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Travelling waves

Reflection & refraction of travelling waves

 Bewley Lattice diagram




 Objective type questions

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Power Related Software

ATP the Alternative Transients Program

Objective type questions

  1. Which one of the following statements is true?

In a protection scheme for a communication line,

  1. The lightning arrester prevents any accumulation of static charge , and the drainage coil relieves the system of any excess voltage
  2. The lightning arrester relieves the system of any excess voltage , and the drainage coil prevents any accumulation of static charge
  3. The lightning arrester prevents any accumulation of static charge on the communication circuit

Ans. b

  1. The correct meaning of 50% dry flash-over test is:

A positive 1/50-microsecond wave is applied 20 times to the insulator. Then a negative 1/50-microsecond wave is applied to the same insulator 20 times.

  1. The amplitude of the wave is such that the insulator flashes over in each case, but is not damage
  2. The amplitude of the wave is such that the insulator is damaged in 50 % of the cases.
  3. The amplitude of the wave is such that 50% of the positive impulses cause flashover and 50 % of the negative impulses cause flashover , but the insulator is not damaged

Ans. c




The transient overvoltages that occur on a power system are either of external origin(for example, a lightning discharge) or are generated internally by switching operations. In general, the transients in transmission systems are cause by any sudden change in the operating condition or configuration of the systems. Lightning is always a potential hazard to power system equipment, but switching operations can also cause equipment damage. At voltages up to about 230 kV the insulation level of the lines & equipment is dictated by the need to protect against lightning. On systems where voltages are above 230 kV but less than 700 kV switching operations as well as lightning are potentially damaging to the insulation. At voltages above 700 kV switching surges are the main determinant of the level of insulation.

Travelling waves

The parameter of the transmission lines, generator & transformer windings are distributed. A distinguishing feature of the circuit with distributed parameters is its ability to support travelling waves of current & voltage. The velocity of propagation of current & voltage waves along a lossless line is

n = 1/Ö (LC) = 1/Ö (e om o) = 3*108 m/sec = velocity of light

for an overhead line .

In some practical cases , the ambient medium is not free space or air. For example , in a cable the permittivity of the dielectric is e oe r where e r may be 3 to 5 or even more. Thus the velocity of wave propagation in cable is reduced by a factor 1/Ö e r. It may be less than half the velocity for an air insulated line. Similarly, where the conductor is buried in steel , as are the conductors of most rotating machines, the permeability m (=m om r) may greatly exceed m o..

The ratio of the amplitudes of voltage and current waves is called the characteristic impedance Zo of the line.

Zo = Ö (L/C)

For a typical overhead transmission line, Zo is about 400 ohms. For an underground cable it is in the range of 30-80 ohms, because the closer spacing of the conductors makes C larger & L smaller.

Reflection & refraction of travelling waves

There is a strict proportionality between the voltage and the current waves in a transmission line. The proportionality factor is the characteristic impedance Zo of the line. When a wave arrives at a discontinuity in a line where the characteristic impedance of the line changes , some adjustment must occur if this proportionality is not to be violated. This adjustment takes place in the form of the initiation of two new wave pairs. The reflected voltage wave and its companion current wave travel back down the line superimposed on the incident wave. The refracted wave penetrates beyond the discontinuity. The amplitudes of the reflected & refracted waves are such that the voltage to current proportionalities are preserved for each, as demanded by the characteristic impedances of the lines on which they are travelling..

Consider the junction between the lines of characteristic impedances Za and Zb. This may be a junction between an overhead line and a cable. If a step function surge of amplitude V1 approaches the junction along the overhead line then the incident (V1), reflected(V2) and refracted(V3) voltage waves are given by

V2= (Zb-Za)V1/(Za+Zb)

V3 = 2 ZbV1/(Za+Zb)

The quantity (Zb-Za)/(Za+Zb) is called the reflection coefficient while the quantity 2 Zb/(Za+Zb) is called the refraction coefficient

The reflected current, I2 = -V2/Za

The refracted current I3 = -V3/Zb

  1. An open-circuited line
  2. A short-circuited line, and
  3. A line terminated in a resistive load , R

Bewley Lattice diagram

The Bewley lattice diagram is a space-time diagram with space measured horizontally and measured time vertically. This diagram show at a glance the position and direction of motion of every incident, reflected, and transmitted wave on the line at every instant of time.. By its means the difficulty of keeping track of the multiplicity of successive reflections is considerably simplified.

  1. An open-circuited lossless line energized with step input voltage V1
  2. A short-circuited lossless line energized with step input voltage V1
  3. A lossless line terminated in a resistive load , R
  4. A long line connected to a cable of finite length with its remote end open-circuited.

a = (R/2Z) + (GZ/2)

where R= resistance per unit length

Z= Characteristic impedance

G= leakage conductance