power system engineering lecture 13

8/3/2019 Power System Engineering Lecture 13

1/23

Review of Last Class

Mechanical designSag and tension calculations


2/23

Mechanical Design

Main FactorsFactors affecting

Conductor load per unit length ( w)Tower spacing, span length (L=2 l)Temperature ( )Conductor tension ( T )

Mechanical loadingsWeight of conductor itself Weight of ice or snow clinging to wireWind blowing against wire


3/23

Calculation of Sag and Tension

Sag is defined as vertical distance between the point wherethe line is joined to the tower to the lowest point on the line.Span is horizontal distance between two towers.Vertical distance between lowest point on line to the ground

plane is called ground clearance .Knowledge of maximum sag is essential in determiningground clearance.

220 kV line GC 7.0 m SL 380 CC 5.1 m

400 kV line GC 8.8 m SL 400 CC 7.0 mSag depends on the tension with which conductors arepulled.


4/23

Calculation of Sag and Tension

L=2l =Span length

O is the lowest point on the wire

ws = weight per unit length

H = tension at point O

T = tension at point P

y b y

a

2l

2l-x 1


5/23

Support at Same Heights

T at Endsor Max

If the towers at same height and span is 2l , i.e. half span is l

Conductor Length

Sag

ConductorTension


6/23

Supports at Different Heights

For tower B

For tower A

Therefore, difference in tower heights


7/23

Approximate Formulae for Sag and Tension

Small Spans

and

and


8/23

Parabolic Approximation

In case of short spans (distribution lines) with small sag(less than 10%), the curve can be considered as parabola.Sag less than 6% could give only 0.5% errorSag between 6-10 % could give only 2% error

For small spans


9/23

Effect of Ice Covering and WindIf the ice thickness is more than 0.5 cm then it is considered.

Effect of ice covering ( wi) is to increase the weight of conductor ( wc) ,and thus increases the vertical sag.

If r is radius of conductor and t is thickness of ice

layer.

icT

T

i

i

W W W

W

rt t W

rt t

r t rt r

r t r V

)(weighttotalTherefore,

kg/m2iceof densitytheisIf

m2

2

2

32

222

22


10/23

t r 2

r 2

Effect of Ice Covering and WindThe wind pressure acts on the conductor inhorizontal direction. Assume that windblows uniformaly.

If p is the wind pressure, wind loading ( ww)

The wind pressure depends on the velocityof the wind.

kg/m2 pr ww

Conductor alone

kg/m2 pt r wwConductor + Ice

22 kg/m006.0 v p


11/23

The resultant weight of the conductor is:

The angle at which loading is acting is:

Effect of Ice Covering and Wind

Conductor alone

Conductor + Ice

kg/m22 wcT www

kg/m22 wicT wwww

w w

w c or (w c + w i ) w T

Conductor alone

Conductor + Ice

cw ww1tan

icw www1tan


12/23

Stringing Chart

The curves of sag and tension with temperature variation are calledthe Stringing Charts .

Stringing chart is helpful in providing sag and tension at anytemperature, if the sag and tension is know at any particulartemperature.

They are useful in erecting line conductors at specified temperatureand loading conditions.

At high temperature, sag is more and tension is less whereas at lowtemperature sag is less but tension is more.


13/23

Stringing Chart

w Load per unit length f Stress (tension per mm 2)

S Conductor length (half span)

d Sag

Temperature

A Area of cross section of conductor

Coefficient of linear expansion

E Youngs modulus

Subscripts 1 and 2 denote temperatures at maximum load conditions andunder stringing conditions (installation or erection of transmission line).


14/23

Stringing Chart

For short spans

and

At temperature

1

At temperature 2

T=A f 22

32

6 f Alw

lS

21

2

321

16 f A

lwlS

22

2

322

26 f A

lwlS

1

21

12 f A

lwd

2

22

22 f A

lwd

and

and


15/23

Stringing Chart

Due to increase in temperature from

1 to

2 ,increase inlength is:

There is another effect increase in temperature from 1

to

2 ,decrease tension or stress from f 1 to f 2 :

Therefore new length is:

lS 1212

l E

f f S

E f f

2121

0

ll

E l f

l 0

l E

f f lSS

21

1212


16/23

Stringing Chart

Simplifying

This is cubic equation in f 2 which can be solved usingmathematical algorithm. Then the sag is:

l E

f f l

f A

lwl

f A

lwl

21

1221

2

321

22

2

322

66

E

f A

E lw f f f

A E lw

1221

2

221

122

22

222

66

2

22

22 f A

lwd


17/23

Stringing Chart

S a g

T e n s i o

n

Temperature


18/23

Sag TemplateIt is plot of curve used for locating the tower positions.

Nowadays, this is done using sophisticated software programs, whichtake input such as cost of tower, foundation requirements, soil quality,etc.


19/23

Ruling or Equivalent SpanThere are several situations span length is not same.Therefore, tension in each span will be different.This is not possible in case of suspension type insulator,because it will swing to equalize the tension.

Therefore, the uniform tension in each span is calculated bydefining the equivalent span (or ruling span).

Le is the equivalent or ruling span Li is the each individual span in line

n

ne L L L L

L L L L L

32

332

32

3

1

1


20/23

Ruling or Equivalent SpanAlso approximate ruling span is:

Lavg is the average span in line L

maxis the maximum span in line

The ruling span is then used to calculate the horizontal component of tension, which is to be applied to all the spans between the anchorpoints. Then the sag at each span is computed using

Span should not be more than twice the ruling span or less than half the ruling span .

avgavge L L L L max32

H lw

d ii 2

2


21/23

Conductor Vibrations

In addition to Horizontal swing due to wind pressure,there are two types of vertical vibrations:Aeolian or resonant vibrations

It is caused by vortex phenomena in light winds.Low magnitude (up to 5 cm) and high frequency (5-40 Hz)Less harmful because of small magnitudeThese vibrations are common in conductor and more or less alwayspresent.The Armour rods or dampers are used to damp these vibrations.

Armour rods Stock-bridge dampers
http://4.bp.blogspot.com/-VtvYTbxPanU/TWYyxc5qWTI/AAAAAAAAEec/LQ3jxxxeOgU/s1600/damper_2.jpg


22/23

Conductor VibrationsGalloping (or dancing conductors)

Generally happened due to asymmetrical layer of ice formation.When this asymmetrical ice coated conductor exposed to light winds(particularly when the slope of ground is higher).High magnitude (up to 6 m) and low frequency (0.25-2 Hz).

These vibration may cause flashover between the conductors.To avoid this flashover horizontal configuration is preferred.Also if conductor is perfectly circular the effect can be minimized.The stranded conductors can be wrapped up with PVC to makeconductor perfectly circular.


23/23

Overview of Next Class

Types of InsulatorsString EfficiencyMethods to improve string efficiency

power system engineering lecture 13

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