transmission line parameter calculations

Transmission Line parameter calculations

Prof. N.VISALI

Dept. of EEE,

JNTUA College of Engineering, Kalikiri

Chittoor District, A.P, India

Prof. N.Visali, Dept. of EEE, JNTUA College of Engineering, Kalikiri, Chittoor District, A.P, India

Outline of Presentation


Basic Structure of a Power System

Conductors

Transmission line Model

Calculation of inductance

Calculation of capacitance

Previous GATE problems

Work for Students

Basic Structure of a Power System


The basic structure of a power system is shown in Fig. 1

It contains a generating plant, a transmission system, a subtransmission

system and a distribution system. These subsystems are interconnected

through transformers T1 , T2 and T3 . Let us consider some typical voltage

levels to understand the functioning of the power system. The electric

power is generated at a thermal plant with a typical voltage of 22 kV

(voltage levels are usually specified line-to-line).


Necessity of Transmission Lines Bulk amount of powers generation

could able to produce on economical basis by employing synchronous

generators at remote locations. The bulk amount of power from the

remote generating station could able to be carried out to the load centre

by using suitable network and the network is called transmission

network (or) transmission lines.

Types of Conductors:-

Mainly we are having four types of conductors.

Solid conductors.

Homogeneous Stranded conductors.

Composite Stranded conductors

Bundled conductors


Solid conductors:-

Fig 2 Solid conductor

Solid conductors is single piece of conductor

These conductors may be of copper (or) Aluminum

It is having high mechanical strength and tensile strength

Circular solid conductor will be preferred to make electrical field same

throughout the surface of the conductor.

There is no application of solid conductors as transmission lines

Flat (or) solid conductors are used for power transformer winding


Homogeneous Stranded Conductors:-

A number of strands are taken and are twisted together to increase the

current carrying capacity by maintaining the same operating voltage.

Fig 3 Stranded Conductors

All strands are of same material

Compared to stranded conductor it is having high mechanical strength

and low tensile strength.

Stringing is easy in stranded conductor so transportation is easy

Prof. N.Visali, Dept. of EEE, JNTUA College of Engineering, Kalikiri, Chittoor District, A P, India

Bundled conductorsWhen voltage is above 230kV, corona loss and interference with the

communication lines is more. Corona occurs when the surface potential

gradient of a conductor exceeds the dielectric strength of the

surrounding air. This causes ionization of the area near the conductor.

The high voltage surface gradient is reduced by using two or more

conductors per phase in close proximity. This is called conductor

bundling.

The conductors of a bundle are separated at regular intervals

with spacer dampers that prevent clashing of the conductors and prevent

them from swaying in the wind.


Bundled conductors Cont.The conductors are bundled in groups of two, three or four as shown in

below Fig.

3s

9 3sb3,s ddDddDD

Fig: Three conductors per phase

416 4

4, 09.12 dddDdddDD ssbs

Fig: Four conductors per phase

dDdDDselfGMDGMR ssbs 4 22,

Fig: Two conductors per phase

d


The performance of transmission line

depends on the parameters of the line.

The transmission line has mainly the

following parameters:

Resistance: It is due to the property of

conductor that it opposes the flow of

current

Inductance: Due to magnetic field around

the conductor

Capacitance: Due to electrostatic field

around the conductor

A transmission line is used for the transmission of electrical power

from generating substation to the various distribution units.

Transmission line Model


The resistance of transmission line conductors is the most important

& cause of power loss in a transmission line. The resistance R of a line

conductor having resistivity ρ, length l and area of cross-section a is given

by

Suppose R1 and R2 are the resistances of a conductor at t1°C and t2°C

(t2 > t1) respectively. If α1 is the temperature coefficient at t1°C then,

Resistance of transmission line

A

lR


Inductance per conductor

Inductance of both the conductors is

given by the formula

Inductance of a two-wire line

r7788.0r '


The inductance of conductor, ‘a’ is

• The inductance of conductors b and c

will also be the same as that of a.

• The inductance of the three-phase line

is equal to the two-wire line.

Inductance of symmetrical three-phase line

Similarly,


The average inductance of phase a is

Thus, it is found that the values of the inductance

for the three phases are equalized by transpositions.

Inductance of unsymmetrical three-phase line


The capacitance between the conductors is

Cab is referred to as line-to-line-capacitance.

The capacitance between each conductor and point of zero potential n

is

Capacitance Cn is called the capacitance to neutral or

capacitance to ground.

Capacitance of two-wire line


Symmetrical Spacing:

Capacitance of conductor A w.r.t neutral,

Unsymmetrical Spacing:

Capacitance from conductor to neutral is

Capacitance of three-phase Overhead line


Effect of earth on transmission line capacitance:

Earth surface is considered as a equipotential surface. To considered

the effect of earth we are considering image conductors below the ground

at a depth equal to the height of the overhead conductor above the

ground with opposite charge (Method of images)

F/mt

F/mt

If conductors are very much above the ground then Hxy=Hxx

With the effect of earth capacitance increases.

xx

xyxy

HH

rD

Clnln

xx

xyn

HH

rD

Clnln

2


mt/FGMRGMDln102L 7

1 mt/F

GMRGMDln

2Can

For Bundled conductors:

S.No Line Description R L XL C Xc

1 Length increases Increases Increases Increases Increases Decreases

2Distance of separation

increasesNo relation Increases Increases Decreases Increases

3Radius of conductor

increasesDecreases Decreases Decreases Increases Decreases

4 Symmetrical spacing No relation decreases Decreases Increases Decreases

5Unsymmetrical

spacingNo relation Increases Increases Decreases Increases

6Effect of earth taken

into accountNo relation No change No change Increases Decreases

7Height of the

conductor increasesNo relation No change No change Decreases Increases


PROBLEM: The inductance of a transmission line

increases with

a)Decrease in line length

b) Increase in diameter of conductor

c)Increase in spacing between the phase

conductors

d)Increase in load current carried by the

conductors



PROBLEM: The insulation resistance of a cable of length 10km is

1 MὨ. For a length of 100km of same cable, the insulation

resistance will be

Sol:



PROBLEM:



PROBLEM: The conductors of a 10km long, single phase, two wire

line are separated by a distance of 1.5m.The diameter of each

conductor is 1cm.If the conductors are of copper ,the inductance of

the circuit is



PROBLEM:



PROBLEM: The horizontally spaced conductors of a single phase line

operating at 50hz are having outside diameter of 1.6cm and spacing

between Centre's of conductors is 6m.The permittivity of free space is

8.854*10-12 f/m. The capacitance to ground per km of each line is



PROBLEM:A single phase transmission line has two conductors each of

10mm radius. These are fixed at a center to center distance of 1m in a

horizontal plane. This is now converted to a three phase transmission

line by introducing a third conductor of same radius. This conductor is

fixed at an equal distance D from the two single phase conductors .The

three phase line is fully transposed. The positive sequence inductance

per phase of the three system is to be 5% more than that of the

inductance per conductor of the single phase system. The distance D ,in

meters is



PROBLEM: A 6.6kv,50 Hz single core lead sheathed cable has the

following data :

Conductor diameter: 1.5cm, length: 4 Km

Internal diameter of the sheath:3cm

Resistivity of insulation: 1.3x10^12 Ὠ-m, relative permittivity of

insulation:3.5

Calculate

a)Insulation resistance

b)The capacitance

c)The max electric stress in the insulation


Q) The insulation level of a 400KV, EHV over head transmission line is deeded on the basis of (GATE-1995)(a)Lightning over voltage (b) Switching over voltage(c) Corona inception voltage (d) Radio and TV interference

Ans:- (b)

Hint:- In any transmission line lightning over voltages are more severe compared to switching over voltages. The lighting voltages are external voltages. Hence the insulation is provided for switching voltage.


Previous GATE questions

Q) A long wire composed of a smooth round conductor runs above parallel to the ground (Assumed to be a large conducting plane). A high voltage exists between the conductor and the ground. The maximum electric stress occurs at (GATE-2002)(a) The upper surface of the conductor (b)The lower surface of the conductor(c) The ground surface (d) Midway between the conductor and the ground

Ans:- (b)


Q) The rated voltage of a 3-phase power system is given as(GATE-2004)

(a) RMS phase voltage (b) PEAK phase voltage(c) RMS line to line voltage (d) PEAK line to line voltage

Ans:- (c)

Q) Bundled conductors are mainly used in high voltage overhead transmission lines to (GATE-2003)

(a) Reduce transmission line losses (b)Increases mechanical strength of the line (c) Reduce corona (d) Reduce sag

Ans:- (c)

For bundle conductors increase in self GMD will be predominantcompared to decrease in

GMRself

GMD.

ln

Hence Electric field intensity at surface of each conductor will be reduced. Hence the corona loss will be reduced, because chances for ionization of air are reduced.




Q) For equilateral spacing of conductors of an untransposed 3-phase

line, we have (GATE-1996)

a) Balanced receiving end voltage and no communication interference

b) Unbalanced receiving end voltage and no communication

interference

c) Balanced receiving end voltage and communication interference

d) Unbalanced receiving end voltage and communication interference

Solution:-

Ans:- (a)

Hint:- For the transmission line with equilateral spacing of

conductors (Inductance/Phase) is equal and (Current/Phase) is equal

Then (Flux/Phase) is equal and (Voltage/Phase) is equal

Hence no communication interference and also the receiving end

voltages are balanced.



Q) For a single phase overhead line having solid copper conductors of

diameter 1 cm, spaced 60 cm between centers, the inductance in mH/km

is (GATE-1999)

(a) 0.05+0.2 In 60 (b) 0.2 In 60 (c) 0.05+0.2 In (60/0.5)

(d) 0.2 In (60/0.5)

Solution:-

Ans:- (c)

externalaernalaa LLL .int.

m/Hrdln10210

21 77

km/mHrdln10210

21 11

km/mH5.0

60ln1021021L 11

a

km/mH5.0

60ln2.005.0La

From given data

Hint:-Given r=0.5cm, d=60cmInductance per conductor


Work for students


The End

transmission line parameter calculations

Documents