Traveling Wave

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Transcript of Traveling Wave

  • Traveling WaveTransient Overvoltages

  • 1.IntroductionTransient Phenomenon : Aperiodic function of timeShort durationExample :Voltage & Current Surge :(The current surge are made up of charging or discharging capacitive currents that introduced by the change in voltages across the shunt capacitances of the transmission system)Lightning SurgeSwitching Surge

  • Impulse Voltage Waveform

  • 2.Traveling WaveDisturbance 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 closedThe first capacitor becomes charged immediatelyBecause of the first series inductor (acts as open circuit), the second capacitor is delayedThis gradual buildup of voltage over the line conductor can be regarded as a voltage wave is traveling from one end to the other end

  • Voltage & Current Functionvf=v1(x-t) vb=v2(x+t) = 1/(LC)v(x,t)=vf + vbvf=Zcifvb=Zcib

    Zc=(L/C) If=vf/ZcIb=vb/ZcI(x,t)=If + IbI(x,t)=(C/L) [v1(x-t) -v2(x+t)]

  • 2.1 Velocity of Surge PropagationIn the air = 300 000 km/s = 1/(LC) m/sInductance single conductor Overhead Line (assuming zero ground resistivity) :L=2 x 10-7 ln (2h/r) H/mC=1/[18 x 109 ln(2h/r)] F/m

    In the cable : = 1/(LC) = 3 x 108 K m/sK=dielectric constant (2.5 to 4.0)

  • 2.2 Surge Power Input & Energy StorageP=vi WattWs= Cv2 ; Wm= Li2 W=Ws+Wm = 2 Ws = 2 Wm = Cv2 = Li2 P=W = Li2 /(LC) = i2 Zc = v2 / Zc

  • 2.3 Superposition of Forward and Backward-Traveling Wave

  • 3. Effects of Line TerminationAssuming vf, if,vb and ib are the instantaneous voltage and current. Hence the instantaneous voltage and current at the point discontinuity are :v(x,t)=vf + vb and I(x,t)=If + IbI=vf/Zc - vb/Zc and iZc=vf vbv + iZc= 2vf so v=2vf=iZcvf = (v+iZc) and vb = (v+iZc) or vb= vf-iZc

  • 3.1 Line Termination in Resistance

  • 3.2 Line Termination in Impedance (Z)

  • Line is terminated with its characteristic impedance :Z=Zc =0, no reflection (infinitely long)Z>Zcvb is positiveIb is negativeReflected surges increased voltage and reduced currentZ

  • 3.3 Open-Circuit Line TerminationBoundary condition for current i=0Therefore if=-ibVb=Zcib=Zif=vfThus total voltage at the receiving endv=vf+vb=2vfVoltage at the open end is twice the forward voltage wave

  • 3.4 Short Circuit Line TerminationBoundary condition for current v=0Therefore vf=-vbIf=vf/Zc=-(vb/Zc)=ibThus total voltage at the receiving endv=if+ib=2ifCurrent at the open end is twice the forward current wave

  • 3.5 Termination Through Capacitor

  • 3.6 Termination Through Inductor

  • 4. Junction of Two Line

  • 5. Junction of Several LineExample:

  • 6. Bewley Lattice Diagram