This document provides an overview of sag-tension calculations for overhead power lines. It discusses key parameters like maximum sag, tension, and span length. Sag determines electrical clearances while tension impacts structure design. The document covers the catenary curve model and factors like conductor weight and elongation. It also summarizes considerations for non-homogeneous conductors like ACSR. Numerical examples show how temperature changes impact sag and tension. Experimental data and computer models are needed due to the nonlinear behavior of composite conductors.
EXECUTIVE SUMMARY
This technical brochure specifies and explains the primary elements of the sag-tension
calculation process, a process which is essential to the design and construction of
overhead lines. The various mathematical tools and conductor data considered herein are
used to predict sag and tension of catenaries at the full range of conductor temperatures
and ice and wind loads that occur over the rather long life of an overhead power line.
The goal of the document is not to develop a unique or “best” calculation method, but to
describe the overall process and explain the common calculation methods.
Introduction
Historically, for most overhead transmission lines, the sag of conductors (or tension) is
measured at the time of construction when the line is not energized. At the time of
installation, the conductors are at a temperature of 10oC to 35oC and tensioned to no more
than 10% to 30% of their rated tensile strength. Once the line is constructed, the phase
conductors may be subject to high temperatures during periods of high electrical loading
and both the lightning shield wires and phase conductors must remain intact during high
ice and wind load events for an expected useful life of 40 years or more. Under all
foreseeable conditions, the conductors must not break under high tension, fatigue under
persistent wind-induced motions, nor sag such that minimum electrical clearances are
compromised.
Cable Conductor Sizing for Minimum Life Cycle CostLeonardo ENERGY
Energy prices are high and expected to rise. All CO2 emissions are being scrutinized by regulators as well as by public opinion. As a result, energy management has become a key factor in almost every business. To get the most out of each kilowatt-hour, appliances must be carefully evaluated for their energy efficiency.
It is an often overlooked fact that electrical energy gets lost in both end-use and in the supply system (cables, busbars, transformers, etc.). Every cable has resistance, so part of the electrical energy that it carries is dissipated as heat and is lost.
Such energy losses can be reduced by increasing the cross section of the copper conductor in a cable or busbar. Obviously, the conductor size cannot be increased endlessly. The objective should be the economic and/or environmental optimum. What is the optimal cross section necessary to maximize the Return on Investment (ROI) and minimize the Net Present Value (NPV) and/or the Life Cycle Cost (LCC)?
This paper will demonstrate that the maximizing of the ROI results in a cross section that is far larger than which technical standards prescribe. Those standards are based entirely on safety and certain power quality aspects. This means there is room for improvement—a great deal of improvement in fact.
Cable sizing to withstand short-circuit current - ExampleLeonardo ENERGY
A short circuit causes very extreme stresses in a cable which are proportional to the square of the current:
A temperature rise in the conducting components such as conductor, screen, metal sheath, armour. Indirectly the temperature of adjoining insulation and protective covers also increases,
electro-magnetic forces between the current-carrying components.
The temperature rise is important for its effect on ageing, heat pressure characteristics etc. and should be limited to a permissible short-circuit temperature. The thermo-mechanical effects of the current shall also be considered.
For the given short-circuit condition the short-circuit capacity of a cable should be investigated with respect to all these parameters. For multi-core cables in most instances the thermal effect - related to the magnitude of fault current and clearance time - is the critical parameter, since the cable will normally have enough mechanical strength. With single-core cables however the mechanical effect - related to the magnitude of the peak short-circuit current - is of such significance that, next to the thermal, the mechanical strength of both cable and its supports should be investigated.
Also accessories must be rated with respect to thermal and mechanical short-circuit stresses.
The short circuit strength of a cable system is not quantitatively defined with regard to permissible number of repeated short circuits, degree of deformation or destruction or impairment quality. It is expected, however, that a cable installation will remain safe in operation and that any deformation remains within tolerable limits even after several short circuits.
This course provides practical overview of short circuit performance of a cable.
EXECUTIVE SUMMARY
This technical brochure specifies and explains the primary elements of the sag-tension
calculation process, a process which is essential to the design and construction of
overhead lines. The various mathematical tools and conductor data considered herein are
used to predict sag and tension of catenaries at the full range of conductor temperatures
and ice and wind loads that occur over the rather long life of an overhead power line.
The goal of the document is not to develop a unique or “best” calculation method, but to
describe the overall process and explain the common calculation methods.
Introduction
Historically, for most overhead transmission lines, the sag of conductors (or tension) is
measured at the time of construction when the line is not energized. At the time of
installation, the conductors are at a temperature of 10oC to 35oC and tensioned to no more
than 10% to 30% of their rated tensile strength. Once the line is constructed, the phase
conductors may be subject to high temperatures during periods of high electrical loading
and both the lightning shield wires and phase conductors must remain intact during high
ice and wind load events for an expected useful life of 40 years or more. Under all
foreseeable conditions, the conductors must not break under high tension, fatigue under
persistent wind-induced motions, nor sag such that minimum electrical clearances are
compromised.
Cable Conductor Sizing for Minimum Life Cycle CostLeonardo ENERGY
Energy prices are high and expected to rise. All CO2 emissions are being scrutinized by regulators as well as by public opinion. As a result, energy management has become a key factor in almost every business. To get the most out of each kilowatt-hour, appliances must be carefully evaluated for their energy efficiency.
It is an often overlooked fact that electrical energy gets lost in both end-use and in the supply system (cables, busbars, transformers, etc.). Every cable has resistance, so part of the electrical energy that it carries is dissipated as heat and is lost.
Such energy losses can be reduced by increasing the cross section of the copper conductor in a cable or busbar. Obviously, the conductor size cannot be increased endlessly. The objective should be the economic and/or environmental optimum. What is the optimal cross section necessary to maximize the Return on Investment (ROI) and minimize the Net Present Value (NPV) and/or the Life Cycle Cost (LCC)?
This paper will demonstrate that the maximizing of the ROI results in a cross section that is far larger than which technical standards prescribe. Those standards are based entirely on safety and certain power quality aspects. This means there is room for improvement—a great deal of improvement in fact.
Cable sizing to withstand short-circuit current - ExampleLeonardo ENERGY
A short circuit causes very extreme stresses in a cable which are proportional to the square of the current:
A temperature rise in the conducting components such as conductor, screen, metal sheath, armour. Indirectly the temperature of adjoining insulation and protective covers also increases,
electro-magnetic forces between the current-carrying components.
The temperature rise is important for its effect on ageing, heat pressure characteristics etc. and should be limited to a permissible short-circuit temperature. The thermo-mechanical effects of the current shall also be considered.
For the given short-circuit condition the short-circuit capacity of a cable should be investigated with respect to all these parameters. For multi-core cables in most instances the thermal effect - related to the magnitude of fault current and clearance time - is the critical parameter, since the cable will normally have enough mechanical strength. With single-core cables however the mechanical effect - related to the magnitude of the peak short-circuit current - is of such significance that, next to the thermal, the mechanical strength of both cable and its supports should be investigated.
Also accessories must be rated with respect to thermal and mechanical short-circuit stresses.
The short circuit strength of a cable system is not quantitatively defined with regard to permissible number of repeated short circuits, degree of deformation or destruction or impairment quality. It is expected, however, that a cable installation will remain safe in operation and that any deformation remains within tolerable limits even after several short circuits.
This course provides practical overview of short circuit performance of a cable.
Infinite bus bar is one which keeps constant voltage and frequency although the load varies. Thus it may behave like a voltage source with zero internal impedance and infinite rotational inertia.
This guide presents a methodology based on standard PN-IEC 60354 to check overloading capacity of transformers. Main changes versus standard PN-71/E-81000 are discussed and step by step examples are given. An essential advantage of the recommended methods of verification of overloading capacity of transformers is that the size and cooling modes of transformers are considered.
Distribution System Voltage Drop and Power Loss CalculationAmeen San
Distribution System Voltage Drop and Power Loss
Calculation
Comparison of Overhead Versus Underground System
Power Loss Calculation,Voltage Drop Calculation
Since the loads having the trends towards growing density. This requires the better appearance, rugged construction, greater service reliability and increased safety. An underground cable essentially consists of one or more conductors covered with suitable insulation and surrounded by a protecting cover. The interference from external disturbances like storms, lightening, ice, trees etc. should be reduced to achieve trouble free service. The cables may be buried directly in the ground, or may be installed in ducts buried in the ground.
Complete details of EHV Transmission Line. Consolidated this presentation from those experts who had contributed separately on slider share and other web pages.Thanks for their valuable inputs.
Infinite bus bar is one which keeps constant voltage and frequency although the load varies. Thus it may behave like a voltage source with zero internal impedance and infinite rotational inertia.
This guide presents a methodology based on standard PN-IEC 60354 to check overloading capacity of transformers. Main changes versus standard PN-71/E-81000 are discussed and step by step examples are given. An essential advantage of the recommended methods of verification of overloading capacity of transformers is that the size and cooling modes of transformers are considered.
Distribution System Voltage Drop and Power Loss CalculationAmeen San
Distribution System Voltage Drop and Power Loss
Calculation
Comparison of Overhead Versus Underground System
Power Loss Calculation,Voltage Drop Calculation
Since the loads having the trends towards growing density. This requires the better appearance, rugged construction, greater service reliability and increased safety. An underground cable essentially consists of one or more conductors covered with suitable insulation and surrounded by a protecting cover. The interference from external disturbances like storms, lightening, ice, trees etc. should be reduced to achieve trouble free service. The cables may be buried directly in the ground, or may be installed in ducts buried in the ground.
Complete details of EHV Transmission Line. Consolidated this presentation from those experts who had contributed separately on slider share and other web pages.Thanks for their valuable inputs.
This is the simple ppt explaining about the main components of the power systems. especially we are determining the insulators and its types with real time pictures which are attractive,
ER Publication,
IJETR, IJMCTR,
Journals,
International Journals,
High Impact Journals,
Monthly Journal,
Good quality Journals,
Research,
Research Papers,
Research Article,
Free Journals, Open access Journals,
erpublication.org,
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Science Journals,
Principles of Cable Sizing; current carrying capacity, voltage drop, short circuit.
Cables are often the last component considered during system design even if in many situations cables are the true system’s lifeline: if a cable fails, the entire system may stop. Cable reliability is therefore extremely important, then a cable system should be engineered to last the life of the system in the installation environment for the required application. Environments in which cable systems are being used are often challenging, as extreme temperatures, chemicals, abrasion, and extensive flexing. These variables have a direct impact on the materials used for cable insulation and jacketing as well as the construction of the cable. Using a systematic approach will help ensure that designer select the best cable for the required application in the installation environment. This lessons will provide students main guidelines for perform this approach.
Load centers get generated electricity from power
stations that are usually far; uninterrupted consumption or usage
of power has increased in last few years. Transmission system is
the system by means of which electricity is transferred from place
of generation to the consumers. Overhead wires or conductors
are the medium used for transmission of power. These wires are
visible to wind, heat and ice. The efficiency of the power system
increases if the losses of these overhead wires are minimal. These
losses are based on the resistive, magnetic and capacitive nature
of the conductor. It is necessary to create or make proper design
of these conductors accompanied by proper installation. To
balance the working and strength of overhead transmission line
and to minimize its capacitive effect the conductors must be
installed in catenary shape. The sag is required in transmission
line for conductor suspension. The conductors are appended
between two overhead towers with ideal estimation of sag. It is
because of keeping conductor safety from inordinate tension. To
permit safe tension in the conductor, conductors are not
completely extended; rather they are allowed to have sag. For
same level supports this paper provides sag and tension
estimation with different wind speeds under low operating
temperature 2 °C. To calculate sag-tension estimation of ACSR
(Aluminum Conductor Steel Reinforced) overhead lines three
different cases are provided with normal and high wind speed
effects. Four different span lengths are taken for equal level
supports. ETAP (Electrical Transient and Analysis Program) is
used for simulation setup. The results shows that wind speed has
great impact upon line tension and with addition of wind speed
the sag of line remains unaltered while tension changes.
Moreover tension gets increase while increase in wind speed.
ASTM developed a collection of documents called material specifications for
standardizing materials of large use in the industry.
• Specifications starting with “A” are for steel.
• Specifications starting with “B” are for non-ferrous alloys (bronze, brass,
copper nickel alloys, aluminum alloys and so on).
• Specifications starting with “D” are for plastic material, as PVC.
An ASTM specification specifies the basic chemical composition of material and the
process through which the material is shaped into the final product. Some of the
common material standards are
Output equation of Induction motor; Main dimensions; Separation of D and L; Choice of Average flux density; length of air gap; Design of Stator core; Rules for selecting rotor slots of squirrel cage machines; Design of rotor bars and slots; Design of end rings; Design of wound rotor; Magnetic leakage calculations; Leakage reactance of polyphase machines; Magnetizing current; Short circuit current; Operating characteristics; Losses and Efficiency.
A tale of scale & speed: How the US Navy is enabling software delivery from l...sonjaschweigert1
Rapid and secure feature delivery is a goal across every application team and every branch of the DoD. The Navy’s DevSecOps platform, Party Barge, has achieved:
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Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdfPaige Cruz
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
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In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
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GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Welocme to ViralQR, your best QR code generator.ViralQR
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Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
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Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
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The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
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Why are attacks on smart factories rising?
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Download the full report from here:
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Sag tension calcs-ohl-tutorial
1. Sag-tension Calculations
A CIGRE Tutorial Based on
Technical Brochure 324
Dale Douglass, PDC
Paul Springer, Southwire Co
14 January, 2013
2. 1/14/13 IEEE Sag-Ten Tutorial
Why Bother with Sag-Tension?
• Sag determines electrical clearances, right-of-
way width (blowout), uplift (wts & strain), thermal
rating
• Sag is a factor in electric & magnetic fields,
aeolian vibration (H/w), ice galloping
• Tension determines structure angle/dead-
end/broken wire loads
• Tension limits determine conductor system
safety factor, vibration, & structure cost
2
3. 1/14/13 IEEE Sag-Ten Tutorial
Sag-tension Calculations – Key
Line Design Parameters
• Maximum sag – minimum clearance to
ground and other conductors must be
maintained usually at high temp.
• Maximum tension so that structures can
be designed to withstand it.
• Minimum sag to control structure uplift
problems & H/w during “coldest month” to
limit aeolian vibration.
3
4. 1/14/13 IEEE Sag-Ten Tutorial
Key Questions
• What is a ruling span & why bother with it?
• How is the conductor tension related to the
sag?
• Why define initial & final conditions?
• What are typical conductor tension limits?
• Modeling 2-part conductors (e.g. ACSR).
4
5. 1/14/13 IEEE Sag-Ten Tutorial
What is a ruling span?
5
Strain Structure Suspension Structure
6. 1/14/13 IEEE Sag-Ten Tutorial
( )max
2
3
Average AverageRS S S S≈ + −
S1 S2 S3
RS
6
S+----+S+S
S+----+S+S
=RS
n21
3
n
3
2
3
1
7. The Ruling Span
• Simpler concept than multi-span line
section.
• For many lines, the tension variation with
temperature and load is the same for the
ruling span and each suspension span.
• Stringing sags calculated as a function of
suspension span length and temperature
since tension is the same in all.
1/14/13 IEEE Sag-Ten Tutorial 7
8. 1/14/13 IEEE Sag-Ten Tutorial
The Catenary Curve
• HyperbolicFunctions & Parabolas
• Sag vs weight & tension
• Length between supports
• What is Slack?
8
9. The Catenary – Level Span
Sag D
H - Horizontal Component of Tension (lb) L - Conductor length (ft)
T - Maximum tension (lb) w - Conductor weight (lb/ft)
x, y - wire location in xy coordinates (0,0) is the lowest point (ft)
D - Maximum sag (ft) S - Span length (ft)
y(x) ≈
𝒘𝒘 𝟐
𝟐𝟐
D (sag at belly)
D ≈
𝒘𝒘 𝟐
𝟖𝟖
Max.
Tension H
(S/2, D)
(end support)
𝑳 ≈ S 𝟏 +
𝑺 𝟐
𝒘 𝟐
𝟐𝟒𝑯 𝟐 ≈ S 𝟏 +
𝟖𝟖 𝟐
𝟑𝟑 𝟐
1/14/13 IEEE Sag-Ten Tutorial 9
Span
10. 1/14/13 IEEE Sag-Ten Tutorial
Catenary Sample Calcs
for Arbutus AAC
2
0.7453 600
12.064 3 678
8 2780
D ft ( . m)
⋅
≅ =
⋅
w=0.7453 lbs/ft Bare Weight H=2780 lbs (20% RBS)
S=600 ft ruling span
600 0.7453 8 12.064
600.647
24 2780 3 600
2 2 2
2 2
L 600 1+ 600 1+ ft
⋅ ⋅
≅ ⋅ = ⋅ =
⋅ ⋅
2
2
8 12.064
0.647
3 600
Slack = L - S = 600 ft
⋅
⋅ =
⋅
( )0.647
12.064 (3.678 )
8
3 600
Sag = ft m
⋅ ⋅
=
10
Notice that 8
inches of slack
produces 12 ft of
sag!!
11. Catenary Observations
• If the weight doubles, and L & D stay the
same, the tension doubles (flexible chain).
• Heating the conductor and changing the
conductor tension can change the length &
thus the sag.
• If the conductor length changes even by a
small amount, the sag and tension can
change by a large amount.
1/14/13 IEEE Sag-Ten Tutorial 11
12. 1/14/13 IEEE Sag-Ten Tutorial
Conductor Elongation
• Elastic elongation (conductor stiffness)
• Thermal elongation
• Plastic Elongation of Aluminum
– Settlement & Short-term creep
– Long term creep
L H
L E A
ε
∆ ∆
= =
⋅
A A
L
T
L
α
∆
= ⋅∆
12
14. 1/14/13 IEEE Sag-Ten Tutorial
Sag-tension Envelope
GROUND LEVEL
Minimum Electrical
Clearance
Initial Installed Sag @15C
Final Unloaded Sag @15C
Sag @ Max Ice/Wind Load
Sag @ Max Electrical
Load, Tmax
Span Length
14
15. Simplified Sag-Tension Calcs
1/14/13 IEEE Sag-Ten Tutorial
w=0.7453 lbs/ft Bare
H=2780 lbs (20% RBS)
S=600 ft
( )( )12.8 6* 167 60 600.647*(1.00137) 601.470L 600.647 1+ e ft≅ ⋅ − −= =
Slack = L - S = 1.470 ft
( )1.470
18.187
8
3 600
D = ft
⋅ ⋅
=
L = 600.647 ft
L-S = Slack = 0.647 ft
D = 12.064 ft
795kcmil 37 strand Arbutus AAC @60F
Now increase cond temp to 167F
2 2
0.7453 600
1844
8 8 18.187
w S
H lbs
D
⋅ ⋅
= = =
⋅ ⋅
15
16. Simplified Sag-Ten Calcs (cont)
1/14/13 IEEE Sag-Ten Tutorial
( )1844 2780
601.470*(0.999786) 601.341
0.6245*7 6
L 601.470 1+ ft
e
−
≅ ⋅ = =
Slack = L - S = 1.341 ft
( )1.341
17.37
8
3 600
D = ft
⋅ ⋅
=
795kcmil 37 strand Arbutus AAC @60F
Increasing the cond temp from 60F to 167F, caused
the slack to increase by 130%, the tension to drop by
from 2780 to 1844 lbs (35%) & sag to increase from
12.1 to 18.2 ft (50%).
After multiple iterations, the exact answer is 1931 lbs
16
18. 1/14/13 IEEE Sag-Ten Tutorial
Tension Limits and Sag
Tension at 15C
unloaded initial
- %RTS
Tension at max
ice and wind
load - %RTS
Tension at max
ice and wind
load - kN
Initial Sag at
100C - meters
Final Sag at
100C - meters
10 22.6 31.6 14.6 14.6
15 31.7 44.4 10.9 11.0
20 38.4 53.8 9.0 9.4
25 43.5 61.0 7.8 8.4
18
19. Modeling Non-Homogeneous
Conductors
• Typically a non-conducting core with outer
layers of hard or soft aluminum strands.
– Core shows little plastic elongation and a
lower CTE than aluminum
– Hard aluminum yields at 16ksi while soft
aluminum yields at 6ksi.
– For Drake 26/7 ACSR, alum is 14/31 of
breaking strength
1/14/13 IEEE Sag-Ten Tutorial 19
20. IEEE Sag-Ten Tutorial 20
Given the link between stress and strain in each component as shown in equations (13),
the composite elastic modulus, EAS of the non-homogeneous conductor can be derived by
combining the preceding equations:
The component tensions are then found by rearranging equations (17):
ASAS
AA
ASA
AE
AE
HH
⋅
⋅
⋅= (18a) and
ASAS
SS
ASS
AE
AE
HH
⋅
⋅
⋅= (18b)
Finally, in terms of the modulus of the components, the composite linear modulus is:
AS
S
S
AS
A
AAS
A
A
E
A
A
EE ⋅+⋅= (19)
SS
S
AA
A
ASAS
AS
AS
EA
H
EA
H
EA
H
⋅
=
⋅
=
⋅
≡ε (17)
Component Tensions – ACSR
CIGRE Tech Brochure 324
1/14/13
21. IEEE Sag-Ten Tutorial 21
Linear Thermal Strain - Non-Homogeneous A1/S1x Conductor
For non-homogeneous stranded conductors such as ACSR (A1/Syz), the composite
conductor’s rate of linear thermal expansion is less than that of all aluminium conductors
because the steel core wires elongate at half the rate of the aluminium layers. The
composite coefficient of linear thermal expansion of a non-homogenous conductor such
as A1/Syz may be calculated from the following equations:
+
=
AS
S
AS
S
S
AS
A
AS
A
AAS
A
A
E
E
A
A
E
E
ααα (20)
Linear Thermal Strain – ACSR
CIGRE Tech Brochure 324
1/14/13
22. IEEE Sag-Ten Tutorial 22
For example, with 403mm2, 26/7 ACSR (403-A1/S1A-26/7) “Drake” conductor, the
composite modulus and thermal elongation coefficient, according to (19) and (20) are:
MPaEAS 74
6.468
8.65
190
6.468
8.402
55 =
⋅+
⋅=
66
1084.18
6.468
8.65
74
190
105.11
6.468
8.402
74
55
623 −−
⋅=
⋅
⋅⋅+
⋅
⋅−= eASα
Example Calculations – ACSR
CIGRE Tech Brochure 324
1/14/13
35% higher than alum
alone
20% less than alum alone
23. Experimental Conductor Data
& Numerical Sag-Tension
Calculations
Paul Springer
Southwire
1/14/13 IEEE Sag-Ten Tutorial 23
24. IEEE Sag-Ten Tutorial 24
Experimental Plastic Elongation Model
• Conductor composite (core component +
conductor component) properties are non-linear
and poorly modeled by linear model
• By the 1920s, the experimental model was
developed:
• Changes in slack from elastic strain, short-term creep, and
long-term creep are determined from tests on finished
conductor
• Algebra used to compute sag and tension
• Graphical computer developed to solve the enormously
complicated problem
• Modern computer programs are based on the graphical
method1/14/13
25. Early work station – analog computer
Alcoa Graphical Method workstation 1920s to 1970s1/14/13 IEEE Sag-Ten Tutorial 25
28. IEEE Sag-Ten Tutorial
28
Modeling thermal strains
• Almost all composite conductors exhibit a “knee
point” in the mechanical response
• At low temperature, thermal strain (or sag with
increasing temperature) is the weighted average
of the aluminum and core strain
• Above the knee point temperature, thermal sag is
governed by the thermal elongation of the core
• Thermal strains cause changes in elastic strains.
The computations are iterative and extremely
tedious – but an ideal computer application
29. 1/14/13 IEEE Sag-Ten Tutorial
SAG10 Calculation Table
From Southwire SAG10 program
29
30. 1/14/13 IEEE Sag-Ten Tutorial
Summary of Some Key Points
• Tension equalization between suspension spans
allows use of the ruling span
• Initial and final conditions occur at sagging and
after high loads and multiple years
• For large conductors, max tension is typically
below 60% in order to limit wind vibration & uplift
• Negative tensions (compression) in aluminum
occur at high temperature for ACSR because of
the 2:1 diff in thermal elongation between alum
& steel
30
31. 1/14/13 IEEE Sag-Ten Tutorial
General Sag-Ten References
• Aluminum Association Aluminum Electrical Conductor Handbook Publication No. ECH-56"
• Southwire Company "Overhead Conductor Manual“
• Barrett, JS, Dutta S., and Nigol, O., A New Computer Model of A1/S1A (ACSR) Conductors, IEEE Trans., Vol.
PAS-102, No. 3, March 1983, pp 614-621.
• Varney T., Aluminum Company of America, “Graphic Method for Sag Tension Calculations for A1/S1A (ACSR)
and Other Conductors.”, Pittsburg, 1927
• Winkelman, P.F., “Sag-Tension Computations and Field Measurements of Bonneville Power Administration, AIEE
Paper 59-900, June 1959.
• IEEE Working Group, “Limitations of the Ruling Span Method for Overhead Line Conductors at High Operating
Temperatures”. Report of IEEE WG on Thermal Aspects of Conductors, IEEE WPM 1998, Tampa, FL, Feb. 3,
1998
• Thayer, E.S., “Computing tensions in transmission lines”, Electrical World, Vol.84, no.2, July 12, 1924
• Aluminum Association, “Stress-Strain-Creep Curves for Aluminum Overhead Electrical Conductors,” Published
7/15/74.
• Barrett, JS, and Nigol, O., Characteristics of A1/S1A (ACSR) Conductors as High Temperatures and Stresses,
IEEE Trans., Vol. PAS-100, No. 2, February 1981, pp 485-493
• Electrical Technical Committee of the Aluminum Association, “A Method of Stress-Strain Testing of Aluminum
Conductor and ACSR” and “A Test Method for Determining the Long Time Tensile Creep of Aluminum Conductors
in Overhead Lines”, January, 1999, The aluminum Association, Washington, DC 20006, USA.
• Harvey, JR and Larson RE. Use of Elevated Temperature Creep Data in Sag-Tension Calculations. IEEE Trans.,
Vol. PAS-89, No. 3, pp. 380-386, March 1970
• Rawlins, C.B., “Some Effects of Mill Practice on the Stress-Strain Behaviour of ACSR”, IEEE WPM 1998, Tampa,
FL, Feb. 1998.
31
32. The End
A Sag-tension Tutorial
Prepared for the IEEE TP&C
Subcommittee by Dale Douglass