# Traveling Wave Transient Overvoltages 1 Introduction Transient Phenomenon

- Slides: 26

Traveling Wave Transient Overvoltages

1. Introduction • Transient Phenomenon : – Aperiodic function of time – Short duration • Example : 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 Surge – Switching Surge

Impulse Voltage Waveform

2. 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

Voltage & Current Function • • • vf=v 1(x- t) vb=v 2(x+ t) = 1/ (LC) v(x, t)=vf + vb vf=Zcif vb=Zcib • • • Zc=(L/C)½ If=vf/Zc Ib=vb/Zc I(x, t)=If + Ib I(x, t)=(C/L) ½ [v 1(x- t) -v 2(x+ t)]

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 (2 h/r) H/m C=1/[18 x 109 ln(2 h/r)] F/m • • In the cable : = 1/ (LC) = 3 x 108 K K=dielectric constant (2. 5 to 4. 0) m/s

2. 2 Surge Power Input & Energy Storage • • P=vi Watt Ws= ½ Cv 2 ; Wm= ½ Li 2 W=Ws+Wm = 2 Ws = 2 Wm = Cv 2 = Li 2 P=W = Li 2 / (LC) = i 2 Zc = v 2 / Zc

2. 3 Superposition of Forward and Backward-Traveling Wave

3. Effects of Line Termination • Assuming 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=vf/Zc - vb/Zc and v + i. Zc= 2 vf so vf = ½ (v+i. Zc) and I(x, t)=If + Ib i. Zc=vf – vb v=2 vf=i. Zc vb = ½ (v+i. Zc) or vb= vf-i. Zc

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>Zc – vb is positive – Ib is negative – Reflected surges increased voltage and reduced current • Z<Zc – vb is negative – Ib is positive – Reflected surges reduced voltage and increased current • Zs and ZR are defined as the sending-end and receiving end. •

3. 3 Open-Circuit Line Termination • • Boundary condition for current i=0 Therefore if=-ib Vb=Zcib=Zif=vf Thus total voltage at the receiving end v=vf+vb=2 vf • Voltage at the open end is twice the forward voltage wave

3. 4 Short Circuit Line Termination • • Boundary condition for current v=0 Therefore vf=-vb If=vf/Zc=-(vb/Zc)=ib Thus total voltage at the receiving end v=if+ib=2 if • Current 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 Line Example:

6. Bewley Lattice Diagram

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