
M. Sc.
Rafael Lucas da Silva França
ORCID: 0000-0001-5100-2979
an der Fakultät IV - Elektrotechnik und Informatik
der Technischen Universität Berlin
und der
Graduiertenprogramm in Elektrotechnik und Computertechnik der
Bundesuniversität von Rio Grande do Norte in Natal, Brasilien
zur Erlangung des akademischen Grades
Doktor der Ingenieurwissenschaften
- Dr.-Ing. -
genehmigte Dissertation
(Cotutelle de Thèse)
Promotionsausschuss:
Vorsitzender:
Prof. Dr.-Ing. Ronald Plath (TU Berlin)
Gutachter:
Prof. Dr. Flavio Bezerra Costa (UFRN, Natal, Brasilien)
Prof. Dr.-Ing. Kai Strunz (TU Berlin)
Prof. Dr. Felipe Vigolvino Lopes (UFPB, João Pessoa, Brasilien)
Prof. Dr. Luiz Felipe de Queiroz Silveira (UFRN, Natal, Brasilien)
Prof. Dr. Washington Luiz Araujo Neves (UFCG, Campina Grande, Brasilien)
Prof. Dr. Dirk Van Hertem (KU Leuven, Leuven, Belgien)
Tag der wissenschaftlichen Aussprache: 28. Februar 2023
per Videokonferenz
Berlin 2024
UNIVERSIDADE DO RIO GRANDE DO NORTEFEDERAL
FEDERAL UNIVERSITY OF RIO GRANDE DO NORTE
GRADUATE PROGRAM IN ELECTRICAL AND COMPUTER ENGINEERING
TECHNICAL UNIVERSITY OF BERLIN
GRADUATE PROGRAM IN ELECTRICAL ENGINEERING AND COMPUTER
SCIENCE
One-Terminal Traveling Wave-Based Protection for
HVAC and HVDC Transmission Lines
Rafael Lucas da Silva França
Supervisors: Prof. Dr. Flavio Bezerra Costa
Prof. Dr. Kai Strunz
Co-supervisor: Prof. Dr. Felipe Vigolvino Lopes
PhD. Thesis presented to UFRN Graduate Pro-
gram in Electrical and Computer Engineering
(Area: Automation and Systems) and TUB
Graduate Program in Electrical Engineering
and Computer Science as part of the require-
ments to obtain the Doctor of Philosophy
degree.
February 2023
To God. To my family, especially my
parents, Sérgio Augusto Nascimento de
França and Eliene Francisca da Silva
França, for their guidance throughout
my life. To my wife, Allany Katywood
Henrique de Miranda, for her
tremendous and valuable support in
completing this work.
Acknowledgment
To my supervisor and friend, Professor Dr. Flavio Bezerra Costa, for his unmatched dedication,
technical contributions, and companionship throughout this journey.
To my supervisors, Professor Dr. Kai Strunz and Professor Dr. Felipe Vigolvino Lopes, for
their essential technical contributions and hard work in supporting the improvement of the text.
To my friends and coworkers, but mainly, Cícero Josean Mateus Nunes da Silva, Francisco
Canindé da Silva Júnior, Mônica Maria Leal, Rodrigo Prado de Medeiros, Daniel Marques da
Silva, and Marcos Sergio Rodrigues Leal, for the significant contributions and support through-
out this work.
To my family, especially my parents, siblings, and wife, for their unconditional support.
To the National Council of Scientific and Technological Development (CNPq) for financial
support.
Abstract
This work proposes developing one-terminal traveling wave-based transmission line protec-
tion methods for HVAC (High Voltage Alternating Current) and HVDC (High Voltage Direct
Current) systems. It considers the effect of the sampling frequency on the protection, which
until now has not been investigated for one-terminal methods. It addresses inaccuracies in wave
velocity estimations, which traditionally lead to problems in methods based on traveling waves,
and presents solutions to these problems. The proposed methods have been evaluated through
computer simulations. The proposed earth fault distance protection for HVAC transmission
lines was evaluated using an actual commercial relay with time-domain-based protection func-
tions. The results related to the proposed earth fault distance protection for HVAC transmission
lines show that the proposed function, when associated with other existing protection functions,
can achieve a remarkable enhancement in the dependability and velocity of the transmission
line protection. The results concerning the method based on traveling wave reflections show
that it is possible to protect most point-to-point transmission lines quickly, without communi-
cation, and independent of the wave speed estimation. Finally, the results concerning distance
protection for meshed HVDC systems demonstrate the applicability of the proposed method for
such systems. The method showed an operating time below 2 ms for a line of 500 km in length.
This operating time meets the likely requirements that HVDC meshed systems will present.
Additionally, the method demonstrated selectivity for a 4-terminal system interconnected by
five transmission lines.
Keywords: Transmission line protection, traveling waves, one-terminal protection, distance
protection, fault location, HVAC systems, meshed HVDC systems, protection selectivity.
Resumo
Este trabalho propõe o desenvolvimento de métodos de proteção de linha de transmissão
baseados em ondas viajantes de um terminal para sistemas ATCA (Alta Tensão em Corrente
Alternada) e ATCC (Alta Tensão em Corrente Contínua). O efeito da frequência de amostragem
na proteção é considerado, o que até agora ainda não foi investigado para métodos de um termi-
nal. As imprecisões nas estimativas da velocidade das ondas, que classicamente são limitações
para métodos baseados em ondas viajantes, são abordadas e são apresentadas soluções para tal
problema. Os métodos propostos foram avaliados por meio de simulações computacionais. A
proteção proposta da distância para faltas envolvendo a terra para linhas de transmissão ATCA
foi avaliada utilizando um relé comercial real com funções de proteção baseadas no domínio
do tempo. Os resultados relacionados à proteção proposta da distância para faltas à terra para
linhas de transmissão ATCA mostram que a função proposta, quando associada a outras funções
de proteção existentes, pode alcançar um incremento bastante notável na confiabilidade e ve-
locidade da proteção da linhas de transmissão. Os resultados relativos ao método baseado em
reflexão de ondas viajantes mostram que é possível proteger a maioria das linhas de transmis-
são ponto a ponto de uma forma rápida, sem necessidade de comunicação e independente da
estimativa da velocidade da onda. Finalmente, os resultados relativos à proteção da distân-
cia para sistemas de ATCC em malha demonstram a aplicabilidade do método proposto para
tais sistemas. O método apresentou um tempo de atuação inferior a 2 ms para uma linha de
500 km de comprimento. Esse tempo de atuação atende aos prováveis requisitos que sistemas
meshed ATCC apresentarão. Além disso, o método apresentou selectividade para um sistema
de 4-terminais interligados por 5 linhas de transmissão.
Palavras-chave: Protecção da linha de transmissão, ondas viajantes, proteção de um ter-
minal, proteção de distância, localização de faltas, sistemas ATCA, sistemas ATCC em malha,
seletividade da proteção.
Table of Contents
Table of Contents i
List of Figures iii
List of Tables vi
List of Symbols viii
List of Abbreviations and Acronyms xi
1 Introduction 1
1.1 HVACSystem................................... 1
1.2 HVDCSystem .................................. 4
1.3 Motivation and Overall Problem . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 ResearchQuestions................................ 6
1.5 Objectives..................................... 6
1.6 Target Protection Functionalities . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.7 LiteratureContribution .............................. 7
1.8 WorkMethodology................................ 10
1.9 WorkStructure .................................. 10
2 State-of-the-Art 11
2.1 One-Terminal HVAC Traveling-Wave-Based Methods . . . . . . . . . . . . . . 11
2.2 Two-Terminal HVAC Traveling-Wave-Based Methods . . . . . . . . . . . . . 13
2.3 State-of-the-Art Summary for HVAC Methods . . . . . . . . . . . . . . . . . . 16
2.4 One-Terminal Traveling-Wave-Based Methods for Meshed HVDC Systems . . 17
2.5 State-of-the-Art Summary for HVDC Methods . . . . . . . . . . . . . . . . . 19
3 Basic Theory of the Traveling Waves 20
3.1 Transmission Line Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Wave Propagation in Discontinuities . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.1 Reflections and Refractions of the Wave . . . . . . . . . . . . . . . . . 21
3.3 ModalComponents................................ 24
3.4 ChapterSynthesis................................. 24
4 Principles of the One-Terminal Transmission Line Protection Based on Reflections
of the Traveling Waves 26
4.1 Traveling Wave Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1.1 Traveling Wave Reflections for a Simple Line . . . . . . . . . . . . . . 26
4.1.2 Traveling Wave Reflections Including Adjacent Lines . . . . . . . . . . 29
4.1.3 ChapterSynthesis ............................ 32
i
5 The Proposed Traveling Wave-Based Earth Fault Distance Protection for HVAC
Transmission Lines 33
5.1 Principles of the Proposed TW-Based Distance Protection Relay . . . . . . . . 33
5.2 The Proposed TW21G Function . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2.1 Sampling Frequency Effects . . . . . . . . . . . . . . . . . . . . . . . 35
5.2.2 TW Velocity Estimation Effects . . . . . . . . . . . . . . . . . . . . . 36
5.3 The Protection Zone of the Proposed TW21G Function . . . . . . . . . . . . . 37
5.3.1 The Maximum Protection Zone . . . . . . . . . . . . . . . . . . . . . 37
5.3.2 Error Margin for the Wave Velocity Estimation . . . . . . . . . . . . . 38
5.3.3 The Minimum Protection Zone . . . . . . . . . . . . . . . . . . . . . . 39
5.4 Proposed TW21G Function Setup Methodology . . . . . . . . . . . . . . . . . 39
5.5 PerformanceAssessment............................. 40
5.5.1 The Proposed Distance Function TW21G . . . . . . . . . . . . . . . . 42
5.5.2 The Proposed TW21G Function with Supervision of Existing Functions 43
5.5.2.1 Effect of Uncertainty in Line Parameters . . . . . . . . . . . 44
5.5.3 The Proposed TW21G Function with Supervision of Existing Functions
Considering Frequency-dependent Parameters . . . . . . . . . . . . . . 44
5.5.3.1 Effect of the Fault Location . . . . . . . . . . . . . . . . . . 45
5.5.3.2 Effect of the Fault Inception Angle . . . . . . . . . . . . . . 45
5.5.3.3 Effect of the Fault Resistance . . . . . . . . . . . . . . . . . 46
5.5.3.4 DTT Protection Scheme . . . . . . . . . . . . . . . . . . . . 46
5.5.4 Operation Time Comparison . . . . . . . . . . . . . . . . . . . . . . . 47
5.6 Conclusion .................................... 49
5.7 ChapterSynthesis................................. 50
6 Proposed One-Terminal Traveling Wave Reflection-Based Transmission Line Pro-
tection 51
6.1 Discrete Time Domain for a Single Line . . . . . . . . . . . . . . . . . . . . . 51
6.1.1 The Protected, Unprotected, and Uncertain Zones . . . . . . . . . . . . 54
6.1.2 Effect of Traveling Wave Speed Estimation . . . . . . . . . . . . . . . 56
6.1.3 Error Margin for Estimation of Wave Speed in the Continuous Time
Domain.................................. 58
6.1.4 Error Margin for Wave Speed Estimation in the Discrete Time Domain 58
6.1.5 Minimum Frequency as a Function of Speed Estimation . . . . . . . . 60
6.2 ProposedMethod................................. 63
6.3 PerformanceAssessment............................. 63
6.3.1 ThePowerSystem ............................ 63
6.3.2 FaultConfiguration............................ 64
6.3.3 Minimum Sampling Frequency . . . . . . . . . . . . . . . . . . . . . 65
6.3.4 MethodPerformance........................... 66
6.4 Conclusion .................................... 69
6.5 ChapterSynthesis................................. 69
7 Applicability of Wave-based Distance Protection for Earth Faults Applied to Meshed
HVDC Systems 70
7.1 The Need for Full Protection Selectivity . . . . . . . . . . . . . . . . . . . . . 70
7.2 Principles of Distance Protection Applied to Meshed HVDC Systems . . . . . 71
7.3 The Proposed Distance Protection Function . . . . . . . . . . . . . . . . . . . 72
7.3.1 Continuous Time Domain . . . . . . . . . . . . . . . . . . . . . . . . 72
7.3.2 Discrete Time Domain . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7.3.2.1 The Search Zone . . . . . . . . . . . . . . . . . . . . . . . . 74
7.4 TheProposedMethod............................... 74
7.4.1 Definition of the Faulty Section . . . . . . . . . . . . . . . . . . . . . 75
7.5 PerformanceAssessment............................. 75
7.5.1 TestSystem1............................... 75
7.5.1.1 Converter Topology and Controls . . . . . . . . . . . . . . . 77
7.5.1.2 Definition of the Faulty Section . . . . . . . . . . . . . . . . 78
7.5.1.3 SearchZone.......................... 79
7.5.1.4 Fault Location Estimation . . . . . . . . . . . . . . . . . . . 81
7.5.1.4.1 Variation of Fault Location on Line L12 . . . . . . 82
7.5.1.4.2 Variation of Fault Location on Line L13 . . . . . . 83
7.5.1.4.3 Variation of Fault Location on Lines L14, L24, and
L34 ......................... 85
7.5.1.5 Negative Pole-to-Ground and Pole-to-Pole Fault Cases . . . . 86
7.5.1.6 Protection Operation Time . . . . . . . . . . . . . . . . . . 86
7.5.2 TestSystem2............................... 89
7.5.2.1 SearchZone.......................... 91
7.5.2.2 Fault Location Estimation . . . . . . . . . . . . . . . . . . . 91
7.5.2.3 Protection Operation Time . . . . . . . . . . . . . . . . . . 94
7.6 Conclusion .................................... 94
7.7 ChapterSynthesis................................. 95
8 Conclusions 96
8.1 Conclusions.................................... 96
Bibliography 104
A Summary Overview of Included Publications 105
List of Figures
3.1 Lattice diagram of the traveling waves for a fault. . . . . . . . . . . . . . . . . 22
4.1 General behavior of the traveling wave reflections. . . . . . . . . . . . . . . . 27
4.2 Lattice diagram to a fault in the first half of the transmission line. . . . . . . . . 27
4.3 Lattice diagram to a fault in the second half of the transmission line. . . . . . . 28
4.4 Lattice diagram for a fault on the remote bus. . . . . . . . . . . . . . . . . . . 29
4.5 Lattice diagram for an upstream external fault. . . . . . . . . . . . . . . . . . . 30
4.6 Lattice diagram for a reverse external fault. . . . . . . . . . . . . . . . . . . . 31
4.7 Lattice diagram for a reverse external fault, considering the upstream external
line smaller than the protected line. . . . . . . . . . . . . . . . . . . . . . . . . 31
4.8 Lattice diagram for an internal fault, considering the upstream external line
smaller than dF................................... 32
5.1 Protection logic using the proposed traveling wave-based distance earth fault
protection function TW21G and the Bewley diagram. . . . . . . . . . . . . . . 34
5.2 Modal wave velocity estimation. . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.3 Flowchart for the relay setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.4 Modeled system 1: 230 kV and 60 Hz power system with distributed parameters. 41
5.5 Modeled system 2: 230 kV and 60 Hz power system with frequency-dependent
parameters and non-ideal line transposition. . . . . . . . . . . . . . . . . . . . 41
5.6 Tower parameters for the system 2. . . . . . . . . . . . . . . . . . . . . . . . . 42
5.7 Protection operation time for: (a) vαunderestimated by 3% and v0overesti-
mated by 3%; (b) vαoverestimated by 3% and v0underestimated by 3%; (c)
correct estimation for vαand v0. ......................... 43
5.8 TD21 and TW21G protection operation times. . . . . . . . . . . . . . . . . . . 44
5.9 TD21 and TW21G protection operation times for: (a) R1,L1, and C1underes-
timated by 3%, and R0,L0, and C0overestimated by 3%; (b) R1,L1, and C1
overestimated by 3%, and R0,L0, and C0underestimated by 3%. . . . . . . . . 45
5.10 TD21 and TW21G protection operation times. . . . . . . . . . . . . . . . . . . 46
5.11 Protection operation time as a function of the fault inception angle to: (a) the
proposed TW21 protection; (b) the existing TD21 protection. . . . . . . . . . . 47
5.12 Protection operation time as a function of the fault resistance to: (a) the pro-
posed TW21 protection; (b) the existing TD21 protection. . . . . . . . . . . . . 47
5.13 Scatter plot of the existing TD21 protection and the proposed TW21G protec-
tionoperationtimes. ............................... 48
5.14 Cumulative frequency of the operation time. . . . . . . . . . . . . . . . . . . . 49
6.1 Lattice diagram of traveling waves seen from a terminal, considering the effect
ofsamplingfrequency. .............................. 52
6.2 Estimated speed higher than the actual speed of the traveling waves for an in-
ternalfault. .................................... 57
iv
6.3 Estimated speed lower than the actual speed of the traveling waves for an exter-
nalfault....................................... 57
6.4 Margin for a positive error in speed estimation. . . . . . . . . . . . . . . . . . 62
6.5 Margin for a negative error in speed estimation. . . . . . . . . . . . . . . . . . 62
6.6 500 kV transmission system. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.7 Minimum sampling frequency as a function of line length. . . . . . . . . . . . 65
6.8 Estimation of the protected and uncertainty zones as a function of line length
for specific frequencies: a) protected zone; b) protected + uncertainty zone. . . 66
6.9 Estimation of the protected and uncertainty zones as a function of sampling
frequency for given line lengths: a) protected zone; b) protected + uncertainty
zone......................................... 67
6.10 Protection operation for a 200 km line and fS=6kHz. ............. 67
6.11 Protection operation for a 200 km line and fS=1.8kHz. ............ 68
6.12 Protection operation for a 200 km line and fS=15kHz. ............ 68
7.1 Principles of the distance protection for earth faults applied to a meshed HVDC
system. ...................................... 71
7.2 Meshed HVDC test system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.3 Geometrical parameters for the transmission line. . . . . . . . . . . . . . . . . 76
7.4 High-level and low-level controllers diagram. . . . . . . . . . . . . . . . . . . 77
7.5 Wavelet transform coefficients for a fault on line L12 for the alpha-mode volt-
ages of all lines connected to: (a) bus 1; (b) bus 2. . . . . . . . . . . . . . . . . 78
7.6 Wavelet transform coefficients for a fault on line L12 for the alpha-mode volt-
ages of all lines connected to: (a) bus 3; (b) bus 4. . . . . . . . . . . . . . . . . 79
7.7 Minimum sampling frequency as a function of the desired length for the search
zone, which varies from: (a) 0 to 35 km; (b) 20 to 70 km; (c) 0 to 8 km. . . . . 80
7.8 Lattice diagram for a fault on line L12, 50 km from bus 1. . . . . . . . . . . . . 81
7.9 Error in the fault location estimation as a function of the fault location for faults
on the line L12 for: (a) estimation on bus 1; (b) estimation on bus 2. . . . . . . 82
7.10 Fault location estimation on bus 1 as a function of the fault location for faults
onthelineL12................................... 83
7.11 Fault location estimation as a function of the fault location for faults on the line
L12 for: (a) estimation on bus 3; (b) estimation on bus 4. . . . . . . . . . . . . 84
7.12 Error in the fault location estimation as a function of the fault location for faults
on the line L13 for: (a) estimation on bus 1; (b) estimation on bus 3. . . . . . . 85
7.13 Fault location estimation as a function of the fault location for faults on the line
L13 and estimation on bus 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7.14 Fault location estimation as a function of the fault location for faults on the line
L13 and estimation on bus 4 for traveling waves coming from the line: (a) L41;
(b)L43. ...................................... 87
7.15 Protection operation time as a function of the fault location referred to bus 1 for
faults on the line L12 and protection function on: (a) bus 1; (b) bus 2. . . . . . 88
7.16 Protection operation time as a function of the fault location referred to bus 1 for
faults on the line L13 and protection function on: (a) bus 1; (b) bus 3. . . . . . 89
7.17 Cumulative frequency for the protection operation time. . . . . . . . . . . . . . 90
7.18 Point-to-point LCC-HVDC test system. . . . . . . . . . . . . . . . . . . . . . 90
7.19 Geometrical parameters for the AC transmission line. . . . . . . . . . . . . . . 90
7.20 Minimum sampling frequency as a function of the desired length for the search
zone for: (a) 0 to 1000 kHz; (b) 20 to 100 kHz; (c) 100 to 1000 kHz. . . . . . . 92
7.21 Error in the fault location estimation as a function of the fault location. . . . . . 93
7.22 Fault location estimation as a function of the fault location. . . . . . . . . . . . 93
7.23 Protection operation time as a function of the fault location. . . . . . . . . . . . 94
List of Tables
1.1 Literature contribution for journal papers. . . . . . . . . . . . . . . . . . . . . 8
1.2 Literature contribution for conference papers. . . . . . . . . . . . . . . . . . . 9
2.1 State-of-the-art summary for HVAC one-terminal methods. . . . . . . . . . . . 16
2.2 State-of-the-art summary for HVAC two-terminal methods. . . . . . . . . . . . 16
2.3 State-of-the-art summary for HVDC methods. . . . . . . . . . . . . . . . . . . 19
5.1 POTT and DTT scheme operations. . . . . . . . . . . . . . . . . . . . . . . . 48
7.1 Electrical parameters for the transmission line. . . . . . . . . . . . . . . . . . . 77
7.2 Fault location estimation for a fault on line L12 at 50 km from bus 1. . . . . . . 81
vii
List of Symbols
αLine attenuation constant
βLine phase constant
cSpeed of light
CPer unit transmission line capacitance
C1Per unit transmission line capacitance in positive sequence component
C0Per unit transmission line capacitance in zero sequence component
dFFault distance from the local bus
dxLength constant
εαError related to the discret instant of the first alpha mode wavefront to
reach the local bus
εFError associated to the discrete fault inception time
εFαTotal error represented by the sum between the error related to the in-
stant of the first alpha mode wavefront to reach the local bus εαand the
error associated to the discrete fault inception time εF
εF0Total error represented by the sum between the error related to the in-
stant of the first zero mode wavefront to reach the local bus ε0and the
error associated to the discrete fault inception time εF
ε0Error related to the discret instant of the first zero mode wavefront to
reach the local bus
fsRelay sampling frequency
GPer unit transmission line conductance
γPropagation constant of the transmission line
Γr1(I)Reflection coefficient in bus 1 of the wave in the current signal
Γr1(U)Reflection coefficient in bus 1 of the wave in the voltage signal
Γr2(I)Reflection coefficient in the fault point of the wave in the current signal
Γr2(U)Reflection coefficient in the fault point of the wave in the voltage signal
Γt1(I)Refraction coefficient in bus 1 of the wave in the current signal
Γt1(U)Refraction coefficient in bus 1 of the wave in the voltage signal
Γt2(I)Refraction coefficient in the fault point of the wave in the current signal
Γt2(U)Refraction coefficient in the fault point of the wave in the voltage signal
iCurrent signal
iACurrent signal in phase A
iαCurrent signal in alpha mode component
iBCurrent signal in phase B
iβCurrent signal in beta mode component
iCCurrent signal in phase C
ir1Traveling wave in currents reflected in bus 1
ir2Traveling wave in currents reflected in the fault point
is1Sum between the incident and reflected current waves in the bus L
it1Traveling wave in currents refracted in bus 1
viii
it2Traveling wave in currents refracted in the fault point
i0Current signal in zero mode component
i1Traveling wave in the current signal
kαSample arrival of the alpha mode traveling wave in bus L
kFSample refering to the fault inception time
k0Sample arrival of the zero mode traveling wave in bus L
LPer unit transmission line inductance
L1Per unit transmission line inductance in positive sequence component
L0Per unit transmission line inductance in zero sequence component
lTotal length of the monitored transmission line
lATotal length of the external transmission line A
lBTotal length of the external transmission line B
mMultiplicative factor dependent on real velocities of modal traveling
waves
margαError margin for overestimating the alpha mode wave velocity
marg0Error margin for underestimating the zero mode wave velocity
m′Multiplicative corrected factor dependent on real velocities of modal
traveling waves
mcEstimated value to the variable m
pαMultiplicative security factor for vα
p0Multiplicative security factor for v0
PlMinimum protection reach
Plmax Maximum protection reach
qThreshold to ensure that an internal fault is properly differentiated from
an external fault
qαOverestimation factor for the the initial alpha mode wave velocity esti-
mation
q0Underestimation factor for the the initial zero mode wave velocity esti-
mation
RPer unit transmission line resistance
RfFault resistance
tTime instant variable
tαAlpha mode wavefront arrival time in continuous time domain in bus L
tFFault inception time in continuous time domain
tF1First wavefront arrival time in continuous time domain in local bus
tF2Second wavefront arrival time in continuous time domain in local bus
tF3Third wavefront arrival time in continuous time domain in local bus
t0Zero mode wavefront arrival time in continuous time domain in bus L
t1
1Arrival time of the first wave to reach the bus 1
t2
1Arrival time of the first wave to reach the bus 2
t3
1Arrival time of the first wave to reach the bus 3
t1
2Arrival time of the second wave to reach the bus 1
t2
2Arrival time of the second wave to reach the bus 2
t3
2Arrival time of the second wave to reach the bus 3
ταDelay between the fault inception timetFand the first alpha mode wave-
front arrival time on the bus L tα
τF1Propagation time of the first wavefront to reach the local bus
τF2Propagation time of the second wavefront to reach the local bus
τ0Delay between the fault inception time tFand the first zero mode wave-
front arrival time on the bus L t0
uVoltage signal
uAVoltage signal in phase A
uαVoltage signal in alpha mode component
uBVoltage signal in phase B
uβVoltage signal in alpha beta component
uCVoltage signal in phase C
ufInstantaneous voltage at the fault point at the fault instant
ur1Traveling wave in voltages reflected in bus 1
ur2Traveling wave in voltages reflected in the fault point
us1Sum between the incident and reflected voltage waves in the bus L
ut1Traveling wave in voltages refracted in bus 1
ut2Traveling wave in voltages refracted in the fault point
u0Voltage signal in zero mode component
u1Traveling wave in the voltage signal
vReal velocity of the traveling waves
vαVelocity of the alpha mode traveling wave
v0Velocity of the zero mode traveling wave
xPosition variable
Z0Characteristic impedance of a specific line
Z1Characteristic impedance of line 1
Z2Characteristic impedance of line 2
List of Abbreviations and Acronyms
AC Alternating Current
ATCA Alta Tensão em Corrente Alternada
ATCC Alta Tensão em Corrente Contínua
CAPES Coordination for the Improvement of Higher Education Personnel
CBA Brazilian Congress of Automatic
CCVT Coupling Capacitor Voltage Transform
CT Current Transformer
DC Direct Current
DMR Dedicated Metalic Return
DTT Direct Transfer Trips
EMTDC Electromagnetic Transients including DC
GPS Global Positioning System
HVAC High Voltage Alternating Current
HVDC High Voltage Direct Current
IEEE Institute of Electrical and Electronics Engineers
IGBT Insulated Gate Bipolar Transistor
IPST The International Conference on Power Systems Transients
OC21 Time domain overcurrent function
PD-SPWM Phase Disposition Sinusoidal Pulse Width Modulation
ProRedes Signal Processing and Smart Grids
RT-BWT Real-time Boundary Wavelet Transform
SBSE Brazilian Symposium on Electrical Systems
SEL Schweitzer Engineering Laboratories
SM Switching Module
SIR System-to-line Impedance Ratio
STATCOM Static synchronous compensator
TD21 Time domain distance protection
TD32 Time domain directional function
TU Berlin Technical University of Berlin
TW21G Proposed traveling wave-based earth fault distance protection for HVAC
OCD Overcurrent Detection
TW32 Traveling wave directional function
UFRN Federal University of Rio Grande do Norte
WCNPS Workshop on Communication Networks and Power Systems
xi
Chapter 1
Introduction
This thesis covers investigations related to HVAC and HVDC transmission systems. There-
fore, for a better understanding, these two topics are, when possible, presented separately in this
chapter.
1.1 HVAC System
The transmission line is a fundamental component of the electrical power system since
it transmits energy from generation plants to load centers. It is estimated that 50% of all
faults occurring in the electric power system are concentrated in overhead transmission lines
(PAITHANKAR; BHIDE, 2003). Therefore, the fast fault clearance in the transmission system
is crucial for reducing damage to the electrical power system, increasing its stability, energy
transmission capacity (GLOVER; SARMA; OVERBYE, 2012), and availability. Such a con-
text has motivated several studies toward developing fast and reliable protection schemes based
on traveling waves (SCHWEITZER; KASZTENNY; MYNAM, 2015; SCHWEITZER et al.,
2015).
Traditional protection schemes for AC (Alternating Current) transmission lines, such as
distance protection, are based on phasor estimation. These techniques present some limitations
that restrict their ability to perform a fast operation (SCHWEITZER et al., 2015), among them
the need for an observation window of a fundamental signal wave cycle for accurate phasor
estimation (SCHWEITZER et al., 2015). According to Schweitzer et al. (2015), protective
relays typically operate between one and one-and-a-half cycles (from 16.67 to 25 ms on a 60 Hz
system). The current interruption time by the circuit breaker is between one-and-a-half cycle
to three cycles, resulting in an average time for the fault interruption of three to four cycles.
Thus, the operation time of the traditional techniques represents 25 to 50% of the total time
for the fault interruption. Although traditional methods operate within a quarter of a cycle in
specific conditions, stability limit considerations should be made assuming conservative times
of protection operation (SCHWEITZER et al., 2015). Eastvedt (1976) demonstrated that, for
a specific transmission line, a reduction of one cycle in the fault interruption time increased
the power transfer capacity by 250 MW, i.e., 15 MW per millisecond, which highlights the
relevance in developing protection methods increasingly fast.
When a fault occurs on an overhead transmission line, high-frequency electromagnetic tran-
sients are induced in voltages and currents. The transients propagate from the fault point toward
the line terminals, as traveling waves, at a velocity close to the speed of light. When a wavefront
arrives at a line terminal, a portion of the traveling wave is reflected and travels back toward the
fault point, whereas another portion is refracted and travels toward the next line terminal if there
are adjacent lines. The traveling waves reflected at the line terminal suffer another reflection
1.1. HVAC SYSTEM 2
and refraction at the fault point, reflecting and refracting toward the line terminals, resulting
in several coexistent traveling waves attending the wave superposition principle. The complete
theory of the traveling wave can be found in Corporation (1964).
The first work related to transients on a distributed parameter line investigated the signal
distortion on the planned Trans-Atlantic telephone cable in 1854 (KELVIN, 1884). In the
1920s and 1930s, several works investigated the traveling waves behavior in transmission lines
(BUSH, 1923; DOWELL, 1931; BEWLEY, 1931). A general theory based on a graphical
method was proposed by Allievi (1902) and applied to the field of hydraulic engineering, which
was a direct application of the traveling-wave concept. Based on Allievi (1902), a solution
to the analysis of transient waves was proposed by Schnyder (1929) and Bergeron (1935) in
order to treat initially transient phenomena in hydraulic systems. It was later applied to electri-
cal transient phenomena. This method is known as Bergeron’s method or Schnyder-Bergeron’s
method. Essential works in the 1960s proposed the analysis of transients on electric power trans-
mission lines based on Bergeron’s method through digital computers (FREY; ALTHAMMER,
1961; ARLETT; MURRAY-SHELLEY, 1965; BRANIN, 1967). Based on Bergeron’s method,
Dommel (1969) proposed a generalized algorithm capable of solving transients in any network
with distributed parameters, which was fundamental to the advance of the traveling waves in
transmission line analysis. These computational techniques are generally called time-domain
methods or traveling-wave techniques.
Traveling-wave-based transmission line protection can be divided into one- and two-terminal
techniques. Two-terminal techniques use information on traveling waves at both line ends, so
communication links and GPS (Global Positioning System) are often reported as a mandatory
requirement (YU, 2010). Nevertheless, practical data synchronization issues have been exten-
sively reported in the literature, such as the possibility of a loss of the time reference signal
(IZYKOWSKI et al., 2010), and the non-installation of common time reference sources in all
substations (YU, 2010). This reduces the reliability of two-terminal techniques in existing sys-
tems. In this context, one-terminal protection solutions have shown to be a good alternative.
This includes traveling wave-based distance protection elements, which require neither com-
munication links nor data synchronization systems. Even so, traveling wave-based functions
commonly face the challenge of distinguishing wavefronts reflected from the fault and other
transmission line terminals (SAHA; IZYKOWSKI; ROSOLOWSKI, 2010).
The first works focused on traveling wave-based protection principles were published in the
1970s (TAGAGI et al., 1977; DOMMEL; MICHELS, 1978; CHAMIA; LIBERMAN, 1978;
JOHNS, 1980). These works mainly investigated the fault directionality employing the voltage
and current traveling wave polarities using one terminal. However, unit protection could be
implemented using the fault directionality information from both line terminals. However, a
communication link between them was required. Crossley and McLaren (1983), Christopou-
los, Thomas and Wright (1988), Shehab-Eldin and McLaren (1988) were the first to publish
transmission line distance protection methods based on traveling waves and using one terminal
without the need for a communication system. Besides the traveling wave polarities and ampli-
tude, these one-terminal protection techniques used the time instant when the traveling waves
reached the local line terminal. However, they depended on the correct detection of the wave-
front reflected from the fault point, which is still a challenging task today. Reliability problems,
such as low sampling frequency available for hardware and limitations in the signal-processing
techniques limited the application of these works.
The advances in high-frequency sampling devices have improved the effectiveness of travel-
ing wave-based functions over the years. From the late 1990s, relevant works on traveling waves
were published focusing mainly on transmission line fault location (MAGNAGO; ABUR, 1998;
1.1. HVAC SYSTEM 3
THOMAS et al., 2004). Considering the experience gained over the years on traveling wave-
based fault analysis, the attention of relay developers has switched to traveling wave-based
ultra-high-speed transmission line protection studies. Dong et al. (2016) proposed a practical
method to detect faults on transmission lines based on the polarity analysis of voltage and cur-
rent traveling waves. Tang et al. (2017) presented a differential protection using equivalent
traveling waves. Using the arrival time of current traveling waves and their respective polarities
at both line ends, a technique for detecting internal faults and the directionality of forward and
reverse faults is proposed by Namdari and Salehi (2017). However, these solutions may fail in
close-in fault cases since successive wave reflections can reach the monitored line end within a
time period smaller than the data window applied in traveling wave filtering techniques, jeopar-
dizing the detection of traveling waves reflected from the fault. The influence of the sampling
frequency in line protection is evaluated by Costa et al. (2017), making it possible to define
unprotected zones, within which a fault will never be detected as internal, and protected zones,
within which a fault will always be detected as internal. However, this function depends on two-
terminal measurements, requiring dedicated communication links and data synchronization.
Although one-terminal traveling wave-based functions are easy to apply in the field, they are
less used than two-terminal approaches, mainly due to difficulties in identifying the reflection
that comes from the fault point. To properly do so, cross-correlation was applied by Crossley
and McLaren (1983), and a technique dependent on line parameters that analyzes the amplitude
of traveling waves was proposed by Christopoulos, Thomas and Wright (1988). The traveling
wave polarity was investigated by Dong, Ge and Xu (1999) to solve this problem. However,
none of the existing techniques reached high levels of accuracy. Thus, further developments
have been pursued toward finding solutions irrespective of the analysis of reflected wavefronts.
Indeed, some techniques analyze the first incident aerial (alpha) and ground (zero) mode trav-
eling waves rather than the incident and reflected alpha-mode (α-mode) waves in earth fault
cases.
Magnago and Abur (1998) used modal traveling waves to differentiate faults between phases
from earth faults in a two-terminal fault location method. Abur and Magnago (2000) proposed
a one-terminal method based on the arriving instants of the modal traveling waves and the
first α-mode traveling wave reflection to pinpoint earth faults. Nonetheless, using only the first
wavefront of modal traveling waves, this method can identify whether the fault is within the first
or second half of the transmission line. Moreover, an earth fault location method based on the
arriving instants of modal waves was also proposed (LIU et al., 2012). However, this method
demands multi-measuring points and communication systems. A two-terminal earth fault loca-
tor was also proposed (LOPES, 2016). It requires neither settings nor data synchronization, but
communication means are still required.
Considering that earth faults represent the majority of fault scenarios on the electrical power
system (SAHA; IZYKOWSKI; ROSOLOWSKI, 2010), where 70 to 80% of transmission line
faults are single-phase earth faults (GRAINGER; JR., 1994), the methods referenced so far are
relevant. Recent patent applications (III; KASZTENNY, 2019b; III; KASZTENNY, 2019a)
also indicate the potential of traveling wave-based distance protection methods, provided that
reliable detections of α-mode waves reflected from the fault point are attained. However, prior
works did not investigate the sampling frequency effects on one-terminal traveling wave-based
line protection functions.
1.2. HVDC SYSTEM 4
1.2 HVDC System
The power system is traditionally divided into generation, transmission, and distribution sys-
tems. The power generation is mainly centralized and provided by hydroelectric power plants
that are far from the load centers. The electric energy is normally delivered to load centers utiliz-
ing high-voltage alternating current transmission lines. However, this traditional configuration
has several drawbacks, such as the reliability dependence of the entire power system on the con-
centrated power plant and restrictions according to the environmental condition. Therefore, to
overcome these drawbacks, the smart grid concept proposes the diversification and distribution
of energy resources, yielding challenges for protecting, controlling, and monitoring the power
system (VAAHEDI et al., 2017).
The advent of new technologies, such as the voltage converter coupled with modern com-
munication networks, has enabled the transformation of the traditional power grid into a smart
grid (BLOOM et al., 2017). In order to provide the best grid optimization, the smart grid con-
cept directs to the modernization of transmission and distribution systems. This concept leads
to the proliferation of renewable energy, distribution of power plants, the resurgence of high-
voltage direct current transmission lines, and more (SANTACANA et al., 2010). The smart grid
also leads to the reliability and resiliency increasing of the power grid and decreases operating
costs and losses. This new reality has faced new challenges related to power grid protection
(SHAHIDEHPOUR et al., 2017).
The distributed generation on the smart grid concept is wider than low distances to the load
centers. Powerful renewable generation, such as offshore wind farms, may be far distant from
the customers, which has demanded the resurgence of HVDC transmission lines. The costs
related to the HVDC transmission system implementation have continuously decreased. More-
over, HVDC systems present several technical advantages for long-distance energy delivery
compared to HVAC transmission systems (BARNES et al., 2017; BAHRMAN; JOHNSON,
2007).
According to CIGRÉ (2013), a meshed HVDC system can be generally defined as a system
composed of multiple converters connected with branches forming at least one mesh, which
creates a parallel path. On the other hand, a multi-terminal HVDC system is composed of sev-
eral converters but without any mesh. Multi-terminal HVDC systems are a viable solution to the
integration of growing renewable energy, such as offshore wind farms. These systems present
several advantages, such as interconnection flexibility, efficiency, power supply reliability, and
capacity to absorb and consume large amounts of renewable energy. Meshed HVDC systems
present all these advantages but with redundancy and higher availability. A parallel path can
ensure transmission continuity if a branch is disconnected in a meshed HVDC system. Con-
versely, a fault in point-to-point or multi-terminal HVDC systems can reduce or completely
interrupt transmission capacity (CIGRÉ, 2018). Therefore, it is expected an increase in the
development of meshed HVDC systems in order to interconnect a wide variety of renewable
generation into the same HVDC grid and improve the power system reliability (CIGRÉ, 2013).
A natural strategy for developing meshed HVDC systems is to build on point-to-point
HVDC systems already in operation. These systems can be interconnected or connected to
new systems to be built, creating multi-terminal or meshed HVDC systems. However, building
a meshed HVDC grid can be more economical when compared with building multiple indi-
vidual point-to-point HVDC systems or an overlay HVAC system (CIGRÉ, 2013). The first
meshed systems are already implemented or under development (TANG et al., 2015; TANG et
al., 2019). Other planning or under development projects predict future expansions to meshed
HVDC systems. This is the case for the German HVDC corridors (THOMAS et al., 2016)
1.3. MOTIVATION AND OVERALL PROBLEM 5
and the HVDC offshore grids in the European North Seas (KOIVISTO; GEA-BERMÚDEZ;
SØRENSEN, 2020).
DC (Direct Current) transmission is more vulnerable to faults than AC (Alternating Current)
transmission due to low DC-side impedances and sensitive power electronics in the converters
(CHANG et al., 2017). Emergent protection solutions based on traveling waves, which have
presented several advantages on the AC transmission lines (COSTA et al., 2017), can han-
dle the DC protection challenges (WU et al., 2017). Moreover, the availability of the power
system can also be improved by accurate fault location since it reduces the maintenance staff
searching area and, consequently, the total time for the transmission line recovery. Fault loca-
tion methods based on traveling waves also presented a good performance for HVDC systems
(NANAYAKKARA; RAJAPAKSE; WACHAL, 2012).
The protection traditionally clears the fault by the AC-side circuit breakers for point-to-
point or multi-terminal HVDC systems. This strategy would lead healthy DC lines to be out
of operation for meshed HVDC grids. This would cause the loss of the advantage of higher
availability. For systems with full bridge converters, it is also possible to control the fault
current to zero. However, the power flow through healthy sections would also be interrupted for
a meshed system. A fully selective fault-clearing strategy could be performed through HVDC
circuit breakers at the line terminals. In this way, continuous operation of the HVDC meshed
grid would be ensured, as only the faulty section would be isolated. In addition, this would
minimize the constraints of the AC grid.
The differential protection of HVDC lines has a prolonged response time due to the telecom-
munication system. It is, therefore, mainly employed as protection for high-impedance faults
or as a backup. Thus, selective fault clearing would hardly be achieved on time for a meshed
system with several HVDC breakers (CIGRÉ, 2018). The protection of a meshed system could
hardly be based solely on communication-dependent functions at the risk of the short-circuit
current exceeding the threshold for opening the HVDC breaker. Therefore, it is necessary that
each station is able to determine if and which local HVDC breakers should be tripped using
only local measurements (CIGRÉ, 2018).
The sampling frequency effect can significantly influence the protection method based on
traveling waves, as demonstrated by Costa et al. (2017) for two-terminal methods. However,
this effect has not been evaluated to one-terminal techniques, as well as it was not evaluated
to HVDC system methods. Therefore, it is necessary to evaluate the influence of the sampling
frequency and to equate its effects in detecting the arrival time of the wavefronts in order to
develop one-terminal techniques to HVAC and HVDC transmission lines effectively.
1.3 Motivation and Overall Problem
The primary motivation for developing this work is reducing the protection operation time
since it results in a lower risk to the system components and greater power transmission capacity
through the transmission lines. Another relevant motivation is the need to analyze the effects
of the sampling frequency and its influence on the reliability of the protection, including the
definition of a protection zone, which facilitates its real-world application. The evaluation of
the effects of errors in the traveling wave velocity estimations is also a strong motivation for
developing this work since methods based on traveling waves usually present relevant sensitivity
to wave velocity variations.
For meshed HVDC systems, there is a demand for the development of faster protections than
those embedded in traditional point-to-point HVDC systems. Furthermore, with the inclusion
of several interconnected lines in the HVDC system, there is also a need for selectivity of
1.4. RESEARCH QUESTIONS 6
protection functions. Thus, with the natural evolution of HVDC systems to meshed topologies,
there is also a strong demand for fast and selective protection.
1.4 Research Questions
This thesis investigates research questions for HVAC/DC protection. Specifically, for AC
protection, they are:
1. Can traveling waves be used to speed up transmission line traditional protection?
2. Can protection zones be accurately defined regardless of traveling wave speed estimation
errors?
3. Can this traveling wave-based protection function be easily parameterized, independent
of the electrical parameters of the transmission lines?
For DC protection, they are:
1. Can traveling waves be used for meshed HVDC transmission line protection?
2. Can this protection function ensure full selectivity?
3. Can it operate within 2 ms according to foreseen CIGRE requirements?
1.5 Objectives
This work’s general objective is to develop one-terminal traveling wave-based protection
and fault location for both HVAC/DC transmission lines.
The specific objectives for HVAC protection are:
• development of a protection method based on modal traveling waves to avoid the need
for detection of wave reflections;
• development of a protection function based on the reflection of traveling waves indepen-
dent of telecommunication, but applied only to point-to-point systems.
The specific objective for HVDC protection is:
• evaluation of the applicability of distance protection based on modal traveling waves for
HVDC meshed systems.
1.6 Target Protection Functionalities
The target functionalities for the proposed wave-based HVAC transmission line protection
for earth faults are:
• no need for detection of wave reflections;
• protection operation time below 2 ms;
• precise definition of the protection zone;
• definition of allowed error margins for the wave velocity estimation;
• easy protection parametrization.
For the proposed HVAC transmission line protection based on the reflection of traveling
waves:
1.7. LITERATURE CONTRIBUTION 7
• application limited to a point-to-point transmission line;
• detection of the reflected traveling wave to avoid the need for telecommunication;
• precise definition of protection zones;
• no need for wave velocity estimation;
• low sampling frequency requirements, e.g., 6 and 15 kHz;
• easy protection parametrization.
For the proposed meshed HVDC transmission line protection:
• application limited to pole-to-ground faults;
• full selectivity only with local measurements and independent of the system topology;
• reliable definition of the protection zone;
• operation time below 2 ms;
• protection threshold parametrization independent of transmission line electrical parame-
ters and based only on simple detection of local transients;
• low sampling frequency requirements, e.g., 25 kHz, available in real HVDC systems.
1.7 Literature Contribution
The publications referent to this work and to works in a partnership are presented in Tables
1.1 and 1.2.
1.7. LITERATURE CONTRIBUTION 8
Table 1.1: Literature contribution for journal papers.
Journal/Event Title Authors
To be defined - 2023 Applicability of Wave-based
Distance Protection for Earth
Faults Applied to Meshed
HVDC Systems*
R. L. S. França, F. B. Costa,
K. Strunz, and F. V. Lopes
Electric Power Systems Re-
search - 2023
One-Terminal Traveling Wave-
Based Transmission Line Pro-
tection for LCC-HVDC Systems
F. B. Costa, R. L. S.
França, F. C. Silva Júnior,
K. Strunz, and A. D. Ra-
japakse
Journal of Control, Automa-
tion and Electrical Systems -
2022
A Meshed MMC-Based MTDC
System with Improved Voltage
Margin Control for Robustness
Towards Disturbances
M. S. Santos, L. S. Barros,
R. L. S. França, F. B. Costa,
and K. Strunz
Electric Power Systems Re-
search - 2021
Comprehensive Analysis of the
Fault Inception Angle Influ-
ence in Fault-induced Traveling
Waves
S. S. B. Azevedo, R. L. S.
França, J. T. L. S. Campos,
and F. B. Costa
International Journal of Elec-
trical Power & Energy Sys-
tems - 2020
Mathematical Development of
the Sampling Frequency Effects
for Improving the Two-terminal
Traveling Wave-based Fault Lo-
cation
F. B. Costa, F. V. Lopes, K.
M. Silva, K. M. C. Dan-
tas, R. L. S. França; M. M.
Leal, and R. L. A. Ribeiro
IEEE Transactions on Power
Delivery - 2020
Traveling Wave-Based Trans-
mission Line Earth Fault Dis-
tance Protection
R. L. S. França, F. C. Silva
Jr., T. R. Honorato, J. P. G.
Ribeiro, F. B. Costa, F. V.
Lopes, and K. Strunz
*To be submitted.
1.7. LITERATURE CONTRIBUTION 9
Table 1.2: Literature contribution for conference papers.
Journal/Event Title Authors
Workshop on Communica-
tion Networks and Power
Systems (WCNPS) - 2020
Performance Assessment of a
Wavelet-Based Differential Pro-
tection scheme in the Inter-Turn
Fault Detection in a Transformer
R. P. Medeiros, M. N. O.
Aires, R. L. S. França, and
F. B. Costa.
Brazilian Symposium on
Electrical Systems (SBSE) -
2020
Power Flow Analysis of MMC-
HVDC System with Margin
Voltage and Voltage Droop Con-
trol Strategies
M. S. Santos, L. S. Barros,
R. L. S. França, F. B. Costa,
and K. Strunz
XXIII Brazilian Congress on
Automation (CBA) - 2020
Analysis of an Eolic-
Photovoltaic Hybrid Generation
with Synchronverter for Fre-
quency and Voltage Supports in
a Microgrid
M. S. Santos, L. S. Bar-
ros, R. L. S. França, F. B.
Costa, C. M. V. Barros, and
K. Strunz
The International Conference
on Power Systems Transients
(IPST) - 2019
Experimental Test Bench for
Traveling-Wave-Based Methods
Evaluations
R. L. S. França, M. M.
Leal, M. S. R. Leal, M. R.
Marques, F. B. Costa, and
R. L. A. Ribeiro
Workshop on Communica-
tion Networks and Power
Systems (WCNPS) - 2018
Methodology to Perform Real-
Time Simulation of Power Sys-
tems Using a FPGA-based Plat-
form
M. S. R. Leal, L. D.
Simões, R. L. S. França, M.
M. Leal, F. B. Costa, and F.
E. Taveiros
Brazilian Congress of Auto-
matic (CBA) - 2018
Comparison of Traveling-Wave-
Based Fault Location Methods
for Transmission Lines of LCC-
HVDC Systems (Portuguese)
F. C. Silva Jr., F. B. Costa,
R. L. S. França, and D. M.
Silva
Brazilian Congress of Auto-
matic (CBA) - 2018
Influence of Fault Parameters
and Devices of LCC-HVDC
Transmission System Convert-
ers on Traveling Wave Detec-
tions (Portuguese)
F. C. Silva Jr., D. M. Silva,
R. L. S. França, and F. B.
Costa
IEEE PES General Meeting -
2018
Wavelet-Based Detection of
Transients Induced by DC
Faults Using Boundary Protec-
tion Principle
D. M. Silva, F. B. Costa, R.
L. S. França, and F. C. Silva
Jr.
Brazilian Symposium on
Electrical Systems (SBSE) -
2018
Graphical Interface to Aid in De-
velopment of Travelling-Wave-
Based Line Protection and Fault
Location Techniques
S. S. B. Azevedo, F. B.
Costa, M. S. R. Leal, R. L.
S. França
Brazilian Symposium on
Electrical Systems (SBSE) -
2018
Method for Fault Detection
on Transmission Lines of
HVDC-VSC Systems Using
High-Frequency Transients
D. M. Silva, F. B. Costa, R.
L. S. França, and F. C. Silva
Jr.
1.8. WORK METHODOLOGY 10
1.8 Work Methodology
This work has been carried out in compliance with the following methodology:
• a historical bibliographic review of the published protection and fault location methods
for transmission lines was carried out. Then, the state-of-the-art survey was carried out
on the latest and most relevant works on developing traveling wave methods for AC and
DC transmission lines.
• a mathematical investigation was developed in order to evaluate the effects of the sam-
pling frequency and the traveling wave velocity estimations resulting in: the development
of two AC one-terminal protection methods; one distance protection for meshed HVDC
systems;
• computational simulations were performed to evaluate all proposed methods;
• the performance of protection functions provided by a real SEL (Schweitzer Engineering
Laboratories)-T400L relay were utilized to evaluate the performance of the proposed AC
distance protection for earth faults.
1.9 Work Structure
This work is organized into eight chapters:
• Chapter 1: An introduction and the contextualization related to AC and DC transmission
line protection and fault location based on traveling waves are presented.
• Chapter 2: The state-of-the-art referring to the main techniques of protection and fault
location on AC transmission lines based on traveling waves is presented.
• Chapter 3: The basic theory of traveling waves is presented.
• Chapter 4: The principles of the one-terminal transmission line protection based on reflec-
tions of traveling waves and the problem of the detection of the traveling wave reflections
are presented.
• Chapter 5: A traveling wave-based AC transmission line earth fault distance protection is
proposed.
• Chapter 6: A method of AC transmission line protection based on the first reflection of
the traveling wave using one terminal is proposed.
• Chapter 7: A fault localization method using one terminal is proposed. Investigation of
the applicability and selectivity of the proposed distance protection applied to meshed
HVDC systems.
Chapter 2
State-of-the-Art
This chapter presents a survey of the state-of-the-art of traveling waves, emphasizing fault
location and transmission line protection methods using one and two terminals.
2.1 One-Terminal HVAC Traveling-Wave-Based Methods
The first paper to propose a transmission line protection method based on traveling waves
using one terminal was published by Crossley and McLaren (1983). The algorithm is based
on the principle of distance protection. The wave polarity of the first two waves that reach the
local terminal is required to determine fault directionality. The arrival instants of these waves
on the local terminal are used to estimate the fault location. Therefore, an internal fault may be
detected based on its location. The method depends on correctly detecting the wave reflected
from the fault point. It utilizes a cross-correlation technique in order to accomplish this task.
However, correctly detecting the wave reflected from the fault point is still challenging today.
The method also depends on the wave velocity estimation, which may lead to a protection
maloperation depending on the error in this estimation. The voltages measurement is required,
which is a limitation of the method due to the poor frequency response of the CCVT (Coupling
Capacitor Voltage Transformer) to high-frequency signals. Posteriorly, improvements on this
method were proposed by Rajendra and McLaren (1985). However, the main limitations could
not be suppressed.
Christopoulos, Thomas and Wright (1988) propose a one-terminal transmission-line dis-
tance protection method based on traveling waves, where the detection of the polarity of the
first wave on currents and voltages to reach the local bus are required in order to detect the
fault directionality. The fault location is estimated from the arrival instants of the first wave
to reach the local bus and its reflection from the fault point. The method requires estimating
the electrical parameter of the transmission line and measuring the amplitude of the waves in
the voltages to detect the correct wave reflected from the fault point. Therefore, errors in the
electrical parameters estimation and the poor frequency response of the CCVT are limitations
for the method in a field application.
A further investigation of the cross-correlation technique was carried out by Shehab-Eldin
and McLaren (1988). The paper demonstrated that the greater the window of the cross-correlation
function, the smaller the chances to distinguish between the wave reflected from the fault point
and the wave reflected from another discontinuity. Conversely, the smaller the window, the
greater the chances of a protection maloperation due to a non-fault transient. Therefore, the
paper proposed a composed correlation, where the sum between the output signals from a cor-
relation with a short window and another with a long one is performed. The proposed technique
can identify when an internal fault occurs very close to the local bus since a high DC (Direct
2.1. ONE-TERMINAL HVAC TRAVELING-WAVE-BASED METHODS 12
Current) component occurs in the output signal of the correlation. The method presents diffi-
culty in detecting traveling waves from low fault inception angles. However, a correction factor
dependent on the fault inception angle may be applied to the correlation signal, which improves
the detection ability of the method. The fault inception angle may be estimated. Despite the pro-
posed improvements to the cross-correlation technique, correctly detecting the wave reflected
from the fault point is still challenging today.
One of the first works to apply the wavelet transform to the electrical power system was
proposed in the late 1990s (MAGNAGO; ABUR, 1998). The paper proposed a one and two-
terminal fault location method based on traveling waves. The synchronized arrival instants of
the first wavefront to reach each line terminal are required to estimate the fault location. The
fault location may also be estimated by using one terminal. In order to do so, the amplitude
of the wavelet coefficients of the aerial and ground modal traveling waves in the voltage signal
is utilized to detect the correct wave reflected from the fault point. However, as currently well
known, the amplitude of the wavelet coefficients of the reflected waves strongly depends on the
electrical parameters of the monitored and adjacent transmission lines, fault resistance, fault in-
ception angle, and impedances connected to the line terminals. Therefore, the proposed method
may not apply to power systems other than the one in which it was evaluated. The method re-
quires wave velocity estimation, a source of errors, and data synchronization, which makes the
communication system more expensive. When using one terminal, the method requires voltage
measurements of successive reflected waves, which is a substantial limitation since the CCVT
presents a poor frequency response.
A one-terminal fault location method based on traveling waves was proposed by Abur and
Magnago (2000). The arrival instants of the aerial and ground mode traveling waves in the
local bus are required to determine if the fault is in the first or second half of the monitored
transmission line. In the local bus, the arrival instant detection of the aerial mode wave reflected
from the fault point is used to estimate the earth-fault location more precisely. Since there is
no ground mode traveling waves, the method can not distinguish if the fault was in the first or
second half of the line to phase-to-phase and three-phase faults. The wave velocity estimation
is required, a source of errors for the correct fault location estimation.
A traveling-wave-based transmission line directional protection method was proposed by
Chen et al. (2003). The work uses the modulus maxima technique for the detection of traveling
waves. The polarities of the first wavefront on the voltage and current signals are used to
determine the fault directionality. Chen et al. (2003) demonstrated that the effect of noise could
be mitigated by filtering the signal on more than one scale of the wavelet transform. However,
this procedure may result in a time delay in detecting the traveling waves. The paper proved that,
even with the use of CCVT in the measurement, the polarity detection of the first wavefront in
the voltage signal could be accomplished appropriately. Using the modulus maxima technique
provided robustness to the method even with noise. The method presents difficulties in detecting
traveling waves generated by faults with low inception angles, which can prevent the protection
for phase-to-ground faults.
Thomas et al. (2004) proposed a one-terminal traveling-wave-based transmission line fault
location method. The method provides fault pre-location information for methods based on
cross-correlation. The method applies the wavelet transform at various scales to the current
signal to furnish a signal with a precise detection of the traveling waves. The method does
not solve the problem of distinguishing the correct wavefront reflected from the fault point.
However, it can estimate two possible fault locations, nearest to the local bus or nearest to the
remote bus. Since the ideal definition of the cross-correlation window size requires the fault
location information, the pre-location estimation provided by the method proposed by Thomas
2.2. TWO-TERMINAL HVAC TRAVELING-WAVE-BASED METHODS 13
et al. (2004) facilitates the definition of this size. However, the window size cannot be precisely
defined since the method cannot determine if the fault occurred in the first or second half of
the transmission line. The method requires the detection of the two first wavefronts to reach
the local bus. It assumes that the second wavefront is reflected in the fault point or the remote
terminal of the monitored transmission line. Nevertheless, the method will not work properly if
a wave reflected from an adjacent line terminal reaches the local bus before the desired reflected
wave.
Lin et al. (2012) proposed a fault location method based on traveling waves using one ter-
minal. An evaluation of the variation of the modal parameters of the transmission line as a
function of the signal frequency was performed. It was demonstrated that the higher the travel-
ing wave frequency, the greater its velocity and the smaller its amplitude. It has been illustrated
that traveling waves suffer attenuation as they propagate along the transmission line. The paper
also demonstrated that the higher-frequency components that compose the traveling wave suffer
a more significant power attenuation, which makes them more challenging to be detected by a
high-frequency filter. The proposed method estimates the frequency of the detected traveling
wave. It estimates its propagation velocity as a function of the estimated frequency. Therefore,
a different wave propagation velocity is assumed for each wave to reach the local bus. Hence,
the fault location can be more precisely estimated. The method requires the polarity detection
of the two first wavefronts to reach the local bus to identify if the fault occurred on the first
or second half of the line. However, the polarities of the traveling waves vary according to
the system’s parameters, so different systems may have different wave polarity patterns, which
limits the application of the method. In addition, the method will not work correctly if the first
reflected wave to reach the local bus comes from an adjacent transmission line terminal.
2.2 Two-Terminal HVAC Traveling-Wave-Based Methods
One of the first works to investigate transmission line protection based on traveling waves
was developed by Chamia and Liberman (1978). A two-terminal transmission-line method
was proposed. The polarity behavior of the traveling waves in each terminal of the protected
transmission line was investigated in the voltage and current signals, considering the pre-fault
voltage signal for internal and external faults. It was demonstrated that the polarities of the
current and voltage traveling waves present different behavior depending on the measurement
position regarding the fault location. The proposed method can detect internal and external
faults and their directionality. However, since the method requires voltage measurement, its
application was limited by the still incipient signal processing methods available at that time,
which presented limitations in detecting the polarity of the traveling waves in voltage signals
due to the poor frequency response of the CCVT.
A method of directional protection for transmission lines using two terminals and based on
traveling waves was proposed by Johns (1980). The method detects the fault directionality at
each terminal of the protected transmission line and, after communication between the two re-
lays, an internal fault can be detected. The directionality of the fault is detected from an equation
whose variables are the amplitude data of the first wavefront on the voltage and current signals
and the characteristic impedance value of the protected line. Since the characteristic impedance
is a value that must be estimated typically from the physical data of the transmission line, this
is an error source. The amplitude data of the voltage and current waves depend on transducer
measurements, so if the transducer does not present a reliable high-frequency response, as in
the case of CCVT, the method may malfunction since the amplitudes of the signals will suffer
distortion.
2.2. TWO-TERMINAL HVAC TRAVELING-WAVE-BASED METHODS 14
Liu et al. (2012) proposed an earth-fault location method based on modal traveling waves
using multiple measurement points, at least two. From the difference between the arrival time
of the air and ground modal waves at each measurement point distributed along the line, the
method can estimate a mean fault location point according to the estimated velocities of the
traveling waves. The paper demonstrated that the propagation velocity of the ground-mode
traveling wave varies according to the fault location. To overcome this problem, the paper
proposes to computationally model the system and simulate several fault points along the line
to estimate the traveling wave velocity in the ground mode as a function of the fault location.
Although the method does not require synchronism, it requires several measuring points and a
communication system that connects all of them, which could make its implementation unfeasi-
ble. In addition, the method’s effectiveness in the field depends on the reliability of the existing
system computationally modeled.
A fault location method based on traveling waves using two terminals was proposed by
Lopes et al. (2015). Although the proposed method requires communication between the two
terminals of the monitored transmission line, it does not require data synchronization between
the relays, i.e., the line terminals do not need to be within the same time frame. The paper
investigates the latency in the processing and sending of data between the line terminals. Thus,
the method does not require the arrival time of the waves in each terminal, but rather the differ-
ence between the arrival times of the first wavefront in each terminal, thus making it possible
to locate a fault within the monitored transmission line. The method can locate faults in data
transmission situations with high latency variation.
Schweitzer et al. (2016) implemented in a real system a fault location method based on the
arrival instants of the traveling waves in the two terminals of the monitored transmission line.
The method uses a high-frequency filter technique known as differentiator-smoother, applied
to traveling wave detection since 1985. This technique uses an interpolation process that may
reduce the error in detecting the wave arrival instant due to the sampling process. For the im-
plementation of the method in the field, the traveling wave velocity was estimated based on the
wave propagation delay along the monitored transmission line, generated from the energization
of the remote bus of the monitored line. The reliability of the data synchronization strategy
limits the method.
A practical implementation of transmission line directional protection based on traveling
waves was developed and applied by Dong et al. (2016). The directionality of the fault is
identified by comparing the polarities of the modulus maxima of the first wavefront in the volt-
age signal with that of the current signal. The work mathematically evaluates the influence of
CCVT and CT (Current Transformer) on the measurement of traveling waves. It concludes that
the CT correctly measures the wave’s polarity for high frequencies and that the CCVT ade-
quately transfers the voltage to frequencies between 10 Hz and 2 kHz. However, this frequency
response cannot be accomplished by most commercial CCVT. Using two terminals, the method
can detect internal faults. A prototype was evaluated through laboratory tests and a real 750
kV transmission system. The method worked properly for sampling frequencies of 500 and 20
kHz.
Lopes (2016) developed a method of earth-fault location in transmission lines based on
modal traveling waves. The method uses the arrival times of the aerial and ground modal com-
ponents of the first wavefront of the current signal at each terminal of the monitored transmis-
sion line. From the ratio between the difference of the arrival times of the modal waves at each
terminal, the proposed method equates the percentage of the line where the fault occurred. The
method does not require any electrical parameters data of the power system or wave velocity
estimations. The method does not require any setting for the relay, which is a relevant improve-
2.2. TWO-TERMINAL HVAC TRAVELING-WAVE-BASED METHODS 15
ment for a field application since its installation in the power system can be easily performed.
The results demonstrated that errors do not influence the method in wave velocity estimation
and data synchronization. However, the method assumes that the velocity of the modal trav-
eling waves is constant during their propagation along the transmission line. This may not be
true, especially for the ground mode wave, which may suffer a more significant attenuation than
the aerial mode wave. Therefore, as with all methods based on traveling waves, the proposed
method presents susceptibility to errors for non-homogeneous transmission lines, i.e., when the
transmission line presents variations in its electrical parameter along its length.
Costa et al. (2017) proposed a transmission line protection method based on traveling waves
using two terminals in which the effect of the sampling frequency was evaluated, which im-
proved its reliability. The method requires the arrival time of the first wavefront in the current
signal to reach each terminal of the protected transmission line. It can detect internal faults and
the directionality of the external ones. The proposed method breaks the paradigm that methods
based on traveling waves require a very high sampling frequency, usually hundreds of kHz, and
presented good results at a sampling frequency of 20 kHz. The method equates zones inside
the protected line: a protection zone, where all the faults will be detected as internals; uncer-
tainty zones, where the faults may be or may not be detected as internals, depending on the
fault inception error; and unprotected zones, where faults will never be detected as internals.
For the method, the greater the sampling frequency, the greater the protected zone. In addition,
the method is independent of line electrical parameters estimation and does not require wave
velocity estimation. However, it is dependent on a synchronization system between the relays.
A method of differential protection of transmission lines based on traveling waves was pro-
posed by Tang et al. (2017). From the principle of superposition, the concept of equivalent
traveling waves was used, which are caused by the DC component of the sudden voltage that
appears in the fault point soon after the fault. The method applies the modulus maxima tech-
nique to the Dyadic wavelet transform of the current signals at each terminal of the monitored
transmission line. The modulus maxima data in each line terminal are sent from one to the
other. These data are used, in each terminal, in order to reconstruct the equivalent traveling
waves of the opposite terminal. Since only a few peak samples of the modulus maxima signal
are required, the data transmitted between the terminals is low. This is a significant contribution
since the high sampling frequency, normally required for the detection of the traveling waves,
would request higher storage capacity of the hardware and a more expensive communication
system between the line terminals. Each relay, connected to each terminal of the protected
transmission line, has the equivalent traveling wave signal relative to the terminal where it is in-
stalled and the equivalent traveling wave signal reconstructed from the opposite terminal. With
this, a differential equation is applied between the two signals to detect internal faults. The
method depends on the synchronization accuracy between the data of the two relays.
Namdari and Salehi (2017) proposed a transmission line protection method using two ter-
minals. A new high-frequency filter was proposed using morphological mathematics capable
of detecting traveling waves and their polarities. From the arrival time and polarity of the first
wavefront of the current signal to reach each terminal of the protected transmission line, the pro-
posed protection method can identify whether the fault was internal to the protected line and its
directionality. The paper demonstrated that the detection method was more efficient when com-
pared to the wavelet transform,. The protection method remained efficient even to fault cases
with high fault impedance and low fault inception angle. These factors negatively influence the
detection of traveling waves. However, the protection method depends on the wave velocity es-
timation, usually performed from the transmission line electrical parameter estimations, which
is a source of errors.
2.3. STATE-OF-THE-ART SUMMARY FOR HVAC METHODS 16
2.3 State-of-the-Art Summary for HVAC Methods
The state-of-the-art of HVAC methods investigated in this work, in chronological order, is
summarized in Tables 2.1 and 2.2, indicating the number of terminals used by the method, the
sampling frequency value adopted in the performance assessment of the method, the need for
parameter estimations of the monitored transmission line, the need for wave velocity estima-
tions, the need for wave polarity detections, the usage of the modal traveling waves, and, in case
of the two-terminal methods, the need for data synchronization.
Table 2.1: State-of-the-art summary for HVAC one-terminal methods.
Reference Objective Freq. Par. Wave Wave Modal
(kHz) Estim. Vel. Pol. Waves
Crossley and McLaren (1983) Protection - - √- -
Rajendra and McLaren (1985) Protection - - √- -
Christopoulos, Thomas and Wright (1988) Protection 25 √ √ √ -
Shehab-Eldin and McLaren (1988) Protection 14.25 - √- -
Magnago and Abur (1998) Fault Location 100 - √-√
Abur and Magnago (2000) Fault Location 303 - √-√
Chen et al. (2003) D. Protection 100 - - √-
Thomas et al. (2004) Fault Location 1.25×103-√- -
Lin et al. (2012) Fault Location 103√-√-
D. - Directional; Estim. - Estimations; Freq. - Sampling Frequency; Par. - Parameters; Pol. - Polarity; Vel. -
Velocity.
Table 2.2: State-of-the-art summary for HVAC two-terminal methods.
Reference Objective Freq. Par. Wave Data Wave Modal
(kHz) Estim. Vel. Sinc. Pol. Waves
Chamia and Liberman (1978) Protection - - - - √-
Johns (1980) Protection - √- - √-
Magnago and Abur (1998) Fault Location 100 - √ √ -√
Liu et al. (2012) Fault Location 103√ √ - - √
Lopes et al. (2015) Fault Location 20 - √- - -
Schweitzer et al. (2016) Fault Location 1.5.103-√ √ - -
Dong et al. (2016) Protection 500 √- - √-
Lopes (2016) Fault Location 100 - - - - √
Costa et al. (2017) Protection 4 - - √- -
Tang et al. (2017) Protection 250 - √ √ √ -
Namdari and Salehi (2017) Protection 103√ √ √ - -
Estim. - Estimations; Freq. - Sampling Frequency; Par. - Parameters; Pol. - Polarity; Sinc. - Synchronization;
Vel. - Velocity.
As shown in Table 2.1, few traveling-wave-based methods developed in recent years use
only one terminal. The last one-terminal transmission line protection method based on travel-
ing waves was proposed in 1988 (SHEHAB-ELDIN; MCLAREN, 1988). The main reason for
this is the great difficulty in correctly detecting the traveling wave reflected from the fault point,
a problem still under investigation by the scientific community. Some methods proposed along
the years (MAGNAGO; ABUR, 1998; ABUR; MAGNAGO, 2000; THOMAS et al., 2004; LIN
2.4. ONE-TERMINAL TRAVELING-WAVE-BASED METHODS FOR MESHED HVDC SYSTEMS17
et al., 2012) depend on the correct detection of the wave reflected from the fault point. How-
ever, their application is restricted to systems with certain conditions and can not be applied to
all transmission systems. From Table 2.2, most of the recently proposed methods of fault loca-
tion and transmission line protection based on traveling waves require measurements on both
terminals of the monitored transmission line. Only one paper (COSTA et al., 2017) analyzed
the effect of the sampling frequency on the effectiveness of the method, which improves its re-
liability. The same analysis has never been done in any one-terminal method based on traveling
waves. Some studies have used the earth modal traveling wave to extract additional informa-
tion from the fault conditions. However, none of them exploited such phenomenon applied to
transmission line protection. Therefore, it is necessary to investigate the effect of the sampling
frequency on a one-terminal transmission line protection method based on traveling waves, as
proposed in this thesis. In addition, the usage of the earth mode of the traveling wave may avoid
the need for detecting the correct traveling wave reflected from the fault point, which would
guarantee the reliability required by a protection method.
Many works have been devoted to the development of methods for detecting high-frequency
transients (COSTA; SOUZA; BRITO, 2010; LOPES; FERNANDES; NEVES, 2013; COSTA,
2014a; SCHWEITZER et al., 2016; NAMDARI; SALEHI, 2017), which have direct applica-
tions for protection based on traveling waves. Therefore, this thesis focuses only on developing
a transmission line protection method based on traveling waves without the objective of devel-
oping a high-frequency transient detection technique.
2.4 One-Terminal Traveling-Wave-Based Methods for Meshed
HVDC Systems
Li, Gong and Jiang (2018) proposed a fault directionality detection method based on the
polarity of the traveling waves. The method can detect the directionality of the fault with time
under 2 ms for transmission lines up to 200 km and a sampling frequency of 1 MHz. Lower
sampling frequencies, up to 50 kHz, have been tested. However, as noted by the authors, the
method’s reliability is higher for higher sampling frequencies. This may make the practical
implementation of the method more difficult. The method can be selective for faults applied on
different transmission lines for a meshed HVDC system. However, it requires communication
between stations. As discussed later in this thesis, the need for communication between stations
can be limiting for the protection of meshed HVDC systems.
Tang et al. (2019) proposed a one-terminal traveling wave-based protection method for a
meshed HVDC system. The method presented total selectivity with low protection operation
time, below 1.2 ms for a sampling frequency of 1 MHz and a fault distance of 183.5 km. This is
a possible sampling frequency for IEDs dedicated to implementing the method, as demonstrated
by the authors in the experimental results. However, in real systems, where each IED is respon-
sible for a vast amount of protection and control functionality, the sampling frequency adopted
is much lower, in the order of a few tens of kHz. The method considers boundary conditions
for a given system’s topology under study. However, the method was developed for boundary
conditions in which all transmission lines are connected to the system. Thus, if the system oper-
ates in a different topology, e.g., with a disconnected transmission line, the boundary conditions
change and the method can no longer be applied to the new topology.
Tong et al. (2019) proposed a distance protection method for earth faults in HVDC transmis-
sion lines. The proposed protection is capable of being selective for a meshed HVDC system
without the need for interstation communication. The method is based on the time difference
2.4. ONE-TERMINAL TRAVELING-WAVE-BASED METHODS FOR MESHED HVDC SYSTEMS18
between the arrival instants of the alpha and zero mode waves. The protection operation time
was below 5 ms even for a transmission line of 1000 km in length. However, as the authors state,
the minimum sampling frequency for the adopted test transmission system should not be less
than 110 kHz. The sampling frequency adopted for the parameterization of the protection was
200 kHz. These sampling frequency values are well above those currently adopted in existing
HVDC systems. This represents a limitation for the practical implementation of the method.
Sabug Jr. et al. (2020) proposed a boundary wavelet transform-based protection for meshed
HVDC systems. The method uses the real-time boundary wavelet transform (RT-BWT) to
compute the energy of transients measured by meters connected between the line inductor and
the line. Thus, the authors determine the faulty section by identifying the transients with the
highest energy. The method does not require communication between stations, i.e., it relies
only on local measurements. Simulation results have shown that the method can perform at a
low sampling frequency, 10 kHz. The method presented reliable operation within 7 ms for a
transmission line of 450 km in length. This operation time delay may not fulfill future speed
requirements for protecting meshed HVDC systems, as further discussed in this thesis. The
method is capable of being fully selective for system-wide faults. To do this, thresholds must be
defined by comparing the energy of transients for faults applied at various points in the system.
However, it is known that transients are strongly affected by the frequency response of the actual
meters installed in an existing system. Thus, it is impossible to establish whether the thresholds
set for transients presented in simulations would be in accordance with transients measured in
a real system. Furthermore, setting thresholds for the energy of fault transients in an existing
system would not be a trivial task.
Liu et al. (2021) proposed a protection method based on traveling wave simulation to de-
tect abrupt transients in a meshed HVDC system. The method applies the concept of median
absolute deviation on locally measured voltages and currents on each line connected to a given
station. The method can be selective for faults applied on all system lines, with operation time
below 2 ms for lines up to 200 km. The method was evaluated for a low sampling frequency
of 10 kHz. However, to parameterize the method to be fully selective, without communication
between stations, it is necessary to define thresholds for the transient variations at each station.
These thresholds are defined from comparisons of transients between stations. However, the
measurement setup installed in the real system strongly affects current and voltage transients.
Thus, the thresholds defined through simulation may not be sufficient for application in the real
system. Furthermore, setting these thresholds in a real system may not be feasible since real
faults must be applied.
Zhao et al. (2023) proposed a one-terminal method based on the rising time of the traveling
wave. The method presented an operating time below 2 ms for a 400 km transmission line.
Results showed that the method can perform for frequencies of 20 and 50 kHz, with low sen-
sitivity to the fault resistance. An important criterion for the correct detection of internal faults
to guarantee the method’s selectivity is the rising time of the traveling wave. This parameter
is defined analytically, considering the fault point and the transmission line parameters. Sim-
ulation results have shown that the rising time of the traveling wave for internal faults can be
reliably established analytically. However, the authors disregarded the effects that transducers
could have on the traveling wave measurement. Thus, the analytically calculated parameters
are not reliable enough to apply the method in actual systems.
2.5. STATE-OF-THE-ART SUMMARY FOR HVDC METHODS 19
2.5 State-of-the-Art Summary for HVDC Methods
The state-of-the-art of HVDC methods investigated in this work, in chronological order, is
summarized in Table 2.3. The table indicates the minimum sampling frequency used by the
method, the protection speed, the longest line length on which the method has been tested,
whether modal waves are used, whether there is a need for communication between the stations
in order to have full selectivity of the method and the level of difficulty for the selectivity
strategy to be applicable in actual systems.
Table 2.3: State-of-the-art summary for HVDC methods.
Reference Samp. Frequency Prot. Speed Length Modal Tel. Selectivity
(kHz) (ms) (km) Waves Applicability
Li, Gong and Jiang (2018) 50 2 200 - √Easy
Tang et al. (2019) 1000 1.2 183.5 - - Medium
Tong et al. (2019) 200 5 1000 √- Easy
Sabug Jr. et al. (2020) 10 7 450 - - Hard
Liu et al. (2021) 10 2 200 - - Hard
Zhao et al. (2023) 20 2 400 - - Hard
Samp. - Sampling; Prot. - Protection; Tel. - Telecommunication.
Table 2.3 points out important factors for the applicability of the methods in actual systems.
Methods with sampling frequencies up to 50 kHz are in accordance with protection methods ap-
plied in actual HVDC systems. Thus, methods that require higher sampling frequencies would
be more difficult and costly to apply in actual systems. As discussed later in this thesis, the op-
timal time for protection operation is below 2 ms. However, since commercial protections can
operate below 2 ms without selectivity, there is still an important contribution if the proposed
method is capable of being selective within 5 ms. This is the estimated time for fault clearing in
meshed HVDC systems. Some methods can operate below 2 ms with low sampling frequency
but have practical limitations to be selective in actual systems. One method presents low op-
eration time at low sampling frequency. However, it requires communication between stations
to be selective, which will make its operation time infeasible for meshed HVDC systems, as
discussed later in this thesis. One method uses modal waves to decrease its complexity for
application in actual systems with short operation times. However, it requires a high sampling
frequency.
Neither method simultaneously meets the best requirements for applicability in actual meshed
HVDC systems. That is, fast operation, low sampling frequency, and easy selectivity strategy to
implement in actual systems. None of the methods investigated the effect of sampling frequency
on the protection. Such investigation can ensure reliability to the protection at a low sampling
frequency. The investigation of the effect of sampling frequency associated with the use of
modal waves has the potential to ensure the development of a method that is easy to implement
in real systems without the need for communication between stations for earth faults.
Chapter 3
Basic Theory of the Traveling Waves
This chapter presents the principles of the traveling waves theory in single-phase transmis-
sion lines, highlighting the basic equation of the transmission line model and the wave propa-
gation equations in discontinuities.
3.1 Transmission Line Equations
As presented by Araújo and Neves (2005), for a given transmission line with inductance L,
capacitance C, resistance R, and conductance G, all per unit length, the time domain transmis-
sion line equations are given by:
−∂u(x,t)
∂x=Ri(x,t)+L∂i(x,t)
∂t,(3.1)
−∂i(x,t)
∂x=Gu(x,t)+C∂u(x,t)
∂t,(3.2)
where u(x,t)and i(x,t)are the voltage and current in the line at instant tand position x. In the
frequency domain, the equations of the transmission line become:
−∂U(x,s)
∂x= (R+sL)I(x,s),(3.3)
−∂I(x,s)
∂x= (G+sC)U(x,s),(3.4)
where U(x,s)eI(x,s)are, respectively, the Laplace transform of u(x,t)and i(x,t).
From the transmission line equations, the wave equations are:
∂2U(x,s)
∂x2=γ2U(x,s),(3.5)
∂2I(x,s)
∂x2=γ2I(x,s),(3.6)
where γis the propagation constant of the transmission line, given by
γ=√︁(R+sL)(G+sC) = α+jβ,(3.7)
composed of a real part (α), called line attenuation constant, and an imaginary part (β), called
line phase constant.
3.2. WAVE PROPAGATION IN DISCONTINUITIES 21
The general solution of the wave equations (3.5) and (3.6) results in:
U(x,s) = U0+e−γx+U0−eγx,(3.8)
I(x,s) = I0+e−γx+I0−eγx,(3.9)
where e−γxrepresents the wave propagation in the positive direction of x, and eγxrepresents the
wave propagation in the negative direction of x. From the general solution of the wave equations
U0+
I0+=−U0−
I0−=Z0,(3.10)
where Z0is the characteristic impedance of the transmission line, given by
Z0=√︄(R+sL)
(G+sC).(3.11)
Therefore, the equation (3.9) can be rewritten as
I(x,s) = U0+
Z0e−γx−U0−
Z0eγx.(3.12)
Considering a lossless transmission line (R=G=0), γ=s√LC eZ0=√︁L/C, the equations
(3.8) and (3.12) become:
U(x,s) = U0+e−s
ux+U0−es
ux,(3.13)
I(x,s) = U0+
Z0e−s
ux−U0−
Z0es
ux,(3.14)
where uis the wave velocity propagation, given by
v=1
√LC.(3.15)
3.2 Wave Propagation in Discontinuities
Figure 3.1 depicts a power system with two transmission lines, line 1 and line 2, with distinct
characteristic impedances (Z1=Z2), with a relay installed between them. There is a fault in line
1 and the occurrence of traveling waves. Some of their respective reflections and refractions at
the discontinuity points are represented in the Lattice diagram. In the Lattice diagram, the
arrival time of the first wave to reach the bus 2 is also illustrated. It is represented by t2
1and
some of the other arrival times in all buses. The propagation times of a traveling wave along
transmission lines 1 and 2 are, respectively, τ1and τ2.
3.2.1 Reflections and Refractions of the Wave
When a fault occurs on line 1, traveling waves in voltages and currents (u1and i1) propa-
gate along both directions of the line from the fault point. As demonstrated by Christopoulos,
Thomas and Wright (1988), the amplitudes of these waves are given by:
u1=−Z1
Z1+2Rf
uf,(3.16)
3.2. WAVE PROPAGATION IN DISCONTINUITIES 22
Fault
Time (s)
Line 2 (Z )2,
u , i
1 1
u , i
t1
u , i
r1
u , i
s1
u , i
r2
u , i
t2 t2
u , i
1 1
u , i
s2 s2
u , i
r3 r3
u , i
t3 t3
Relay
Bus 3 Bus 1 Bus 2
t1
2
t2
2
t1
1
t2
1
t1
3
t2
3
2Line 1 (Z )1,1
s1
t1
r1
r2
Figure 3.1: Lattice diagram of the traveling waves for a fault.
i1=−u1
Z1=1
Z1+2Rf
uf,(3.17)
where Rfis the fault resistance, ufis the instantaneous voltage at the fault point at the fault
instant, and Z1is the characteristic impedance of line 1.
Traveling waves in the voltage and current signals u1and i1propagate towards line 2 and,
when reaching bus 1, suffer reflection (ur1eir1) and refraction (ut1eit1). The reflected waves
propagate back toward the fault point, and the refracted waves follow along line 2. As demon-
strated by Bewley (1931), the reflected waves are given by:
ur1=Γr1(U)u1,(3.18)
ir1=Γr1(I)i1,(3.19)
where Γr1(U)is the reflection coefficient of the wave in the voltage signal, given by
Γr1(U)=Z2−Z1
Z2+Z1,(3.20)
and Γr1(I)is the reflection coefficient of the wave in the current signal, given by
Γr1(I)=−Γr1(U)=Z1−Z2
Z1+Z2,(3.21)
whereas the refracted waves are given by:
ut1=Γt1(U)u1,(3.22)
it1=Γt1(I)i1,(3.23)
where Γt1(U)is the refraction coefficient of the wave in the voltage signal, given by
Γt1(U)=1+Γr1(U)=2Z2
Z1+Z2,(3.24)
3.2. WAVE PROPAGATION IN DISCONTINUITIES 23
and Γt1(I)is the refraction coefficient of the wave in the current signal, given by
Γt1(I)=1+Γr1(I)=2Z1
Z1+Z2.(3.25)
The reflected waves in bus 1 (ur1and ir1) propagate back toward the fault point. When
reaching the discontinuity point of the fault, new reflected waves (ur2and ir2) and refracted
waves (ut2and it2) arise. The reflected and refracted voltage waves at the fault point are given
by:
ur2=Γr2(U)ur1,(3.26)
ut2=Γt2(U)ur1,(3.27)
where Γr2(U)is the reflection coefficient of the wave in the voltage signal, given by
Γr2(U)=
Z1Rf
Z1+Rf−Z1
Z1Rf
Z1+Rf+Z1
,(3.28)
and Γt2(U)is the refraction coefficient of the wave in the voltage signal, given by
Γt2(2)=
2Z1Rf
Z1+Rf
Z1Rf
Z1+Rf+Z1
.(3.29)
The current waves reflected and refracted at the fault point along the remainder of the line
are given by:
ir2=Γr2(I)ir1,(3.30)
it2=Γt2(I)ir1,(3.31)
where Γr2(I)is the reflection coefficient of the wave in the current signal, given by
Γr2(I)=−Γr2(U)=
Z1−Z1Rf
Z1+Rf
Z1+Z1Rf
Z1+Rf
,(3.32)
and Γt2(I)is the refraction coefficient of the wave in the current signal that propagates toward
the rest of the line, given by
Γt2(I)=2Rf
Z1+2Rf
.(3.33)
According to Christopoulos, Thomas and Wright (1988), a relay installed in the bus 1 is not
able to measure the incident waves (u1and i1) and the reflected waves (ur1eir1) separately. As
the relay is normally installed a few meters from the bus, when a traveling wave reaches the
relay at speed close to the speed of light, its reflection occurs soon after. In this way, when a
traveling wave reaches the bus, due to the sampling process, the signal collected by the relay
is the sum between the incident and reflected waves in the bus. The traveling wave equations
measured by the relay are given by:
us1=u1+ur1=u1(1+Γr1(U)) = 2Z2u1
Z2+Z1,(3.34)
3.3. MODAL COMPONENTS 24
is1=i1+ir1=i1(1+Γr1(I)) = −2u1
Z2+Z1.(3.35)
3.3 Modal Components
In studying traveling waves in transmission lines, it is important to analyze the voltage
and current signals considering the electromagnetic coupling between the phases. Thus, for
studying traveling waves, the voltage and current signals measured on phase components should
be transformed into independent modal components. Clarke’s transformation (CLARKE, 1938)
can be used for this purpose. The matrix adopted for Clarke’s transformation was the same
published by Namdari and Salehi (2017), as follows:
⎡
⎣
u0
uα
uβ⎤
⎦=⎡
⎢
⎣
1 1 1
√2−1
√2−1
√2
0√3
√2−√3
√2
⎤
⎥
⎦⎡
⎣
uA
uB
uC⎤
⎦(3.36)
and
⎡
⎣
i0
iα
iβ⎤
⎦=⎡
⎢
⎣
1 1 1
√2−1
√2−1
√2
0√3
√2−√3
√2
⎤
⎥
⎦⎡
⎣
iA
iB
iC⎤
⎦,(3.37)
where uA,uB,uC,iA,iB, and iCare the voltages and currents in the phase domain; u0,uα,uβ,i0,
iα, and iβare the voltages and currents in zero, alpha, and beta modal components, respectively.
In this way, each modal component behaves as a single-phase circuit signal. This work will
always analyze the traveling waves in the alpha or zero mode signals.
Similarly, during a fault transient, a bipolar or symmetric monopolar HVDC system can be
seen as a two-phase system. Thus, it is possible to apply a modal decoupling transformation
designed for two-phase systems to these systems (FERNANDES et al., 2020). This thesis will
apply the Karrenbauer transformation to the voltages and currents of HVDC systems. The
modal components of the Karrenbauer transformation are given by:
[︃u0
uα]︃=1
2[︃1 1
1−1]︃[︃u+
u−]︃,(3.38)
and [︃i0
iα]︃=1
2[︃1 1
1−1]︃[︃i+
i−]︃,(3.39)
where u+and u−are the positive and negative pole voltages; i+and i−are the positive and
negative pole currents; u0,uαi0, and iαare the voltages and currents in zero and alpha modal
components, respectively.
3.4 Chapter Synthesis
In this chapter, the theoretical basis of traveling waves was presented, and the equations of
the single-phase transmission line model were demonstrated. The line equations, the character-
istic impedance of the line, and the traveling wave velocity to a lossless line were deducted.
The propagation equations of the traveling waves along the transmission line were also
presented. The reflection and refraction equations of the waves in the fault point and the line
3.4. CHAPTER SYNTHESIS 25
connections were demonstrated. It also presented the equations of the waves seen by a relay
installed between two transmission lines. Finally, a brief discussion was held on modal traveling
waves.
The simplified analysis presented in this chapter is sufficient for understanding the methods
proposed in this thesis, and it is possible to find a more detailed theory of traveling waves in
Zanetta Jr. (2003).
Chapter 4
Principles of the One-Terminal
Transmission Line Protection Based on
Reflections of the Traveling Waves
This chapter presents the principles of one-terminal transmission line protection based on
reflections of traveling waves. It also presents the main problems identified for correctly de-
tecting the traveling wave reflected from the fault point, an issue still under investigation by the
scientific community.
4.1 Traveling Wave Reflections
Figure 4.1 depicts the general behavior of traveling wave reflections. When a fault occurs on
the transmission line, traveling waves propagate toward the line terminals, suffering reflection
and refraction. The reflected waves propagate back toward the fault point, whereas the refracted
waves propagate toward the terminal of an adjacent transmission line. New reflections and
refractions occur when the traveling waves reach the fault point or other line terminals. A relay
may detect traveling waves that reach a terminal of the protected transmission line and identify
whether an internal fault occurred on the protected line. As detailed in the following sections,
internal fault detection can be performed from detecting the arrival instants of the traveling
waves on one terminal of the protected transmission line.
4.1.1 Traveling Wave Reflections for a Simple Line
Figure 4.2 depicts a fault in the first half of a simple line (without adjacent lines), with a
fault inception time tFand distanced dFfrom the local bus, where dF=dxand dF<l/2. Thus,
the second wavefront will always come from a reflection at the fault point, so the propagation
times of the first and second wavefronts are given respectively by:
τF1=tF1−tF=tF2−tF1
2=dF
v,(4.1)
τF2=tF2−tF= (tF2−tF1)3
2=3dF
v,(4.2)
where vis the speed of the traveling wave; tF1and tF2are the arrival times of the first and second
wavefronts, respectively, at the local bus.
Figure 4.3 depicts a fault in the second half of the line (dF>l/2), distanced dxfrom the
26
4.1. TRAVELING WAVE REFLECTIONS 27
Protected line
Internal fault
Trip
Time (s)
Traveling wave
Fault inception
Traveling wave
Traveling waves
Refracted wave
Reflected wave
First wavefront
Wavefront
Relay
Figure 4.1: General behavior of the traveling wave reflections.
Internal fault
Time (s)
tF
Local bus Protected line with kml
dl d-
FF
Remote bus
tF1
tF2
tF3
= dx
F1
F2
Relay
Trip
Figure 4.2: Lattice diagram to a fault in the first half of the transmission line.
remote bus and dFfrom the local bus, where dF=l−dx. Therefore, the second wavefront will
always come from a reflection on the remote bus. Thus, the propagation times of the first and
second wavefronts are given respectively by:
τF1=tF1−tF=l
v−tF2−tF1
2=dF
v,(4.3)
τF2=tF2−tF=l
v+tF2−tF1
2=2l−dF
v.(4.4)
According to equation (4.1), the distance between the local bus and a fault in the first half
of the line is given by
dF=dx= (tF1−tF)v=(tF2−tF1)v
2,(4.5)
whereas, according to the equation (4.3), the distance between the local bus and a fault in the
4.1. TRAVELING WAVE REFLECTIONS 28
Internal fault
Time (s)
tF
Local bus Protected line with kml
d
dx
F
Remote bus
tF1
tF2
= l - dx
F1
F2
Relay
Trip
Figure 4.3: Lattice diagram to a fault in the second half of the transmission line.
second half of the line is given by
dF=l−dx= (tF1−tF)v=l−(tF2−tF1)v
2.(4.6)
From the equations (4.5) and (4.6), for two distinct faults, one in the first half of the line, at
a distance dxfrom the local bus, and the other in the second half of the line, distanced dxfrom
the remote bus and l−dxfrom the local bus, the difference between the arrival times of the
first and second wavefronts (tF2−tF1) are equal. Therefore, at first, it would not be possible to
identify whether a fault occurred on the first or second half of the transmission line only from
the arrival times of the traveling waves.
The propagation time of the traveling wave along the entire transmission line (transit time)
with length lis given by
τ=l
v.(4.7)
For faults in the first half of the line, the difference between the arrival times of the first
and second wavefronts in the local bus is less than one transit time since the arrival time of
the second wavefront is due to the reflected wave from the fault point (Figure 4.2). Regarding
the faults in the second half of the line, the difference between the arrival times of the first and
second wavefronts in the local bus is also smaller than one transit time since the arrival time of
the second wavefront is due to the reflected wave from the remote bus of the transmission line
(Figure 4.3). The maximum difference between the arrival times of the first two wavefronts on
the local bus occurs for a fault in the middle of the line. Therefore, internal faults are detected
if
tF2−tF1≤l
v.(4.8)
Figure 4.4 depicts a fault exactly on the remote bus (external fault). In this situation, the
first wavefront will reach the local bus after a transit time τand will be reflected back toward
the remote bus, where it will undergo further reflection and propagate again toward the local
bar. Therefore, the difference between the arrival times of the first and second wavefronts, due
4.1. TRAVELING WAVE REFLECTIONS 29
to a fault in the remote bus, is given by
tF2−tF1=2l
v.(4.9)
For a fault exactly in the local bus, the time difference between the first and second wave-
fronts is also given by the equation (4.9).
External fault
Time (s)
tF
Local bus Protected line with kml
l d=F
Remote bus
tF1
tF2
Relay
Trip
Figure 4.4: Lattice diagram for a fault on the remote bus.
According to equations (4.8) and (4.9), the difference between the arrival times of the first
two wavefronts will never be in the range l/v<tF2−tF1<(2l)/v. It is possible to adopt a
threshold for detecting internal faults with no detriment to the protection method, considering
only the continuous time domain. Therefore, it is proposed that an internal fault is detected if
tF2−tF1≤ql
v,(4.10)
where qis a threshold to ensure that an internal fault is properly differentiated from an external
fault, attending to
l
v≤ql
v<2l
v,(4.11)
where 1 ≤q<2.
4.1.2 Traveling Wave Reflections Including Adjacent Lines
The protection scheme must distinguish between internal and external faults to avoid a false
trip due to a fault outside the protected line. Traditionally, the two-terminal methods based
on traveling waves require only the first wavefront to reach each terminal of the monitored
transmission line, i.e., wave reflections are not required. However, more than the first wavefront
is required for the correct protection performance for one-terminal methods based on traveling
4.1. TRAVELING WAVE REFLECTIONS 30
waves. Therefore, the protection scheme reliability of one-terminal methods is dependent on
the reliability of the correct detection of the reflected traveling waves.
Figure 4.5 depicts an upstream external fault on the external line A, lAlong, distanced dx<l
from the local bus of the protected line. In this fault configuration, the difference between the
arrival times of the first two wavefronts to reach the local bus is less than twice the transit
time of a traveling wave along the protected line (tF2−tF1= (2l)/v). Thus, the equation (4.9)
is not respected, i.e., an external fault would be identified as internal, leading to a protection
maloperation.
Protected line
External fault
Time (s)
External line BExternal line A
dx
tF
tF1
tF2
Relay
Trip
Figure 4.5: Lattice diagram for an upstream external fault.
The same occurs for a reverse external fault, on the external line B, lBlong, distanced dx<l
from the remote bus of the protected line (Figure 4.6). Therefore, the difference between the
arrival times of the first two traveling wavefronts can be the same for at least four different fault
scenarios: internal fault at a distance dx<l/2 from the local bus of the protected line (Figure
4.2); internal fault at a distance dx<l/2 from the remote bus of the protected line (Figure 4.2);
external fault at a distance dx<lfrom the local bus of the protected line (Figure 4.5); external
fault at a distance dx<lfrom the remote bus of the protected line (Figure 4.6). Therefore, any
one-terminal transmission line protection scheme based on traveling waves has to distinguish
such fault situations to avoid that external faults being confused with internal ones. A solution
to this problem would be the correct detection of the traveling wave reflected from the fault
point.
Figure 4.7 depicts another possible situation that could lead to a protection maloperation: a
reverse external fault considering the upstream external line (line A) smaller than the protected
line (lA<l). In this situation, the instant tF2would be relative to a traveling wave reflected from
the terminal end of the external line A, whereas the reflected wave from the remote bus of the
protected line would reach the local bus at the instant tF3. Therefore, an external fault would
sensitize the protection.
Figure 4.8 depicts an internal fault distanced dFfrom the local bus, where dF>l. The
second traveling wave to reach the local bus comes from a reflection at the terminal end of the
external line A. Despite this situation does not lead to a protection maloperation, it could lead
to errors in the fault location estimation based on traveling waves.
Several works have proposed techniques to detect the correct wave reflected from the fault
point. Cross-correlation was the first strategy applied to the problem (CROSSLEY; MCLAREN,
4.1. TRAVELING WAVE REFLECTIONS 31
Protected line
External fault
Time (s)
External line BExternal line A
dx
tF
tF1
tF2
Relay
Trip
Figure 4.6: Lattice diagram for a reverse external fault.
Time (s)
External
line A
tF
tF1
tF2
Local
bus Protected line
l
Remote
bus
l < l
A
External
fault
tF3
External
line B
Relay
Trip
Figure 4.7: Lattice diagram for a reverse external fault, considering the upstream external line
smaller than the protected line.
1983). However, as mentioned by Magnago and Abur (1998), this technique depends on the cor-
rect correlation window size definition, which depends on the fault location, which is unknown
information. In order to mitigate the problem of defining the correlation window size, Shehab-
Eldin and McLaren (1988) proposed a method that combines short and long window sizes.
Christopoulos, Thomas and Wright (1988) proposed a method based on the amplitude of the
traveling waves to detect the correct wave reflected from the fault point. However, the method
depends on the correct line parameter estimations, a source of errors. The polarities of the
traveling waves were also investigated to solve this problem (DONG; GE; XU, 1999; KALE;
BHIDE; BEDEKAR, 2012). However, the polarities of the traveling waves vary according to
system parameters so that different systems may have different wave polarity patterns. None
of the existing techniques was consolidated as a feasible and reliable solution for detecting
the correct wave reflection in real-world fault cases. Therefore, this is a problem still under
investigation by the scientific community.
4.1. TRAVELING WAVE REFLECTIONS 32
Time (s)
External line A
tF
tF1
tF2
Local bus Protected line
dF
Remote bus
l < dF
Internal fault
tF3
Relay
Trip
Figure 4.8: Lattice diagram for an internal fault, considering the upstream external line smaller
than dF.
4.1.3 Chapter Synthesis
This chapter presented the principles of one-terminal transmission line protection based
on reflections of traveling waves. The main problems regarding detecting the traveling waves
reflected in the singularity points were discussed. As presented, the difficulty in distinguishing
the traveling wave reflected in the fault point from the ones reflected in other singularity points
is a strong limitation for the one-terminal methods based on the reflections of the traveling
waves.
Chapter 5
The Proposed Traveling Wave-Based
Earth Fault Distance Protection for HVAC
Transmission Lines
Most of this chapter was published in França et al. (2020). The work is licensed under a Cre-
ative Commons Attribution 4.0 License. For more information, see <https://creativecommons.
org/licenses/by/4.0/>.
A traveling wave-based earth fault distance AC protection method (FRANÇA et al., 2020)
is proposed in this chapter. The proposed method requires only the modal components of the
first wavefront, i.e., detecting traveling wave reflections is not required. However, the method
is valid only for earth faults.
5.1 Principles of the Proposed TW-Based Distance Protec-
tion Relay
Fig. 5.1 depicts the Bewley diagram and the arrival times of earth-fault-induced α- and 0-
mode TWs, with fault inception time at tF, at a distance dFaway from the local bus and l−dF
away from the remote bus on a line of length equal to l. Fig. 5.1 also depicts the proposed
TW21G protection operation logic.
Considering that the α-mode propagation velocity is greater than the 0-mode one on over-
head lines (vα>v0) (LIU et al., 2012), the α-mode wave reaches the local bus before the 0-mode
one (Fig. 5.1). The relay, positioned at the local bus, samples voltages and currents at a fixed
sampling frequency fS, so the wavefront arrival times in the continuous-time domain (tαand t0)
are unknown and replaced by respective detectable discrete wavefront arrival times, i.e., kα/fS
and k0/fS, where kαand k0are samples that represent tαand t0in the digital time domain,
respectively. The continuous reference time tFgives the true fault inception time. It is also re-
placed by its discrete version kF/fS, where both tFand kF/fSare unknown. Thus, the proposed
TW21G function only requires kαand k0, i.e., it does not require the detection of reflections.
In this chapter, the detection of the discrete wavefront arrival times kα/fSand k0/fSis
carried out by using the DS (differentiator-smoother) filter (SCHWEITZER et al., 2016) in the
currents. This is a TW filtering method used in a commercially available relay. It provides
the relevant information to the proposed TW21G function (Fig. 5.1). Even so, other existing
methods could be alternatively used, such as those based on the wavelet transform (SILVA et
al., 2019; COSTA, 2014a; COSTA, 2014b).
The proposed TW21G function requires auxiliary overcurrent and directional supervision
functions to avoid protection maloperation in non-fault situations and reverse faults. Combining
33
5.1. PRINCIPLES OF THE PROPOSED TW-BASED DISTANCE PROTECTION RELAY34
Internal earth fault
Time (s)
α-mode
tF
W alavefront arriv
discrete time
k f/S
F
Sampling
time
Local bus Remote busProtected line with kml
dd l d= -
FFF
0-mode
t0
k f/S
0
k f/S
t
Trip
α
α
Relay
Directional supervision
Overcurrent supervision (OC21)
kαand k0detection (DS filter)
The proposed TW21G
distance protection
k0kα
- <
Other distance
protections
(e.g., TD21)
The proposed distance
function (TW21G)
Yes
1/fS
1/fS
1/fS
TD32
TW32
lf mS´
Figure 5.1: Protection logic using the proposed traveling wave-based distance earth fault pro-
tection function TW21G and the Bewley diagram.
the proposed TW21G function with overcurrent and directional supervision functions yields the
proposed TW21G distance protection. This work considers an OR (∪) operation between the
time domain directional function (TD32) (SCHWEITZER et al., 2015) and the TW directional
function (TW32) (SCHWEITZER et al., 2015) as the directional supervision element, as well as
the time-domain overcurrent function (OC21) (SCHWEITZER et al., 2015) as the overcurrent
supervision function. These auxiliary functions were chosen because they are commercially
available in actual relays for high-speed protection. Nevertheless, other existing fast overcurrent
and directional functions could be used. Therefore, the proposed TW21G distance protection
performs the following logic TW21G ∩OC21 ∩(TD32 ∪TW32) (Fig. 5.1), where ∩is an
AND operation. In addition, the proposed distance protection can run in parallel with any
existing fast distance protection such as the TD21 protection (SCHWEITZER et al., 2015) (Fig.
5.1) in order to accelerate the protection operation.
The proposed TW21G distance protection includes the voltage TW detection due to the
usage of the TW32 function. As well known, in real systems, the poor high-frequency response
of the Coupling capacitor voltage transformer (CCVT) can impair the voltage TW detection.
Nevertheless, thanks to the added TD32 function, which does not require TW detection, the
directional supervision element in the proposed TW21G distance protection can operate even
when the TW32 function cannot.
5.2. THE PROPOSED TW21G FUNCTION 35
5.2 The Proposed TW21G Function
The proposed TW21G function is derived by considering the sampling frequency effects,
accommodating errors in estimated modal traveling wave velocities. To do so, a detailed anal-
ysis of these aspects is performed, as addressed next.
5.2.1 Sampling Frequency Effects
The true arrival times of the first modal TWs to reach the local bus in the continuous-time
domain, tαand t0, are unknown due to the sampling process. However, these instants are re-
placed by their counterparts kα/fSand k0/fSin the discrete-time domain in practical applica-
tions considering an IED (Intelligent Electronic Device), such as a protective relay. Therefore,
the sampling frequency effects must be considered in traveling-wave-based protection functions
(COSTA et al., 2017).
The discrete fault inception time kF/fSis defined in Fig. 5.1 as the reference time and is the
first sampling instant following the continuous true fault inception time tF, given by:
kF
fS=⌊tFfS⌋
fS+1
fS,(5.1)
where ⌊∗⌋returns the largest integer value not greater than ∗.
The error in the discrete fault inception time corresponds to the time difference between the
discrete and continuous fault inception times as follows:
εF=kF
fS−tF,(5.2)
where 0 ≤εF<1/fS, i.e., εFis lower than a sampling interval.
The discrete arrival time of the α-mode TW is given by:
kα
fS=⌊tαfS⌋
fS+1
fS,(5.3)
which is the sampling instant following the true arrival time in the continuous-time domain of
the α-mode TW at the local bus.
Similarly to εF, the error related to the discrete arrival time of the first incident α-mode TW
at the local bus is given by:
εα=kα
fS−tα,(5.4)
where 0 ≤εα<1/fS. Therefore, from (5.2) and (5.4), the total error for the α-component is
obtained as:
εFα=εα−εF=kα−kF
fS−(tα−tF),(5.5)
where −1/fS≤εFα<1/fS.
From (5.2), (5.4), and (5.5), considering a fault at the remote bus (dF=l), the number of
samples covered by the α-mode TW to travel across the line from the fault point to the local bus
is represented by:
kα−kF=(︃dF
vα
+εFα)︃fS,(5.6)
5.2. THE PROPOSED TW21G FUNCTION 36
where vαis the actual α-mode propagation velocity, given by:
vα=dF
tα−tF.(5.7)
The development for the 0-mode component follows the same steps as for the α-mode com-
ponent. Therefore, replacing αby 0 yields:
k0−kF=(︃dF
v0+εF0)︃fS,(5.8)
where v0is the actual 0-mode propagation velocity, given by:
v0=dF
t0−tF.(5.9)
From (5.6) and (5.8):
k0−kα=dFfSm+(ε0−εα)fS,(5.10)
where mis a variable dependent on actual modal TW propagation velocities defined as follows
(LIU et al., 2012):
m=vα−v0
vαv0.(5.11)
Knowing that 0 ≤εα<1/fS, 0 ≤ε0<1/fS, and k0and kα∈N, the lower limit of (5.10) is
given by:
k0−kα=⌊dFfSm⌋.(5.12)
Considering a fault in the remote bus or further away, k0−kαwill be equal to or greater
than the limit in (5.12). Therefore, to ensure that an internal fault will not be confused with an
external one at the remote bus or on the downstream adjacent lines, an internal fault is detected
only if:
k0−kα<⌊l fSm⌋.(5.13)
5.2.2 TW Velocity Estimation Effects
In real-world conditions, the actual velocities vαand v0are unknown. Therefore, they
are replaced by their respective estimations vαand v0. These velocities may be estimated as
vα=l/τα(l)and v0=l/τ0(l), where τα(l)and τ0(l)are estimated line propagation times of
modal TWs. These line propagation times may be estimated in real-world systems during line
commissioning procedures (SCHWEITZER et al., 2016). As the protection reliability depends
on the correct estimation of modal TW velocities, errors in this estimation may lead to misoper-
ations. Nevertheless, the proposed TW21G function considers the effect of uncertainties in TW
velocity estimations to avoid misoperation.
From (5.11), if the estimated α-mode velocity is greater than the true one (vα>vα) and the
estimated 0-mode velocity is smaller than the true one (v0<v0), then the estimated value for m
is greater than its true counterpart. In this situation, external faults at the remote bus or beyond
it could satisfy (5.13), i.e., the relay may overreach and fail. In order to avoid this situation, the
wave velocity estimations must result in values of mthat are always smaller than the true one.
Nevertheless, vαand v0may be higher or lower than vαand v0, respectively. Therefore, in this
work, it is proposed to systematically overestimate v0, increasing v0by a security factor p0, and
to underestimate vα, decreasing vαby a security factor pα. Thus, the overestimation of v0is
5.3. THE PROTECTION ZONE OF THE PROPOSED TW21G FUNCTION 37
given by v0↑=p0v0, where p0>1. The underestimation of vαis given by vα↓=pαvα, where
0<pα<1. This assumption results in a smaller estimated value for m, avoiding false trips
to improve the protection function security. Thus, following this recommendation, the protec-
tion inequality (5.13) to detect internal faults is to consider overestimated and underestimated
velocities v0↑and vα↓instead of the true ones v0and vα, respectively, as follows:
k0−kα<⌊l fSm′⌋,(5.14)
where:
m′=vα↓−v0↑
vα↓v0↑
=pαvα−p0v0
pαvαp0v0(5.15)
and
pαvα>p0v0.(5.16)
5.3 The Protection Zone of the Proposed TW21G Function
Inaccuracies in TW velocity estimations (vαand v0) and errors in the detection time of TWs
(kα/fSand k0/f0) due to the sampling process lead to variations on the reach of the proposed
function. This section defines the protection zone considering error margins in the modal TW
velocity estimations.
5.3.1 The Maximum Protection Zone
As aforementioned, 0 ≤εα<1/fSand 0 ≤ε0<1/fS, then −1<(ε0−εα)fS<1. Therefore,
based on (5.10), the maximum k0−kα, obtained when (ε0−εα)fS→1, with true velocities vα
and v0, and with a given internal fault located at a distance dFfrom the local bus, is smaller
than dFfSm+1. Conversely, based on (5.10) and (5.15), the minimum k0−kα, obtained when
(ε0−εα)fS→−1 with estimated velocities vαand v0for a fault located at the remote bus, at a
distance lfrom the local bus, is greater than l fSm′−1. Therefore, in order to avoid an external
fault being detected as an internal one, l fSm′−1 must be greater than dFfSm+1, yielding:
dF≤lm′
m−2
fSm,(5.17)
which in percentage is given by:
dF% ≤(︃m′
m−2
l fSm)︃100%.(5.18)
For a hypothetical fStending to infinity, the maximum protection zone within which the method
will detect a fault as an internal one is given by:
PZmax =(︃m′
m)︃100(%).(5.19)
By defining PZmax =100% in (5.19), the protection inequality given by (5.14) ensures that
no downstream external fault will be detected as internal one. However, (5.19) uses true propa-
gation velocities in m, as defined in (5.11), which are unknown. Therefore, error margins in the
wave velocity estimations must be considered to define the protection zone.
5.3. THE PROTECTION ZONE OF THE PROPOSED TW21G FUNCTION 38
5.3.2 Error Margin for the Wave Velocity Estimation
In what follows, the estimated modal TW propagation velocities vαand v0are expressed
as approximations of the respective true TW propagation velocities vαand v0employing error
factors gαand g0, i.e., vα=gαvαand v0=g0v0. Therefore, (5.15) is given by:
m′=pαgαvα−p0g0v0
pαgαvαp0g0v0.(5.20)
To avoid external faults being detected as internal ones, PZmax in (5.19) must be smaller
than 100%. Therefore, the maximum value for m′in (5.20) must be equal to the correct value
of min (5.11), as follows: pαgαvα−p0g0v0
pαgαvαp0g0v0=vα−v0
vαv0.(5.21)
Thus, ideal conditions are satisfied with pα=1/gαand p0=1/g0. However, gα=vα/vα
and g0=v0/v0are unknown because vαand v0are unknown. Therefore, pαand p0are to be
obtained through expected percentage error margins gα%and g0% for the modal wave velocity
estimations instead of gαand g0, respectively. These margins must ensure that errors below gα%
and g0% are acceptable for vαand v0, respectively.
Fig. 5.2 depicts the effect of the security factors pαand p0in the modal wave velocity
estimations, where gα↑=1+ (gα%/100),gα↓=1−(gα%/100),g0↑=1+ (g0%/100), and
g0↓=1−(g0%/100)are upper- and lower-limit (↑and ↓) error factors. Fig. 5.2 shows that
by respecting gα%and g0%,vαand v0may be estimated in within regions A or B. However,
as discussed in subsection 5.2.2, vα>vαand v0<v0must be avoided, i.e., regions A must be
avoided. Thereby, the security factors pαand p0must be computed considering the worst case,
which is vα=vα1=gα↑vαand v0=v01 =g0↓v0, in the external limit of zones A. Therefore, pα
and p0are given by:
pα=1
gα↑
=100
100+gα%(5.22)
and
p0=1
g0↓
=100
100−g0% .(5.23)
From (5.22) and (5.23), pαand p0are automatically computed since gα%and g0% have been
defined previously. In turn, the adopted values for the error margins gα%and g0% must result
in security factors pαand p0that ensure (5.16). Thus, considering that the percentage errors on
the estimated modal TW propagation velocities vαand v0are lower than the adopted margins
gα%and g0%, then m′<min (5.21) and PZmax <100% in (5.19). Therefore, (5.14) ensures that
faults in the remote bus or downstream external lines will not be detected as internal ones.
vα1
p vαα1
vα
g vαα↑
g vαα↓
p g vαα α↓
vα2
p vαα2
vα3
p vαα3
Region Aα
Region Bα
v01
p v001
v0
g v00↑
g v00↓
p g v00 0↑
v02
p v0 02
v03
p v003
Region 0A
Region 0B
(a) (b)
α-mode velocity
estimation
0-mode velocity
estimation
Figure 5.2: Modal wave velocity estimation.
5.4. PROPOSED TW21G FUNCTION SETUP METHODOLOGY 39
5.3.3 The Minimum Protection Zone
The definition of the minimum protection zone PZmin is necessary for reliable protection
because it defines the minimum zone in which all faults are detected as internal ones. When vα
and v0are estimated in regions B (Fig. 5.2), i.e., when vα<vαand v0>v0, the protection reach
is reduced. In addition, the effect of the security factors pαand p0is to reduce it even more. As
Fig. 5.2 shows, the boundary condition for PZmin occurs when vαand v0are estimated at the
limit of regions B, where vα=vα3=gα↓vαand v0=v03 =g0↑v0. It is now possible to estimate
a compensated value of m, named here as mc, which allows to express mwithout the need to
use the true values of vαand v0:
mc=(︂1
gα↓)︂vα−(︂1
g0↑)︂v0
(︂1
gα↓)︂vα(︂1
g0↑)︂v0
=(︂100
100−gα%)︂vα−(︂100
100+g0% )︂v0
(︂100
100−gα%)︂vα(︂100
100+g0% )︂v0
.(5.24)
Therefore, in the presented boundary condition, when vα=gα↓vαand v0=g0↑v0,mcis equal
to the actual value of m.
From (5.18) and (5.24), the minimum protection zone, within which all faults will be de-
tected as internal ones, is given by:
PZmin =(︃m′
mc−2
l fSmc)︃100(%).(5.25)
For any other values of vαand v0and corresponding gα%and g0%, then the protection reach
may be greater than PZmin, but will always be lower than PZmax =100%.
It is recommended that the adopted values for gα%and g0% ensure PZmin >50%, from
(5.25). Thereby, by connecting relays with the proposed TW21G protection implemented in
both line terminals, a DTT (Direct Transfer Trip) protection scheme can be applied in order to
protect 100% of the monitored transmission line.
5.4 Proposed TW21G Function Setup Methodology
Fig. 5.3 depicts the methodology for the offline setup of the proposed TW21G function.
The settings can be easily obtained since the protection threshold given by (5.14) can be au-
tomatically estimated after defining the input relay parameters. The line length, the sampling
frequency, the modal TW propagation velocity estimations, and error margins for the modal
wave velocity estimations are input parameters to be set in the relay. The variables pα,p0,m′,
and mcare all automatically calculated using the demonstrated equations. Finally, the relay
parametrization calculates the reach setting ⌊l fSm′⌋and the minimum protection zone PZmin.
For instance, consider a transmission line with l=200 km and estimated modal wave velocities
equal to vα=0.9285cand v0=0.7143c, where cis the speed of light. Adopt the error mar-
gins gα%=g0% =3%, so that PZmin >50% according to (5.25). Then, from (5.22) and (5.23),
pα≈0.9709 and p0≈1.0309, which ensure (5.16). From (5.15) and (5.24), m′≈8.2881×10−7
and mc≈1.3242. From (5.25), PZmin ≈61.8337%, which means that all internal earth faults
occurring before 123.66 km will be detected as internal. Finally, according to (5.14), a fault
will be detected as internal one when k0−kα<165. Therefore, provided that the errors in
modal wave propagation velocity estimations do not exceed 3%, k0−kα<165 will ensure
PZmax =100%.
As aforementioned, the relay setup may also be performed considering the estimated modal
5.5. PERFORMANCE ASSESSMENT 40
mc
(22)
(23)
pα
p0(15)
vαv0l fS
m´(14)
gα%
g0%PZmin
(24)
vαv0l fS
(25)
lf mS´
Figure 5.3: Flowchart for the relay setup.
travel times by replacing vαand v0by l/τα(l)and l/τ0(l)(SCHWEITZER et al., 2016) in Fig.
5.3.
5.5 Performance Assessment
Two test systems were modeled in order to assess the proposed method. Both were modeled
based on actual 230 kV and 60 Hz transmission networks. In the first one, shown in Fig.
5.4, the transmission lines were modeled using the Bergeron frequency-independent distributed
parameter model. In this model, the TW velocity depends on line series inductance and shunt
capacitance, as follows:
vα=1/√︁LαCα(5.26)
and
v0=1/√︁L0C0.(5.27)
Therefore, as the exact values of the modal wave velocities are known, it was possible to eval-
uate the precision of the protection zone of the proposed method as a function of the adopted
error margins gα%and g0%. The protected line is 200 km long, and adjacent lines of 15 km were
connected at buses 2 and 3. The system-to-line impedance ratio (SIR) is equal to 0.1 at buses
2 and 3, and a power system loading angle equal to −15◦was considered. This corresponds to
a moderate power system loading. CCVTs and current transformers (CTs) were, respectively,
implemented as described in (CARVALHO; FREIRE; OLIVEIRA, 2009) and (IEEE, 2004), in
both systems.
In the second system, shown in Fig. 5.5, the transmission lines were modeled with the JMarti
frequency-dependent distributed parameter line model with a frequency response up to 10 MHz.
Fig. 5.6 depicts the parameters of the tower for this system. The protected transmission line
TL 3 was transposed employing four transposition points, following the well-known scheme
1/6 + 1/3 + 1/3 + 1/6. Two perfectly transposed parallel adjacent lines of 10 km in length
were added at each terminal of the protected line. An SNR (signal-to-noise ratio) of 40 dB
was considered to hinder the wavefront detection. In this system, the wave velocity varies
depending on the fault position due to the frequency-dependent line parameters, especially the
0-modal component. Therefore, the wave velocity can no longer be estimated with (5.26) and
(5.27). Furthermore, fault-induced transients present more attenuation than the Bergeron-based
counterparts, so traveling waves that reach the line terminals do not present sharp step variation.
This is in accordance with traveling wave behavior in real systems. Due to this characteristic,
5.5. PERFORMANCE ASSESSMENT 41
detecting the true arrival instant of the wavefront becomes more challenging.
Faults were simulated using the ATP software at a sampling frequency of 1 MHz. All the
oscillographic records at the relays connected at bus 2, designed to protect the transmission
line between buses 2 and 3 in each modeled system, were stored in a database. After that, five
procedures were accomplished:
1. the performance assessment of the proposed TW21G distance function, in the first system,
as addressed in subsection 5.5.1;
2. the performance assessment of the existing distance protection TD21 in an actual relay
by means of its playback functionality (GUZMÁN et al., 2018), in the first system, as
addressed in subsection 5.5.2;
3. the performance assessment of the proposed TW21G protection with the logic operation
TW21G ∩OC21 ∩(TD32 ∪TW32) in Fig. 5.1, in the first system, where OC21, TD32,
and TW32 were available in an actual relay, as addressed in subsection 5.5.2;
4. the procedures 2) and 3) were performed for the second system in order to evaluate the
method in a more realistic scenario, as addressed in subsection 5.5.3;
5. complementary operation time comparisons between the proposed TW21G protection
and the existing distance protection TD21 were performed, as addressed in subsection
5.5.4.
Z0
= 0.522 + j1.432 /kmΩ
Z1
= 0.098 + j0.53 /kmΩ
Y0
= 2.293 /kmμΩ
Y1
= 3.252 /kmμΩ
Transmission lines
TL 2 (protected)
TL 1
Bus 1
Relay
Bus 2 Bus 3 Bus 4
Generator 1
U
= 230.091 1.536 kV∟
Z1
= 2.156 + j11.660 Ω
Z0
= 11.484 + j31.504 Ω
o
TL 3
Generator 2
U
= 230.053 -16.46 kV∟
Z1
= 2.156 + j11.660 Ω
Z0
= 11.484 + j31.504 Ω
o
Figure 5.4: Modeled system 1: 230 kV and 60 Hz power system with distributed parameters.
TL 3 (protected)
TL 1
Bus 1
Relay
Bus 2 Bus 3 Bus 4
TL 2
Generator 1
U
= 230 0 kV∟
Z1
= 2.156 + j11.660 Ω
Z0
= 11.484 + j31.504 Ω
o
Generator 2
U
= 230 -15 kV∟
Z1
= 2.156 + j11.660 Ω
Z0
= 11.484 + j31.504 Ω
o
TL 4
TL 5
Figure 5.5: Modeled system 2: 230 kV and 60 Hz power system with frequency-dependent
parameters and non-ideal line transposition.
5.5. PERFORMANCE ASSESSMENT 42
All the applied earth faults were phase-A-to-ground type (AG faults). However, all eval-
uations performed here can be extended to other earth fault types. The Clarke transformation
referenced to phase A was applied to currents so that the arriving instants of the TWs were
always detected in the modal domain from the DS filter outputs.
In the first system, where the Bergeron-based distributed parameter transmission line model
was implemented, the actual α- and 0-modal TW velocities for the protected line, in the sim-
ulation environment, are vα=1/
√L1C1=2.8716×105km/s (0.9572c) and v0=1/
√L0C0=
2.0805 ×105km/s (0.6935c), respectively. As a result, the travel time of the alpha and zero
mode TWs along the protected line are, respectively, 0.6965 ms and 0.9613 ms. However, these
values are not used in the proposed protection because they are unknown in a practical situation,
and vα=vαand v0=v0were considered, as further discussed in the following subsections. The
proposed TW21G function was set considering gα%=g0% =3% for all the evaluated scenarios
for the system 1, respecting (5.16). So if follows that PZmin >50% from (5.25).
In the second system, the modal wave velocity estimation was performed through an en-
ergization procedure applied in real transmission systems (SCHWEITZER et al., 2016). The
protected transmission line TL 3 was energized from bus 3, while the terminal connected to bus
2 was open. A circuit breaker interpole switching delay of 3.3 ms was considered in accordance
with what has been observed in real scenarios (MOORE, 2004). The time stamps of the pole
closing and the TW reflected from bus 2 were used in order to estimate the modal wave veloc-
ities, which were vα= 2.9957 ×105km/s (0.9986c) and v0=2.7523×105km/s (0.9174c). In
order to respect (5.16) and maintain PZmin >50%, in accordance with (5.25), gα%=0.8 and
g0% =1.79% were adopted for all the tests performed for the system 2.
Ground resistivity = 531 mΩ
19.555 m 9.220 m
11.582 m
7.267 m
3.429 m
Conductors: ACSR 636 MCM 26/7
Number of conductors per phase: 1
Ground conductors:
ACC HS 3/8'' 7 wires
Figure 5.6: Tower parameters for the system 2.
5.5.1 The Proposed Distance Function TW21G
In order to analyze the effect of fault location variations on the proposed TW21G function,
faults from 1 to 199 km, at steps of 1 km, were considered for system 1, amounting to 199
faults being investigated. In this evaluation, solid faults were initiated at a fault inception angle
of 90◦in the faulted phase in order to result in the highest content of electromagnetic tran-
sients (COSTA; SOUZA; BRITO, 2012), avoiding TW detection problems due to the transient
attenuation. However, the effect of this parameter is considered in subsection 5.5.3.
Fig. 5.7 depicts the proposed TW21G function operation time for different estimations of
vαand v0. Fig. 5.7(a) considers vαwith underestimation of 3% (vα=0.97vα) and v0with
overestimation of 3% (v0=1.03v0), i.e., estimation errors higher than expected ones, which
are supposed to be less than 2% (WANG; XU, 2015). According to (5.25), PZmin =61.8337%
(123.66 km). Fig. 5.7(b) also considers significant estimation errors: vαwith overestimation of
3% (vα=1.03vα) and v0with underestimation of 3% (v0=0.97v0), yielding PZmin =72.0358%
5.5. PERFORMANCE ASSESSMENT 43
(144.07 km). Fig. 5.7(c) considers an exact estimation of both vαand v0, i.e., vα=vαand
v0=v0, yielding PZmin =67.7445% (135.49 km).
The relay performed in these situations as follows: 1) no fault within PZmin was detected
as external; 2) most faults beyond PZmin, but inside the protected line, were detected as inter-
nals; 3) as the errors for the modal wave velocity estimations were not higher than the adopted
margins gα%and g0% of 3%, no fault at the remote bus or beyond it was detected as internal.
The maximum protection operation time in Fig. 5.7(a) was 0.697 ms, whereas the maximum
operation time of the two-terminal TW-based protection in (COSTA et al., 2017) was 2.5 ms,
considering a protected line of 200 km length. The maximum operation time in Figs. 5.7(b)
and 5.7(c) were 1.057 ms and 0.879 ms, respectively.
0 20 40 60 80 100 120 140 160 180 200
0
0.4
0.8
1.2
Operation
time (ms)
0
0.4
0.8
1.2
Operation
tme (ms)
(b)
(c)
0
0.4
0.8
1.2
Operation
time (ms)
(a)
No operation
Operation
Pzmin =144.07 km
Pzmin =123.66 km
Pzmin =135.49 km
Fault ocation (km)l
(c)
Figure 5.7: Protection operation time for: (a) vαunderestimated by 3% and v0overestimated
by 3%; (b) vαoverestimated by 3% and v0underestimated by 3%; (c) correct estimation for vα
and v0.
According to Fig. 5.7, there is an uncertainty zone between PZmin and the remote bus
where faults may or may not be detected as internal faults, depending on the error in modal TW
velocity estimations. In addition, the adopted margins gα%and g0% ensure that no fault within
PZmin is detected as external, and no fault at the remote bus or beyond it is detected as internal.
Therefore, no protection misoperation was verified.
5.5.2 The Proposed TW21G Function with Supervision of Existing Func-
tions
Performances of the proposed distance protection with the logic TW21G ∩OC21 ∩(TD32
∪TW32) and of the existing distance protection TD21 were evaluated and compared for system
1. The results consider variations on line parameters to verify the effect of inaccuracies of relay
settings on the operation of its functions. They also consider errors in modal wave velocity
estimations to verify the minimum and maximum reaches of the proposed protection TW21G.
5.5. PERFORMANCE ASSESSMENT 44
5.5.2.1 Effect of Uncertainty in Line Parameters
Fig. 5.8 depicts the operation time of the proposed TW21G and the existing TD21 protec-
tions as a function of the fault distance considering the correct estimation of the modal wave
velocities (vα=vαand v0=v0). Faults from 1 to 199 km, at steps of 1 km, were considered,
totaling 199 faults. The TD21 protection resulted in a maximum operation time equal to 10.133
ms and mean operation time equal to 4.08 ms, giving a very fast operation time when compared
to the one to one-and-a-half cycle typical operating time of traditional phasor-based protection
(SCHWEITZER et al., 2015). In addition, it detects faults up to 124 km, which is at 62% of the
line. The proposed TW21G protection was able to speed up the distance protection operation
in all simulated scenarios, with maximum and mean operation times of 1.5 ms and 1.09 ms,
respectively. In addition, the proposed TW21G protection detected faults beyond the maximum
reach of the TD21 protection.
Fig. 5.9 depicts the operation times of the existing TD21 protection and the proposed
TW21G protection, considering uncertainties in line parameters. In Fig. 5.9(a), the α-mode
line parameters, which are equal to the positive sequence parameters, were underestimated by
3%. The 0-mode line parameters, which are equal to the zero sequence parameters, were over-
estimated by 3%. Regarding Fig. 5.9(b), the aerial mode line parameters were overestimated by
3%, whereas the 0-mode line parameters were underestimated by 3%. In these cases, the relay
parameters were not modified for both TD21 and TW21G protections. Since there is a cer-
tainty that all faults within the minimum protection zone PZmin are properly detected as internal
events, only the results for faults from 100 to 199 km, at steps of 1 km, are presented, amounting
to 100 fault cases, demonstrating the uncertainty zone variation from the end of PZmin to the
remote bus.
0 20 40 60 80 100 120 140 160 180 200
0
3
6
9
12
Operation
time (ms)
TW21G protection
TD21 protection No trip
Trip
Fault ocation (km)l
Figure 5.8: TD21 and TW21G protection operation times.
According to Fig. 5.9, the operation time and reach of the TD21 protection did not present
relevant variation, proving its robustness regarding deviations of line parameters. As mathemat-
ically predicted and according to what was presented in subsection 5.5.1, the TW21G protection
presented variation in its reach. However, no fault at the remote bus or beyond was detected as
internal. The proposed TW21G protection was again able to significantly speed up the distance
protection scheme, with a maximum operation time of 1.6 ms.
5.5.3 The Proposed TW21G Function with Supervision of Existing Func-
tions Considering Frequency-dependent Parameters
A more realistic scenario was considered to evaluate and compare the performance of the
proposed distance protection with the logic TW21G ∩OC21 ∩(TD32 ∪TW32) and the existing
distance protection TD21. Frequency-dependent line electrical parameters, a non-ideal line
transposition, electrical noise, and fault inception angle variations, which may affect the wave
5.5. PERFORMANCE ASSESSMENT 45
0
3
6
9
12
Operation
time (ms)
100 120 140 160 180 200
Fault ocation (km)l
0
3
6
9
12
Operation
time (ms)
(a)
(b)
No trip
TW21G protection
TD21 protection
The proposed protection
is the fastest
The proposed protection
detects more faults
Figure 5.9: TD21 and TW21G protection operation times for: (a) R1,L1, and C1underestimated
by 3%, and R0,L0, and C0overestimated by 3%; (b) R1,L1, and C1overestimated by 3%, and
R0,L0, and C0underestimated by 3%.
velocity estimation and wave detection, were considered in different fault situations for system
2.
5.5.3.1 Effect of the Fault Location
Fig. 5.10 depicts the operation time of the proposed TW21G and of the existing TD21 pro-
tections as a function of the fault distance. Faults from 0 to 210 km, at steps of 5 km, were con-
sidered, amounting to 43 faults being evaluated. Despite the errors in the modal wave velocity
estimations being unknown, the adopted error margins gαand g0ensured the protection reliabil-
ity since no fault in the remote bus or beyond it was detected. The proposed TW21G protection
detected all applied faults up to 160 km, which corresponds to 76.19% of the transmission line
length and is in accordance with the projected PZmin >50%. The maximum operation time was
1.3 ms. The maximum reach of the existing TD21 protection was 125 km, which corresponds
to 59.52% of the transmission line, while the maximum operation time was 9.7 ms.
5.5.3.2 Effect of the Fault Inception Angle
Fig. 5.11 depicts the operation time of the proposed TW21G and of the existing TD21
protections as a function of the fault inception angle. Faults were applied from 0 to 210 km,
at steps of 15 km, considering fault inception angles equal to 0◦, 30◦, 60◦, and 90◦, totaling
60 faults being investigated. As expected for TW-based algorithms, the proposed TW21G dis-
tance protection did not detect faults with an inception angle equal to 0◦since the fault-induced
transients were severely damped. This is a challenge to be faced by the TW filtering method.
However, the development or detailed analysis of the TW filtering method is out of the scope
of this work. Moreover, the protection reach was slightly lower to faults with a fault inception
angle equal to 30◦. In addition, the mean and the maximum operation times were about 1.1 ms
and 1.5 ms, respectively.
Although the fault inception angle variation modifies the TD21 protection operation, it does
not present a clear tendency. The existing TD21 protection detected faults with fault-induced
transients severely damped. The mean operation time was about 3.2 ms, whereas the maximum
5.5. PERFORMANCE ASSESSMENT 46
operation time was about 9.4 ms. Therefore, considering cases in which TW21G operations
were verified, the proposed method was the fastest.
5.5.3.3 Effect of the Fault Resistance
Fig. 5.12 shows the effects of the fault resistance on the operation time of the proposed
TW21G and the existing TD21 protections. Faults were applied from 0 to 210 km, at steps of
15 km, considering fault inception angle of 90◦and fault resistances equal to 10, 50, 100, and
200 Ω, amounting to 60 faults in total. The TD21 and the TW21G protections presented higher
operation times for fault resistance values. The existing TD21 protection had its reach decreased
with the increase of the fault resistance and could not detect faults with resistances greater than
100 Ω. The proposed TW21G protection was able to detect all the applied faults up to 150 km
with a maximum operation time of 1.6 ms. Thus, the TD21 protection is more influenced by
the fault resistance variation. Therefore, the proposed TW21G protection could accelerate the
existing TD21 protection for all the jointly detected faults and detect some others that the TD21
protection could not detect. The increase in the operation time of the proposed TW21G distance
protection performing the logic TW21G ∩OC21 ∩(TD32 ∪TW32) (Fig. 5.1) occurred due
to the increase in the operation time of the OC21 function. The traveling-wave-based functions
TW21G and TW32 did not present variations in their operation times.
TW21G protection
TD21 protection No trip
Trip
0 30 60 90 120 150 180 210
Fault Location (km)
0
3
6
9
12
Operation
Time (ms)
Figure 5.10: TD21 and TW21G protection operation times.
5.5.3.4 DTT Protection Scheme
As the proposed TW21G distance protection is under-reach protection and presents good
dependability, it can be applied in a DTT protection scheme. Two of the used actual relay were
employed in order to evaluate this application. Table 5.1 shows the operation time of the POTT
(Permissive Overreaching Transfer Trip) and the DTT protection schemes for the actual relay
and the operation time of the proposed TW21G distance protection in a DTT scheme. The op-
eration time is related to the instant when both relays give trip signals. Since the adopted optical
fiber to connect both relays is very small, the observed communication delays in these test cases
were smaller than expected for a real transmission system. The same communication delays ob-
served for the DTT scheme with the proposed TW21G distance protection were adopted for the
DTT scheme of the actual relays. Those delays were 77 µs and 23 µs for the local and remote
terminals, respectively.
Table 5.1 shows that the proposed TW21G distance protection accelerated the trip of the
actual relay for all the evaluated test cases. These results demonstrate the potential of the
proposed TW21G distance protection to speed up the earth-fault protection, even considering
existing ultra-fast two-terminal methods.
5.5. PERFORMANCE ASSESSMENT 47
0
2.5
5
7.5
10
Operation
Time (ms)
0 30 60 90 120 150 180 210
Fault Location (km)
0
2.5
5
7.5
10
Operation
Time (ms)
(a)
(b)
Ang. 30oAng. 60oAng. 90o
Ang. 0o
Ang. 30o
Ang. 60o
Ang. 90o
Figure 5.11: Protection operation time as a function of the fault inception angle to: (a) the
proposed TW21 protection; (b) the existing TD21 protection.
0
2.5
5
7.5
10
Operation
Time (ms)
0 30 60 90 120 150 180 210
Fault Location (km)
0
2.5
5
7.5
10
Operation
Time (ms)
10
50
100
0
50
100
200
(a)
(b)
Figure 5.12: Protection operation time as a function of the fault resistance to: (a) the proposed
TW21 protection; (b) the existing TD21 protection.
5.5.4 Operation Time Comparison
The operation times between the proposed TW21G protection and the existing TD21 pro-
tection was compared to verify the ability of the proposed TW21G function to speed up the
time-domain distance protection. Fig. 5.13 depicts the scatter plot to compare the operation
time between the TD21 protection and the proposed TW21G protection for all the 225 jointly
detected by both protection schemes in the assessments presented in subsections 5.5.2, 5.5.3.1,
5.5.3.2, and 5.5.3.3.
5.5. PERFORMANCE ASSESSMENT 48
Table 5.1: POTT and DTT scheme operations.
Fault Operation Time (µs)
Location (km) Actual Relay Proposed TW21G Protection
POTT DTT DTT
20 1790 1313 890
80 1636 1336 1136
100 1509 1286 1186
120 1556 1333 1156
180 1797 1374 897
Mean 1657.6 1328.4 1053
As shown in Fig. 5.13, in some cases, the proposed TW21G protection scheme was six
times faster than the TD21 protection, being about two times faster in the remaining cases. The
operation time of the proposed TW21G protection did not exceed 1.4 ms, whereas the TD21
element presented operation times varying from 1.6 ms to about 10.1 ms. Therefore, for all the
225 fault cases jointly detected by both protection schemes, the proposed TW21G protection
accelerated the TD21 protection.
Fig. 7.17 depicts the cumulative frequency of the operation time for the TD21 protection and
the proposed TW21G protection for all detected internal faults. The maximum operation times
of the proposed TW21G protection and the TD21 protection were about 1.6 ms and 10.1 ms,
respectively. When the proposed TW21G protection reached a cumulative frequency of 100%,
the TD21 protection detected only one fault. These results demonstrate that using the proposed
TW-based earth fault distance protection to speed up the protection operation is efficient and
reliable.
tTD21 protection (ms)tTD21 protection (ms)
tTW21G protection
(ms)
0 1 2 3 4 5 6 7 8 9 10 11 12
0
2
4
6
8
10
6x faster
2x faster
Faster
Slower
Figure 5.13: Scatter plot of the existing TD21 protection and the proposed TW21G protection
operation times.
5.6. CONCLUSION 49
0 1 2 3 4 5 6 7 8 9 10 11
Operation time (ms)
0
20
40
60
80
100
Cumulative
frequency (%)
TW21G protection
TD21 protection
Figure 5.14: Cumulative frequency of the operation time.
5.6 Conclusion
This chapter proposes a traveling wave-based earth fault transmission line distance pro-
tection, which only requires arrival instants of the first incident modal traveling waves at one
line terminal and the estimation of modal propagation velocities with uncertainties. Therefore,
the proposed protection overcomes traditional limitations of one-terminal traveling-wave-based
methods, which require the challenging task of detection of reflected waves and accurate wave
propagation velocity estimations. The proposed function setup procedure is straightforward,
facilitating practical implementation.
A thorough investigation of the sampling frequency effect allowed the definition of error
margins for the modal wave velocity estimations, ensuring the reliability of the protection in
well-defined protection zones. The proposed function provides a protection reach, considering
the adopted error margins for the modal wave velocity estimations, wherein all the internal
faults will always be detected. This facilitates the application of the proposed function in real-
world systems. Reach values greater than 60% in the worst evaluated cases were achieved. A
greater portion of the transmission line may be protected, depending on the error in velocity
estimations. Therefore, unitary protection, where 100% of the transmission line is inside the
protected zone, may be achieved via a DTT scheme whether a relay is connected at each line
terminal of the protected line, considering the additional cost of applying a communication
channel.
When associated with other existing auxiliary protection functions„ the proposed function
presented an ultra-fast operation time well below those presented by a commercially existing
time domain distance protection. Errors in the wave velocity estimations and inaccuracies in line
parameters were evaluated. The effect of the fault location was also evaluated. The proposed
method accelerated the evaluated time-domain distance element available in the analyzed actual
relay for all detected earth faults. The presented maximum operation time was smaller than 2
ms for all detected internal faults, without misoperations in cases of external faults. In addition,
it was demonstrated that the proposed distance protection has the potential to speed up earth-
fault protection, even considering existing ultra-fast two-terminal methods. This represents an
important contribution since fast fault detection provides greater stability to the electrical system
and reduces the risk of damage to its components. The results have also demonstrated that the
method presents good dependability, even considering errors in the wave velocity estimations.
5.7. CHAPTER SYNTHESIS 50
5.7 Chapter Synthesis
This chapter proposed a traveling wave-based earth fault distance protection method for AC
lines. The effects of the sampling frequency and the velocity estimations of the modal compo-
nents of the traveling waves on the protection reliability were evaluated. From these evaluations,
a protection zone was delimited, as well as error margins for the modal wave velocity estima-
tions were defined, with no loss of protection reliability.
Chapter 6
Proposed One-Terminal Traveling Wave
Reflection-Based Transmission Line
Protection
This chapter will present the proposed method for transmission line protection based on
traveling wave reflections using one terminal. The correct detection of the reflected wave at
the fault point is an issue still under investigation by the scientific community. Therefore, the
proposed method only applies to point-to-point lines without adjacent lines.
A previous version of the method presented here was investigated in (FRANÇA, 2017).
However, this chapter has carried out a thorough and unprecedented investigation of the effect
of traveling wave speed estimation. In this way, a more robust method has been developed.
6.1 Discrete Time Domain for a Single Line
For application in protection relays, the voltage and current signals are discretized. There-
fore, the effect of the sampling frequency needs to be considered. Costa et al. (2017) has
investigated such an effect for a protection method using two terminals. However, this effect
has not been investigated so far for one-terminal methods.
Figure 6.1 depicts the arrival time of traveling waves at the local terminal due to a dFdis-
tant fault from the L-bar on a lkm long line. It also depicts the discrete time instants of the
wavefronts due to the effect of sampling frequency.
Considering the effect of the sampling frequency, the first and second wavefront arrival
times tF1and tF2, as well as the fault inception time tF, all in the continuous time domain,
should be converted to their respective discrete times. These can be detected with high accuracy
by various high-frequency digital filtering methods (COSTA; SOUZA; BRITO, 2010; COSTA,
2014a; NAMDARI; SALEHI, 2017). Therefore, this work assumes that the discrete times of
wavefront detections are known, and no detection method will be investigated. The times in the
discrete-time domain are given by:
kF
fs
=⌊tFfs⌋
fs
,(6.1)
where
tF−1
fs
<kF
fs≤tF,(6.2)
kF1
fs
=⌊tF1fs⌋
f s +1
fs
,(6.3)
51
6.1. DISCRETE TIME DOMAIN FOR A SINGLE LINE 52
Internal fault
Time (s)
F1 S
tF
Discrete instant of arrival
of the wavefront
k /f
FSDiscrete time
Bus L Bus R
Protected line with kml
dd l d= -
FFF
k /f
tF1
F2 S
k /f
tF2
Relay
Trip
Reference for discrete
fault inception time
Figure 6.1: Lattice diagram of traveling waves seen from a terminal, considering the effect of
sampling frequency.
where
tF1<kF1
fs≤tF1+1
f s,(6.4)
and kF2
fs
=⌊tF2fs⌋
f s +1
fs
,(6.5)
where
tF2<kF2
fs≤tF2+1
f s,(6.6)
where kFis the reference sample and represents the discrete time of fault incidence; kF1and kF2
are the samples at which the relay detects the first and second wavefronts; ⌊⌋ is the floor opera-
tion, which returns the minimum integer value of the argument; fsis the sampling frequency.
Due to the sampling process, the variables in the discrete-time domain have errors concern-
ing the correct values in the continuous-time domain. According to equations (6.1)-(6.5), the
errors associated with the instant of fault incidence (εF) and arrival times of the first and second
wavefronts (εF1and εF2) are given by:
εF=tF−kF
fs
,(6.7)
where
0≤εF<1
fs
,(6.8)
εF1=kF1
fs−tF1,(6.9)
where
0≤εF1<1
fs
,(6.10)
and
εF2=kF2
fs−tF2,(6.11)
6.1. DISCRETE TIME DOMAIN FOR A SINGLE LINE 53
where
0≤εF2<1
fs
.(6.12)
The difference between the discrete arrival times of the second and first wavefronts is given
by:
kF2
fs−kF1
fs
= (tF2+εF2)−(tF1+εF1) = (tF2−tF1)+(εF2−εF1),(6.13)
which makes it possible to calculate a total error associated with the difference between the
discrete times:
εT= (εF2−εF1) = kF2−kF1
fs−(tF2−tF1),(6.14)
where −1/fs<εT<1/fs, since 0 ≤εF1<1/fsand 0 ≤εF2<1/fs.
From equations (4.8) and (6.14), a fault will be detected as internal when:
kF2−kF1
fs
+(εF1−εF2)≤l
v∴kF2−kF1
fs−εT≤l
v∴kF2−kF1≤(︃l
v+εT)︃fs.(6.15)
Considering the upper limit of the total error, the inequality (6.15) becomes:
kF2−kF1<(︃l fs
v+1)︃,(6.16)
on the other hand, considering the lower limit, the inequality (6.15) becomes:
kF2−kF1<(︃l fs
v−1)︃.(6.17)
Since kF2≥kF1and (kF2−kF1)∈N, then from equations (6.16) and (6.17), an internal
fault will be detected when:
kF2−kF1≤⌊︃l fs
v⌋︃+1.(6.18)
From equations (4.9) and (6.14), an external fault will be detected when:
kF2−kF1
fs
+(εF1−εF2) = 2l
v∴kF2−kF1
fs−εT=2l
v∴kF2−kF1=(︃2l
v+εT)︃fs.(6.19)
Therefore, considering the upper and lower limits of the total error, an external fault will be
detected when: (︃2l fs
v−1)︃<kF2−kF1<(︃2l fs
v+1)︃.(6.20)
Since kF2≥kF1and (kF2−kF1)∈N, the inequality (6.20) becomes:
⌊︃2l fs
v⌋︃≤kF2−kF1≤⌊︃2l fs
v⌋︃+1.(6.21)
According to equations (6.18) and (6.21), to ensure a correct distinction between internal
and external faults, a threshold (p) for the detection of internal faults can be adopted as follows:
⌊︃l fs
v⌋︃+1≤⌊︃pl fs
v⌋︃<⌊︃2l fs
v⌋︃,(6.22)
6.1. DISCRETE TIME DOMAIN FOR A SINGLE LINE 54
where 1 ≤p<2. Therefore, the inequality (6.22) is the discrete analog of the inequality (4.11).
6.1.1 The Protected, Unprotected, and Uncertain Zones
In the sampling process, it is taken as true that the relay is unable to identify multiple wave-
fronts arriving between two consecutive samples. Suppose the first and second wavefronts reach
the local terminal in the same sampling period. In that case, the relay will identify them as only
one wavefront. Therefore, when:
kF2−kF1≤1,(6.23)
it is not possible to guarantee that only two wavefronts arrived at the local bus, as multiple
wavefronts may have arrived at the local bus before sample kF1and between samples kF1and
kF2, which could have occurred due to a switching at one of the line terminals.
In terms of wavefront arrival times, the inequality (6.23) becomes:
kF2
fs−kF1
fs≤1
fs
∴(tF2+εF2)−(tF1+εF1)≤1
fs
∴(tF2−tF1)+εT≤1
fs
.(6.24)
To ensure that any event at the line terminal is not mistaken for an internal fault, it is required
that for an internal fault to be detected, the first and second wavefronts must reach the local
terminal in non-consecutive samples, as follows:
kF2−kF1≥2.(6.25)
In terms of the arrival times of the traveling waves, the inequality (6.25) becomes:
kF2
fs−kF1
fs≥2
fs
∴(tF2+εF2)−(tF1+εF1)≥2
fs
∴(tF2−tF1)+εT≥2
fs
.(6.26)
Due to the limitation given by the inequation (6.25), whenever the inequation (6.23) is true,
the fault should be detected as external. This means there will be an unprotected zone in the
local terminal and another, of the same length, in the remote terminal.
Maneuvers at the line terminals, such as transformer energization, capacitor bank switching,
or load switching, may result in multiple wavefronts arriving at the local terminal within the
same sampling period. This leads the relay to detect wavefronts in consecutive samples. A
fault too close to the line terminals will also result in detections of wavefronts in consecutive
samples by the relay. Therefore, the defined unprotected zones are important to avoid unwanted
protection sensitization. Thus the need for a backup protection scheme to detect faults near the
line terminals is evident.
According to the inequality (6.26), and considering that −1/fs<εT<1/fs, the limit for the
difference between the arrival times of the first two wavefronts, in the continuous time domain,
in which an internal fault may be detected as internal, sensitizing the protection, is given by:
(tF2−tF1)>1
fs
,(6.27)
which means that a fault will be detected as external whenever:
(tF2−tF1)≤1
fs
,(6.28)
That is, the fault will have occurred in an unprotected zone.
6.1. DISCRETE TIME DOMAIN FOR A SINGLE LINE 55
According to the inequation (6.24), and considering that −1/fs<εT<1/fs, the limit for
the difference between the arrival instants of the first two wavefronts, in the continuous time
domain, in which an internal fault could be detected as external, not sensitizing the protection,
is given by:
(tF2−tF1)<2
fs
,(6.29)
which means that for an internal fault to be reliably detected as internal, one has to:
(tF2−tF1)≥2
fs
,(6.30)
which will define that a fault has occurred in the protected zone.
According to the inequations (6.27)-(6.30), there is an uncertainty zone where a fault can
be detected as internal or external, depending on the value of the total error (εT). Therefore, the
fault will have occurred in the uncertainty zone if:
1
fs
<tF2−tF1<2
fs
.(6.31)
According to the inequation (6.28), the boundary of the unprotected zone occurs when
tF2−tF1=1
fs
.(6.32)
Knowing that the distance traveled by the traveling wave in one sample period (1/fs) is
given by:
∆d=v
fs
,(6.33)
then, according to equations (6.32) and (6.33), the length of the unprotected zones at each end
of the line is given by:
∆d
2=v
2fs
,(6.34)
since the traveling wave must travel the distance between the fault point and the line terminal
twice in one sampling period. Thus, the total length of the unprotected zone is given by:
UPZ =2∆d
2=∆d=v
fs
.(6.35)
The beginning of the protected zone, according to the inequation (6.30), occurs when:
tF2−tF1=2
fs
.(6.36)
Thus, the protected zone starts at:
∆d=v
fs
,(6.37)
and its length is given by:
PZ =l−2∆d=l−2v
fs
.(6.38)
Two uncertainty zones are positioned between the end of each unprotected zone at the line
terminal and the beginning of the protected zone. The length of each of the uncertainty zones
6.1. DISCRETE TIME DOMAIN FOR A SINGLE LINE 56
at each end of the line is given by:
l−(l−2∆d)−2∆d
2
2=∆d
2=v
2fs
.(6.39)
Consequently, the total length of the uncertainty zone in the transmission line is given by:
UZ =2∆d
2=∆d=v
fs
.(6.40)
In summary, according to equations (6.34)-(6.35) and (6.37)-(6.40), faults in the region
≤d≤dF≤l− ≤ dare always detected as internal, while faults in the 0 ≤dF≤∆d
2and l−
∆d
2≤dF≤lare always detected as external. Furthermore, for the regions ∆d
2<dF<∆dand
l−∆d<dF<l−∆d
2, faults can be detected as internal or external, depending on the total error
(εT).
Percentage-wise, with respect to the total line length l, the zones given by the equations
(6.35), (6.38) and (6.40) can be given, respectively, by:
UPZ(%) = 2∆d
2
l100% =∆d
l100% =v
l fs
100%,(6.41)
PZ(%) = l−2∆d
l100% =(︃1−2v
l fs)︃100%,(6.42)
and
UZ(%) = 2∆d
2
l100% =∆d
l100% =v
l fs
100%.(6.43)
6.1.2 Effect of Traveling Wave Speed Estimation
A significant problem for traveling wave-based protection schemes is the error in estimating
the traveling wave speed, which depends on the transmission line parameters. In turn, the line
parameters are estimated with possible errors in a real system so that the exact value of the real
traveling wave speed is unknown. Thus, the discrete-time internal fault detection inequality
from inequality (6.22) becomes:
⌊︃l fs
vT⌋︃+1≤⌊︃pl fs
vT⌋︃<⌊︃2l fs
vT⌋︃,(6.44)
where vTis the estimated speed of the traveling wave.
The error in estimating the traveling wave speed increases the possibility of operation error
in the protection scheme. For example, in Figure 6.2 the estimated speed of the traveling waves
is greater than the actual speed (vT>v). With this, the difference between the wavefront detec-
tion samples (kF2−kF1) is greater than the left-hand portion of the inequality (6.44). Thus, the
protection will not be sensitized, depending on the value of p, even though the fault occurred in
the transmission line’s protected zone (PZ).
Similarly, an external fault can be detected as internal if the estimated speed of the traveling
waves is less than the actual speed (vT<v). Figure 6.3 depicts an external fault where the
difference between the wavefront detection samples (kF2−kF1) is smaller than the portion to
the right of the inequation (6.44). Therefore, due to the error in estimating the traveling wave
speed, the protection could act, depending on the value of p.
6.1. DISCRETE TIME DOMAIN FOR A SINGLE LINE 57
Internal fault
Time (s)
Local bus Remote bus
tF
Discrete time
( )vT
( )v
Estimated speed
Actual speed
lf
(k - k )
F2 F1
l/2
l/2
Protected line with kml
S
vT+1
Relay
Trip
Figure 6.2: Estimated speed higher than the actual speed of the traveling waves for an internal
fault.
It is then evident that the effect of the error in estimating the wave speed needs to be over-
come to ensure the robustness of the protection method.
Protected line with kml
External fault
Time (s)
External line
tF
(k - k )
F2 F1
2lfS
vT
Relay
Trip
Discrete time
( )vT
()v
Estimated speed
Actual speed
Figure 6.3: Estimated speed lower than the actual speed of the traveling waves for an external
fault.
6.1. DISCRETE TIME DOMAIN FOR A SINGLE LINE 58
6.1.3 Error Margin for Estimation of Wave Speed in the Continuous Time
Domain
According to equation (4.9) and inequations (4.8), (4.10) and (4.11), in the continuous time
domain, for an internal fault to be detected as an external fault, in the most critical case - which
is a fault in the center of the protected line (Figure 6.3) -, and for an external fault to be detected
as internal, the following inequalities must be satisfied, respectively:
l
v>ql
vT⇒vT
v>q(6.45)
and 2l
v≤ql
vT⇒vT
v≤q
2.(6.46)
According to the inequation (6.45), when the estimated speed vTis greater than the actual
speed v, the maximum tolerated error for an internal fault not to be detected as external is
(q−1)100%. Consequently, if this limit is exceeded, analyzing only from the continuous time
domain point of view, an internal fault may be detected as external. On the other hand, when
the estimated speed is lower than the actual speed, the maximum tolerated error for an external
fault not to be detected as internal is (1−q/2)100%. Thus, if this limit is exceeded, an external
fault may be detected as internal.
6.1.4 Error Margin for Wave Speed Estimation in the Discrete Time Do-
main
In the discrete-time domain, according to equation (6.13) and inequation (6.44), for an inter-
nal fault to be detected as external, in the most critical case, and an external fault to be detected
as internal, the following inequalities must be respected, respectively:
kF2−kF1
fs
>⌊︃pl fs
vT⌋︃1
fs
∴εT+l
v>⌊︃pl fs
vT⌋︃1
fs
(6.47)
and kF2−kF1
fs≤⌊︃pl fs
vT⌋︃1
fs
∴εT+2l
v≤⌊︃pl fs
vT⌋︃1
fs
.(6.48)
Similar to what was done for the continuous time domain, it is possible to determine an
acceptable value for the error in the speed estimation. Considering that:
pl
vT−⌊︃pl fs
vT⌋︃1
fs
=εx(6.49)
and
εR=εT+εx,(6.50)
where
0≤εx<1
fs
(6.51)
and
−1
fs
<εR<2
fs
.(6.52)
6.1. DISCRETE TIME DOMAIN FOR A SINGLE LINE 59
Then, from inequality (6.47), we have:
εT+l
v>pl
vT−εx∴l
v>pl
vT−εR.(6.53)
Therefore, an internal fault is detected as external when the ratio between the estimated speed
and the actual speed satisfies: vT
v>p
1+εRv
l
.(6.54)
To ensure that there is an acceptable margin of error where the estimated speed is greater
than the actual speed without resulting in the possibility of an internal fault being detected as
external (Figure 6.2), the forward term in the inequation (6.54) must be greater than one. In this
situation, respecting the error margin, an internal fault within the protection zone will never be
detected as external.
Analyzing now the possibility of an external fault being detected as internal, from inequality
(6.48), we have:
εT+2l
v≤pl
vT−εx∴2l
v≤pl
vT−εR.(6.55)
Therefore, an external fault will be detected as internal when the ratio between the estimated
speed and the actual speed satisfies:
vT
v≤
p
2
1+εRv
2l
.(6.56)
To ensure that there is an acceptable margin of error where the estimated speed is less than
the actual speed without resulting in the possibility of an external fault being detected as internal
(Figure 6.3), the forward term in the inequation (6.56) must be less than one. In this situation,
respecting the error margin, an external fault will never be detected as internal.
The smallest margin for the estimated speed to be greater than the actual speed occurs when
the right-hand term in the inequation (6.54) has the largest value for the denominator, which
occurs for εR=2/fs. In this situation, which is the most critical for an overestimation of the
wave speed, the inequation (6.54) is rewritten as:
vT
v>p
1+2v
l fs
.(6.57)
In turn, the smallest margin for the estimated speed to be smaller than the actual speed
occurs when the term to the right of (6.56) has the smallest value for the denominator, which
occurs for εR=−1/fs. In this situation, which is the most critical for an underestimation of the
wave speed, (6.56) is rewritten as:
vT
v≤
p
2
1−v
2l fs
.(6.58)
According to the above discussion, there is no margin for error in estimating the wave speed
when the right-hand terms in inequations (6.57) and (6.58) are both equal to one, as follows,
respectively:
p
1+2v
l fs
=1∴p=1+2v
l fs
(6.59)
6.1. DISCRETE TIME DOMAIN FOR A SINGLE LINE 60
and p
2
1−v
2l fs
=1∴p=2−v
l fs
.(6.60)
According to equations (6.59) and (6.60), it follows that there is a minimum sampling fre-
quency at which there is a positive and negative margin of error for the estimation of the travel-
ing wave speed, and it is given by:
1+2v
l fs
=2−v
l fs
∴fs=3v
l.(6.61)
Substituting equation (6.61) into equation (6.59) or equation (6.60) gives:
p=1+2
3=1.6,(6.62)
which means that, considering p=1.6, for fS<3v/l, it is not possible to obtain a speed esti-
mation that guarantees the correct detection of internal and external faults simultaneously, since
there is no simultaneous positive and negative margin for error in speed estimation. On the other
hand, for fS≥3v/l, the higher the sampling frequency, the higher the positive and negative error
margins for speed estimation.
6.1.5 Minimum Frequency as a Function of Speed Estimation
For easier mathematical manipulation and future practical implementation, p=1.7 is adopted
in the method. However, the minimum sampling frequency that ensures positive and negative
error margins for the estimation of the traveling wave speed must be computed. From equation
(6.59), the minimum sampling frequency that ensures a positive margin of error for the speed
estimation is given by:
fs>2v
l(1.7−1)∴f s >2.86v
l∴l fs
v>2.86.(6.63)
From equation (6.60), the minimum sampling frequency that ensures a negative margin of error
in the speed estimation is given by:
fs>v
l(2−1,7)∴fs>3,3v
l∴l fs
v>3,3.(6.64)
Considering p=1.7, according to inequations (6.63) and (6.64), the minimum frequency
that simultaneously ensures that the term on the right in inequation (6.57) is greater than one
and the term on the left in inequation (6.58) is less than one, i.e., the minimum frequency
that guarantees positive and negative error margin without a fault in the protection zone being
considered external or an external fault being considered internal, must be greater than 3.3v/l.
However, it is necessary to prove that the inequation (6.22) is always true, i.e., that the left-
hand portion in the inequation (6.22) is the minimum value of the inequation and the right-hand
portion is the maximum value, for p=1.7 and a given sampling frequency. A property of the
floor function (⌊⌋) is that when x−y≥1 then ⌊x⌋−⌊y⌋⌋ ≥ 1. Thus, to prove the right-hand
portion in the inequality (6.22), one has:
2l fs
v−1.7l fs
v≥1∴l fs
v≥3.3∴fs≥3.3v
l.(6.65)
6.1. DISCRETE TIME DOMAIN FOR A SINGLE LINE 61
Similarly, to prove the left-hand side in the inequality (6.22), one has:
1.7l fs
v−l fs
v≥1∴l fs
v≥1.43 ∴fs≥1.43v
l.(6.66)
Therefore, for p=1.7 and fs≥3,3v/l, the inequality (6.22) will be respected. The protection
will act correctly even if the estimated speed has presented a positive or negative error, within
the error margin given by the inequalities (6.57) and (6.58).
According to the inequations (6.57) and (6.58), it is possible to calculate positive and neg-
ative error margins for estimating the speed as a function of the actual traveling wave speed.
However, the actual speed of the traveling wave is unknown information. Thus, to determine
the tolerable margin of error for a particular transmission line, it is necessary to vary the actual
value of the speed in the inequations (6.57) and (6.58) and compute the corresponding values
for the positive and negative margins of error. Although the exact value of the wave speed
is unknown, it is known that for alternating current transmission lines, the speed of the alpha
component of the traveling wave is approximately 98% of the value of the speed of light (c)
(ZIMATH; RAMOS; FILHO, 2010). Thus, it can be guaranteed that the actual speed of the
alpha-mode component of the traveling wave lies between 0.9cand c, where c=3x105km/s.
Figures 6.4 and 6.5 depict the positive and negative error margins, respectively, for sampling
frequencies equal to f s =5 kHz and f s =960 kHz, as a function of the actual speed, which
ranges from 0.9cto c. For both cases, the wave speed was estimated to be equal to the speed of
light c. Figures 6.4 and 6.5 depict that the margin of error for a positive error in speed estimation
is always larger than the margin for a negative error. Figure 6.4 depicts that for actual wave
speeds greater than 0.91c, the error in the speed estimation - for an estimated speed of 0.9c-
is always smaller than the margin of error for f s =5 kHz. Therefore, it is possible to identify
a minimum sampling frequency at which estimating vT=cguarantees that the protection will
act correctly. For instance, when considering vT=cand the actual speed of the wave equal to
90% of the speed of light (v=0.9c), from the inequation (6.57), one has:
f s ≥(︃2∗v
l)︃(︃ 1+εv
0.7−εv)︃∴f s ≥(︃2∗0.9c
l)︃(︄1+0.1
0.9
0.7−0.1
0.9)︄,(6.67)
where εvis the error between the estimated speed (vT=c) and the actual speed (v=0.9c), and
is given by:
εv=c−0.9c
0.9c=1
9.(6.68)
6.1. DISCRETE TIME DOMAIN FOR A SINGLE LINE 62
Actual traveling wave speed
Positive error (%)
0
20
40
60
80
Error in speed estimation
Error margin for fs= 5 kHz
Error margin for fs= 960 kHz
0.90c 0.91c 0.92c 0.93c 0.94c 0.95c 0.96c 0.97c 0.98c 0.99c c
Figure 6.4: Margin for a positive error in speed estimation.
Actual traveling wave speed
Negative error (%)
0
20
40
60
80
Error margin for fs= 5 kHz
Error margin for fs= 960 kHz
0.90c 0.91c 0.92c 0.93c 0.94c 0.95c 0.96c 0.97c 0.98c 0.99c c
Figure 6.5: Margin for a negative error in speed estimation.
The inequality (6.67) was obtained from the inequality (6.57), which defines a positive error
margin so that an internal fault is not detected as an external fault. Therefore, the inequation
establishes a minimum sampling frequency for any value of vgreater than 0.9c
The minimum sampling frequency that enables a positive margin of error in speed estimation
is lower than the minimum sampling frequency that enables a negative margin of error for
external faults not to be detected as internal, as shown by inequations (6.63) and (6.64). It is
necessary to ensure that the sampling frequency given by inequation (6.67) ensures that there
is room for negative error in the speed estimation, i.e., the sampling frequency must respect the
inequation (6.65) as well. This procedure is necessary to ensure that even if the wave velocity
is overestimated (vT=c), the right-hand plot in the inequation (6.58) is not greater than one
because if it is, even if the estimated wave velocity is greater than the real one, an external fault
could be considered as internal due to the low sampling frequency. Therefore, by multiplying
the frequency given by the inequality (6.67) by a constant n, it is possible to ensure that the
inequality (6.65) is respected, as follows:
n(︃2∗0.9c
l)︃(︄1+0.1
0.9
0.7−0.1
0.9)︄>3,3v
l∴v<c(︃n+1,6
2.83 )︃,(6.69)
6.2. PROPOSED METHOD 63
where, to ensure that v<c, we have:
(︃n+1,6
2.83 )︃≥1∴n≥1.16.(6.70)
According to the inequation (6.69), adopting n=1.17, for any actual value of the traveling
wave speed between 0.9cand c, the minimum sampling frequency that guarantees a correct
protection operation for internal and external faults, when estimating the wave speed as being
equal to the speed of light (vT=c), is given by:
fs≥1.17(︃2∗v
l)︃(︃ 1+εv
0.7−εv)︃∴fs≥1.17(︃2∗0.9c
l)︃(︄1+0.1
0.9
0.7−0.1
0.9)︄.(6.71)
According to the inequation (6.71), the higher the actual value of the traveling wave speed
v, the lower the value of the error εvand, consequently, the lower the value of the sampling
frequency (fs). Therefore, by adopting the lowest sampling frequency considering v=0.9c, the
protection scheme will act correctly for any actual traveling wave speed equal to or greater than
90% of the speed of light (v≥0.9c).
6.2 Proposed Method
According to the above, estimating the wave speed always equal to the speed of light is a
good strategy, respecting the inequality (6.71). When estimating the wave speed equal to the
speed of light, there is no need to try to estimate the actual speed of the wave. Therefore, an
internal fault will be detected if:
kf2−kf1≤⌊︃1.7l fs
c⌋︃.(6.72)
Whereas an external fault will be detected if:
kf2−kf1>⌊︃1.7l fs
c⌋︃(6.73)
and, according to inequality (6.23), if:
kf2−kf1≤1.(6.74)
6.3 Performance Assessment
Due to the limitation of the method regarding the correct distinction between the wave
reflected from the fault point and waves reflected at adjacent line terminals, all faults were
performed inside the protected line and at its terminals.
6.3.1 The Power System
Figure 6.6 depicts the electrical system used. The system contains three transmission lines
at a base voltage level of 500 kV. There are two transmission line configurations, type 1 and
type 2. The type 1 transmission line was modeled based on a real transmission line from Chesf,
6.3. PERFORMANCE ASSESSMENT 64
whose parameters are the same as those published by Costa et al. (2017). The type 2 line was
modeled based on a real transmission line from a system in China, whose geometric data refers
to the first type of line described by Pathirana, Dirks and McLaren (2003). The lines were
modeled from distributed parameters. All lines are 200 km long. A relay at bus 2 measured the
signals to protect the line between buses 2 and 3.
Type 1 Line
(protected)
Type 2 LineType 2 Line
Bus 1
Relay
Transmission line type 1
Z0
= 0.3996 + j0.9921 /kmΩ
Z1
= 0.0333 + j0.317 /kmΩ
Y0
= 3.0839 /kmμ
Ω
Y1
= 5.2033 /kmμ
Ω
Generator at bus 1
V
= 1.02 0 p.u.∟
Z1
= 0.871 + j25.661 /kmΩ
Z0
= 1.014 + j18.754 /kmΩ
o
Bus 2 Bus 3 Bus 4
Generator at bus 4
V
= 0.98 20 p.u.∟
Z1
= 0.9681 + j28.513 /kmΩ
Z0
= 1.1268 + j20.838 /kmΩ
o
Transmission line type 2
Z0
= 0.0360 + j0.5787 /kmΩ
Z1
= 0.0164 + j0.317 /kmΩ
Y0
= 2.7979 /kmμ
Ω
Y1
= 4.8759 /kmμ
Ω
Figure 6.6: 500 kV transmission system.
6.3.2 Fault Configuration
The traveling wave-based method presented in this chapter depends on accurately detecting
the arrival times of traveling waves. However, the performance evaluation of a detection method
is beyond the scope of this paper. Therefore, critical cases of traveling wave detection, such as
high fault resistance and low angle of fault incidence, were not analyzed, making it possible
to evaluate the performance of the protection algorithm exclusively. The detector used was
the redundant wavelet transform (COSTA; SOUZA; BRITO, 2010), whose wavelet family was
Daubechies 4, as suggested in (COSTA; SOUZA; BRITO, 2010).
The simulations were performed with an integration step ten times larger than the sampling
step. All faults were of phase A to ground type, the fault resistance was set at 10 Ωand the fault
incidence angle at 90ofor the phase A voltage, providing a higher incidence of electromagnetic
transients. The Clark transform was applied to the voltage and current signals so that traveling
waves were always detected in alpha or ground mode signals.
All evaluations were conducted with faults applied at the line terminals and inside the line,
from 5 km from the local bus up to 195 km, with a 5 km step. The faults were applied with in-
ception time tFassuming random values between kF/fSand kF/fS+1 with a step of (kF/fS)/10
(Figure 6.1), i.e., the fault inception error (εF) assuming random values between 0 and 0.9/fs
with step of 0.1/fs.
In computing the operation time for internal fault detection, the time relative to one sam-
pling period was added, which is more than enough time for digital processing of the relay and
sending the trigger signal to the circuit breaker.
6.3. PERFORMANCE ASSESSMENT 65
6.3.3 Minimum Sampling Frequency
Figure (6.7) depicts the minimum sampling frequency as a function of line length from the
inequation (6.71). According to the theory presented, this sampling frequency should guarantee
that the error in the estimation of the wave speed will always be smaller than the acceptable error
margin so that an internal fault is not considered external (Figure 6.4) and an external fault is
not considered internal (Figure 6.5), regardless of the line parameters. For this, the actual speed
of the traveling wave must be equal to or greater than 90% of the speed of light (v≥0.9c), and
the speed of light must be adopted as the estimated speed of the wave (vT=c).
Line length (km)
0
2
4
6
8
10
12
14
16
18
20
22 Actual speed 0.9c≥
Minimum sampling
frequency (kHz)
50 100 200 300 400 500 600 700 800 900 1000
Figure 6.7: Minimum sampling frequency as a function of line length.
From equations (6.41)-(6.43), we have the percentages of the protected, uncertainty, and
unprotected zones of the transmission line as a function of the sampling frequency, line length,
and wave speed. Figure 6.8(a) depicts the variation of the protected zone as a function of line
length for different sampling frequencies, while Figure 6.8(b) depicts the same parameter but
added to the uncertainty zone. The higher the sampling frequency, the higher the percentages of
these zones. As depicted in Figure 6.8(a), adopting 20 kHz sampling frequency, the protected
zone will be equivalent to 80% of the line length for lines longer than 150 km, a value tradi-
tionally adopted for distance protection. Whereas, if the goal is to achieve such a percentage by
adding the protected zone with the uncertainty zone for 20 kHz, this is achieved for lines from
75 km. Almost 100% of the line can be protected for lengths longer than 50 km by adopting
a sampling frequency of 1 MHz. On the other hand, when adopting 2 kHz, it is impossible to
guarantee a protected zone of 80% for lines shorter than 500 km.
6.3. PERFORMANCE ASSESSMENT 66
Protected +
Line length (km)
0
20
40
60
80
100
fS= 2 kHz
fS= 20 kHz
fS= 100 kHz
fS= 1 MHz
uncertainty zones (%)
Protected zone (%)
(b)
(a)
0
20
40
60
80
100
0 50 100 150 200 250 300 350 400 450 500
Figure 6.8: Estimation of the protected and uncertainty zones as a function of line length for
specific frequencies: a) protected zone; b) protected + uncertainty zone.
By analyzing Figures 6.7 and 6.8, it can be seen that by adopting a minimum sampling
frequency that guarantees 80% of the protected line, necessarily the minimum frequency for a
fault in the protection zone not to be detected as external and an external fault not to be detected
as internal will be respected. Thus, the minimum frequency to be adopted for the protection to
act correctly can be defined as ensuring 80 percent of the protected line. Suppose the desired
percentage of the protected zone is below 80%. In that case, care must be taken to respect the
minimum frequency depicted in Figure 6.7 for the length of the protected line.
From equations (6.41)-(6.43), it is also possible to plot the relation between sampling fre-
quency and protection zone for given line lengths. Such a relation is depicted in Figure 6.9(a)
for 50, 200, and 500 km line lengths. The same relation is depicted in Figure 6.9(b) but with
the sum between the protected and uncertainty zones. The longer the line length, the lower the
sampling frequency needed to guarantee certain percentages of the zones. Note that for lines
longer than 50 km, the protected zone of 80% is guaranteed for a frequency of 60 kHz, while
if the objective is that the protected zone added to the uncertainty zone reaches this percentage,
the frequency drops to 30 kHz for lines longer than 50 km. For a 200 km line, which will be
analyzed in more detail in this chapter, a protected zone of 80% is guaranteed with a sampling
frequency of 15 kHz.
As in Costa et al. (2017) for two-terminal methods, this method breaks the paradigm of
high sampling frequencies for one-terminal methods if the goal is to protect a percentage of the
transmission line. To have broader protection, higher rates will be required.
6.3.4 Method Performance
According to Figure 6.7, a sampling frequency of 6 kHz guarantees that, for a 200 km long
line, a fault in the protected zone is not detected as external, and an external fault is not detected
6.3. PERFORMANCE ASSESSMENT 67
Sampling frequency (kHz)
(b)
(a)
l = 50 km
l = 200 km
l = 500 km
Protected +
0
20
40
60
80
100
uncertainty zones (%)
Protected zone (%)
0
20
40
60
80
100
0 10 20 30 40 50 60 70 80 90 100
Figure 6.9: Estimation of the protected and uncertainty zones as a function of sampling fre-
quency for given line lengths: a) protected zone; b) protected + uncertainty zone.
as internal. Adopting this frequency, the protected zone of the line is 50%, and the unprotected
zones in each line terminal compose 12.5% of the line and the uncertainty zones.
Figure 6.10 illustrates the method’s performance for a frequency of 6 kHz and a line length
of 200 km. As mathematically predicted, no faults were detected as internal in the unprotected
zones, whereas all faults in the protected zone were detected, as well as some in the uncertainty
zones. Therefore, the method was 100% correct. The maximum operating time was 1.2 ms, and
the average was 1.01 ms. This is considerably below the average operating time for traditional
distance protections, which operate after one wave cycle of the fundamental signal, which is
16.67 ms for 60 Hz. For specific cases, such as faults close to the local terminal of the line, the
operating time of traditional distance protections is 8 ms. The two-terminal protection method
based on traveling waves proposed by Costa et al. (2017) showed a maximum operating time of
2.85 ms for 4 kHz and 2.5 ms for 20 kHz, i.e., more than double the time required for the method
proposed here, thus evidencing the potential of one-terminal methods for fast performance.
Fault location (km)
Operation time (ms)
0
0 2
.
0 4.
0 6.
0 8.
1
1 2.
1 4. UPZ UPZUZPZUZ
0 20 40 60 80 100 120 140 160 180 200
Figure 6.10: Protection operation for a 200 km line and fS=6 kHz.
6.3. PERFORMANCE ASSESSMENT 68
Figure 6.11 depicts the protection behavior for a sampling frequency of 1.8 kHz, well be-
low the minimum required for external faults not to be detected as internal. For the 1.8 kHz
frequency, the line has no protected zone, but only the unprotected zones, composing 83.33%
of the line, and an uncertainty zone in the center of the line, which composes 16.67% of the
line. Therefore, only one fault was detected inside the line in the uncertainty zone. However,
an external fault at the remote terminal was detected as internal. It is evident, therefore, that
frequencies below the defined theoretical minimum do not guarantee the correct performance
of the protection.
UPZ
0
0 4.
0 8.
1 2.
1 6.
2
2 4.
2 8. UZ UPZ
Fault location (km)
0 20 40 60 80 100 120 140 160 180 200
Operation time (ms)
Figure 6.11: Protection operation for a 200 km line and fS=1.8 kHz.
In Figure 6.12, the method’s performance is presented for a sampling frequency of 15 kHz,
which is the frequency from which 80% of the 200 km line will be within the protected zone.
The protection operated correctly for the faults within the protection zone. It was not sensitized
for any fault in the unprotected zone or at the terminals of the protected line. The maximum
operating time was 1.11 ms and the average was 0.806 ms, demonstrating that the method’s
operating time is inversely proportional to the value of the sampling frequency.
UPZ
0
0 2
.
0 4.
0 6.
0 8.
1
1 2.
UZ UZ UPZPZ
Operation time (ms)
Fault location (km)
020 40 60 80 100 120 140 160 180 200
Figure 6.12: Protection operation for a 200 km line and fS=15 kHz.
A sampling frequency rate of 15360 Hz is commercially viable for relays. It ensures that
at least 80% of a transmission line of up to 200 km is protected very quickly, regardless of its
electrical parameters. Faults very close to the line terminals would be handled by traditional
protections, which are efficient for close faults.
6.4. CONCLUSION 69
Although the method proposed here, based only on arrival instants of traveling waves, is
insufficient to protect systems with adjacent lines, directional fault information would complete
the method, making it applicable to any system.
6.4 Conclusion
This chapter proposed a method for protecting transmission lines using only one terminal.
An extensive mathematical investigation of the effect of sampling frequency and error on esti-
mating the traveling wave speed was performed.
The method establishes a clear mathematical parameter for defining a minimum sampling
frequency, which makes it possible to adopt low sampling frequencies. Such a mathematical
definition is unprecedented for one-terminal traveling wave-based methods. This also represents
a paradigm break since traveling wave-based methods require high sampling frequencies of
hundreds of kHz. The method is also independent of the estimation of the traveling wave
velocity. This also represents a paradigm break for traveling wave-based methods, especially
those based on one terminal.
The proposed method achieved 100% accuracy for the protected zone defined by the adopted
sampling frequency, regardless of the line’s electrical parameters. The operation time of the
method was well below those presented by traditional methods. It also performed well when
compared to traveling wave-based two-terminal methods.
The correct and reliable distinction between the reflected wave from the fault point and
reflected waves at line terminals when adjacent lines occur has not been investigated in this
thesis. Thus, this is still an open issue for the scientific community. Therefore the method is
only valid for point-to-point lines, not connected to adjacent lines. Furthermore, the method
only applies to transmission lines where the actual speed of the traveling wave is between 90
and 100% percent of the speed of light. This covers almost all overhead lines, whose wave
speed is around 98% of the speed of light.
6.5 Chapter Synthesis
In this chapter, a one-terminal method based on traveling waves has been presented. The
method applies to simple, point-to-point transmission lines with no adjacent lines. It is also
limited to transmission lines with traveling waves with speed above 90% of the speed of light.
An extensive investigation of the effect of sampling frequency and error on estimating the trav-
eling wave speed has been performed. Consequently, the method is independent of estimating
the traveling wave speed and can also be applied for low sampling frequencies.
Chapter 7
Applicability of Wave-based Distance
Protection for Earth Faults Applied to
Meshed HVDC Systems
This chapter investigates the applicability of a distance protection method for earth faults
applied to a meshed HVDC system. A traveling wave-based fault location method is proposed,
starting from the analysis of the effect of sampling frequency. Traveling wave detections are
also used to define the faulty section and guarantee selectivity to the method.
7.1 The Need for Full Protection Selectivity
The objective of the protection in both HVAC and HVDC systems can be summarized as
fault clearing in the system. That is, after detecting the fault, protection needs to act to prevent
the system from continuing to supply the short-circuit current. However, HVDC systems are
more flexible concerning the mode of operation after the fault has been eliminated. For example,
in the case of a permanent fault on one pole of the transmission line, symmetrical monopolar
or bipolar systems can decouple from the transmission line. Their converters can enter in static
synchronous compensator (STATCOM) mode, supplying reactive power to the HVAC system.
A flexible bipolar system, on the other hand, would be able to act in monopolar mode through,
for example, a DMR (Dedicated Metalic Return). However, for the correct ,operating mode
selection, the protection must be fully selective and inform the system of the correct fault zone.
Traditional HVDC protection functions can protect the system for transmission line faults
quickly and without communication between stations. This is the case for the 76DC (IEEE...,
2008) overcurrent protection. HVDC converters have a dedicated and highly sensitive over-
current detection (OCD) function with a short trip time. However, these functions have no
selectivity capability and can be sensitized by faults at any point in the system.
Commercial HVDC systems can achieve full selectivity capability for transmission line
faults through station communication. However, the need for communication slows down sig-
nificantly the protection selectivity (CIGRÉ, 2018).
For meshed HVDC systems, the protection must operate below 2 ms, and the fault must
be cleared within 5 ms (CIGRÉ, 2018). Thus, even if non-selective protection can detect the
fault below 2 ms, selectivity should still be achieved below 5 ms. After this time, there would
be no more fault currents, and determining the fault zone would no longer be possible. For
transmission line faults, the currently commercially available protection functions for HVDC
systems cannot be selective without communication between the terminals. Therefore, due to
the communication delay, full fault selectivity cannot be achieved within 5 ms.
70
7.2. PRINCIPLES OF DISTANCE PROTECTION APPLIED TO MESHED HVDC SYSTEMS71
In this context, fast-acting distance protection would be of great relevance for HVDC sys-
tems without a communication system between the system terminals. This protection would
guarantee protection selectivity for most faults on the transmission line. For meshed HVDC
systems, it could be of even more relevance if it is able to guarantee protection selectivity on
multiple interconnected transmission lines.
7.2 Principles of Distance Protection Applied to Meshed HVDC
Systems
The general idea of traveling-wave-based distance protection for earth faults as described
in the section 5.1. Fig. 7.1 depicts the Lattice diagram for an earth fault applied to one of the
transmission lines of a meshed HVDC system. Due to the difference in speed of the modal
waves (LIU et al., 2012), they arrive at each system bus at different times. This time difference
can be used to estimate the location of the fault. Due to the sampling process of the voltages and
currents at each bus, the arrival times in the continuous-time domain (tαand t0) are unknown.
Thus, they are replaced by their counterparts in the discrete-time domain, kα/fSand k0/fS,
where kαand k0are samples that represent tαand t0in the digital time domain, respectively.
Since multiple lines are in the system, a fault on any line may lead to buses not being
connected to the faulty line detecting these waves. Thus, without a correct estimation of the
location of the fault, protections on different buses may mistakenly detect the fault as internal.
Earth fault
Bus 3 Bus 4
d = 50 km
F
Time (s)
α-mode
tF
W alavefront arriv
discrete time
k f/S
F
Sampling time
0-mode
t0
k f/S
0
k f/S
t
α
α
1/fS
Inductor
Current meter
Voltage meter
1/fS
1/fS
Bus 1 Bus 2
Figure 7.1: Principles of the distance protection for earth faults applied to a meshed HVDC
system.
7.3. THE PROPOSED DISTANCE PROTECTION FUNCTION 72
In addition, as it propagates through a faulty line, the traveling wave reaches the bus and is
transmitted to a subsequent line, also connected to the same bus. In this way, all the voltage
and current measurements for the lines connected to the same bus can simultaneously detect
the traveling wave. Therefore, it becomes a challenge to correctly detect from which line the
traveling wave propagated, making it difficult to estimate the location of the fault.
For full selectivity of protection in a meshed HVDC system, the traveling wave-based dis-
tance protection function at each bus must detect which section of line the traveling wave came
from. From there, the protection function must estimate the location of the fault and be able to
define whether the fault is internal to the protected line.
7.3 The Proposed Distance Protection Function
The proposed earth fault distance protection function is developed by considering the sam-
pling frequency effects on the fault location estimation. Modal traveling waves are required to
detect the faulty section and the fault location on the faulty line. Below is addressed a detailed
analysis.
7.3.1 Continuous Time Domain
The time delay between the fault inception time tFand the first wavefront arrival times in
the bus L tαand t0depends on the modal traveling wave speeds and fault distance from the bus
L, as follows:
tα−tF=dF
vα
(7.1)
and
t0−tF=dF
v0.(7.2)
The difference between the time delays is given by:
(t0−tF)−(tα−tF) = t0−tα=dF
v0−dF
vα
=vα−v0
vαv0dF.(7.3)
Therefore, the fault distance from the local bus is given by (LIU et al., 2012):
dF=t0−tα
m,(7.4)
where mis a variable dependent on the modal traveling wave speeds, given by (LIU et al.,
2012):
m=vα−v0
vαv0.(7.5)
7.3.2 Discrete Time Domain
The IEDs (Intelligent Electronic Devices) that measure the voltages and currents at the
transmission line terminals are digital devices. Thus, the measured signals must be discretized
employing a fixed sampling frequency. Therefore, the exact arrival time of the modal traveling
waves at the local bus tαand t0are unknown and are replaced by their respective discrete time
7.3. THE PROPOSED DISTANCE PROTECTION FUNCTION 73
(kα/fSand k0/fS). The discrete wavefront arrival times are given by:
kα
fS
=⌊tαfS⌋
fS
+1
fS
,(7.6)
where
tα<kα
fS≤tα+1
fS
,(7.7)
and k0
fS
=⌊t0fS⌋
fS
+1
fS
,(7.8)
where
t0<k0
fS≤t0+1
fS
,(7.9)
where ⌊∗⌋is the largest integer value not greater than ∗(floor function).
The discrete fault inception time kF/tS, which is the new reference time, is given by:
kF
fS
=⌊tFfS⌋
fS
,(7.10)
where
tF−1
fS
<kF
fS≤tF.(7.11)
The sampling frequency process yields errors in the wavefront arrival times and the refer-
ence time. The error on the fault inception time is given by:
εF=tF−kF
fS
,(7.12)
where
0≤εF<1
fS
.(7.13)
The errors on the wavefront arrival times are given by:
εα=kα
fS−tα,(7.14)
where
0≤εα<1
fS
,(7.15)
and
ε0=k0
fS−t0,(7.16)
where
0≤ε0<1
fS
.(7.17)
Therefore, the difference between the time delays may also be given by:
t0−tα=k0−kα
fS
+(εα−ε0),(7.18)
7.4. THE PROPOSED METHOD 74
where −1
fS
<εα−ε0<1
fS
.(7.19)
From (7.4) and (7.18), the fault distance, considering the sampling frequency process, be-
comes:
dF=k0−kα+(εα−ε0)fS
m fS
.(7.20)
Assuming the limit values for εα−ε0, which are −1/fSand 1/fS, the fault location can be
estimated by:
k0−kα−1
m fS
<dF<k0−kα+1
m fS
.(7.21)
(7.4) is a particular case of (7.21). The methods that perform the fault location estimation
by (7.4) assume εα−ε0=0 in (7.21), as follows:
dF=k0−kα
m fS
,(7.22)
which is not true, for the most faults.
7.3.2.1 The Search Zone
Analyzing the sampling frequency effect on the fault location enables the definition of a
desired search zone for the fault location. The left and right sides of (7.21) are the minimum
and maximum limits for estimating the fault location. Thus, if a search zone of pkm is desired,
then: k0−kα+1
m fS−k0−kα−1
m fS≤p∴2
m fS≤p,(7.23)
or
fS≥2
mp.(7.24)
Therefore, the fault location can be estimated with 100% assurance for a specific desired search
zone when a minimum sampling frequency is adopted.
From (7.24), the length of the search zone can be estimated by adopting a specific sampling
frequency as follows:
p=2
m fs
.(7.25)
The distance from dFgiven by (7.22) to the inferior and the superior limits of the search
zone, given by (7.21), are equal. Therefore, the estimated point for the fault location given by
(7.22) returns a maximum error equal to p/2.
7.4 The Proposed Method
This work proposes a methodology where the fault location is estimated within a range
of search as a function of the sampling frequency. The range for the fault location is given
by (7.21), where the length of the desired search zone pis respected by adopting a minimum
sampling frequency given by (7.24). A mean fault location is given by (7.22), positioned in the
center of the search zone.
7.5. PERFORMANCE ASSESSMENT 75
For instance, assuming a particular transmission line where vα=2.9429×105km/s and v0=
1.5975×105km/s, according to (7.5), m=2.8620×10−6. Adopting fS=100 kHz, according
to (7.25), p ≈7 km. Considering a fault where k0−kα=15, according to (7.21), the range for
the fault location is from 48.92 to 55.90 km, i.e., the length of the range is 6.98 km. According
to (7.22), the mean location for the fault is 52.41 km.
7.4.1 Definition of the Faulty Section
When reaching a bus in a meshed HVDC system like the one in Fig. 7.1, a traveling wave is
attenuated by the inductor connected to the line. Thus, before being transmitted to another line
connected to the same bus, it is again attenuated by the inductor of the neighboring line. There-
fore, the voltage and current meters connected to the line after the inductor detect a transmitted
wave that is more attenuated than before the inductor on the originating line.
Sabug Jr. et al. (2020) calculates the wavelet transform the energy of transients measured by
meters connected between the line inductor and the line. Thus, the authors determine the faulty
section by identifying the transients with the highest energy.
This thesis compares the amplitudes of traveling waves detected at each line terminal con-
nected to the same bus. Measurements should be taken between the inductor connected to the
line and the line, as Fig. 7.1 depicts. In this way, it is possible to define from which line section
the traveling wave originated.
7.5 Performance Assessment
Two HVDC test systems were modeled in order to evaluate the proposed method. The first
is a multiterminal meshed system whose transmission lines have been modeled with Bergeron’s
model. In this model, the traveling wave speeds can be accurately computed. Therefore, the
effect of the sampling frequency and the mathematics presented in this work can be precisely
evaluated in section 7.5.1.
The second system is a point-to-point LCC system based on an actual system. The trans-
mission line is modeled with the JMarti frequency-dependent distributed parameter line model.
This is a more realistic line model in which the traveling wave speed is unknown and needs to be
estimated. Thus, the proposed fault location estimation method can be evaluated by accounting
for errors in the modal traveling wave speed estimation in section 7.5.2.
7.5.1 Test System 1
Fig. 7.2 depicts the meshed HVDC grid considered in this work. The system is based on
the one proposed by Leterme et al. (2015). The system is a symmetrical monopolar with a ±
320 kV voltage. It consists of four terminals with modular multilevel converters (MMC). The
terminals are connected by five overhead transmission lines, forming a meshed system. All
converters are connected to AC equivalents. The AC systems connected to buses 1 and 2 supply
power to the DC system. Whereas the AC equivalents at buses 3 and 4 consume power from
the DC system.
The AC systems are modeled as ideal 370 kV, 60 Hz voltage sources connected in series to a
concentrated impedance equivalent. Fig. 7.3 depicts the parameters of the HVDC transmission
lines. The lines are based on a real Brazilian HVDC system, the Madeira River system (LUZ;
JUNIOR; JUNIOR, 2014). The transmission lines are modeled using the Bergeron frequency-
independent distributed parameter model. Table 7.1 depicts the transmission line parameters
7.5. PERFORMANCE ASSESSMENT 76
Bus 3 Bus 4
Inductor
Current meter
Voltage meter
Bus 1 Bus 2
Y D
AC
grid
YD
YD
Y D
Line L12 = 100 km
Line L14 =
Line L24 =
Line L13
Line L34 = 200 km
100 km
200 km
200 km
AC
grid
AC
grid
AC
grid
Figure 7.2: Meshed HVDC test system.
for the Bergeron model. The modal wave speeds are vα≈2.9429 ×105(0.9921c) and v0≈
1.5975×105(0.5325c), and computed as follows:
vα=1/√︁LαCα≈2.9429×105(7.26)
and
v0=1/√︁L0C0≈1.5975×105.(7.27)
Ground resistivity = 1000 mΩ
10 m
5.83 m
Conductors: Thrasher 2312 MCM ACSR
Number of conductors per phase: 1
Ground conductors: 3/8'' Steel
Tower: cc600
16.40 m
31.27 m
0.4572 m
Mid-Span Sag:
18.04 m for conductors
7.51 m for ground wires
Figure 7.3: Geometrical parameters for the transmission line.
Faults were simulated using MATLAB/Simulink®at a sampling frequency of 100 kHz. On
each line, faults were applied by varying the fault location at a 5 km step. Also, faults were
applied at 3 km from the stations at each line’s terminal. The faults applied were of the positive
pole-to-ground, negative pole-to-ground, and pole-to-pole fault types. 63 faults were applied
on each of the lines L12 and L24. Each of the lines L14, L13, and L34 had 123 faults applied.
7.5. PERFORMANCE ASSESSMENT 77
In total, 495 faults were applied to all five lines in the system. Subsequently, the following
performance assessment methodology was adopted:
1. the detection of the faulty section for all 495 faults applied was performed in the subsec-
tion 7.5.1.2;
2. a discussion about the sampling frequency to be adopted depending on the search zone
was addressed in subsection 7.5.1.3;
3. the performance assessment of the proposed fault location method for all 330 earth faults
applied to all transmission lines, as addressed in subsection 7.5.1.4;
4. the evaluation of the protection operation time for all earth faults detected as internal ones,
as addressed in 7.5.1.6.
7.5.1.1 Converter Topology and Controls
Each MMC converter has six arms consisting of five switching modules (SMs) connected in
series with an impedance RL. The SMs are of the half-bridge type composed of insulated-gate
bipolar transistors (IGBTs).
Fig. 7.4 depicts the diagram of high-level and low-level controllers of MMCs. The low-
level control consists of a phase disposition sinusoidal pulse width modulation (PD-SPWM).
It is responsible for voltage balancing for the SMs. The high-level control, in turn, is divided
into two sub-controls, one for active power control and one for reactive power control. Each
sub-control consists of two control loops, external and internal. The external control provides
the internal control’s current reference dq. The internal control loop provides voltage reference
for the PD-SPWM.
The high-level control follows a master-slave strategy. The converter station at bus 4 is the
main master station for voltage control on the daxis. The bus 3 station assumes the backup
master position. The stations at buses 1, 2, and 3 perform active power control with references
at -200 MW, -100 MW, and 150 MW, respectively. All the MMCs perform reactive power
control on the qaxis. A detailed system description can be found in Santos (2021).
Figure 7.4: High-level and low-level controllers diagram.
Table 7.1: Electrical parameters for the transmission line.
Aerial Mode Ground Mode
R(Ω/km) L(mH/km) C(µF/km) R(Ω/km) L(mH/km) C(µF/km)
0.00702 0.860602 0.0134166 0.008028 3.88784 0.0100794
7.5. PERFORMANCE ASSESSMENT 78
7.5.1.2 Definition of the Faulty Section
All the buses are connected to more than one line for the HVDC meshed system under
analysis. Thus, the traveling wave is transmitted to the other lines when propagating through a
specific line and colliding with a bus. Therefore, the traveling wave can be detected through the
voltage measurements of all lines. By defining the line from which the traveling wave originally
arrived, it is possible to estimate the location of the fault more accurately. To do this, the method
compares the intensity of the wavefront measured on all lines connected to the bus at the arrival
time of the first alpha-mode wavefront. The wavefront with the highest intensity indicates the
faulty section.
Fig. 7.5 depicts the wavelet transform coefficients for the alpha-mode voltage signals at
buses 1 and 2 for a fault on line L12 located 50 km from bus 1. Fig. 7.5(a) depicts that
the highest intensity traveling wavelet is detected on line L12 for bus 1. Although it cannot
be determined if the fault occurred at line L12, it can be determined that the traveling wave
propagated through that line. Fig. 7.5(b) depicts that for the bus 2, the method correctly detected
that the wave propagated from line L12 as well. If there was communication between these two
buses, it would be possible to determine that the fault occurred on line L12. However, since
the method does not rely on telecommunication, it is not possible to determine the faulty line
without first estimating the location of the fault.
(a)
-4
-2
0
2
4
6
Wavelet Transform
Coefficients
×10 4
Line L12
Line L13
Line L14
12345
Samples
-4
-2
0
2
4
6
Wavelet Transform
Coefficients
×10 4
Line L12
Line L24
(b)
Figure 7.5: Wavelet transform coefficients for a fault on line L12 for the alpha-mode voltages
of all lines connected to: (a) bus 1; (b) bus 2.
7.5. PERFORMANCE ASSESSMENT 79
Fig. 7.6 depicts that for buses 3 and 4, the method correctly detected the faulty section. For
bus 3, the traveling wave came from line L31. For bar 4, the wave came from line L24. For all
495 faults applied in the system, the method could correctly detect the faulty section. This was
possible even for the pole-to-pole faults since they generate alpha-mode traveling waves.
7.5.1.3 Search Zone
Fig. 7.7 depicts the minimum sampling frequency as a function of the desired length for
the search zone, considering the transmission line depicted on 7.2. The greater the sampling
frequency the smaller the search zone. 7.7(a) depicts the sampling frequency required for search
zones varying from 0 to 35 km. For instance, a sampling frequency of 100 kHz ensures a search
zone of about 7 km. Fig. 7.7(b) depicts the search zone for a sampling frequency within a range
traditionally adopted in real HVDC systems. For example, for a sampling frequency of 25 kHz,
the search zone is approximately 28 km. On the other hand, for higher sampling frequencies
and commercially available for HVAC systems, Fig. 7.7(c) depicts a search zone between 1 and
7 km. For 1 MHz, the search zone is 700 meters, which represents an error for the mean fault
location close to a typical tower span, approximately 300 m.
-2000
0
2000
4000
6000
Wavelet Transform
Coefficients
Line L31
Line L34
12345
Samples
-4000
-2000
0
2000
4000
6000
Wavelet Transform
Coefficients
Line L14
Line L24
Line L34
(a)
(b)
Figure 7.6: Wavelet transform coefficients for a fault on line L12 for the alpha-mode voltages
of all lines connected to: (a) bus 3; (b) bus 4.
7.5. PERFORMANCE ASSESSMENT 80
(a)
20 100 200 300 400 500 600 700 800 900 1000
0
5
10
15
20
25
30
35
Length of Search Zone (km)
10 12 14 16 18 20 22 24 26 28 30
20
30
40
50
60
70
Length of Search Zone (km)
(b)
100 200 300 400 500 600 700 800 900 1000
Minimum Sampling Frequency (kHz)
0
2
4
6
8
Length of Search Zone (km)
(c)
Figure 7.7: Minimum sampling frequency as a function of the desired length for the search
zone, which varies from: (a) 0 to 35 km; (b) 20 to 70 km; (c) 0 to 8 km.
7.5. PERFORMANCE ASSESSMENT 81
7.5.1.4 Fault Location Estimation
Fig. 7.8 depicts the Lattice diagram for a positive pole to ground fault on line L12, distanced
50 km from bus 1. The adopted sampling frequency was 100 kHz. The difference in samples
between the arrival times of the alpha and zero mode waves measured on bus 1 was 15 samples.
The range for the fault location estimation on bus 1 given by (7.21) is from 48.92 to 55.90 km.
The mean fault location estimation on bus 1 given by (7.22) is 52.41 km.
Earth fault
Time
α-mode
Bus 1 Bus 2
0-mode
d = 50 km
F
15 Samples
Modal
voltages
Samples
Inductor
Current meter
Voltage meter
Figure 7.8: Lattice diagram for a fault on line L12, 50 km from bus 1.
Table 7.2 summarizes the fault location estimations and their respective errors at all buses
for this specific fault. The faulty transmission line is connected to buses 1 and 2. Considering
only the fault location estimated by these two buses, the maximum error was 5.9 km. This value
is below the mathematically predicted search zone, which is 7 km. Similarly occurs for bus 4.
However, for bus 3, the maximum error was 8.9 km. Thus bus is 250 km from the fault point
and is not connected to a faulty line. Thus, the traveling wave detection becomes less accurate,
which influences the accuracy of the fault location estimation. However, even less precise, this
is still relevant information since it was estimated without communicating with the other buses
in the system.
Table 7.2: Fault location estimation for a fault on line L12 at 50 km from bus 1.
Inferior Limit Mean Location Superior Limit
Bus 1 Estimation (km) 48.92 52.41 55.90
Error (km) -1.08 2.41 5.90
Bus 2 Estimation (km) 48.92 52.41 55.90
Error (km) -1.08 2.41 5.90
Bus 3 Estimation (km) 241.1 244.59 248.08
Error (km) -8.90 -5.41 -1.92
Bus 4 Estimation (km) 146.75 150.25 153.74
Error (km) -3.25 0.25 3.74
7.5. PERFORMANCE ASSESSMENT 82
7.5.1.4.1 Variation of Fault Location on Line L12
Fig. 7.9 depicts the error in fault location estimation for a positive pole to ground faults
applied on line L12 and estimations made on buses 1 and 2. The faults were applied from 5 to
95 km from bus 1, at steps of 5 km. Additionally, faults were applied at 3 and 97 km so that the
boundary of the search zone could be checked. This makes a total of 21 fault cases. Both buses
1 and 2 performed equally well in fault location estimation. Fig. 7.10 depicts the fault location
estimation on bus 1 as a function of the fault location for the same fault cases.
-10
-5
0
5
10
Error in the Fault
Location Estimation (km)
0 10 20 30 40 50 60 70 80 90 100
Fault Location (km)
-10
-5
0
5
10
Error in the Fault
Location Estimation (km)
(b)
(a) Sup. Lim.
Mean Loc.
Inf. Lim.
Search Zone
Theoretical Lim.
Figure 7.9: Error in the fault location estimation as a function of the fault location for faults on
the line L12 for: (a) estimation on bus 1; (b) estimation on bus 2.
All wavefronts were correctly detected so that all faults were estimated within the math-
ematically predicted search zone. The fault applied at 3 km had its mean location estimated
at 0 km, with the search zone outside the L12 line. The fault applied at 97 km had its mean
estimated location within line L12 but with a search zone extending to line L24. For these
fault cases, the previous detection of the faulty line would be fundamental for the correct fault
location estimation and eventual protection operation.
Fig. 7.11 depicts the fault location estimation for the faults applied on line L12 and estima-
tions performed on buses 3 and 4. For both buses, several faults were located slightly outside
the search zone. This is due to incorrect detection of the wavefronts. Wavefronts are attenu-
7.5. PERFORMANCE ASSESSMENT 83
0 10 20 30 40 50 60 70 80 90 100
Fault Location (km)
-20
0
20
40
60
80
100
120
Fault Location Estimation (km)
Sup. Lim.
Mean Loc.
Inf. Lim.
Search Zone
Zero Error Line
Figure 7.10: Fault location estimation on bus 1 as a function of the fault location for faults on
the line L12.
ated when they reach the line terminals and are transmitted to an adjacent line. In addition, the
greater the distance from the fault point, the greater the attenuation of the wave. These factors
make it difficult to detect the correct arrival sample of the wavefront. Thus, the estimation of
the fault location performed by buses not connected to the faulty line can be used efficiently to
determine whether the fault is internal or external to the lines connected to these buses. How-
ever, the buses connected to the faulty line can estimate more accurately the fault location due
to the lower attenuation of the wavefronts arriving at these buses.
7.5.1.4.2 Variation of Fault Location on Line L13
Positive pole-to-ground faults were applied on the L13 line from 5 to 195 km, at steps of 5
km. Additionally, faults were applied at 3 and 197 km. Thus totaling 41 fault cases. Fig. 7.12
depicts the error in fault location estimation as a function of the fault point for buses 1 and 3.
All fault locations were estimated within the mathematically defined search zone.
Fig. 7.13 depicts the fault location estimation as a function of the fault location for mea-
surements taken at bus 2. This bus is not directly connected to the faulty line. Therefore, the
traveling waves arrived at bus bar 2 with higher attenuation. This resulted in inaccuracy in
detecting the correct sample arrival of the waves. Thus, in some cases, the fault was located
slightly outside the search zone stipulated by the method.
Fig. 7.14 depicts the fault location estimation as a function of the fault location for measure-
ments performed at bus 4. Fig. 7.14(a) depicts the estimation performed for waves that arrived
at bus 4 from line L41. Whereas Fig. 7.14(b) depicts the estimation for waves coming from
7.5. PERFORMANCE ASSESSMENT 84
200 210 220 230 240 250 260 270 280 290 300
180
200
220
240
260
280
300
Fault Location Estimation (km)
Sup. Lim.
Mean Loc.
Inf. Lim.
Search Zone
Zero Error Line
100 110 120 130 140 150 160 170 180 190 200
Fault Location (km)
80
100
120
140
160
180
200
Fault Location Estimation (km)
(b)
(a)
Figure 7.11: Fault location estimation as a function of the fault location for faults on the line
L12 for: (a) estimation on bus 3; (b) estimation on bus 4.
7.5. PERFORMANCE ASSESSMENT 85
Fault Location (km)
(b)
(a)
-10
-5
0
5
10
Error in the Fault
Location Estimation (km)
0 20 40 60 80 100 120 140 160 180 200
-10
-5
0
5
10
Error in the Fault
Location Estimation (km)
Sup. Lim.
Mean Loc.
Inf. Lim.
Search Zone
Theoretical Lim.
Figure 7.12: Error in the fault location estimation as a function of the fault location for faults
on the line L13 for: (a) estimation on bus 1; (b) estimation on bus 3.
line L43. This is because, for the first half of the faults applied on line L13, the shortest path to
bus 4 is through line L41, which is 200 km long. For faults applied on the second half of line
L13, the shortest path for traveling waves is through line L43, which is also 200 km long. This
way, even varying the fault point on line L13 with a range of approximately 200 km, the fault
location at bus 4 was correctly estimated with a range of approximately 100 km.
7.5.1.4.3 Variation of Fault Location on Lines L14, L24, and L34
The same methodology was applied for pole-to-ground faults on lines L14, L24, and L34.
Therefore, 41 faults were applied on lines L14, 21 on L24, and 41 on L34. This makes a total of
103 additional fault cases. The proposed method performed similarly to the results presented for
the faults in lines L12 and L13. For all cases, the buses connected to the faulty line estimated the
fault location within the previously calculated search zone. For the other buses, in some cases,
the traveling wave arrival samples were not detected with complete accuracy, which resulted in
an estimation of the fault location slightly outside the search zone.
7.5. PERFORMANCE ASSESSMENT 86
Sup. Lim.
Mean Loc.
Inf. Lim.
Search Zone
Zero Error Line
100 120 140 160 180 200 220 240 260 280 300
Fault Location (km)
50
100
150
200
250
300
350
Fault Location Estimation (km)
Figure 7.13: Fault location estimation as a function of the fault location for faults on the line
L13 and estimation on bus 2.
7.5.1.5 Negative Pole-to-Ground and Pole-to-Pole Fault Cases
All the fault cases mentioned so far were repeated for negative pole-to-ground and pole-to-
pole faults. Thus, 165 negative pole-to-ground and 165 inter-pole faults were applied on lines
L12, L13, L14, L24, and L34. For the negative pole-to-ground faults, the results were the same
as for the positive pole-to-ground faults. The method could not estimate the faults’ location for
the inter-pole faults since there was no detection of zero-mode waves.
7.5.1.6 Protection Operation Time
The distance protection was parameterized to operate for faults with a location range of
less than 90% of the line length. The operation time of the protection corresponds to the time
between the fault inception time and the arrival of the zero-mode traveling wave, added to a
sampling time of the IED.
Fig. 7.15 depicts the operation time of the protection as a function of the fault location for
positive pole-to-ground faults. The faults were applied on line L12. The protection functions
on buses 1 and 2 were sensitized. Fig. 7.15(a) depicts the operation time of the protection at
bus 1. Fig. 7.15(b) depicts the operation time of the protection at bus 2 with the fault location
taking as reference bus 1. All faults up to 80 km were detected as internal for both buses. The
fault applied at 85 km was estimated at 83.86 and 90.85 km. Thus, above 90 km of the defined
protection zone. The maximum operation time was 0.54 ms.
Fig. 7.16 depicts the operation time of the protection for fault applied on line L13. Only the
protections on buses 1 and 3 were sensitized. All applied faults up to 175 km were correctly
7.5. PERFORMANCE ASSESSMENT 87
(b)
(a)
150
200
250
300
350
400
Fault Location Estimation (km)
Sup. Lim.
Mean Loc.
Inf. Lim.
Search Zone
Zero Error Line
200 220 240 260 280 300 320 340 360 380 400
Fault Location (km)
150
200
250
300
350
400
Fault Location Estimation (km)
Figure 7.14: Fault location estimation as a function of the fault location for faults on the line
L13 and estimation on bus 4 for traveling waves coming from the line: (a) L41; (b) L43.
7.5. PERFORMANCE ASSESSMENT 88
(a)
No operation
Operation
0
0.2
0.4
0.6
Operation Time (ms)
0 10 20 30 40 50 60 70 80 90 100
Fault Location (km)
0
0.2
0.4
0.6
Operation Time (ms)
(b)
Figure 7.15: Protection operation time as a function of the fault location referred to bus 1 for
faults on the line L12 and protection function on: (a) bus 1; (b) bus 2.
detected as internal. From 180 km onwards, all faults were correctly detected outside the defined
protection zone.
Similar results were found for the faults applied to lines L14, L24, and L34. The same
operating times for the positive pole-to-ground faults were also performed for the negative pole-
to-ground faults. The method was not able to detect any pole-to-pole faults.
The method can detect the fault in both terminals connected to the faulty line only when
the fault is within the protection zone for both buses. Otherwise, only one of the line terminals
can detect the fault as internal. In this situation, it would not be possible to have full protection
selectivity without communication between the terminals.
A DTT protection scheme could be achieved for the proposed distance protection. In this
way, getting full protection selectivity with only local measurement data would be possible.
However, in this situation, communication between the terminals would still be required for a
direct trip transfer signal to be sent to the remote terminal.
Fig. 7.17 depicts the cumulative frequency of the protection operation time for the cases
in which the protection tripped. Among the 330 cases of pole-to-ground faults applied in the
system, the distance protection tripped for 284 cases. All were correctly detected as internal
faults. Thus, defined for a protection zone of 90% in each line, the protection operated in 86%
of the grounded faults. All faults were correctly detected by at least one of the buses in less
7.5. PERFORMANCE ASSESSMENT 89
than 1.2 ms. Thus, it is evident that traveling wave-based distance protection applied to HVDC
meshed systems is fast. Furthermore, such protection can be of great relevance in the context
of the need for total selectivity of protection in the occurrence of faults on transmission lines
when there is no communication between the system terminals.
7.5.2 Test System 2
Fig. 7.18 depicts the simplified topology of the LCC-HVDC transmission system used to
assess the performance of the proposed protection system. This benchmark model is based on
the Madeira River system of ±600 kV and 3150 MW/pole (LUZ; JUNIOR; JUNIOR, 2014).
It is modeled on the EMTP/ATPDraw software and is available for download in (LUZ, 2016).
The protected DC transmission line is 500 km long and modeled with the JMarti frequency-
dependent distributed parameter line model according to its geometrical parameters shown in
Fig. 7.3. Additionally, the adjacent AC transmission lines are 100 km long and modeled with
the JMarti model. The geometrical parameters of the AC transmission lines are based on an
actual 230-kV system and are depicted in Fig. 7.19.
In the JMarti frequency-dependent model, the traveling wave speed is unknown, so it needs
to be estimated. In the design of real HVDC transmission lines, the system is completely mod-
(a)
No operation
Operation
(b)
0 20 40 60 80 100 120 140 160 180 200
0
0.5
1
1.5
Operation Time (ms)
0 20 40 60 80 100 120 140 160 180 200
Fault Location (km)
0
0.5
1
1.5
Operation Time (ms)
Figure 7.16: Protection operation time as a function of the fault location referred to bus 1 for
faults on the line L13 and protection function on: (a) bus 1; (b) bus 3.
7.5. PERFORMANCE ASSESSMENT 90
0 0.2 0.4 0.6 0.8 1 1.2
Operation Time (ms)
0
20
40
60
80
100
Cumulative Frequency (%)
Figure 7.17: Cumulative frequency for the protection operation time.
Bus 1 Bus 2
AC line 1 AC line 2
Protected DC line
Local Station Remote Station
Inductor Current meter Voltage meter
Figure 7.18: Point-to-point LCC-HVDC test system.
Ground resistivity = 531 mΩ
11.582 m
7.267 m
9.220 m
19.555 m
Conductors: ACSR 636 MCM 26/7
Number of conductors per phase: 1
Ground conductors:
ACC HS 3/8'' 7 wires
3.429 m
Figure 7.19: Geometrical parameters for the AC transmission line.
eled in an EMTDC (Electromagnetic Transients including DC) software. The modeling is done
with high accuracy since all data for all components of the real system to be implemented is
known. In addition, the entire control and protection design is implemented based on simula-
tions of the modeled system. Thus, a viable strategy for estimating the modal traveling wave
speeds would be through simulation. Additionally, the estimation could be performed on a real
system employing an energization procedure. This procedure has been adopted before for real
HVAC systems (SCHWEITZER et al., 2016) and has been proven to be suitable in simulations
for estimating modal wave speeds (FRANÇA et al., 2020).
7.5. PERFORMANCE ASSESSMENT 91
For test system 2, modal wave speeds were estimated from the simulation of a pole-to-
ground fault at the end of the protected DC line at the remote station connection. The modal
wave propagation time was measured from the fault inception time to the instants of modal
wave arrival at the local station. The modal wave speeds were estimated as vα≈2.9429×105
(0.9921c) and v0≈2.6042×105(0.8681c).
Simulations were performed with a simulation step-size equal to 1 µs. The adopted relay
sampling frequency was 25 kHz. Positive pole-to-ground faults were applied by varying the
fault location at a 5 km step from 0 to 500 km of the protected DC line. In total, 101 faults were
applied. The following performance assessment methodology was adopted:
1. a discussion about the sampling frequency to be adopted depending on the search zone
was addressed in subsection 7.5.2.1;
2. the performance assessment of the proposed fault location method, as addressed in sub-
section 7.5.2.2;
3. the evaluation of the protection operation time for all faults detected as internal ones, as
addressed in 7.5.2.3.
7.5.2.1 Search Zone
Fig. 7.20 depicts the minimum sampling frequency as a function of the desired length for
the search zone, considering the system depicted in Fig. 7.18. In test system 2 the zero-mode
wave speed is considerably higher than in test system 1. This is because the transmission line
is modeled with the JMarti frequency-dependent model. As a consequence, the length of the
search zone becomes larger, according to 7.25. For the sampling frequency of 25 kHz, the
search zone now becomes approximately 166 km. A sampling frequency of 1 MHz would
result in a search zone of approximately 4 km.
Since in actual HVDC systems, the sampling frequency is 25 kHz, the 166 km search zone
given by the proposed method would need to be more accurate for fault location estimation.
However, with the proposed mathematics, it would still be possible to determine a maximum
range of the distance protection in order to guarantee the selectivity of the protection, even
with the lack of communication between the stations. This is further discussed in the following
sections.
7.5.2.2 Fault Location Estimation
For systems with transmission lines modeled with frequency-dependent models, as in real
systems, there is expected to be greater uncertainty in the estimation of the traveling wave
speed. This occurs especially with the zero-mode wave. The greater the distance from the
fault to the measuring point, this mode suffers greater propagation attenuation. Thus, there is a
higher dependency between the fault point and the real speed of the zero-mode traveling wave
(LIU et al., 2012). This can influence the estimation of the fault location. This is an important
motivation for the need to know the uncertainty in fault location estimation precisely due to the
effect of sampling frequency in order to minimize uncertainties in distance protection.
Fig. 7.21 depicts the error in fault location estimation. Fig. 7.22 depicts the fault location
estimation as a function of the fault location for the same fault cases. Among the 101 faults
applied, 6 presented an estimated search zone with an error above the theoretically predicted
one. These six faults were applied at points 85, 170, 180, 265, 275, and 335 km. The errors for
the search zone’s theoretical limit were approximately 1.6, 3.3, 13.3, 15, 25, and 1.6 km. These
errors are due to the error in estimating modal wave speeds.
7.5. PERFORMANCE ASSESSMENT 92
There is expected to be a greater error between the value of the estimated zero-mode wave
speed and the actual value of the speed for faults closer to the local station. This is because the
modal wave speeds have been estimated from the application of a fault at the remote terminal.
Thus, the closer the fault is to the remote terminal, the closer the zero-mode wave speed will
be to the previously estimated value. Consequently, the fault search zone estimation should
(a)
(b)
(c)
0 100 200 300 400 500 600 700 800 900 1000
0
50
100
150
200
250
Length of Search Zone (km)
20 30 40 50 60 70 80 90 100
0
50
100
150
200
Length of Search Zone (km)
100 200 300 400 500 600 700 800 900 1000
Minimum Sampling Frequency (kHz)
0
10
20
30
40
50
Length of Search Zone (km)
Figure 7.20: Minimum sampling frequency as a function of the desired length for the search
zone for: (a) 0 to 1000 kHz; (b) 20 to 100 kHz; (c) 100 to 1000 kHz.
7.5. PERFORMANCE ASSESSMENT 93
be more accurate for faults closer to the remote station. The results presented reinforce this
statement, since all faults applied from 340 km were located within the theoretical search zone.
This represents 68% of the line length.
0 50 100 150 200 250 300 350 400 450 500
Fault Location (km)
-200
-100
0
100
200
Error in the Fault
Location Estimation (km)
Sup. Lim.
Mean Loc.
Inf. Lim.
Search Zone
Theoretical Lim.
Figure 7.21: Error in the fault location estimation as a function of the fault location.
Sup. Lim.
Mean Loc.
Inf. Lim.
Search Zone
Zero Error Line
0 50 100 150 200 250 300 350 400 450 500
Fault Location (km)
-100
0
100
200
300
400
500
600
Fault Location Estimation (km)
Figure 7.22: Fault location estimation as a function of the fault location.
7.6. CONCLUSION 94
7.5.2.3 Protection Operation Time
The distance protection was parameterized to operate for faults with a location range of less
than 90% of the line length, 450 km. The operation time of the protection corresponds to the
time between the fault inception time and the arrival of the zero-mode traveling wave, added to
a sampling time of the IED.
Fig. 7.23 depicts the operation time of the protection as a function of the fault location. All
faults applied up to 375 km were detected as internal. This represents 75% of the line length.
The faults applied at 385 and 395 km were also detected as internal. 395 km represents 79%
of the line length. All the remaining faults were detected as outside of the protection zone of
90% of the line. The fault at 385 km presented a search zone estimation ranging from 250 to
416 km. This is less than 90% of the line length. On the other hand, the fault at 380 km had a
search zone estimation ranging between 333 and 500 km, which is more than 450 km. For this
reason, this fault was detected as external. Similarly occurred for the remaining faults detected
as external ones.
Therefore, even with the definition of a high search zone for the fault location, the method
is reliable for defining a protection zone. This ensures selectivity of protection for most faults
when communication fails between stations. In addition, the method presented a maximum
operation time of less than 1.6 ms, representing a very fast operation time.
No operation
Operation
0 50 100 150 200 250 300 350 400 450 500
Fault Location (km)
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
Operation Time (ms)
Figure 7.23: Protection operation time as a function of the fault location.
7.6 Conclusion
This chapter evaluated the applicability of traveling wave-based distance protection for
meshed HVDC systems. A distance protection method was proposed for earth faults in over-
head transmission lines. A thorough investigation of the effect of sampling frequency was
performed.
The method defines a mathematical equation for defining the minimum sampling frequency
as a function of the search zone to estimate the fault location. Therefore, the fault location
presents greater reliability for its application in distance protection since the error in estimating
the fault location is mathematically predicted. In addition, there is a paradigm breaking con-
cerning the need for a high sampling frequency for traveling wave-based fault location. For
7.7. CHAPTER SYNTHESIS 95
example, a sampling frequency of 25 kHz, which is commercially adopted in actual systems,
could be used in distance protection.
Two systems were modeled for the assessment of the proposed method. The first system
contains four terminals interconnected by five transmission lines modeled by the Bergeron dis-
tributed parameter model. Thus, the traveling waves’ modal speeds are known, enabling the
accurate evaluation of the mathematics presented. The method was able, at each terminal, to
correctly distinguish internal faults from external faults for faults applied on all system lines.
For the terminals connected to the faulty line, the method was able to locate 100% of the faults
within the mathematically predicted search zone. For the other terminals, some faults were
located slightly outside the search zone due to lower accuracy in wavefront detection.
The second is a point-to-point LCC system with transmission lines modeled with the frequency-
dependent JMarty model. In this way, it was possible to evaluate the proposed method in a more
real-world scenario, where the traveling wave speed is unknown and needs to be estimated. As
expected in an actual system, in this line model, the speed of the zero-mode wave approaches
the speed of the alpha-mode wave. Hence, the search zone predicted by the proposed method
becomes larger. The search zone for the test system used was approximately 166 km for a 500
km line, which is significantly long. However, the precise evaluation of the effect of the sam-
pling frequency made it possible to guarantee with high reliability the search zone as a function
of the sampling frequency. This has made distance protection more reliable. By defining a
protection zone of 90% of the line, the method detected all faults up to 75% of the line.
The proposed method showed a maximum operation time below 1.6 ms for all detected
internal faults. This value is below the 2 ms maximum trip time requirement of the protection for
meshed HVDC systems (CIGRÉ, 2018). This operation time is also achieved by the overcurrent
protection that monitors the converter, the OCD. However, the OCD protection does not have
any selectivity. Thus, the proposed method can act selectively and ensure greater selectivity to
the system below 2 ms since additional communication delays do not affect it. Thus, the method
shows promise for its applicability in meshed HVDC systems.
7.7 Chapter Synthesis
This chapter evaluates the applicability of traveling wave-based distance protection for earth
faults for meshed HVDC systems. A distance protection method was proposed from the analysis
of the effect of sampling frequency on fault location. The method presented selectivity and
operation time below 2 ms, without the need for communication between stations, for a 4-
terminal system interconnected by five transmission lines.
Chapter 8
Conclusions
8.1 Conclusions
This thesis investigated the application of traveling waves for developing protection and
fault location methods for transmission lines. Three one-terminal methods have been proposed.
The proposed methods assume that the system needs to guarantee the protection’s reliability,
fast operation, and selectivity in the context of a lack of communication between stations. The
first method is based on modal wave detection for earth faults in HVAC systems. The second
method is also applied to HVAC systems and is based on detecting the reflected wave at the
fault point. The third method is a distance protection applied to meshed HVDC systems. The
development of all the proposed methods has in common the thorough investigation of the
sampling frequency effects on the protection.
The first proposed method is a traveling wave-based earth fault transmission line distance
protection, which only requires arrival instants of the first incident modal traveling waves at one
line terminal and the estimation of modal propagation velocities with uncertainties. Therefore,
the proposed protection overcomes traditional limitations of one-terminal traveling-wave-based
methods„ which require detecting reflected waves and accurate wave propagation velocity esti-
mations. The proposed function setup procedure is straightforward, facilitating practical imple-
mentation.
A thorough investigation of the sampling frequency effect allowed the definition of error
margins for the modal wave velocity estimations, ensuring the reliability of the protection in
well-defined protection zones. The proposed function provides a protection reach, considering
the adopted error margins for the modal wave velocity estimations, wherein all the internal
faults will always be detected. This facilitates the application of the proposed function in real-
world systems. Reach values greater than 60% in the worst evaluated cases were achieved. A
greater portion of the transmission line may be protected, depending on the error in velocity
estimations. Therefore, unitary protection, where 100% of the transmission line is inside the
protected zone, may be achieved via a DTT scheme whether a relay is connected at each line
terminal of the protected line, considering the additional cost of applying a communication
channel.
When associated with other existing auxiliary protection functions, the proposed function
presented an ultra-fast operation time well below those presented by a commercially existing
time domain distance protection. Errors in the wave velocity estimations and inaccuracies in line
parameters were evaluated. The effect of the fault location was also evaluated. The proposed
method accelerated the evaluated time-domain distance element available in the analyzed actual
relay for all detected earth faults. The presented maximum operation time was smaller than 2
ms for all detected internal faults, without misoperations in cases of external faults. In addition,
it was demonstrated that the proposed distance protection has the potential to speed up earth-
8.1. CONCLUSIONS 97
fault protection, even considering existing ultra-fast two-terminal methods. This represents an
important contribution since fast fault detection provides greater stability to the electrical system
and reduces the risk of damage to its components. The results have also demonstrated that the
method presents good dependability, even considering errors in the wave velocity estimations.
The second proposed method is an one-terminal protection for transmission lines. An ex-
tensive mathematical investigation of the effect of sampling frequency and error on estimating
the traveling wave speed was performed.
The method establishes a clear mathematical parameter for defining a minimum sampling
frequency, which makes it possible to adopt low sampling frequencies. Such a mathematical
definition is unprecedented for one-terminal traveling wave-based methods. This also repre-
sents a paradigm break since traveling wave-based methods require high sampling frequencies
in the order of hundreds of kHz. The method is also independent of the estimation of the trav-
eling wave velocity. This also represents a paradigm break for traveling wave-based methods,
especially those based on one terminal.
The proposed method achieved 100% accuracy for the protected zone defined by the adopted
sampling frequency, regardless of the line’s electrical parameters. The operation time of the
method was well below those presented by traditional methods. It also performed well when
compared to traveling wave-based two-terminal methods.
This thesis has not investigated the correct and reliable distinction between the reflected
wave from the fault point and reflected waves at line terminals when adjacent lines occur. Thus,
this is still an open issue for the scientific community. Therefore the method is only valid for
point-to-point lines, not connected to adjacent lines. Furthermore, the method only applies to
transmission lines where the actual speed of the traveling wave is between 90 and 100% percent
of the speed of light. This covers almost all overhead lines, whose wave speed is around 98%
of the speed of light.
The last chapter of this work evaluated the applicability of traveling wave-based distance
protection for meshed HVDC systems. A distance protection method was proposed for earth
faults in overhead transmission lines. A thorough investigation of the effect of sampling fre-
quency was performed.
The method defines a mathematical equation for defining the minimum sampling frequency
as a function of the search zone for the estimation of the fault location. Therefore, the fault
location presents greater reliability for its application in distance protection since the error in
estimating the fault location is mathematically predicted. In addition, there is a paradigm break-
ing concerning the need for a high sampling frequency for traveling wave-based fault location.
For example, a sampling frequency of 25 kHz, which is commercially adopted in actual sys-
tems, could be used in distance protection.
Two systems were modeled for the assessment of the proposed method. The first system
contains four terminals interconnected by five transmission lines modeled by the Bergeron dis-
tributed parameter model. Thus, the traveling waves’ modal speeds are known, enabling the
accurate evaluation of the mathematics presented. The method was able, at each terminal, to
correctly distinguish internal faults from external faults for faults applied on all lines of the
system. For the terminals connected to the faulty line, the method was able to locate 100% of
the faults within the mathematically predicted search zone. For the other terminals, some faults
were located slightly outside the search zone due to lower accuracy in wavefront detection.
The second test system is a point-to-point LCC system with transmission lines modeled with
the frequency-dependent JMarty model. In this way, it was possible to evaluate the proposed
method in a more real-world scenario, where the traveling wave speed is unknown and needs to
be estimated. As expected in an actual system, in this line model, the speed of the zero-mode
8.1. CONCLUSIONS 98
wave approaches the speed of the alpha-mode wave. Hence, the search zone predicted by the
proposed method becomes larger. The search zone for the test system used was approximately
166 km for a 500 km line, which is significantly long. However, the precise evaluation of the
effect of the sampling frequency made it possible to guarantee with high reliability the search
zone as a function of the sampling frequency. This has made distance protection more reliable.
By defining a protection zone of 90% of the line, the method could detect all faults up to 75%
of the line.
The proposed method showed a maximum operation time below 1.6 ms for all detected
internal faults. This value is below the 2 ms maximum trip time requirement of the protection for
meshed HVDC systems (CIGRÉ, 2018). This operation time is also achieved by the overcurrent
protection that monitors the converter, the OCD. However, the OCD protection does not have
any selectivity. Thus, the proposed method can act selectively and ensure greater selectivity to
the system below 2 ms since it is not affected by additional communication delays. Thus, the
method shows promise for its applicability in meshed HVDC systems.
Finally, this thesis demonstrates the applicability of using modal traveling waves and trav-
eling wave reflection detection in fault location and protection of HVAC and HVDC transmis-
sion lines. In doing so, it proposes the commercial use of one-terminal traveling wave-based
methods to increase the speed of operation, reliability, and higher protection selectivity even
in communication loss between stations. In addition, this thesis also demonstrates the poten-
tial application of traveling waves for ultra-fast protection operation in HVDC meshed systems,
whose protection operation times are expected to be much lower than current HVAC and HVDC
systems.
Bibliography
ABUR, A.; MAGNAGO, F. H. Use of time delays between modal components in wavelet based
fault location. International Journal of Electrical Power & Energy Systems, v. 22, n. 6, p. 397–
403, 2000.
ALLIEVI, L. Teoria generale del moto perturbato dell’acqua nei tubi in pressione. In: Annali
della Societa degli Ingegneri ed Architette Italiani, 1902. (English translation, E. E. Halmos,
1925. Theory of water hammer, American Society of Mechanical Engineering).
ARAÚJO, A. E. A. de; NEVES, W. L. A. Cálculo de Transitórios Eletromagnéticos em Sistemas
de Energia. Belo Horizonte: UFMG, 2005.
ARLETT, P. L.; MURRAY-SHELLEY, R. An improved method for the calculation of transients
on transmission lines using a digital computer. In: Proc. Power Industry Computer Applications
Conf., 1965. p. 195–211. Sponsored by the IEEE Power Group.
BAHRMAN, M. P.; JOHNSON, B. K. The abcs of hvdc transmission technologies. IEEE power
and energy magazine, IEEE, v. 5, n. 2, p. 32–44, 2007.
BARNES, M. et al. Hvdc systems in smart grids. Proceedings of the IEEE, v. 105, n. 11, p.
2082–2098, 2017.
BERGERON, L. Etude das variations de regime dans les conduits d’eau: Solution graphique
generale. Rev. Generale de L’hydraulique, v. 1, p. 12, 1935.
BEWLEY, L. V. Traveling waves on transmission systems. Transactions of the American Insti-
tute of Electrical Engineers, v. 50, n. 2, p. 532–550, 1931.
BLOOM, A. et al. It’s indisputable: Five facts about planning and operating modern power
systems. IEEE Power and Energy Magazine, IEEE, v. 15, n. 6, p. 22–30, 2017.
BRANIN, F. H. Transient analysis of lossless transmission lines. Proceedings of the IEEE, v. 55,
n. 11, p. 2012–2013, 1967.
BUSH, V. Transmission line transients. Transactions of the American Institute of Electrical
Engineers, XLII, p. 878–893, 1923.
CARVALHO, A. V.; FREIRE, A. R. F.; OLIVEIRA, H. M. Transient interaction between cou-
pling capacitors voltage transformers and transmission lines. In: IEEE. 2009 IEEE Power &
Energy Society General Meeting, 2009. p. 1–8.
CHAMIA, M.; LIBERMAN, S. Ultra high speed relay for ehv/uhv transmission lines – devel-
opment, design and application. IEEE Transactions on Power Apparatus and Systems, PAS-97,
n. 6, p. 2104–2116, 1978.
99
BIBLIOGRAPHY 100
CHANG, B. et al. Review of different fault detection methods and their impact on pre-emptive
vsc-hvdc dc protection performance. High voltage, IET, v. 2, n. 4, p. 211–219, 2017.
CHEN, W. et al. Study of wavelet-based ultra high speed directional transmission line protec-
tion. IEEE Transactions on Power Delivery, v. 18, n. 4, p. 1134–1139, 2003.
CHRISTOPOULOS, C.; THOMAS, D. W. P.; WRIGHT, A. Scheme, based on travelling-waves,
for the protection of major transmission lines. IEE Proceedings C - Generation, Transmission
and Distribution, v. 135, n. 1, p. 63–73, 1988.
CIGRÉ, C. J. W. G. B. Protection and local control of HVDC-grids, 2018.
CIGRÉ, C. W. G. B. HVDC Grid Feasibility, 2013.
CLARKE, E. Problems solved by modified symmetrical components. General Electric Review,
v. 41, n. 11 and 12, p. 488–449, 1938.
CORPORATION, C. S. E. of the W. E. Electrical Transmission and Distribution Reference
BookUSA: , 1964.
COSTA, F. B. Boundary wavelet coefficients for real-time detection of transients induced by
faults and power-quality disturbances. IEEE Transactions on Power Delivery, v. 29, n. 6, p.
2674–2687, 2014.
COSTA, F. B. Fault-induced transient detection based on real-time analysis of the wavelet co-
efficient energy. IEEE Trans. Power Del., v. 29, n. 01, p. 140–153, Fev. 2014.
COSTA, F. B. et al. Two-terminal traveling-wave-based transmission-line protection. IEEE
Transactions on Power Delivery, v. 32, n. 3, p. 1382–1393, 2017.
COSTA, F. B.; SOUZA, B. A.; BRITO, N. S. D. Real-time detection of fault-induced transients
in transmission lines. Electronics Letters, v. 46, n. 11, p. 753–755, 2010.
COSTA, F. B.; SOUZA, B. A.; BRITO, N. S. D. Effects of the fault inception angle in fault-
induced transients. IET Generation, Transmission & Distribution, IET, v. 6, n. 5, p. 463–471,
2012.
CROSSLEY, P. A.; MCLAREN, P. G. Distance protection based on traveling waves. IEEE
Power Engineering Review, PER-3, n. 9, p. 30–31, 1983.
DOMMEL, H. W. Digital computer solution of electromagnetic transients in single-and multi-
phase networks. IEEE Transactions on Power Apparatus and Systems, PAS-88, n. 4, p. 388–399,
1969.
DOMMEL, H. W.; MICHELS, J. M. High speed relaying using traveling wave transient analy-
sis. In: IEEE Power Eng. Soc. Winter MeetingNew York: , 1978.
DONG, X. et al. Implementation and application of practical traveling-wave-based directional
protection in uhv transmission lines. IEEE Transactions on Power Delivery, v. 31, n. 1, p. 294–
302, 2016.
DONG, X. Z.; GE, Y. Z.; XU, B. Y. Research of fault location based on current travelling waves.
Proc. CSEE, v. 19, n. 4, p. 76–80, 1999.
BIBLIOGRAPHY 101
DOWELL, J. C. Attenuation and successive reflections of traveling waves. Transactions of the
American Institute of Electrical Engineers, v. 50, n. 2, p. 551–557, 1931.
EASTVEDT, R. B. The need for ultra-fast fault clearing. In: Third Annual Western Protective
Relay ConferenceSpokane, EUA: , 1976.
FERNANDES, P. C. et al. Evaluation of travelling wave-based fault location methods applied
to hvdc systems. Electric Power Systems Research, Elsevier, v. 189, p. 106619, 2020.
FRANÇA, R. L. S. Proteção de Linhas de Transmissão de Corrente Alternada Baseada em
Ondas Viajantes Utilizando um Terminal. Master’s Thesis, 2017.
FRANÇA, R. L. S. et al. Traveling wave-based transmission line earth fault distance protection.
IEEE Transactions on Power Delivery, IEEE, v. 36, n. 2, p. 544–553, 2020.
FREY, W.; ALTHAMMER, P. The calculation of electromagnetic transients on lines by means
of a digital computer. Brown Boveri Rev., v. 48, n. 5/6, p. 344–355, 1961.
GLOVER, J. D.; SARMA, M. S.; OVERBYE, T. J. Power System Analysis and Design. 5. ed.,
2012.
GRAINGER, J. J.; JR., W. D. S. Power System Analysis. New York, USA: McGraw-Hill, 1994.
GUZMÁN, A. et al. Testing traveling-wave line protection and fault locators. In: 14th Interna-
tional Conference on Developments in Power System Protection, 2018.
IEEE, I. P. S. R. C. EMTP Reference Models for Transmission Line Relay Testing. 2004. Avail-
able at: <http://www.pes-psrc.org>.
IEEE Standard Electrical Power System Device Function Numbers, Acronyms, and Contact
Designations. IEEE Std C37.2-2008 (Revision of IEEE Std C37.2-1996), p. 1–48, 2008.
III, E. O. S.; KASZTENNY, B. Z. Distance protection using traveling waves in an electric
power delivery system: Google Patents, Mar. 28 2019. US Patent App. 16/137,343.
III, E. O. S.; KASZTENNY, B. Z. Secure Traveling Wave Distance Protection in an Electric
Power Delivery System: Google Patents, Mar. 28 2019. US Patent App. 16/137,350.
IZYKOWSKI, J. et al. Accurate noniterative fault location algorithm utilizing two-end unsyn-
chronized measurements. IEEE Transactions on Power Delivery, v. 25, n. 1, p. 72–80, 2010.
JOHNS, A. T. New ultra-high-speed directional comparison technique for the protection of
e.h.v. transmission lines. IEE Proceedings C - Generation, Transmission and Distribution,
v. 127, n. 4, p. 228–239, 1980.
KALE, V.; BHIDE, S.; BEDEKAR, P. Fault location estimation based on wavelet analysis of
traveling waves. In: 2012 Asia-Pacific Power and Energy Engineering Conference, 2012. p. 1–
5.
KELVIN, L. Collected mathematical and physical papers, v. 2, p. 71–72, 1884.
KOIVISTO, M.; GEA-BERMÚDEZ, J.; SØRENSEN, P. North sea offshore grid development:
combined optimisation of grid and generation investments towards 2050. IET Renewable Power
Generation, Wiley Online Library, v. 14, n. 8, p. 1259–1267, 2020.
BIBLIOGRAPHY 102
LETERME, W. et al. A new hvdc grid test system for hvdc grid dynamics and protection stud-
ies in emt-type software. In: IET. 11th IET International Conference on AC and DC Power
Transmission, 2015. p. 1–7.
LI, Y.; GONG, Y.; JIANG, B. A novel traveling-wave-based directional protection scheme for
mtdc grid with inductive dc terminal. Electric Power Systems Research, Elsevier, v. 157, p.
83–92, 2018.
LIN, S. et al. Travelling wave time-frequency characteristic-based fault location method for
transmission lines. IET Generation, Transmission & Distribution, v. 6, n. 8, p. 764–772, 2012.
LIU, L. et al. A fast protection of multi-terminal hvdc system based on transient signal detection.
IEEE Transactions on Power Delivery, v. 36, n. 1, p. 43–51, 2021.
LIU, Y. et al. A traveling wave fault location method for earth faults based on mode propagation
time delays of multimeasuring points. Przeglad Elektrotech., v. 2012, p. 254–258, 2012.
LOPES, F. V. Settings-free traveling-wave-based earth fault location using unsynchronized two-
terminal data. IEEE Transactions on Power Delivery, v. 31, n. 5, p. 2296–2298, 2016.
LOPES, F. V.; FERNANDES, D.; NEVES, W. L. A. A traveling-wave detection method based
on park’s transformation for fault locators. IEEE Transactions on Power Delivery, v. 28, n. 3, p.
1626–1634, 2013.
LOPES, F. V. et al. Real-time traveling-wave-based fault location using two-terminal unsyn-
chronized data. IEEE Transactions on Power Delivery, v. 30, n. 3, p. 1067–1076, 2015.
LUZ, G. S. R2-MAD-NEW4D. 2016. (Accessed: 2021-03-23). Available at: <https://www.
atpdraw.net/showpost.php?id=52&kind=0>.
LUZ, G. S.; JUNIOR, D. S. C.; JUNIOR, S. G. Hvdc transmission line modeling analysis in
pscad and atp programs. In: XIII Symposium of Specialists in Electric Operational and Expan-
sion Planning, 2014.
MAGNAGO, F. H.; ABUR, A. Fault location using wavelets. IEEE Transactions on Power
Delivery, v. 13, n. 4, p. 1475–1480, 1998.
MOORE, P. J. Radiometric measurement of circuit breaker interpole switching times. IEEE
Transactions on Power Delivery, IEEE, v. 19, n. 3, p. 987–992, 2004.
NAMDARI, F.; SALEHI, M. High-speed protection scheme based on initial current traveling
wave for transmission lines employing mathematical morphology. IEEE Transactions on Power
Delivery, v. 32, n. 1, p. 246–253, 2017.
NANAYAKKARA, O. M. K. K.; RAJAPAKSE, A. D.; WACHAL, R. Traveling-wave-based
line fault location in star-connected multiterminal hvdc systems. IEEE Transactions on Power
Delivery, v. 27, n. 4, p. 2286–2294, Oct 2012. ISSN 0885-8977.
PAITHANKAR, Y. G.; BHIDE, S. R. Fundamentals of Power System Protection. Nova Delhi,
India: PHI Learning, 2003.
PATHIRANA, V.; DIRKS, E.; MCLAREN, P. G. Using impedance measurement to improve
the reliability of traveling-wave distance protection. In: 2003 IEEE Power Engineering Society
General Meeting (IEEE Cat. No.03CH37491), 2003. v. 3, p. 1879 Vol. 3.
BIBLIOGRAPHY 103
RAJENDRA, S.; MCLAREN, P. G. Travelling-wave techniques applied to the protection of teed
circuits: Multi-phase/multi-circuit system. IEEE Power Engineering Review, PER-5, n. 12, p.
49–50, 1985.
Sabug Jr., L. et al. Real-time boundary wavelet transform-based dc fault protection system for
mtdc grids. International Journal of Electrical Power & Energy Systems, Elsevier, v. 115, p.
105475, 2020.
SAHA, M. M.; IZYKOWSKI, J.; ROSOLOWSKI, E. Fault Location on Power Networks. New
York, USA: Springer, 2010.
SANTACANA, E. et al. Getting smart. IEEE Power and Energy Magazine, IEEE, v. 8, n. 2, p.
41–48, 2010.
SANTOS, M. d. S. Improved Voltage Margin Control Strategy for Multi-terminal High Voltage
Direct Current Systems based on the Modular Multilevel Converter. Master’s Thesis (Master’s
Thesis) — Federal University of Rio Grande do Norte, 2021.
SCHNYDER, O. Druckstosse in pumpensteigleitungen. Schweiz. Bouzeitungen, v. 94, n. 2, p.
22–23, 1929.
SCHWEITZER, E. et al. Speed of line protection - can we break free of phasor limitations? In:
68th Annual Conference for Protective Relay Engineers, 2015.
SCHWEITZER, E. O. et al. Protective relays with traveling wave technology revolutionize fault
locating. IEEE Power and Energy Magazine, v. 14, n. 2, p. 114–120, 2016.
SCHWEITZER, E. O.; KASZTENNY, B. Z.; MYNAM, M. V. Performance of time-domain line
protection elements on real-world faults. In: 42nd Annual Western Protective Relay Conference,
2015.
SHAHIDEHPOUR, M. et al. Networked microgrids: Exploring the possibilities of the iit-
bronzeville grid. IEEE Power and Energy Magazine, IEEE, v. 15, n. 4, p. 63–71, 2017.
SHEHAB-ELDIN, E. H.; MCLAREN, P. G. Travelling wave distance protection-problem areas
and solutions. IEEE Transactions on Power Delivery, v. 3, n. 3, p. 894–902, 1988.
SILVA, D. M. da et al. Wavelet-based analysis and detection of traveling waves due to dc faults
in lcc hvdc systems. International Journal of Electrical Power & Energy Systems, Elsevier,
v. 104, p. 291–300, 2019.
TAGAGI, T. et al. Fault protection based on travelling wave theory, part 1: Theory. In: IEEE
Power Eng. Soc. Summer Meeting, 1977.
TANG, G. et al. Basic topology and key devices of the five-terminal dc grid. CSEE Journal of
Power and Energy Systems, CSEE, v. 1, n. 2, p. 22–35, 2015.
TANG, L. et al. A new differential protection of transmission line based on equivalent travelling
wave. IEEE Transactions on Power Delivery, v. 32, n. 3, p. 1359–1369, 2017.
TANG, L. et al. A high-speed protection scheme for the DC transmission line of a MMC-HVDC
grid. Electric Power Systems Research, Elsevier, v. 168, p. 81–91, 2019.
BIBLIOGRAPHY 104
THOMAS, D. W. P. et al. Single ended travelling wave fault location scheme based on wavelet
analysis. In: 2004 Eighth IEE International Conference on Developments in Power System
Protection, 2004. v. 1, p. 196–199 Vol.1.
THOMAS, H. et al. Efficiency of superconducting transmission lines: An analysis with respect
to the load factor and capacity rating. Electric Power Systems Research, Elsevier, v. 141, p.
381–391, 2016.
TONG, N. et al. Local measurement-based ultra-high-speed main protection for long distance
vsc-mtdc. IEEE Transactions on Power Delivery, v. 34, n. 1, p. 353–364, 2019.
VAAHEDI, E. et al. The emerging transactive microgrid controller: Illustrating its concept,
functionality, and business case. IEEE Power and Energy Magazine, v. 15, n. 4, p. 80–87, July
2017. ISSN 1540-7977.
WANG, Y.; XU, W. Algorithms and field experiences for estimating transmission line param-
eters based on fault record data. IET Generation, Transmission Distribution, v. 9, n. 13, p.
1773–1781, 2015. ISSN 1751-8687.
WU, J. et al. An improved traveling-wave protection scheme for lcc-hvdc transmission lines.
IEEE Transactions on Power Delivery, IEEE, v. 32, n. 1, p. 106–116, 2017.
YU, C.-S. An unsynchronized measurements correction method for two-terminal fault-location
problems. IEEE Transactions on Power Delivery, v. 25, n. 3, p. 1325–1333, 2010.
Zanetta Jr., L. C. Transitórios Eletromagnéticos em Sistemas de Potência: Editora da Universi-
dade de São Paulo, 2003.
ZHAO, Z. et al. Wave front rising time based traveling wave protection for multi-terminal vsc-
hvdc grids. International Journal of Electrical Power & Energy Systems, Elsevier, v. 144, p.
108534, 2023.
ZIMATH, S. L.; RAMOS, M. A. F.; FILHO, J. E. S. Comparison of impedance and travelling
wave fault location using real faults. In: IEEE PES T D 2010, 2010. p. 1–5.
Appendix A
Summary Overview of Included
Publications
Chapter 5 is composed mostly by a published paper. This appendix includes bibliographic
details of the paper:
Rafael Lucas da Silva França, Francisco Caninde da Silva Júnior, Tiago R. Honorato, Joao
Paulo G. Ribeiro, Flavio Bezerra Costa, Felipe V. Lopes, and Kai Strunz. "Traveling Wave-
Based Transmission Line Earth Fault Distance Protection". IEEE Transactions on Power De-
livery, vol. 36, no. 2, pp. 544-553, April 2021.
Published version.
<https://doi.org/10.1109/TPWRD.2020.2984585>.
105
