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Sag-Tension Calculation Methods for Overhead Lines

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Sag-Tension Calculation Methods for Overhead Lines 324 SAG-TENSION CALCULATION METHODS FOR OVERHEAD LINES Task Force B2.12.3 First edition: June 2007 Revision : April 2016 Sag-Tension Calculation Methods for Overhead Lines Task Force B2.12.3 Convenor of WG B2.12: D. Douglass (United States) Secretary of WG B2.12: M. Gaudry (France) Task Force 3 Leader D. Douglass (United States) Task Force 3 Secretary S. Hoffmann (United Kingdom) H. Argasinska (Poland), K. Bakic (Slovenia), Anand Goel (Canada), S. Hodgkinson (Australia), S. Hoffmann (United Kingdom), J. Iglesias Diaz (Spain), F. Jakl (Slovenia), D. Lee (Korea), T. Kikuta (Japan), Ryuzo Kimata (Japan), F. Massaro (Italy), A. Maxwell (Sweden),G. Mirosevic (Croatia), D. Muftic (South Africa), Y. Ojala (Finland), R. Puffer (Germany), J. Reding (United States), B. Risse (Belgium), T.O.Seppa (United States), R. Stephen (South Africa), S. Ueda (Brazil), L. Varga (Hungary) Former Members of WG B2.12 who contributed to this brochure: Y. Motlis (Canada, deceased), V. Morgan (Australia) Other members of Study Committee B2 who participated in the writing, editing, and reviewing of this document are: WG B2.11 – C. B. Rawlins (United States), D. Havard (Canada), K. Papailiou (Switzerland) WG B2.6 – J. Rogier (Belgium) Designated Study Committee B2 Reviewers G. Brennan (Australia), J. Peralta (Portugal) Study Committee B2 Members P. Riisio (Finland), E. Ghannoum (Canada), C. Hardy (Canada), P. Meyere (Canada) Members of IEEE Subcommittee 15.11 Towers, Poles, and Conductors who contributed: Neal Schmidt (US), Rea Berryman (US), Steve Barrett (Canada), Alain Peyrot (US) Copyright © 2007 “Ownership of a CIGRE publication, whether in paper form or on electronic support only infers right of use for personal purposes. Are prohibited, except if explicitly agreed by CIGRE, total or partial reproduction of the publication for use other than personal and transfer to a third party; hence circulation on any intranet or other company network is forbidden”. Disclaimer notice “CIGRE gives no warranty or assurance about the contents of this publication, nor does it accept any responsibility, as to the accuracy or exhaustiveness of the information. All implied warranties and conditions are excluded to the maximum extent permitted by law”. N° ISBN : 978-2-85873-010-0 Sag-Tension calculation methods for overhead lines REVISIONS FIRST EDITION: JUNE 2007 MODIFICATION HISTORY Amended Updated Modifications Part Date Section 3 : Equation reference : (14) instead of (9) Section 4 : Equation reference : (8) instead of (5) Page 55 April 2016 Section 5 : Equation reference : 13 instead of 8 Section 7 : Equation reference : (14) instead of (9) CIGRE - copyright 2016 WG B2-12 “Calculation of Sag-tension for Overhead Power Lines” Table of Contents List of Figures....................................................................................................................iii List of Tables ...................................................................................................................... v EXECUTIVE SUMMARY ................................................................................................. i Introduction...................................................................................................................... i The Catenary Equation ................................................................................................... ii Mechanical Coupling of Spans ......................................................................................iii Conductor Tension Limits ............................................................................................. iv Conductor Elongation – Elastic, Plastic, and Thermal .................................................. iv Sag-tension Calculation Methods ................................................................................... v Parameter Sensitivity ...................................................................................................... v Conclusions.................................................................................................................... vi ABSTRACT........................................................................................................................1 KEY WORDS..................................................................................................................... 1 DEFINITIONS.................................................................................................................... 2 TERMS ............................................................................................................................... 5 1.0 INTRODUCTION .................................................................................................. 7 1.1 Conductor Naming Convention.......................................................................... 7 1.2 The Catenary Clearance Envelope...................................................................... 7 2.0 THE CATENARY................................................................................................ 10 2.1 Catenary and parabolic solutions for sag in level spans ................................... 10 2.2 Total Conductor Length.................................................................................... 12 2.3 Conductor Slack................................................................................................ 12 2.4 Total and Horizontal Tension ........................................................................... 14 2.5 Engineering accuracy of sag calculations......................................................... 16 2.6 Effect of change in conductor loading per unit length...................................... 17 2.7 Inclined spans....................................................................................................18 3.0 MODELING MECHANICALLY COUPLED SPANS ....................................... 21 3.1 Mechanical Equilibrium at Suspension Points ................................................. 22 3.2 Ruling Span Sag-tension Calculations.............................................................. 26 4.0 CONDUCTOR TENSION LIMITS ..................................................................... 28 4.1 Conductor tension limits under high ice and wind loading .............................. 28 4.2 Avoiding Aeolian Vibration Fatigue ................................................................ 29 5.0 CONDUCTOR ELONGATION - ELASTIC, PLASTIC, AND THERMAL...... 31 5.1 Overview of Conductor Elongation Models..................................................... 31 5.2 Linear Thermal and Elastic Elongation ............................................................ 34 5.2.1 Linear Elastic Strain - All Aluminium Conductors .................................. 34 5.2.2 Linear Thermal Strain – All Aluminium Conductor................................. 36 5.2.3 Linear Elastic Strain - Non-Homogeneous ACSR (A1/Syz) Conductors 37 5.2.4 Linear Thermal Strain - Non-Homogeneous A1/S1x Conductor ............. 38 5.3 Simplified Plastic Elongation (SPE) Model ..................................................... 39 5.4 Experimentally Measured “Plastic” Elongation of Stranded Conductors ........ 43 5.4.1 Stress-strain testing of stranded conductors.............................................. 43 5.4.2 Plastic elongation under initial high loading ............................................ 47 5.4.3 Long-time “Metallurgical” Creep - Plastic Elongation for Persistent Moderate Loading..................................................................................................... 49 i WG B2-12 “Calculation of Sag-tension for Overhead Power Lines” 5.4.4 Long-time Creep Plastic Elongation with non-homogeneous stranded conductors................................................................................................................. 53 5.4.5 Summing Plastic Elongation..................................................................... 53 6.0 SAG-TENSION CALCULATION METHODS.................................................. 54 6.1 Sag-tension for A1 Conductor with LE (Linear Elongation) Model ................ 56 6.2 Sag-tension for A1/S1A Conductor at high temperature with Simplified Plastic Elongation (SPE) Model............................................................................................... 58 6.3 Sag-tension Calculation with Experimental Plastic Elongation (EPE) Model ....... 61 6.3.1 Maximum conductor tension with the EPE model ................................... 61 6.3.2 Final sag-tension accounting for aluminum creep with the EPE model... 63 6.3.3 Calculating Final sag-tension at high temperature with EPE model ........ 65 7.0 CONDUCTOR PARAMETER STUDIES........................................................... 68 7.1 Conductor Weight............................................................................................. 68 7.2 Elastic Elongation............................................................................................. 69 7.3 Plastic Elongation............................................................................................. 70 7.4 Thermal elongation........................................................................................... 71 7.5 Errors at elevated temperature .......................................................................... 73 7.6 Thermal elongation at low temperature. ........................................................... 74 8.0 References............................................................................................................
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