Sag tension calcs-ohl-tutorial
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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.
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
- 13. 1/14/13 IEEE Sag-Ten Tutorial Conductor Elongation Manufactured Length Thermal Strain Elastic Strain Long-time Creep Strain Settlement &1-hr creep Strain 13
- 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
- 17. Numerical Calculation 1/14/13 IEEE Sag-Ten Tutorial 17
- 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
- 26. Stress-Strain Model – Type 13 ACSR Initial Modulus Core Initial Modulus Aluminum Initial Modulus 10-year Creep Modulus Aluminum 10-year Creep 26
- 27. Stress-Strain Model – Type 13 ACSS 27
- 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