Sag & Tension

Sag & Tension

Prepared by .

Email : [email protected] [email protected] co.th

Tel : 0 02 2-436436 -134 -1342 1342

Electricity Generating Authority Authority of Thailand ( EGAT EGAT )

Sag and tension are calculated to have three basic principles : Sa ety

 Reliability  Economy


Sag and tension are calculated to have three basic principles : Sa ety

 Reliability  Economy


Influence on Sag and Tension  Conductor behavior

•Weight of conductor • Creep

 Additional Loads

 Change in Temperature  Short circuit Force  Span Length


 Conductor behavior  Weight of conductor  Creep

 Additional Loads  Iced or snow  Wind


 Chan e in Tem erature  Ambient  Load flow  Fault current

 Short circuit force


 Level Span

Electricity Generating Authority of Thailand ( EGAT )

 Inclined Span


Calculation Method The calculation has two methods that comprises

1.

Catenary method

2. Parabola method This method is used for span length less than

metres


ree o y

agram o

eve span y-axis

A

T y

D=Sag

Tx

L

H

x1

O

x2

x-axis

w

S Electricity Generating Authority of Thailand ( EGAT )

The shape of the conductor that is strung on support (A and B) is a function of the conductor weight per unit length , w , the horizontal component of c

,

,

, ,

,

.


Which : w = Conductor weight per unit length [kg/m] =

on uc or ens on

g

H = Horizontal component of tension [kg] L

= =

X1,X2 S

=

Actual conductor length [m]

=

Distance along X-axis (X-Y Coordinate) [m]

Span length [m]


Catenary Method

D = L =

H ⎛ w

⎜ cosh

2 H

sinh

w

T = H cosh

wS

⎞ −1⎟ = Sag

wS 2 H

wS 2 H

= H + wD

Parabola Method

D =

wS

2

= Sag

⎛ (wS ) ⎞ ⎟ L = S ⎜1 + ⎜ 24 H ⎟ 2

2

⎛ (wS ) ⎞ ⎟ T = H ⎜1 + ⎜ 8 H ⎟ = H + wD ⎝ ⎠ 2

2


Free body diagram of Inclined span


c :

= y2 = x = x2 = y1

Short support height [m] Tall support height [m] Distance between short support and lowest point of conductor [m] Distance between tall support and lowest point of conductor [m]

= Actual conductor length of x1 side [m] L2 = Actual conductor length of x2 side [m] L1


S = x1 + x2 h = y2 − y1

Catenary method S

1

x2

y1 y2

= − 2

H

⎛ ⎜ − ⎜ 2 H

wc

⎞ ⎟ ⎟

h

1

Parabola method

wc S

⎜ w sinh 2 H ⎟ ⎝ c ⎠ ⎛ S H h ⎟ = + sinh − ⎜ ⎜ 2 H wc S ⎟ wc 2 ⎜ w sinh 2 H ⎟ ⎝ c

S

= −

Hh

2

wc S

S

Hh

x

1

L =

H ⎛

wc

=

2 H 2

=

y

wc x2

⎛ (w S ) h ⎞ ⎟ L = S ⎜1+ c + 2

w x ⎞ ⎜ cosh c − 1⎟ wc ⎝ H ⎠ H ⎛ w x = ⎜ cosh c − 1⎟ wc ⎝ H ⎠

=

= +

2

wc x1

2

1

2

⎜ sinh wc ⎝

wc x1 H

+ sinh

wc x2 H

wc S ⎟ ⎠

8T

S

2

3

+h

2


Effect of Tension Tension Stress = Conductor tension to cross section area ratio =

T A

[kg/mm2]

Strain = Elongation to original length ratio

δ L

δ


E

=

ress Strain

Δ L =

T

= Δ L A = A Δ L

TL

en e onga e con uc or eng

w c

s ue o ens on s

t

=

TL AE


Creep Cree is the lastic deformation that occurs in metal at stresses below its yield strength. Metal that is stressed below the yield point will normally return to its original shape and size when unloaded because of its elasticity. However, if the metal is held under stress for a long period of time, permanent deformation will occur. This deformation is in addition to the expecte

ncrease n engt resu t ng rom t e stress-stra n c aracter st cs

of the metal.


Effect of Temperature

- In case of high temperature and/or an increase of power flow, the temperature o con uctor w

e

g er caus ng t e e ongat on o t e

conductor and more sag.

- In case of low temperature and/or an decrease of power flow, the temperature of conductor will be lower causing the shrinking of the conductor and less sag. The elongation of the conductor which is due to temperature

Δ L = α L Δ t Electricity Generating Authority of Thailand ( EGAT )

Conductor Elongation


Effect of of suspension insulator

or s ort spans, suc as su stat on stra n uses, t e suspens on nsu ators can ave an appreciable effect on span sags. , the conductor sag for the total bus sag.


C I = C c =

⎡⎛

T

D BC = C I ⎢⎜⎜ cosh

wi T

⎛ X BC ⎞ ⎟⎟ C ⎝ I ⎠ − ⎛ l ⎞ X AC = C I sinh ⎜⎜ AC ⎟⎟ ⎝ C I ⎠ l AC = l AB + C I sinh ⎜⎜

wc

X BC =

⎤ ⎟⎟ − 1⎥ C

X BC ⎞

C I C c

X BD

S ⎛ ⎞ ⎜ Assume X BD = − l AB ⎟ 2 ⎝ ⎠

1

⎡⎛ X AC ⎞ ⎤ ⎜ ⎟⎟ − 1⎥ D AC = C I ⎢⎜ cosh C D I = D AC − D BC D = D

+ Dc


c : C I = Insulator catenary constant [m] C c AC

= Conductor catenary constant [m] = Horizontal distance from insulator support point to center of insulator catenary [m]

X BC

= Horizontal distance from connection point of insulator string and conductor to center of insulator catenary [m]

X BD

= Horizontal distance from connection oint of insulator string and conductor to center of conductor catenary [m]


AB

L AC

=

eng

o nsu a or s r ng m

= Arc length from insulator support point to center of insulator catenary [m]

D = Total bus sag D AC = Sag from insulator support point to center of insulator

catenary [m] D BC = Sag from connection point of insulator string and

conductor to center of insulator catenar [m]


D I = Insulator sag [m] D =

T = Horizontal conductor tension [m]

wi = Insulator string weight [N/m] c

=

S = Span length [m]


ect o

n

oa

e e ec o w n pressure on con uc or s o ncrease

e ransverse

wind load. It can be calculated by

w p

= 0.0047 x Aero x V x Dc 2

Give : w

=

Wind force [kg/m]

Dc

=

Overall diameter of conductor [m]


〈 12.5 mm for 12.5 ≤ D 15.8 mm for D ≥ 15.8 mm

Aero. = Aerodynamic Factor = 1.0 for D c = 1.1 = 1.2

c

V = Wind speed [km/hr]


Effect of of iced or snow If ice loading has to be considered in the design it is usual to consider

thickness with a density of 900 kg / m3



wi

= 2.87 x10 r Dc + r 3

Which :

wi = Iced weight [kg/m] r = Radial ice thickness [m] Dc = Conductor diameter [m]


Total conductor pressure The total conductor pressure consist of wind pressure, ice loading and conductor weight. It can be calculated according to

w=

w

+w

2

+ w + k 2

Which : =

wc = Conductor weight [kg/m] wi = Iced weight [kg/m] w = Wind ressure [k /m]

k = NESC constant Electricity Generating Authority of Thailand ( EGAT )

Tension Calculated 0

=

3

T 2

⎡ ⎛ C + ⎢⎜ ⎣

C 1 C 2

1

w 1 L ⎞

2

⎟ −

T 1

+

−

C 2 (t 2

t 1

1

⎤ )⎥ T − (C ⎦ 2

2

AE

w p1

= 0.0047 xAeroxV x Dc

= α AE

w p 2

= 0.0047 xAeroxV x Dc

=

1

w2L

2

1

2

2

w1

= (wc + wi ) + w p + k

w2

= (wc + wi ) + w p + k

2

1

1

2

2

2

2

2


)

2

Which : T1 T2 A E

= Initial conductor tension at t1 [kg/m] = Final conductor tension at t2 kg/m = Cross section area conductor [mm2] = Final Modulus Elasticity of Conductor [kg/mm2] o

t1 t2

= Initial temperature [oC] = New temperature [oC]


c

wc w p1

= =

w p2 w1 w2

Conductor weight [kg/m] Wind pressure on conductor at temperature t1 [kg/m] n pressure on con uc or a empera ure 2

= =

gm

Total pressure on conductor at temperature t1 [kg/m] Total pressure on conductor at temperature t2 [kg/m]


Tension Limits The NESC recommends limits on the tension of conductors based on a percentage of their Rated Breaking Strength (RBS). – T

< 60% RBS @ NESC Loading, Initial.

– Tinitial < 35% RBS, upon installation, 16oC. –

final

<

, un oa a ter max mum oa ng,

.



If fault current flowed in conductor, it will be swing that may be flashover. The desi ner will consider this event.


Conductor Swing under fault current flow in conductor

Sag

Conductor

Phase to Phase Fault

Three Phase Fault


Short circuit force can be calculated according to below equation. F sc

=

μ 0 2π

0.75

I sc2 S D

− 2 Li S

1

g

Which Fsc

= =

0

sc

=

Short circuit force [kg/m] 4π x 10

−7

ymmetr ca au t current

D = Distance between stringing point conductor [m] S = Span Length [m]

g

=

Reach of conductor [m]


One lace have fault and this cause will be occurred to follow fault in the another. This event is called cascade fault. The cascade fault cannot occurred when sag allowable shall be less than maximum sag.


The sag allowable can be calculated according to below equation. 2

Dalw

= R

sc

2

c

F sc

Which S

= Sa allowable [m]

R

= Reach [m]

Fsc

= Short circuit force [kg/m]

n

= The number of conductor er hase

wc = Conductor weight [kg]


The reach can be calculated according to below equation. R =

−

c

−

a

−

s

2

R = Reach [m] D = Distance between stringing point conductor [m] c

Da = Minimum phase to phase clearance [m] Ds = Spacer distance [m]


D


D

D


Reach


The cascade fault cannot occur when Dmax ≤

Dalw


Data

477

795

1272

3/8 OHG

Unit

A

280.99

423.49

677.71

51.07

mm

Wc

0.978

1.524

2.04

0.406

kg/m

Dc

0.02181

0.02772

0.03391

0.009144

m

E

7700

6200

7000

19300

kg/mm

α

1.80E-05

2.13E-05

2.07E-05

1.15E-05

per C

V

52.5

52.5

52.5

52.5

Aero.

1

1

1

1.2

2

2

2

kg/m


Example The single per phase conductors 477 MCM ACSR (HAWK) are strung

current kA flow in this conductor.


⎡ T + ⎢ ⎜ ⎢⎣ ⎝

1

2

=

w1 C

=

1

=

AeroxP

2

wc

2

2

1

T 1

C 1

w p 1

⎤ ⎥ T − (C w S ) = − + ( − ) T C t t ⎟ ⎥⎦ ⎠ 2

3

xD c

w1

2

= α A E =

2

1

2

.

=

24

w p 1

2

=

24

1

2

0

3 0 0 .2 5 1 5

= 1 x 52 . 50 x 0 . 02181 = 1 . 145 kg

=

1.8 x 1 0

.

−5

2

.

2

=

x 2 8 0 .9 9 x 7 7 0 0

=

.

g

/ m

m

3 8. 9 4 5 2


w p 2

2

give T = 1

T 6

and

= AeroxP

= T2

xD c

w2

2

2

c

p 2

=

= 1 x 0 x 0 . 02181 = 0 kg / m 2

.

2

=

.

= T

65

Then 3

T 65

+ ⎢⎜ ⎣⎝

.

x

.

x

750

2

⎟ − ⎠

750

+

.

65

=

wS

3 8. 9 4 5 2 ( 6 5

− 6) ⎥T − ( 3 0 0.2 5 1 5x 0. 9 7 8x 4 5) = ⎦ .

27

2

8T 65

2

65

2

=

0.978 x 45

8 x 261.906

=

.


2

0

Sag & Tension

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