A01048771--Tesis-Final

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Instituto Tecnológico y de Estudios Superiores de Monterrey
Campus Monterrey
School of Engineering and Sciences
Assessment of the opportunities for integrating a Dynamic
Line Rating System in the Mexican National Electric Grid
A thesis presented by
Ana Victoria Taŕın Santiso
Submitted to the
School of Engineering and Sciences
in partial fulfillment of the requirements for the degree of
Master of Science
in
Energy Engineering
Monterrey, Nuevo León. December 4th, 2017
Declaration of authorship 
I, Ana Victoria Tarín Santiso, declare that this thesis titled: Assessment of the • 
opportunities for integrating a Dynamic Line Rating System, in the Mexican National 
Electric Grid and the work presented in it are my own. I confirm that: 
• This work was done wholly while in candidature for the degree of Master of Science 
in this institution. 
• I have given credit to any previously published work that has been consulted in 
this thesis. 
• I have cited the work consulted by other authors, and the source from which I 
obtained them. 
• I have given credit to all sources of help used. 
• I have given credence to the contributions of the co-authors, when the results 
correspond to a collaborative work. 
Ana Victoria Tarín Santiso 
Monterrey, Nuevo León. December 4th, 2017 
©2017 by Ana Victoria Tarín Santiso 
AH rights reserved 
Dedication
Yahveh, My Lord.
For blessing me every day, for giving me lessons that allowed me to grow as a person
and for providing me the strength to achieve this dream.
Acknowledgements
To Osvaldo Micheloud, Federico Viramontes and Armando Llamas, for forming the
Industrial Consortium to Foster Applied Research in México and allowing
professionals to receive a scholarship to continue their studies.
For each of their classes, just wonderful.
To Oliver Probst and Armando Llamas for proposing me this amazing, interesting
and challenging thesis project. For providing me with the necessary means and
resources for the development of the research. For their time, guide, support, advice
and for allowing me to learn from them.
To Sergio Castellanos, for his collaboration and support in the collection of
information from the National Renewable Energy Laboratory database, and for his
willingness to be part of the Thesis Committee.
To my mother, for providing me intangible tools to help me build this dream. For
teaching me by example: discipline and constancy, her example has taught me that
success is based on effort and hard work. For her support while I was studying my
professional career, because I was able to devote myself completely to school.
To my father, for teaching me by example: responsibility, perseverance and
dedication. For his support while I was studying my professional career, because I
was able to devote myself completely to school.
To Ivan and Cristian, for a careful revision of the manuscript and useful discussion.
To Ivan, the light of my heart. For supporting me at every step, for always trying to
lighten my path when I was exhausted from school. For worrying with me in each
Subject. For motivating me in every challenge. For his patience and support every
sleeplessness night. For helping me as much as possible, even more than that.
For always believing that I could reach the goal.
If I have seen further, it is by standing on the shoulders of giants.
Letter from Isaac Newton to Robert Hooke
Contents
Abstract i
List of Figures iii
List of Tables vii
1 Chapter 1 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Problem statement and context . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Solution overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6 Thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Chapter 2 7
2.1 Loadability of overhead transmission lines . . . . . . . . . . . . . . . . 7
2.1.1 Surge impedance . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 Loadability limits in overhead transmission lines . . . . . . . . . 8
2.2 Thermal behavior of bare overhead conductors . . . . . . . . . . . . . . 12
2.2.1 Convective cooling . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.2 Radiative cooling . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.3 Solar heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.4 Joule effect heating . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.5 Steady-state thermal rating . . . . . . . . . . . . . . . . . . . . 17
2.3 Fundamentals of Dynamic Line Rating technologies . . . . . . . . . . . 18
2.3.1 Dynamic Line Rating in Smart Grids development . . . . . . . . 18
2.3.2 Monitoring systems for Dynamic Line Rating . . . . . . . . . . 19
2.3.3 Economic and market implications of Dynamic Line Rating . . . 21
2.3.4 Applications and limitations of Dynamic Line Rating . . . . . . 23
3 Chapter 3 27
3.1 The representation of the Mexican National Electric Grid in ArcGIS . . 27
3.1.1 Conversion of transmission lines to points . . . . . . . . . . . . 28
3.2 Analysis of environmental and geographical conditions in the National
Electric Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Azimuth of the transmission lines . . . . . . . . . . . . . . . . . 28
3.2.2 Wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.3 Wind direction . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.4 Solar radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.5 Air temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.6 Elevation of the transmission lines above sea level . . . . . . . . 49
3.2.7 Hour angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3 Electrical conductor considered in each transmission line . . . . . . . . 57
4 Chapter 4 61
4.1 Program to calculate Dynamic Line Rating . . . . . . . . . . . . . . . . 61
4.2 Dynamic thermal rating results from monthly analysis . . . . . . . . . 66
4.3 Dynamic thermal rating results from hourly analysis . . . . . . . . . . 81
4.4 Analysis of thermal rating exceedance probabilities . . . . . . . . . . . 97
4.5 Operational status of the Mexican National Electric Grid . . . . . . . . 104
4.6 Congestion analysis in distributes nodes . . . . . . . . . . . . . . . . . 107
5 Chapter 5 123
5.1 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
A Appendix A 125
B Appendix B 143
B.1 Wind speed maps conversion to gray scale . . . . . . . . . . . . . . . . 143
B.2 Association of the transmission lines points to the nearest point of The
Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.3 Monthly average calculation of the variable wind direction using Circular
Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
B.4 Dynamic Line Rating calculation based on IEEE Standard 738-2012 . . 149
C Appendix C 155
C.1 About ArcGIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
C.2 Referencing a map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
C.3 Creating a shapefile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
C.4 Digital map conversion: .tif format to raster format . . . . . . . . . . . 162
C.5 Digital map conversion: shapefile format to raster format . . . . . . . . 164
Assessment of the opportunities for integrating a Dynamic
Line Rating System in the Mexican National Electric Grid
by
Ana Victoria Taŕın Santiso
Abstract
Transmission lines limited by thermal constraints are conservatively operated with the
worst case scenario, resulting in a typically lower utilization level than their maximum
transmissioncapacity. With the development of modern information technologies,
however, the actual thermal rating of a given transmission line can at least in principle
be known in real-time, opening a realm of opportunities for the more efficient operation
of the electric grid.
The aim of this research is to conduct the first systematic assessment of the potential
for dynamic uprating of transmission lines in the Mexican National Electric Grid and
to propose the incorporation of a Real Time Rating System in strategic overhead lines.
The possibility of using variable line ratings to increase its utilization brings with it the
potential for improved economic dispatch and reductions in the average cost of energy
because of the relief of congested transmission connections, as well as higher renewable
energy integration in the grid. A natural consequence of the former is the avoidance
or reduction of renewable energy curtailment and the reduced use of inefficient and
therefore often contaminating power plants, leading to a generally cleaner generation
of electricity.
The research is based on an implementation of IEEE Std. 738-2012, which
provides a methodology for relating weather conditions and the ampacity in a bare
stranded overhead conductor. The IEEE Standard is based on a balance between
heat absorbed and dissipated in the conductor, being the wind speed, wind direction,
ambient temperature and solar radiation the most significant variables in this thermal
equilibrium.
ArcGIS software was used for the analysis of environmental and geographical
conditions in the Mexican National Electric Grid, while the IEEE Std. 738-2012
implementation was done through an algorithm developed in MATLAB. The project
includes the study of the power transmission system at 115 kV, 230 kV and 400 kV based
on information published by CENACE and other public data sources; the databases
used to obtain the environmental and geographical conditions are: INERE of SENER,
MERRA-2 of NASA, NSRDB of NREL and INEGI.
i
List of Figures
1 Sag and clearance in an overhead transmission line . . . . . . . . . . . 9
2 Thermal, voltage drop and stability load limits as a function of the line
length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Mexican National Electric Grid represented in ArcGIS . . . . . . . . . 27
4 Transmission line: Kilometro 20 - Mezcalapa Switcheo . . . . . . . . . . 28
5 Span with positive azimuth . . . . . . . . . . . . . . . . . . . . . . . . 30
6 Span with negative azimuth . . . . . . . . . . . . . . . . . . . . . . . . 30
7 Metal towers used in high voltage . . . . . . . . . . . . . . . . . . . . . 31
8 Wind speed color map, for the month of March at 80 meters height . . 31
9 INERE color scale for wind speed maps . . . . . . . . . . . . . . . . . . 32
10 INERE gray scale for wind speed maps . . . . . . . . . . . . . . . . . . 33
11 Flowchart of the color map conversion to gray scale . . . . . . . . . . . 33
12 National Electric Grid overlapped with a wind speed map . . . . . . . . 34
13 Wind speed along the transmission line La Angostura - El Sabino . . . 34
14 Transmission line Bahia Asuncion - Vizcaino . . . . . . . . . . . . . . . 36
15 Mexican Republic representation to 522 points . . . . . . . . . . . . . . 37
16 Flowchart of the nearest point assignment: OHL - The Mesh . . . . . . 37
17 Transmission line Torreon Sur - Lerdo . . . . . . . . . . . . . . . . . . 38
18 Transmission line: Rio Escondido - Carbon II . . . . . . . . . . . . . . 40
19 φ in one section of the overhead line Rio Escondido - Carbon II, hour 1
of the year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
20 Flowchart of the circular mean calculation . . . . . . . . . . . . . . . . 42
21 φ in one section of the overhead line Rio Escondido - Carbon II, month
of June . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
22 Solar radiation components behavior for summer solstice. Lat:25.5◦,
Long:-108◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
23 National Electric Grid overlapped with a direct radiation map . . . . . 45
24 Direct radiation along the transmission line Camargo II - Santiago II . 46
25 Transmission line Kanasin Potencia - Ticul II . . . . . . . . . . . . . . 46
26 Transmission line Tecali-Cruz Azul Maniobras . . . . . . . . . . . . . . 48
27 National Electric Grid overlapped with an elevation map . . . . . . . . 49
28 Transmission line Hermosillo IV - Guaymas Cereso . . . . . . . . . . . 50
29 Solar heating along the summer solstice for Zline = 0
◦, 45◦, 90◦,−45◦ . . 51
30 Graph of the Equation of Time according to the day of the year . . . . 53
31 Solar heating behavior in summer solstice for different transmission line
azimuths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
32 Kangle factor as a function of the angle φ . . . . . . . . . . . . . . . . . 62
33 Angle between wind direction and the conductor axis greater than 90◦ . 62
34 Kangle factor as a function of the angle φ
′
. . . . . . . . . . . . . . . . . 63
35 Multidimensional cell array structure . . . . . . . . . . . . . . . . . . . 64
36 Flowchart for the dynamic line ratings calculation . . . . . . . . . . . . 65
37 OHL ID: 1, Voltage level: 115 kV. Monthly dynamic thermal rating profile 66
iii
38 OHL ID: 7, Voltage level: 115 kV. Monthly dynamic thermal rating profile 66
39 OHL ID: 16, Voltage level: 115 kV. Monthly dynamic thermal rating
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
40 OHL ID: 47, Voltage level: 115 kV. Monthly dynamic thermal rating
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
41 Environmental conditions behavior. Overhead line Sabancuy - Cd. del
Carmen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
42 Heat comparative, transmission line Sabancuy - Cd. del Carmen,
points:246/249 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
43 The most frequent critical spans location for the transmission system at
115 kV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
44 OHL ID: 25, Voltage level: 230 kV. Monthly dynamic thermal rating
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
45 OHL ID: 64, Voltage level: 230 kV. Monthly dynamic thermal rating
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
46 OHL ID: 83, Voltage level: 230 kV. Monthly dynamic thermal rating
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
47 OHL ID: 120, Voltage level: 230 kV. Monthly dynamic thermal rating
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
48 Environmental conditions behavior. Overhead line Escobedo - Hylsa Norte 73
49 Heat comparative, overhead line Escobedo - Hylsa Norte, points:981/986 74
50 Transmission line Escobedo - Hylsa Norte . . . . . . . . . . . . . . . . . 75
51 The most frequent critical spans location for the transmission system at
230 kV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
52 OHL ID: 70, Voltage level: 400 kV. Monthly dynamic thermal rating
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
53 OHL ID: 88, Voltage level: 400 kV. Monthly dynamic thermal rating
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
54 OHL ID: 135, Voltage level: 400 kV. Monthly dynamic thermal rating
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
55 OHL ID: 151, Voltage level: 400 kV. Monthly dynamic thermal rating
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
56 Environmental conditions behavior. Overhead line Tecali - Cruz Azul
Maniobras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
57 Heat comparative, transmission line Tecali - Cruz Azul Maniobras,points:1695/1700 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
58 Transmission line Tecali - Cruz Azul Maniobras . . . . . . . . . . . . . 80
59 The most frequent critical spans location for the transmission system at
400 kV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
60 OHL ID: 10, Voltage level: 115 kV. Hourly dynamic thermal rating profile 82
61 OHL ID: 10, Voltage level: 115 kV. Dynamic thermal rating histogram 82
62 OHL ID: 22, Voltage level: 115 kV. Hourly dynamic thermal rating profile 83
63 OHL ID: 22, Voltage level: 115 kV. Dynamic thermal rating histogram 83
64 OHL ID: 34, Voltage level: 115 kV. Hourly dynamic thermal rating profile 84
65 OHL ID: 34, Voltage level: 115 kV. Dynamic thermal rating histogram 84
iv
66 OHL ID: 84, Voltage level: 115 kV. Hourly dynamic thermal rating profile 85
67 OHL ID: 84, Voltage level: 115 kV. Dynamic thermal rating histogram 85
68 Heat comparative. OHL ID: 84, Voltage level: 115 kV. . . . . . . . . . 86
69 OHL ID: 29, Voltage level: 230 kV. Hourly dynamic thermal rating profile 87
70 OHL ID: 29, Voltage level: 230 kV. Dynamic thermal rating histogram 87
71 OHL ID: 74, Voltage level: 230 kV. Hourly dynamic thermal rating profile 88
72 OHL ID: 74, Voltage level: 230 kV. Dynamic thermal rating histogram 88
73 OHL ID: 96, Voltage level: 230 kV. Hourly dynamic thermal rating profile 89
74 OHL ID: 96, Voltage level: 230 kV. Dynamic thermal rating histogram 89
75 OHL ID: 113, Voltage level: 230 kV. Hourly dynamic thermal rating profile 90
76 OHL ID: 113, Voltage level: 230 kV. Dynamic thermal rating histogram 90
77 Heat comparative. OHL ID: 113, Voltage level: 230 kV. . . . . . . . . . 91
78 OHL ID: 77, Voltage level: 400 kV. Hourly dynamic thermal rating profile 92
79 OHL ID: 77, Voltage level: 400 kV. Dynamic thermal rating histogram 92
80 OHL ID: 94, Voltage level: 400 kV. Hourly dynamic thermal rating profile 93
81 OHL ID: 94, Voltage level: 400 kV. Dynamic thermal rating histogram 93
82 OHL ID: 109, Voltage level: 400 kV. Hourly dynamic thermal rating profile 94
83 OHL ID: 109, Voltage level: 400 kV. Dynamic thermal rating histogram 94
84 OHL ID: 119, Voltage level: 400 kV. Hourly dynamic thermal rating profile 95
85 OHL ID: 119, Voltage level: 400 kV. Dynamic thermal rating histogram 95
86 Heat comparative. OHL ID: 119, Voltage level: 400 kV. . . . . . . . . . 96
87 OHL ID: 9, Voltage level: 115 kV. Empirical CDF . . . . . . . . . . . . 98
88 EPV > SLR for transmission lines at 115 kV, month of January . . . . 99
89 EPV > SLR for transmission lines at 115 kV, month of December . . . 99
90 EPV > SLR for transmission lines at 230 kV, month of January . . . . 100
91 EPV > SLR for transmission lines at 230 kV, month of December . . . 101
92 EPV > SLR for transmission lines at 400 kV, month of January . . . . 102
93 EPV > SLR for transmission lines at 400 kV, month of November . . . 102
94 Location of transmission lines with a great potential to increase their
capacity most of the year . . . . . . . . . . . . . . . . . . . . . . . . . . 103
95 OHL ID: 28, Voltage level: 400 kV. Hourly dynamic thermal rating profile106
96 Hourly dynamic thermal rating profile for the month of July . . . . . . 106
97 Location of distributed nodes and transmission line with thermal constraint108
98 Difference in the energy congestion price, throughout the year 2016.
Guaymas - Hermosillo link . . . . . . . . . . . . . . . . . . . . . . . . . 110
99 Difference in the energy congestion price, throughout the year 2017.
Guaymas - Hermosillo link . . . . . . . . . . . . . . . . . . . . . . . . . 110
100 Location of the distributed nodes Guaymas and Hermosillo . . . . . . . 111
101 OHL ID: 6, Voltage level: 230 kV. Hourly dynamic thermal rating profile 111
102 Difference in the energy congestion price, throughout the year 2016.
Navojoa - Obregon link . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
103 Difference in the energy congestion price, throughout the year 2017.
Navojoa - Obregon link . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
104 Location of the distributed nodes Navojoa and Obregon . . . . . . . . . 113
105 OHL ID: 213, Voltage level: 230 kV. Hourly dynamic thermal rating profile113
v
106 OHL ID: 214, Voltage level: 230 kV. Hourly dynamic thermal rating profile114
107 Difference in the energy congestion price, throughout the year 2016.
Saltillo - Monterrey link . . . . . . . . . . . . . . . . . . . . . . . . . . 114
108 Difference in the energy congestion price, throughout the year 2017.
Saltillo - Monterrey link . . . . . . . . . . . . . . . . . . . . . . . . . . 115
109 Location of the distributed nodes Saltillo and Monterrey . . . . . . . . 115
110 OHL ID: 25, Voltage level: 230 kV. Hourly dynamic thermal rating profile116
111 OHL ID: 26, Voltage level: 230 kV. Hourly dynamic thermal rating profile117
112 Difference in the energy congestion price, throughout 2016. Villahermosa
- Chontalpa link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
113 Difference in the energy congestion price, throughout 2017. Villahermosa
- Chontalpa link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
114 Location of the distributed nodes Villahermosa and Chontalpa . . . . . 118
115 OHL ID: 266, Voltage level: 230 kV. Hourly dynamic thermal rating profile119
116 OHL ID: 315, Voltage level: 230 kV. Hourly dynamic thermal rating profile119
117 Difference in the energy congestion price, throughout the year 2016.
Cancun - Merida link . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
118 Difference in the energy congestion price, throughout the year 2017.
Cancun - Merida link . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
119 Location of the distributed nodes Cancun and Merida . . . . . . . . . 121
120 OHL ID: 19, Voltage level: 115 kV. Hourly dynamic thermal rating profile121
121 ArcGIS integrates many types of spatial data . . . . . . . . . . . . . . 155
122 Importing a image in the ArcGIS work space . . . . . . . . . . . . . . . 156
123 Fitting the image to georeference . . . . . . . . . . . . . . . . . . . . . 156
124 Selecting the points that will be associated . . . . . . . . . . . . . . . . 156
125 3rd order polynomial transformation for georeferencing a digital map . 157
126 Creating a shapefile in ArcGIS . . . . . . . . . . . . . . . . . . . . . . . 158
127 Polyline configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
128 Management of the shapefile in Table Of Contents section . . . . . . . 159
129 Creating lines associated to the same shapefile . . . . . . . . . . . . . . 159
130 Creating lines associated to the same shapefile, second part . . . . . . . 160
131 Creating lines associated to the same shapefile, third part . . . . . . . . 160
132 Drawing the polyline trace . . . . . . . . . . . . . . . . . . . . . . . . . 161
133 Managing polylines through an attribute table . . . . . . . . . . . . . . 161
134 Polyline name assignment . . . . . . . . . . . . . . . . . . . . . . . . . 161
135 Management of the digital map in Table Of Contents section . . . . . . 162
136 Digital maps conversion: .tif format to raster format . . . . . . . . . . 162
137 Displaying pixel values in the Table Of Contents section . . . . . . . . 163
138 Wind speed query for 400 kV transmission line points . . . . . . . . . . 163
139 Digital map in shapefile format imported to work space . . . . . . . . . 164
140 Digital map in shapefile format imported to work space . . . . . . . . . 164
141 Attribute table of the solar radiation map . . . . . . . . . . . . . . . . 164
142 Digital map conversion:shapefile format to raster format . . . . . . . . 165
vi
List of Tables
1 Solar azimuth constant as a function of hour angle and solar azimuth
variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 Coordinates of the transmission line points: Kilometro 20 - Mezcalapa
Switcheo . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 29
3 Azimuth of the transmission line as a function of its slope . . . . . . . . 29
4 Wind speed as a function of pixel value in gray scale . . . . . . . . . . 33
5 Wind speed at 50 m height along the transmission line La Angostura -
El Sabino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6 Wind speed at 20 m height along the transmission line: Bahia Asuncion
- Vizcaino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7 Coordinates comparison. Torreon Sur - Lerdo and The Mesh . . . . . . 38
8 Wind speed at 80m height in the first six hours of the year, for The Mesh
point:306 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
9 Wind speed at 30m height in the first six hours of the year, for The Mesh
point:306 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
10 Coordinates of the transmission line points: Rio Escondido - Carbon II 40
11 Coordinates comparison. Rio Escondido - Carbon II and The Mesh . . 40
12 Wind direction in the first six hours of the year, for The Mesh point:426 41
13 φ in one section of the transmission line Rio Escondido - Carbon II . . 41
14 Monthly average wind direction for The Mesh point:426 . . . . . . . . . 42
15 Direct radiation along the transmission line Camargo II - Santiago II . 45
16 Coordinates of the transmission line points: Kanasin Potencia - Ticul II 46
17 Coordinates comparison. Kanasin Potencia - Ticul II and The Mesh . 47
18 First six hours of the year with solar radiation, for The Mesh point:160 47
19 Range of hours of the year grouped by month . . . . . . . . . . . . . . 47
20 Coordinates of the transmission line points: Tecali-Cruz Azul Maniobras 48
21 Coordinates comparison. Tecali - Cruz Azul Maniobras and The Mesh . 48
22 Air temperature in the first six hours of the year, for The Mesh point:80 49
23 Monthly average air temperature throughout a typical year for The Mesh
point:80 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
24 Elevation of the transmission line Hermosillo IV - Guaymas Cereso . . 50
25 Selected transmission lines at 230 kV to analyze the solar heating behavior 52
26 Sunrise and Sunset time in the summer solstice for the transmission lines
analyzed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
27 Average solar heating for different azimuths throughout the year . . . . 55
28 Angle of incidence of the Sun’s rays according to monthly average of qS 55
29 Hour angle at which monthly averages of qS are recorded . . . . . . . . 56
30 Zbase for different voltage levels . . . . . . . . . . . . . . . . . . . . . . 57
31 Electrical resistance at different temperatures for: 477, 795, 900 & 1113
ACSR bare conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
32 Static current capacity for: 477, 795, 900 & 1113 ACSR bare conductors 59
33 Static Line Rating in MW for: 477, 795, 900 & 1113 ACSR bare conductors 59
vii
34 Environmental conditions in the transmission line Sabancuy - Cd. del
Carmen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
35 Heat analysis in the transmission line Sabancuy - Cd. del Carmen,
points:246/249 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
36 Environmental conditions in the transmission line Escobedo - Hylsa Norte 73
37 Heat analysis in the transmission line Escobedo - Hylsa Norte,
points:981/986 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
38 Analysis of direct radiation absorbed for transmission line Escobedo -
Hylsa Norte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
39 Environmental conditions in the transmission line Tecali - Cruz Azul
Maniobras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
40 Heat analysis in the transmission line Tecali - Cruz Azul Maniobras,
points:1695/1700 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
41 Analysis of direct radiation absorbed for transmission line Tecali - Cruz
Azul Maniobras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
42 Environmental conditions comparative. OHL ID: 84, Voltage level: 115
kV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
43 Environmental conditions comparative. OHL ID: 113, Voltage level: 230
kV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
44 Environmental conditions comparative. OHL ID: 119, Voltage level: 400
kV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
45 Exceedance probabilities for the transmission line Villa Constitucion -
Las Pilas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
46 EPV > SLR for transmission lines at 115 kV . . . . . . . . . . . . . . . 98
47 EPV > SLR for transmission lines at 230 kV . . . . . . . . . . . . . . . 100
48 EPV > SLR for transmission lines at 400 kV . . . . . . . . . . . . . . . 101
49 Operational status of alert . . . . . . . . . . . . . . . . . . . . . . . . . 104
50 Alert operational status by power flow limitations . . . . . . . . . . . . 105
51 Distributed nodes of the Mexican National Electric Grid . . . . . . . . 109
52 Comparative of possible congestion solutions. Saltillo-Monterrey link . 116
53 Comparative of possible congestion solutions. Cancun-Merida link . . . 122
54 Transmission lines at 115 kV . . . . . . . . . . . . . . . . . . . . . . . . 127
55 Transmission lines at 115 kV, second part . . . . . . . . . . . . . . . . 128
56 Transmission lines at 115 kV, third part . . . . . . . . . . . . . . . . . 129
57 Transmission lines at 230 kV . . . . . . . . . . . . . . . . . . . . . . . . 129
58 Transmission lines at 230 kV, second part . . . . . . . . . . . . . . . . 130
59 Transmission lines at 230 kV, third part . . . . . . . . . . . . . . . . . 131
60 Transmission lines at 230 kV, fourth part . . . . . . . . . . . . . . . . . 132
61 Transmission lines at 230 kV, fifth part . . . . . . . . . . . . . . . . . . 133
62 Transmission lines at 230 kV, sixth part . . . . . . . . . . . . . . . . . 134
63 Transmission lines at 230 kV, seventh part . . . . . . . . . . . . . . . . 135
64 Transmission lines at 230 kV, eighth part . . . . . . . . . . . . . . . . . 136
65 Transmission lines at 230 kV, ninth part . . . . . . . . . . . . . . . . . 137
66 Transmission lines at 230 kV, tenth part . . . . . . . . . . . . . . . . . 138
67 Transmission lines at 400 kV . . . . . . . . . . . . . . . . . . . . . . . . 138
viii
68 Transmission lines at 400 kV, second part . . . . . . . . . . . . . . . . 139
69 Transmission lines at 400 kV, third part . . . . . . . . . . . . . . . . . 140
70 Transmission lines at 400 kV, fourth part . . . . . . . . . . . . . . . . . 141
71 Transmission lines at 400 kV, fifth part . . . . . . . . . . . . . . . . . . 142
ix
Chapter 1
1.1 Introduction
The Mexican Department of Energy, known as Secretaŕıa de Enerǵıa (SENER),
through Estrategia Nacional de Enerǵıa 2013-2027, recognizes that one of the most
important challenges for the electricity sector is increasing the capacity, efficiency,
availability, reliability and safety of electrical power transmission and distribution
systems; which implies, among other things, the deployment of Smart Grids that should
be strengthened and the capacity across regions should be increased, making it feasible
to exchange energy; this could prevent the installation of new generation capacity [1].
Historically utilities have operated transmission systems conservatively in order to
provide high reliability through moderate transmission line loading and redundancy.
This is because the system is planned in order to guarantee the highest possible security
and quality of supply, which involves using conservative worst-case assumptions at the
planning stage. However, environmental, regulatory and economic pressures have forced
utilities to look for ways to increase line loading, [2]and [3].
The loadability of long transmission lines is often limited by surge impedance
loading or stability constraints, voltage profile and energy losses, but for short lines
the maximum load capacity is dictated for their thermal rating, which depends on the
maximum allowable conductor temperature [4].
Both IEEE and CIGRE have developed standards based on the same concept of
evaluating the conductor temperature, their differences are analyzed in full detail in [5]
and [6]. CIGRE Standard is most commonly used in Europe [7], while IEEE Standard
in America; the methodology used in this thesis to analyze the dynamic ratings of the
transmission lines is based on the IEEE Standard [8].
IEEE Std. 738-2012 describes a numerical method, by which the core and surface
temperatures of a bare stranded overhead conductor are related to the steady or time-
varying electrical current and weather conditions. The method may also be used to
determine the conductor current that corresponds to conductor temperature limits.
IEEE method is based on the steady state heat balance equation considering
the balance between heat dissipated (convective cooling and radiative cooling) and
absorbed (solar heating and Joule effect heating). Convective cooling depends mainly
on wind speed (Ws) and φ (angle between wind direction (Wd) and the conductor
axis (ϕline)), whilst radiative cooling is influenced by the temperature at which the
conductor operates (Ts) and ambient temperature (Ta). Direct and diffuse solar
radiation (QB, QD), and the position of the Sun in relation to the conductor are
important for solar heating calculation; some geographic conditions are also relevant
such as the transmission line azimuth (Zline), and the latitude (Lat) where it is located.
Joule effect heating is a consequence of the electric current (I), this is precisely the
variable to be solved for when the described weather conditions are analyzed.
In practice, the current capacity obtained applying the IEEE Standard with the
worse environmental conditions defines the capacity of the transmission lines limited
by thermal constraints, giving rise to: Static Line Rating. Weather conditions are not
1
static; therefore, the thermal rating of a transmission line is not either. Recognizing
that certain weather conditions can impact conductor temperature and cause a change
in the capacity of the transmission lines reveals that the possibility of using variable
line ratings could increase the overhead lines utilization, bringing with it the relief
of congested transmission connections and higher renewable energy integration in the
grid, as well as a better grid management in case of contingencies.
Dynamic Line Rating (also referred to as dynamic thermal rating or real time
thermal rating) is a technology that can dynamically increase current carrying capacity
of electric transmission lines. In a Dynamic Line Rating framework, ampacity is
considered as a dynamic variable giving a conservative estimate of the critical value
at which the line may be operated at each time unit of operation. This phenomenon
is particularly obvious on overhead transmission lines, where Dynamic Line Rating
can provide considerable uprating. In the current power system scenario, where
the rise of power from intermittent renewable sources puts stress on the existing
infrastructure, making network reinforcements necessary, Dynamic Line Rating can
represent a solution for accommodating higher renewable production whilst minimizing
or postponing network reinforcements [2].
1.2 Motivation
Operational status of alert are registered daily in different transmission regions of the
Mexican National Electric Grid due to transmission constraints, which indicates that
being able to increase the transmission capacity may result in the relief of bottlenecks
and an optimal economic dispatch, this would have a positive impact on the price of
energy. The possibility of monitoring the real-time conditions in which the transmission
system operates allows to improve its utilization, for that it is necessary to analyze the
relation between the environment and power systems.
Motivated for the mentioned challenges, this research proposes the first systematic
assessment of the potential for increasing dynamically the capacity of the transmission
lines in México, where the electricity market scheme is emerging, thereby implementing
a Dynamic Line Rating System from an early stage of the market could bring great
benefits to the power system, as it is in other countries.
1.3 Problem statement and context
The ampacity of a conductor is defined as the maximum constant current which
meet the design, security and safety criteria of a particular line on which the conductor
is used and it is limited by a maximum temperature in order to respect these constraints
and preserve mechanical integrity [2].
The conductor temperature is a function of: a) conductor material, b) conductor
diameter, c) conductor surface conditions, d) ambient weather conditions, and e)
electrical current. The first two of these properties are specific chemical and physical
properties. The third may vary with time and be dependent upon ambient atmospheric
conditions other than weather. The fourth, weather, varies greatly depending on the
hour and season. The fifth, conductor electrical current, may be constant or may vary
with power system loading, generation, dispatch, and other factors [8].
2
Ampacities proposed by bare stranded overhead conductors manufacturers (those
governed by the Aluminum Electrical Conductor Handbook) are calculated with very
conservative weather conditions: QB = 1000 W/m
2, Ta = 25
◦C and Ws = 0.61 m/s,
this last consideration arose from a study realized in the 1930s, where it was determined
that this wind speed was not registered more than 5% of the time during a summer
season. Consequently the possibility of overheating the conductor is almost negligible.
Therefore the static rating is stable under such conservative conditions, when favorable
weather conditions occur the transmission lines operates with a low utilization level.
Then an increase in the capacity of power transmission systems can be achieved by
monitoring in real time weather conditions.
The idea of a Real Time Rating System for overhead conductors and power
equipment was conceived by Murray Davis in the 1970s, it was not technologically
feasible to implement in that time, but the development of the technology allowed the
maturation of the concept and today, it can be seen implemented in several countries.
In the Mexican scenario SENER through Programa de Redes Electricas Inteligentes
[9], recognizes the importance of evaluating the feasibility to integrate a Dynamic
Line Rating System in the National Electric Grid to alleviate congestion problems, to
improve network management in contingencies and to achieve the inclusion of greater
renewable energy generation.
There are outstanding related works documented in the Dynamic Line Rating
scenario: The dynamic transmission lines capacity in the north of Chile was studied
by Soto in [10], based on meteorological data of the Department of Geophysics of the
University of Chile. Overhead lines closer to the coast are those that possess greater
dynamic capacity in contrast to the extreme lines that penetrate the continent which
have less capacity according to the observed results. Additionally, the optimal location
and number of sensors needed to estimate the dynamic transmission capacity for each
line were determined.
A portion of the Scottish Power Energy Network was studied by Roberts, Taylor and
Michiorri [11], hourly weather data was used for estimating weather parameter values
in each point of a transmission line and to calculate a real time thermal ratings series
(system in 132 kV, a single line connects two towns that are 7 km apart). The real
transmission capacity in MVA was calculated and compared with the static rating, as
well as other more conventional alternatives, suchas re-tensioning the line or reinforcing
the network. From the comparison, of installation costs and energy transfer capacity, a
Dynamic Thermal Rating System could be able to offer the greatest potential benefits
with the lowest cost.
A solution based on Real Time Thermal Rating System to alleviate electric
transmission congestion and to keep a section of the Power System of Pakistan intact
in contingencies is presented by Zafran, Naeem, Ahmad and Karim [12]. As a case
study, a 132 kV transmission line in Lahore region of Pakistan was chosen, keeping
in view meteorological data availability and prevailing overloading issue in the area.
The analysis discovered that smart adaptions based upon varying weather conditions
provide a feasible scenario for dynamic rating of transmission lines, additional capacity
can be increased up to 51.34% on average.
Black, Connor and Colandairaj described case studies at three 110 kV lines on
3
which Northern Ireland Electricity has successfully installed Dynamic Line Rating
equipment [13]. They examined how re-conductoring certain sections of overhead lines
with higher temperature in conjunction with Dynamic Line Rating implementation
allows a greater increase in ampacity of the lines than Dynamic Line Rating alone. The
analysis showed that Dynamic Line Rating provides, on average, an additional 50 MVA
above static rating of the conductor (109 MVA for summer, and 124 MVA for winter,
at 75◦C of conductor surface temperature), while a combination of re-conductoring and
dynamically rating the overhead line up-rates it by 130 MVA.
In contrast Cradden and Harrison analyzed the impacts of climate change on
overhead line ratings due to the increase in the Earth’s temperature [14]. Using the
UKCP09 climate projections with additional wind modelling, this work has shown
that the likely climate change effects on the thermal limits of the overhead lines in
the United Kingdom are relatively modest. Authors emphasize the importance of
monitoring systems, Dynamic Rating Systems offer the opportunity to eliminate the
risk of exceeding nominal ratings values when the weather conditions do not permit
it, and open up additional capacity when they do; they offer the additional advantage
that they can be retrofitted relatively quickly to existing circuits without upgrading
the line itself.
Wind power researchers at Idaho National Laboratory are developing a Java-based
software package called General Line Ampacity State Solver (GLASS), which calculates
real-time ampacity and thermal conductor limits; the software is based on the use of
computational fluid dynamics (CFD) simulations coupled with weather stations data,
this method can potentially be used to give more accurate predictions [15]. A field
implementation comprises two transmission corridors of AltaLink in a southern part
of Alberta, Canada; findings revel that real-time ratings are above the seasonal static
ratings for up to 95.1% of the time, with a mean increase of 72% over static rating [16].
The first application in which an Energy Market operates with real-time line ratings
is managed by ERCOT, in the south of the United States, [17] and [18]. ERCOT
receives the real time dynamic ratings from Oncor Electric Delivery Company, who
developed and deployed an extensive and advanced Dynamic Line Rating installation
to demonstrate that this technology is capable of solving many transmission capacity
constraint problems with a system that is reliable, safe and very cost competitive. This
system feeds and loads a dispatch program, which optimizes the matching of generation
with load demand on a security, reliability and economic basis. Study results show that
Dynamic Line Rating provides an increase from 6% to 10% for transmission lines at
345 kV and from 8% to 10% for 138 kV, the availability of that added capacity ranged
from 83.5% to 90.5% of the time; while the effective congestion mitigation can be in
the range of 60% to 100% on the lines monitored.
1.4 Research questions
The following research questions were formulated:
• What is the subset of the high-voltage transmission lines in México limited by
their thermal conduction capacity, and therefore subject to dynamic uprating,
4
as opposed to lines limited by transient stability, voltage drop, and reliability
considerations?
• What are the main factors governing thermal transmission line limits in the
Mexican context?
• What is the dynamic thermal capacity of the transmission lines limited by thermal
constraints for each hour in a typical year?
• What are the values of the thermal rating at exceedance probabilities of 90%,
95%, and 99%, respectively?
• Which are the transmission lines that are consistently showing capacity
limitations?
• What is the theoretical impact of dynamic thermal line limits on the load-carrying
capacity of critical transmission corridors?
1.5 Solution overview
The aim of the present research is to conduct the first systematic assessment of the
potential for dynamic uprating of the Mexican National Electric Grid. This will allow
to identify strategic overhead lines in which to integrate a Real Time Rating System
will bring high benefits to the power transmission system.
The project includes the power transmission system study at 115 kV, 230 kV and
400 kV based on information published by the Regional Transmission Organization in
México, known as Centro Nacional de Control de Enerǵıa (CENACE). The databases
used to obtain the environmental and geographical conditions are: National Renewable
Energy Inventory (INERE), Modern-Era Retrospective Analysis for Research and
Applications, Version 2 (MERRA-2), National Solar Radiation Database (NSRDB)
and National Institute of Statistics and Geography (INEGI).
A first study of dynamic capacities of transmission lines considering monthly
averages of environmental variables will be carried out, if the results indicate that the
transmission lines have a capacity increase potential, an intensive study considering
hourly data of the environmental variables will proceed.
The general objectives of the project are to:
• calculate the dynamic capacity of the power transmission system in a typical
year and to compare with the respective static ratings, for determining a possible
increase in the capacity of the overhead lines;
• determine the critical span in each transmission line under study in order to
identify the weakest section where a weather monitoring system could be installed;
• analyze transmission lines with records of congestion problems to determine if an
increase in capacity could contribute to a bottleneck solution;
• realize an economic dispatch simulation with the dynamic capacities obtained, to
determine if the uprating has a positive impact on the price of energy.
5
1.6 Thesis structure
This document is structured as follows:
• Chapter 2 provides a review in line loadability theory, thermal behavior of the
conductors, as well as the benefits and limitations of Dynamic Line Rating.
• Chapter 3 reports the methodology to be followed to collect the information of
the environmental and geographical conditions in the National Electric Grid.
• Chapter 4 describes the IEEE Std.738-2012 implementation and the results of the
dynamic capacity study for the power transmission system, both in the monthly
and hourly analysis, as well as the thermal rating exceedance probabilities and
the possible relief of some congested corridors.
• Finally, Chapter 5 presents the conclusions and suggestions to integrate a Real
Time Rating System in the Mexican National Electric Grid, and a discussion of
future work is presented.
6
Chapter 2
This section presents an overview of the real time thermal rating approach developed
for overhead transmission lines, analyzing the complex interconnection between the
environment and power systems. The basic theory of line loadability will be presented to
know in what type of overhead lines a real time thermal study can be applied, therefore
theDynamic Line Rating concept will be introduced, as well as their applications and
limitations.
2.1 Loadability of overhead transmission lines
The expression line loadability is used to describe the load carrying ability of
a transmission line operating under a specified set of performance criteria. The
transmission line power-transfer capability curves, also known as “St.Clair curves”,
analyze the loadability of transmission lines in terms of their surge impedance loading
for line lengths up to 400 miles. These curve have been a valuable tool for planning
engineers ever since their publication [19].
2.1.1 Surge impedance
The general equations that relate voltage and current on a transmission line are
analyzed in [20], and they recognize the fact that the parameters of a transmission
line: Resistance R in Ohms, Inductance L in Henrys, Capacitance C in Farads, and
Conductance G in Siemens are uniformly distributed along the line.
In order to distinguish between the total series impedance of a line and the series
impedance per unit length, the following nomenclature is adopted:
z = Series impedance per unit length per phase
y = Shunt admittance per unit length per phase to neutral
l = Length of line
Z = zl = Total series impedance per phase
Y = yl = Total shunt admittance per phase to neutral
Zc =
√
z/y and γ =
√
zy are called characteristic impedance and propagation
constant of the line, respectively. Both Zc and γ are complex quantities.
In power system work characteristic impedance is sometimes called surge impedance.
The term however, is usually reserved for the special case of a lossless line. If a line
is lossless, its series resistance and shunt conductance are zero and the characteristic
impedance reduces to the real number
√
L/C which has the dimensions of ohms when L
is the series inductance of the line and C is the shunt capacitance. Also, the propagation
constant for the line of length l reduces to the imaginary number jβ = jω
√
LC/l since
the attenuation constant resulting from line losses is zero. When dealing with high
frequencies or with surges due to lightning, losses are often neglected and the surge
impedance becomes important. Surge impedance loading (SIL) of a line is the power
7
delivered by a line to a purely resistive load equal to its surge impedance. When loaded,
the line supplies a current of:
|I| = VL√
3 · |Zc|
[A] (1)
where:
VL: Line-to-line voltage at the load in kV
Zc: Characteristic impedance in Ω
Since the load is pure resistance:
SIL =
V 2L
|Zc|
[MW] (2)
Power system engineers sometimes find it convenient to express the power
transmitted by a line in terms of per unit of SIL, that is, as the ratio of the power
transmitted to the surge impedance loading. For instance, the permissible transmission
line loading may be expressed as a fraction of its SIL, and SIL provides a comparison
of the load carrying capabilities of lines.
When the line is loaded below its SIL, the lines supplies (lagging) reactive power;
if the line is loaded above the SIL, it absorbs reactive power.
2.1.2 Loadability limits in overhead transmission lines
Dunlop, Gutman and Marchenko in [19], consider that of all limiting factors that
normally set a ceiling on how much power can be carried by a particular transmission
line, three major line loading limitations are:
• Thermal limitation
• Line voltage drop limitation
• Steady state stability limitation
The capacity of most transmission lines under approximately 60 miles (100 km) in
length is generally limited by thermal limits, voltage drop generally impacts the power
flow on transmission lines between 60 and 180 miles (100 and 300 km) in length and
the relevant steady-state stability limit becomes the limiting factor only for long lines
(greater than 300 km) [21].
Thermal constraints are dictated by the necessity to maintain statutory clearances
between the transmission line and other objects or the ground; variable conductor
temperatures on the line can modify the span sag by up to several meters, depending
on the mechanical tension and the length of the span. In fact, a rise in temperature
causes the conductor to elongate which, in turn, increases the sagging [2], as Figure 1
illustrates.
8
Figure 1: Sag and clearance in an overhead transmission line
Balangó, Németh and Göcsei in [22] describe the sag by the catenary curve:
S =
σh
γ
[
cosh
aγ
2σh
− 1
]
[m] (3)
where:
γ: Force of conductor per unit length in kg/m
σh: Horizontal tension of the conductor in kg ·m/s2
a: Length of the specific span in m
The length of the conductor in a specific state can be calculated as:
l = a
a3γ2
24σh
[m] (4)
Any temperature change in the conductor results in an immediate change in
conductor length and sag. Elongation of the line has two components, a thermal one
(Equation 5) and an elastic one (Equation 6):
∆t = l0 · α · (t− t0) [m] (5)
where:
α: Linear expansion coefficient in ◦C−1
t: Final temperature in ◦C
t0: Initial temperature in
◦C
l0: Initial length of the conductor in m
∆σ =
l0
E
· (σh − σh0) [m] (6)
where:
E: Young’s modulus in N/m2
σh: Final horizontal tension of the conductor in kg ·m/s2
σh0: Initial horizontal tension of the conductor in kg ·m/s2
l0: Initial length of the conductor in m
9
The total change in conductor length within a span can be calculated by the addition
of the two above mentioned factors:
∆l = ∆t + ∆σ [m] (7)
The change in conductor length within a simple span can also be calculated by
subtracting lengths calculated for two specific states:
∆l = l − l0 =
[
a+
a3γ2
24σ2h
]
−
[
a+
a3γ20
24σ2h0
]
[m] (8)
l − l0 = ∆t + ∆σ [m] (9)
a3γ2
24σ2h
− a+ a
3γ20
24σ2h0
= l0 · α · (t− t0) +
l0
E
· (σh − σh0) [m] (10)
Sag and conductor length represent average conductor temperature along line-spans.
Conductor sag-temperature calculations and prediction are necessary to avoid cases
where electrical clearance might be violated.
Regarding line voltage drop limitation, the conductor manufacturer CTC GLOBAL
describes this constraint proportionally with line length primarily as a result of electrical
phase shifting and conductor impedance [21]. Voltage drop is usually limited from 5%
up to 10% along a line, which becomes increasingly difficult to control as line length
increases. Appropriate conductor selection can reduce voltage drop allowing longer lines
between fewer substations and reduce the need for substations. These aspects include
non-uniform current density due to the skin effect and transformer effect (particularly
with steel-cored conductors) that influence conductor inductance. The presence of
steel will give rise to magnetic hysteresis, eddy currents and the redistribution of
current density between the nonferrous wires which impacts resistance and impedance.
Highly magnetic steel alloys such as invar can exacerbate these effects. The addition
of shunt capacitors at the ends of the transmission line can also be used to reduce
these constraints, which can allow greater levels of current to flow at higher operating
temperatures.
In alternating current lines, impedance Z depends on the spacing and dimensions
of the conductors, the frequency of the current and the magnetic permeability of the
conductor and its surroundings. Voltage drop (E) in an alternating current line is
the product of the current and the impedance of the circuit, E = I · Z. Over longer
distances, extremely large conductors may not be economically attractive. It is usually
preferable to move to higher voltages. Higher voltage circuit requires less current to
transmit the same power, which also serves to reduce line losses.
In contrast with the line voltage drop limitation, the steady state stability limitation
has been discussed quite extensively in the technical literature. However, one important
point is rarely made or given proper emphasis; that is, the stability limitation should
take the complete system into account, not just the line alone. This has been a common
oversight which, for thelower voltage lines generally considered in the past, has not led
to significant misinterpretations concerning line loadability. This is because at lower
10
voltage levels, say 345-kV and below, the line impedance comprises a major portion
of the total equivalent reactance from source to load provided this line is long enough
(over 200 miles) in the first place, to be limited by stability rather than voltage drop
considerations.
Steady state stability limitation is defined by Dunlop, Gutman and Marchenko [19]
in terms of the desired margin between the maximum power transfer ability of the
system Pmax and the operating level Prated:
% Stability margin =
Pmax − Prated
Pmax
· 100 (11)
This margin is chosen so as to provide for stable system operating performance
following a variety of credible contingencies which may cause steady state and/or
transient increases in a given line loading. Such changes in loading may be caused
by line switching operations, by changes in generation dispatch, and by transient
disturbances such as temporary faults or generation loss. The margin amount which is
desirable in a given situation is dependent on many factors. For the general application
of developing conceptual guides to line loadability, the level of margin becomes a matter
of judgment which reflects the on-going philosophy of a particular system with regard
to planning criteria and desired operating reliability level. Authors propose that a
steady state stability margin from 30% to 35% is a reasonable level for typical heavy
line loading situations.
Figure 2 illustrates a typical loadability curve. It is observed how the thermal limit is
considered static and it is well above voltage drop and steady state stability limitation.
Figure 2: Thermal, voltage drop and stability load limits as a function of the line length
11
2.2 Thermal behavior of bare overhead conductors
IEEE Standard 738-2012 describes a numerical method by which the core and
surface temperatures of a bare stranded overhead conductor are related to the steady
or time-varying electrical current and weather conditions. The method may also be
used to determine the conductor current that corresponds to conductor temperature
limits [8].
IEEE method is based on the steady state heat balance equation considering the
balance between heat absorbed and dissipated:
qC + qR = qS + qJ (12)
where:
qC : Convective cooling
qR: Radiative cooling
qS: Solar heating
qJ : Joule effect heating
2.2.1 Convective cooling
The movement of wind around an overhead line conductor results in a heat removal
mechanism known as the convective cooling. This mechanism is determined by the
speed and direction of the wind, as well as the surrounding air properties [23].
For the convective cooling calculation it is necessary to consider:
• Average temperature of the boundary layer
Tfilm =
Ts + Ta
2
[◦C] (13)
where:
Ts: Conductor surface temperature in
◦C
Ta: Ambient air temperature in
◦C
• Density of air
ρf =
1.293− 1.525 · 10−4He + 6.379 · 10−9H2e
1 + 0.00367 · Tfilm
[kg/m3] (14)
where:
He: Elevation of conductor above sea level in m
Tfilm: Average temperature of the boundary layer in
◦C
12
• Dynamic viscosity of air
µf =
1.458 · 10−6(Tfilm + 273)1.5
Tfilm + 383.4
[kg/m · s] (15)
where:
Tfilm: Average temperature of the boundary layer in
◦C
• Thermal conductivity of air
kf = 2.424 · 10−2 + 7.477 · 10−5Tfilm − 4.407 · 10−9T 2film [W/m◦C] (16)
where:
Tfilm: Average temperature of the boundary layer in
◦C
Natural convection, or free convection, occurs during still air conditions; where, in
a continuous process, cool air surrounding the hot conductor is heated and rises, and
is replaced by cool air.
qcn = 3.645 · ρ0.5f ·D0.750 · (Ts − Ta)1.25 [W/m] (17)
where:
ρf : Density of air in kg/m
3
D0: Outside diameter of conductor in m
Ts: Conductor surface temperature in
◦C
Ta: Ambient air temperature in
◦C
Forced convection occurs when blowing air moving past the conductor carries the
heated air away. Equation 18 is correct at low wind speeds but underestimates forced
convection at high wind speeds. Equation 19 is correct at high wind speeds but
underestimates forced convection at low wind speeds. At any wind speed, this standard
recommends calculating convective heat loss with both equations, and using the greater
calculated convection heat loss rates.
qc1 =
[
1.01 + 1.35
(
D0 · ρf ·Ws
µf
)0.52]
· kf ·Kangle · (Ts − Ta) [W/m] (18)
qc2 = 0.754
(
D0 · ρf ·Ws
µf
)0.6
· kf ·Kangle · (Ts − Ta) [W/m] (19)
where:
D0: Outside diameter of conductor in m
ρf : Density of air in kg/m
3
13
Ws: Wind speed in m/s
µf : Dynamic viscosity of air in kg/m · s
kf : Thermal conductivity of air in W/m
◦C
Kangle: Wind direction factor
Ts: Conductor surface temperature in
◦C
Ta: Ambient air temperature in
◦C
Convective heat loss rate, calculated with Equation 18 and Equation 19, must be
multiplied by wind direction factor, Kangle.
Kangle = 1.194− cos(φ) + 0.194 cos(2φ) + 0.368 sin(2φ) (20)
where:
φ: Angle between wind direction and the conductor axis in degrees.
Kangle can take values from 0.3881 to 1.0; it takes its minimum value when φ = 0
◦
(wind direction is parallel to the transmission line) and Kangle takes its maximum value
when φ = 90◦ (wind direction is perpendicular to the transmission line).
Finally convective cooling qC is the largest of the heat losses due to both natural
and forced heat convection, given in W/m.
2.2.2 Radiative cooling
When a bare overhead conductor is heated above the temperature of its
surroundings, energy is transmitted by radiation to the surroundings. The rate at
which the energy is radiated is dependent primarily on the difference in temperature
between the conductor and its surroundings, which are assumed to be at ambient
temperature. The surface condition of the conductor, its emissivity, also affects the
radiative heat transfer; emissivity is the proportion of thermal radiation emitted by an
object due to its temperature.
qR = 17.8 ·D0 · ε ·
[(
Ts + 273
100
)4
−
(
Ta + 273
100
)4]
[W/m] (21)
where:
D0: Outside diameter of conductor in m
ε: Emissivity
Ts: Conductor surface temperature in
◦C
Ta: Ambient air temperature in
◦C
2.2.3 Solar heating
The Sun provides heat energy to the conductor. The amount of solar heat energy
delivered to the conductor depends on the Sun’s position in the sky, the solar constant
(the amount of energy per m2 outside of the Earth’s atmosphere), the amount of
14
that energy that is transmitted through the Earth’s atmosphere to the conductor, the
orientation of the conductor, and its surface condition (its absorptivity). Bright, shiny
conductors reflect most of the Sun’s energy and black weathered conductors absorb
most of the Sun’s energy.
Below is described the solar heating calculation:
• Solar declination
δ = 23.4583 · sin
[
284 +N
365
· 360
]
[degrees] (22)
where:
N : Day of the year
• Altitude of the Sun
Hc = arcsin[cos(Lat) · cos(δ) · cos(ω) + sin(Lat) · sin(δ)] [degrees] (23)
where:
Lat: Latitude in degrees
δ: Solar declination in degrees
ω: Hour angle in degrees
• Solar azimuth variable
χ =
sin(ω)
sin(Lat) · cos(ω)− cos(Lat) · tan(δ)
(24)
where:
ω: Hour angle in degrees
Lat: Latitude in degrees
δ: Solar declination in degrees
• Azimuth of the Sun
Zc = C + arctan(χ) [degrees] (25)
where:
C: Solar azimuth constant in degrees
χ: Solar azimuth variable
15
The solar azimuth constant (C) is a function of the hour angle (ω) and the solar
azimuth variable (χ), as shown in Table 1.
Table 1: Solar azimuth constant as a function of hour angle and solar azimuth variable
ω C if χ ≥ 0 C if χ < 0
−180◦ ≤ ω < 0◦ 0◦ 180◦
0◦ ≤ ω < 180◦ 180◦ 360◦
• Effective angle of incidence of the Sun’s rays
θ = arccos[cos(Hc) · cos(Zc − Zline)] [degrees] (26)
where:
Hc: Altitude of the Sun in degrees
Zc: Azimuth of the Sun in degrees
Zline: Azimuth of the transmission line in degrees
Finally solar heating can be calculated:
qS = α · A′ · [QB· sin(θ) +QD] [W/m] (27)
where:
α: Solar absorptivity
θ: Effective angle of incidence of the Sun’s rays in degrees
A′: Projected area of conductor per unit length in m2/m
QB: Direct solar radiation in W/m
2
QB: Diffuse solar radiation in W/m
2
2.2.4 Joule effect heating
The Joule effect is an irreversible phenomenon by which if an electric current
circulates in a conductor, part of the kinetic energy of the electrons is transformed
into heat. This effect is a function of the current and the electrical resistance of the
conductor:
qJ = I
2 ·R(Ts) [W/m] (28)
where:
I: Electrical current in A
R(Ts): AC electrical resistance of conductor in Ω, at temperature Ts
16
The electrical resistance of a bare stranded conductor varies with frequency, average
current density, and temperature. For 60 Hz ac, at temperatures of 25◦C to 75◦C, the
Aluminum Electrical Conductor Handbook gives calculated values of electrical resistance
for most standard aluminum power conductors.
These calculated values include the frequency-dependent “skin effect” for all types of
stranded conductor, but, for other than single-layer ACSR, do not include a correction
for current density dependent magnetic core effects, which is significant for ACSR
conductors having odd numbers of layers of aluminum strands.
In IEEE Standard, electrical resistance is calculated solely as a function of conductor
temperature; however, the resistance values entered may be a function of frequency and
current density. For example, the values of conductor resistance at high temperature,
Thigh, and low temperature, Tlow, may be taken from the tabulated values in the
Aluminum Electrical Conductor Handbook, in [24]. The conductor resistance at any
other temperature, Ts, is found by linear interpolation according to:
R(Ts) =
[
R(Thigh)−R(Tlow)
Thigh − Tlow
]
(Ts − Tlow) +R(Tlow) [Ω] (29)
where:
R(Thigh): AC electrical resistance of conductor in Ω, at temperature Thigh
R(Tlow): AC electrical resistance of conductor in Ω, at temperature Tlow
Thigh: High average conductor temperature in
◦C
Tlow: Low average conductor temperature in
◦C
Ts: Conductor surface temperature in
◦C
This method of resistance calculation allows the user to calculate the high and low
temperature resistance values by whatever means is appropriate. Since the resistivity
of most common metals used in stranded conductors increases somewhat faster than
linearly with temperature, the resistance calculated by Equation 29 will be somewhat
high as long as conductor temperature is between Tlow and Thigh. If the conductor
temperature exceeds Thigh, however, the calculated resistance will be somewhat low.
2.2.5 Steady-state thermal rating
The steady-state thermal rating (maximum rated current) given by a maximum
allowable conductor temperature, weather conditions, and conductor characteristics,
can be found using Equation 30:
I =
√
qC + qR − qS
R(Ts)
[A] (30)
where:
qC : Convective cooling in W/m
qR: Radiative cooling in W/m
qS: Solar heating in W/m
R(Ts): AC electrical resistance of conductor in Ω, at temperature Ts
17
2.3 Fundamentals of Dynamic Line Rating technologies
The term Dynamic Rating is defined as the technique that allows increasing the
capacity of a power system component, without violation of the safety margins.
Dynamic Rating uses data about physical and electrical properties of power system
components to improve power system transmission capability. The dynamic rating
of overhead lines is usually referred to as the Dynamic Line Rating. The correct
application of the Dynamic Line Rating requires the calculation of the heat balance of
the conductor [25].
Dynamic Line Rating recognizes that certain weather conditions, such as wind speed
and direction, ambient temperature, solar radiation, rainfall, and ice loading on a line,
can impact conductor temperature and cause a change in the capacity along the line
and throughout the day. Dynamic Line Ratings provide a more accurate assessment
of transmission line ratings and operating margins than static ratings or ambient-
adjusted ratings, allowing operators to optimize the utilization of the transmission
grid. A Dynamic Line Rating System does not increase line capacity by itself; rather,
it reveals the real-time line capacity. Although dynamic ratings are often greater than
static ratings, in a minority of cases, Dynamic Line Rating Technologies reveal that a
dynamic line rating is less than the static line rating [26].
2.3.1 Dynamic Line Rating in Smart Grids development
There are many Smart Grid definitions, a common element to most definitions
is: the presence of digital processing together with information and communication
technologies applied to the power grid in order to efficiently deliver sustainable,
economic and secure electricity supplies [2]. A Smart Grid employs innovative products
and services together with intelligent monitoring, control, communication, and self-
healing technologies and integrates them into utility processes and systems.
As the electricity network was originally designed to hold power flows from
centralized generation units to distributed consumption areas, the increased penetration
of decentralized and intermittent renewable sources significantly changes the power
flows patterns, making them more dynamic, and thus modifying the way to manage
them. This is one of the main issues from which Smart Grids technologies originated.
In order to efficiently deal with those new power flows patterns, different
complementary methods can be implemented to improve network flexibility and they
can be summarized in four points:
• Controlling power flows with FACTS
• Monitoring network and the status of components
• Introduce active components at the planning stage
• Managing load and generation with active network management, demand side
management, and virtual power plants
The consequence of the application of these technologies and the coordination
between different actors coming with them results in a series of advantages reducing
18
the necessity of new investments and facilitating the operation of the power system.
In particular it is possible to: a) minimize power reserves and peak power plants, b)
enhance power system security with regard to failures of transmission or generation
components, and c) reduce volatility of the electricity prices, by mitigating the
consequences or removing the causes of high demand or excess power.
In the light of this, Dynamic Line Rating can be considered a Smart Grid technology.
Although it is based on traditional physical properties of power system components, its
implementation and exploitation are made possible only by improvements in monitoring
and communication technologies. Furthermore its application will be enhanced by the
flexibility provided by all power system actors, network operators, market players,
producers or consumers through automatic control, when information on eventual
variable constraints is available. In this framework, combined implementation of
smart grids technologies increases the overall efficiency. Therefore, even a few percent
increases of dynamic rating scan significantly enhance network operation and flexibility
when other smart grids tools are being used simultaneously. This can then benefit all
stakeholders by increasing overall social welfare.
2.3.2 Monitoring systems for Dynamic Line Rating
Dynamic Line Rating requires use of a monitoring system that will collect all the
necessary data. The type of data that is used for system evaluation influences the
quality of the Dynamic Rating. Therefore, ratings can vary from very detailed ones,
which change several times per hour, to seasonal ratings, when the system experiences
changes in ratings several times per year. The evaluation of system ratings is based on
stored data of several years, or the information from online monitoring systems.
Different companies produce different equipment for Dynamic Rating data
collection. Monitoring equipment can beinstalled on the overhead line at some point
close to the control room, and will send the on-line data to the control system with a
small delay. Monitoring systems can have different functions. Some of them are used
for monitoring weather conditions, measuring conductor temperature or monitoring
the tension in the conductor. Morozovska divided all of the methods into the following
categories for evaluating system monitoring [25]:
• Static rating (STR): a standard rating of transmission lines and transformers,
which is specified by international or national standards.
• Seasonal rating (SER): also known as summer-winter rating, or in several cases
summer autumn-winter rating.
• Weather model (WM): rating based on the collected average weather data for
several years. It has better accuracy than the seasonal rating.
• Weather forecast (WF): online monitoring method, in which real time weather
data is collected near the conductor or transformer and ratings are set according
to the forecast.
• Conductor temperature evaluation (CTE): an on-line monitoring method, in
which the conductor temperature is measured with a sensor.
19
• Tension monitoring (TM): the process of tension monitoring is done by placing
load cells in series with insulator strings. The loads cells must be electrically
insulated from the conductor. Tension monitoring is useful, because there is a
direct relation between the sag and tension of the conductor. Most of the tension
monitoring systems require weather monitoring equipment installation for further
evaluation of system parameters and calculation of the ampacity of the line.
• Line sag measurement (CSM): it is a more advanced system that can actually
measure the sag of the line by placing such equipment in the worst case parts of
the power system can be operated within safety margins.
• Clearance-to-ground measurement (CTGM): new generation of on-line monitoring
systems for overhead lines are measuring not sag, but a clearance-to-ground. This
is a relevant measurement, because it directly gives information about the distance
of the conductors to the ground.
• Full scale monitoring (FSM): this method can be a combination of the several cases
proposed above. The main feature of the following category is the placement of
small sensors along the line. However, placing numerous devices along the power
line is expensive today.
The U.S. Department of Energy perceives that all devices share a common goal,
regardless of the type of Dynamic Line Rating measurement [26]. The goal is to measure
specific parameters to calculate the dynamic rating and capacity margin. This goal is
accomplished by measuring key operating conditions that affect the capacity of the
transmission line in real time: a) weather conditions—such as ambient temperature,
solar radiation, wind speed, wind direction, and rainfall—and b) the characteristics of
the line itself, such as conductor temperature, clearance, sag and tension.
Devices that make direct weather measurements are the least expensive and are
highly reliable. They are also the simplest to implement because they do not need to
be installed on the line itself, their components are more reliable, and they provide
data that is easy to interpret. However, these devices are point sensors, so they may
not accurately reflect average operating conditions along the entire length of the line.
Installation sites must be carefully considered, especially for collecting data from remote
sections of a transmission line.
For Dynamic Line Rating devices measuring conductor temperature, sag, or
tension, line loading determines whether the effective wind speed—and, by extension,
the dynamic rating—can be accurately calculated. Effective wind speed can only
be determined when the line is loaded heavily enough to increase the conductor
temperature several degrees Celsius above the temperature it would reach due to the
impacts of ambient temperature and net solar radiation (dead-end to dead-end, which
may be up to several miles). Generally, the line must be carrying a minimum load
of 20% to 30% of its static rating or have a minimum current density of 0.5 A per
thousand circular mils (kcmil). This condition is often unmet, especially for 69 kV
to 230 kV lines. When the effective wind speed cannot be determined, the software
conservatively approximates the impact of wind on the line. The resulting dynamic
rating is correspondingly conservative. For lightly loaded lines, transmission owners
20
may need to rely on other Dynamic Line Rating technologies or direct wind speed
measurements if they wish to take full advantage of the available real-time capacity.
The devices themselves are reliable, but transmission owners must be aware of their
potential limitations.
The Dynamic Line Rating device, which measures conductor clearance, is unique
among conductor temperature-measuring devices in that it has no contact with the
transmission line itself. Promethean Devices’ Real-Time Transmission Line Monitoring
System (RT-TLMS) is an example of this technology [27]. Rather than measuring
conductor temperature directly, the RT-TLMS utilizes three ground-based sensors to
measure the magnetic field around the conductor. The magnetic field strength is
proportional to the amount of current flowing through the line. By monitoring the
phase currents of a transmission line and performing calculations of the installation
geometry, the conductor height (example, clearance) and the conductor temperature
may be calculated and therefore monitored. Additional technologies, such as Lindsey
Manufacturing’s Transmission Line Monitor (TLM) [28], measure the natural frequency
and/or inclination of the conductor to characterize its catenary curve, as well as
conductor temperature and clearance.
Some academic projects which have resulted in temperature monitoring system
prototypes have also mentioned, as stressed in [29]. The Georgia Institute of Technology
has developed two different prototypes to measure conductor temperature and current
intensity, the objective is to design cheap and self-supplied devices; the first system,
called Power Line SensorNet (PLSN), is designed using commercially available low
power devices, the second system is a stick-on sensor. Furthermore, the Isfahan
University of Technology and the University of Manitoba have developed a device that
measures temperature based on radio frequency cavity resonance.
2.3.3 Economic and market implications of Dynamic Line Rating
Michiorri, Nguyen, Alessandrini, Bjørnar, Dierer, Ferrero, Nygaard, Pinson,
Thomaidis and Uski, in [2], analyze the constant attention that Dynamic Line Rating
has received from the power system and academic community as a promising strategy
for maximizing the utilization of the infrastructure of the network and bringing low-
cost energy to heavily loaded sections of the grid. Undoubtedly, the great majority
of research studies focus on how flexible line-rating policies could be used to tackle
operational and safety issues in grid management. Little has yet been written on the
extent to which consumers might benefit from flexible rating mechanisms or how much
capital could be released from the required network extension/upgrade projects. These
questions are very important when it comes to convincing grid operators or regulators
to adopt new, and perhaps radical, network management rules. Furthermore, where as
it may be easier to compare a conventional network reinforcement (example: building
additional transmission lines, and adhering to static line ratings) investment and an
investment on Dynamic Line Rating implementation on specific congested power lines
as an alternative, the assessment of overall economic implications may be very difficult.
Generally, the discussion on whether Dynamic Line Rating presents an economically
feasible and rational solution focuses on two dimensions that mainly represent the
viewpoints of different network stakeholders (utilities and consumers).
21
Switching to