Sag TensionCalcs OHL Tutorial 14Jan2013

7/29/2019 Sag TensionCalcs OHL Tutorial 14Jan2013

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Sag-tension Calculations

A CIGRE Tutorial Based onTechnical Brochure 324

Dale Douglass, PDCPaul Springer, Southwire Co

14 January, 2013


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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 cost2


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Sag-tension Calculations KeyLine Design Parameters

Maximum sag minimum clearance toground and other conductors must bemaintained usually at high temp.

Maximum tension so that structures canbe designed to withstand it.

Minimum sag to control structure upliftproblems & H/w during coldest month tolimit aeolian vibration.

3


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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).

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What is a ruling span?

5

Strain Structure Suspension Structure


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( )max23 Average Average RS S S S +

S 1 S 2 S 3

RS

6

S +----+S +S

S +----+S +S = RS n21

3n

32

31


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The Ruling Span

Simpler concept than multi-span linesection.

For many lines, the tension variation withtemperature and load is the same for theruling span and each suspension span.

Stringing sags calculated as a function ofsuspension span length and temperaturesince tension is the same in all.

1/14/13 IEEE Sag-Ten Tutorial 7


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The Catenary Curve

HyperbolicFunctions & Parabolas Sag vs weight & tension

Length between supports What is Slack?

8


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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)

D (sag at belly)

D

Max .

Tension H

(S/2, D) (end support)

S + S +


Span


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Catenary Sample Calcsfor Arbutus AAC

20.7453 60012.064 3 678

8 2780D ft ( . m) =

w=0.7453 lbs/ft Bare Weight H=2780 lbs (20% RBS)S=600 ft ruling span

600 0.7453 8 12.064 600.64724 2780 3 600

2 2 2

2 2 L 600 1 + 600 1 + ft

= = 2

2

8 12.0640.647

3 600Slack = L - S = 600 ft

=

( )0.64712.064 (3.678 )

8

3 600Sag = ft m

=

10

Notice that 8inches of slackproduces 12 ft ofsag!!


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Catenary Observations

If the weight doubles, and L & D stay thesame, the tension doubles (flexible chain).

Heating the conductor and changing theconductor tension can change the length &thus the sag.

If the conductor length changes even by asmall amount, the sag and tension canchange by a large amount.



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Conductor Elongation

Elastic elongation (conductor stiffness)

Thermal elongation

Plastic Elongation of Aluminum

Settlement & Short-term creep Long term creep

L H L E A

= =

A A

LT

L

=

12


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Conductor Elongation

Manufactured Length

T h e rm a l S tr a i n

Elastic Strain

Long-time

Creep Strain Settlement &1-hr creep Strain

13


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Sag-tension Envelope

GROUND LEVEL

Minimum ElectricalClearance

Initial Installed Sag @15C

Final Unloaded Sag @15C

Sag @ Max Ice/Wind Load

Sag @ Max ElectricalLoad, Tmax

Span Length

14


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Simplified Sag-Tension Calcs


w=0.7453 lbs/ft BareH=2780 lbs (20% RBS)S=600 ft

( )( )12.8 6* 167 60 600.647*(1.00137) 601.470 L 600.647 1 + e ft = = Slack = L - S = 1.470 ft

( )1.470 18.1878

3 600 D = ft =

L = 600.647 ftL-S = Slack = 0.647 ftD = 12.064 ft

795kcmil 37 strand Arbutus AAC @60F

Now increase cond temp to 167F

2 20.7453 6001844

8 8 18.187w S

H lbs D

= = =

15


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Simplified Sag-Ten Calcs (cont)


( )1844 2780601.470* (0.999786) 601.341

0.6245*7 6 L 601.470 1 + ft

e

= =

Slack = L - S = 1.341 ft

( )1.34117.37

8

3 600 D = ft

=

795kcmil 37 strand Arbutus AAC @60F

Increasing the cond temp from 60F to 167F, causedthe slack to increase by 130%, the tension to drop byfrom 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

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Numerical Calculation



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Tension Limits and Sag

Tension at 15Cunloaded initial- %RTS

Tension at maxice and windload - %RTS

Tension at maxice and windload - kN

Initial Sag at100C - meters

Final Sag at100C - meters

10 22.6 31.6 14.6 14.615 31.7 44.4 10.9 11.020 38.4 53.8 9.0 9.425 43.5 61.0 7.8 8.4

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IEEE Sag-Ten Tutorial 20

Given the link between stress and strain in each component as shown in equations (13),the composite elastic modulus, E AS of the non-homogeneous conductor can be derived bycombining the preceding equations:

The component tensions are then found by rearranging equations (17):

AS AS

A A AS A A E

A E H H = (18a) and

AS AS

S S AS S A E

A E H H = (18b)

Finally, in terms of the modulus of the components, the composite linear modulus is:

AS

S S

AS

A A AS A

A E

A

A E E += (19)

S S

S

A A

A

AS AS

AS AS E A

H E A

H E A

H == (17)

Component Tensions ACSRCIGRE Tech Brochure 324

1/14/13


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IEEE Sag-Ten Tutorial 22

For example, with 403mm2, 26/7 ACSR (403-A1/S1A-26/7) Drake conductor, thecomposite modulus and thermal elongation coefficient, according to (19) and (20) are:

MPa E AS 746.4688.65

1906.4688.402

55 =

+

=

66 1084.186.468

8.65

74

190105.11

6.468

8.402

74

55623 =

+

= e AS

Example Calculations ACSRCIGRE Tech Brochure 324

1/14/13

35% higher than alumalone

20% less than alum alone


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Experimental Conductor Data& Numerical Sag-Tension

CalculationsPaul Springer

Southwire



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Early work station analog computer

Alcoa Graphical Method workstation 1920s to 1970s1/14/13 IEEE Sag-Ten Tutorial 25


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Stress-Strain Model Type 13 ACSR

Initial Modulus

Core Initial Modulus

Aluminum Initial Modulus

10-year Creep Modulus

Aluminum 10-year Creep

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Stress-Strain Model Type 13 ACSS

27


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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 extremelytedious but an ideal computer application


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SAG10 Calculation Table

From Southwire SAG10 program 29


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Summary of Some Key Points

Tension equalization between suspension spansallows use of the ruling span

Initial and final conditions occur at sagging andafter high loads and multiple years

For large conductors, max tension is typicallybelow 60% in order to limit wind vibration & uplift

Negative tensions (compression) in aluminum

occur at high temperature for ACSR because ofthe 2:1 diff in thermal elongation between alum& steel

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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 W orld, 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 Conductorsin 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.

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The End

A Sag-tension Tutorial

Prepared for the IEEE TP&CSubcommittee by Dale Douglass

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Sag TensionCalcs OHL Tutorial 14Jan2013

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