lattice diagram.ppt

Bewley lattice diagram

1. Traveling Wave
Transient Overvoltages

2. •Any disturbance on a transmission line or system such
as sudden opening or closing of a line, a short circuit
or a fault results in the development of over voltages
or over currents at that point
•disturbance propagates as a travelling wave to the ends
of the line or to a termination, such as, a sub-station.
•these travelling waves are high frequency disturbances
and travel as waves
•They may be reflected, transmitted, attenuated or
distorted during propagation until the energy is
absorbed.

3. Traveling Wave
•Disturbance represented by closing
or opening the switch S.
•If Switch S closed, the line suddenly
connected to the source.
•The whole line is not energized
instantaneously.
•Processed :
–When Switch S closed
–The first capacitor becomes
charged immediately
–Because of the first series inductor
(acts as open circuit), the second
capacitor is delayed
•This gradual buildup of voltage over
the line conductor can be regarded
as a voltage wave is traveling from
one end to the other end

4. 2.1 Velocity of Surge Propagation
•In the air = 300 000 km/s
•= 1/(LC) m/s
•Inductance single conductor Overhead Line (assuming zero
ground resistivity) :
L=2 x 10
-7
ln (2h/r) H/m
C=1/[18 x 10
9
ln(2h/r)] F/m
•
•In the cable : = 1/(LC) = 3 x 10
8
K m/s
K=dielectric constant (2.5 to 4.0)

1
2/1
9
7
/2ln1018
/2ln1021





















rh
rh
LC
v

5. Attenuation and Distortion of Travelling
Waves
•The decrease in the magnitude of the wave as it
propagates along the line is called attenuation
•The elongation or change of wave shape that
occurs is called distortion
•Sometimes, the steepness of the wave is reduced
by distortion.
•Attenuation is caused due to the energy loss in
the line and distortion is caused due to the
inductance and capacitance of the line

6. •The changes in the inductance are due to the skin
effect, the proximity effect and the non-uniform
distribution effect of currents, and the nearness to
steel structures such as transmission towers.
•The variation is capacitance is due to capacitance
change in the insulation nearest to the ground
structures etc
•The other factor that contributes for the attenuation
and distortion is the corona on the lines.

7. Reflection and Transmission of Waves
at Transition Points
•Whenever there is an abrupt change in the parameters of a
transmission line, such as an open circuit or a termination,
the travelling wave undergoes a transition
•part of the wave is reflected or sent back and only a
portion is transmitted forward.
•At the transition point, the voltage or current wave may
attain a value which can vary from zero to two times its
initial value
•The incoming wave is called the incident wave and
•the other waves are called the reflected and transmitted
waves at the transition point

8. Bewley Lattice Diagram
•Thisdiagramshowsataglancethepositionand
directionofmotionofeveryincident,reflected,and
transmittedwaveonthesystemateveryinstantof
time.
•Thediagramovercomesthedifficultyofotherwise
keepingtrackofthemultiplicityofsuccessive
reflectionsatthevariousjunctions.

9. •Consider a transmission line having a resistance r, an
inductance l, a conductance g and a capacitance c, all per unit
length.
•let be the propagation constant of the transmission line,
and E be the magnitude of the voltage surge at the sending
end,

12. Analysis of an open-circuit line fed
from ideal source

15. •The corresponding reflection coefficient at the
receiving end would be (β-Z1)/(R+Z1) and the
reflection factor at the sending end would still be -1.

16. Reflections at 3 substation system