Traveling Wave Transient Overvoltages 1 Introduction Transient Phenomenon
![Traveling Wave Transient Overvoltages Traveling Wave Transient Overvoltages](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-1.jpg)
![1. Introduction • Transient Phenomenon : – Aperiodic function of time – Short duration 1. Introduction • Transient Phenomenon : – Aperiodic function of time – Short duration](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-2.jpg)
![Impulse Voltage Waveform Impulse Voltage Waveform](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-3.jpg)
![2. Traveling Wave • • Disturbance represented by closing or opening the switch S. 2. Traveling Wave • • Disturbance represented by closing or opening the switch S.](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-4.jpg)
![Voltage & Current Function • • • vf=v 1(x- t) vb=v 2(x+ t) = Voltage & Current Function • • • vf=v 1(x- t) vb=v 2(x+ t) =](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-5.jpg)
![2. 1 Velocity of Surge Propagation • In the air = 300 000 km/s 2. 1 Velocity of Surge Propagation • In the air = 300 000 km/s](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-6.jpg)
![2. 2 Surge Power Input & Energy Storage • • P=vi Watt Ws= ½ 2. 2 Surge Power Input & Energy Storage • • P=vi Watt Ws= ½](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-7.jpg)
![2. 3 Superposition of Forward and Backward-Traveling Wave 2. 3 Superposition of Forward and Backward-Traveling Wave](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-8.jpg)
![3. Effects of Line Termination • Assuming vf, if, vb and ib are the 3. Effects of Line Termination • Assuming vf, if, vb and ib are the](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-9.jpg)
![3. 1 Line Termination in Resistance 3. 1 Line Termination in Resistance](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-10.jpg)
![3. 2 Line Termination in Impedance (Z) 3. 2 Line Termination in Impedance (Z)](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-11.jpg)
![• Line is terminated with its characteristic impedance : – Z=Zc – =0, • Line is terminated with its characteristic impedance : – Z=Zc – =0,](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-12.jpg)
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![3. 3 Open-Circuit Line Termination • • Boundary condition for current i=0 Therefore if=-ib 3. 3 Open-Circuit Line Termination • • Boundary condition for current i=0 Therefore if=-ib](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-14.jpg)
![3. 4 Short Circuit Line Termination • • Boundary condition for current v=0 Therefore 3. 4 Short Circuit Line Termination • • Boundary condition for current v=0 Therefore](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-15.jpg)
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![3. 5 Termination Through Capacitor 3. 5 Termination Through Capacitor](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-17.jpg)
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![3. 6 Termination Through Inductor 3. 6 Termination Through Inductor](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-19.jpg)
![4. Junction of Two Line 4. Junction of Two Line](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-20.jpg)
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![5. Junction of Several Line Example: 5. Junction of Several Line Example:](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-23.jpg)
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![6. Bewley Lattice Diagram 6. Bewley Lattice Diagram](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-25.jpg)
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- Slides: 26
![Traveling Wave Transient Overvoltages Traveling Wave Transient Overvoltages](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-1.jpg)
Traveling Wave Transient Overvoltages
![1 Introduction Transient Phenomenon Aperiodic function of time Short duration 1. Introduction • Transient Phenomenon : – Aperiodic function of time – Short duration](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-2.jpg)
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 Impulse Voltage Waveform](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-3.jpg)
Impulse Voltage Waveform
![2 Traveling Wave Disturbance represented by closing or opening the switch S 2. Traveling Wave • • Disturbance represented by closing or opening the switch S.](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-4.jpg)
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 vfv 1x t vbv 2x t Voltage & Current Function • • • vf=v 1(x- t) vb=v 2(x+ t) =](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-5.jpg)
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 kms 2. 1 Velocity of Surge Propagation • In the air = 300 000 km/s](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-6.jpg)
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 Pvi Watt Ws ½ 2. 2 Surge Power Input & Energy Storage • • P=vi Watt Ws= ½](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-7.jpg)
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 BackwardTraveling Wave 2. 3 Superposition of Forward and Backward-Traveling Wave](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-8.jpg)
2. 3 Superposition of Forward and Backward-Traveling Wave
![3 Effects of Line Termination Assuming vf if vb and ib are the 3. Effects of Line Termination • Assuming vf, if, vb and ib are the](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-9.jpg)
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. 1 Line Termination in Resistance](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-10.jpg)
3. 1 Line Termination in Resistance
![3 2 Line Termination in Impedance Z 3. 2 Line Termination in Impedance (Z)](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-11.jpg)
3. 2 Line Termination in Impedance (Z)
![Line is terminated with its characteristic impedance ZZc 0 • Line is terminated with its characteristic impedance : – Z=Zc – =0,](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-12.jpg)
• 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. •
![](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-13.jpg)
![3 3 OpenCircuit Line Termination Boundary condition for current i0 Therefore ifib 3. 3 Open-Circuit Line Termination • • Boundary condition for current i=0 Therefore if=-ib](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-14.jpg)
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 v0 Therefore 3. 4 Short Circuit Line Termination • • Boundary condition for current v=0 Therefore](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-15.jpg)
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
![](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-16.jpg)
![3 5 Termination Through Capacitor 3. 5 Termination Through Capacitor](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-17.jpg)
3. 5 Termination Through Capacitor
![](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-18.jpg)
![3 6 Termination Through Inductor 3. 6 Termination Through Inductor](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-19.jpg)
3. 6 Termination Through Inductor
![4 Junction of Two Line 4. Junction of Two Line](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-20.jpg)
4. Junction of Two Line
![](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-21.jpg)
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![5 Junction of Several Line Example 5. Junction of Several Line Example:](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-23.jpg)
5. Junction of Several Line Example:
![](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-24.jpg)
![6 Bewley Lattice Diagram 6. Bewley Lattice Diagram](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-25.jpg)
6. Bewley Lattice Diagram
![](https://slidetodoc.com/presentation_image/1413ced169103d412a4174237935e92c/image-26.jpg)
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