Electro-Magnetic Transients

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2 Copyright 2017 Industry, Inc., Power Technologies International. All rights reserved. Reproduction in whole or in part in any form or medium without the express written permission of Industry, Inc., Power Technologies International is prohibited. Industry, Inc., Power Technologies International 0-2 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

3 Table of Contents Tab 1 Time Functions & Transients Tab 2 Sine & Cosine Transients Tab 3 Travelling Waves Tab 4 EMTP Travelling Wave Results Tab 5 Lightning Surges Tab 6 Transients in Lumped Parameter Circuits Tab 7 Fundamentals of Traveling Waves Single Phase Tab 8 Multiphase Traveling Waves Tab 9 Lightning Surges on Transmission Lines Tab 10 Impulse Overvoltages - Terminals Industry, Inc., Power Technologies International 0-3 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

4 Course Outline Class 1 Class 2 Time Functions First Order Transients Sine & Cosine Functions Capacitor Bank Opening Second Order Transients Damping Class 3 Class 4 Traveling Waves Reflection Coefficients EMTP Simulation Results Lightning Surges Shielding Models Overhead Line Lightning Performance Industry, Inc., Power Technologies International 0-4 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

6 Time Functions & Transients Steady state analysis assumes perfect cosine waves that do not change over time. Transient analysis considers many types of time varying functions: Sine & Cosine waves Unit Step function Exponential functions Surge functions Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

7 Sources of Transients Switching circuits Faults Lightning Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

8 Impacted by Transients Insulation Levels Surge Arresters Relaying Circuit Breakers Equipment Design System Operation Other Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

9 Basic Circuit Elements First and second order electrical systems are based upon linear elements of Voltage and Current Sources Resistance Inductance Capacitance A solid understanding of the fundamental physical behavior of these elements is KEY to the understanding of electromagnetic transients. Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

10 Ideal Sources Ideal Voltage Source current voltage power power Ideal Current Source Internal Z = 0 Internal Y = 0 The external circuit does not affect the voltage. The external circuit does not affect the current. can supply an infinite amount can supply an infinite amount Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

11 Resistance (Ohm) Dissipates power (Watts): P=i 2 R P=V 2 /R Dissipates energy (Joules): E=P t Industry, Inc., Power Technologies International i = v R Unit 5 Electro-Magnetic Transients 2005 PTI June

12 Inductance (Henry) and Capacitance (Farad) L - Inductance C - Capacitance Stores Energy: Magnetic Fields Electric Fields Energy Stored: Differential eq: for Impedance: Ohm s Law: Integral eq.: Li 2 d v = - dt N = = Li di v = L dt i = Isin t v LIcos t X L Industry, Inc., Power Technologies International L v = XLIcos t v 1 2 Cv dq i = dt Q Cv dv i = C dt Vsin t i = CVcos t X C V i = X = 1 c C cos t t 1 1 v i v(t)dt i(0) i(t)dt v(0) C 0 L 0 t Unit 5 Electro-Magnetic Transients 2005 PTI June

13 Single Circuit Ideal Element Response to a Step Source + V + V + I Industry, Inc., Power Technologies International C R L V I V I I V Unit 5 Electro-Magnetic Transients 2005 PTI June

14 Unit Step Function Is equal to 1 for all positive values of the independent variable (term between parenthesis) u(t) = 1 t > 0 Is equal to zero for all negative values of the independent variable (term between parenthesis) u(t) = 0 t < 0 Industry, Inc., Power Technologies International 1 0 t Unit 5 Electro-Magnetic Transients 2005 PTI June

15 Unit Step Function (continued) In general, the start of a step function can be delayed by t 0 seconds and its magnitude adjusted to A Y = Au (t-t 0 ) Industry, Inc., Power Technologies International A 0 t 0 t Unit 5 Electro-Magnetic Transients 2005 PTI June

16 Unit Step Function Example The function Y above can be expressed as the sum of two unit step functions: First starts at t=2 with a magnitude +5 Second starts at t=4 with a magnitude -5 Y = 5 u(t-2) - 5 u(t-4) Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

17 First Order Circuits A first order circuit has only 1 element that stores energy, either: 1 inductor (L) or 1 capacitor (C) RL or RC circuits The circuit response is an exponential wave with a time constant determined by the values of R & L or R & C Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

18 The Exponential Function slope 1 1 e t e t t t e Industry, Inc., Power Technologies International time/time constant e t Unit 5 Electro-Magnetic Transients 2005 PTI June

19 Points on the Exponential Curve A(0) A(1) A(2) t(0) t(1) A(1) A(0) e t 1 t 0 t(2) A(2) A(0) e t 2 t0 t2 t1 A(1) e If you know any 2 points, you can determine the time constant and any other point! Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

20 The Time Response of Any First Order System 1) Find initial value: 2) Find final (steady state) value: 3) Calculate the time constant: 4) The time response is: or A ( A ( t ) = A ( Industry, Inc., Power Technologies International 0 + ) e t - A(0 + ) + A ( + - t ) = [ A ( ) - A ( ) ] 0 e transient A( ) L = or = R C R ) [ 1 - t e t - ] + A ( ) s.s. Unit 5 Electro-Magnetic Transients 2005 PTI June

21 Step Response Values In Damped Circuits L V(0 + ) =? i(0 + ) = i(0 - ) X(0 + ) = V( ) = 0 i( ) =? X( ) = 0? = to be determined Industry, Inc., Power Technologies International C V(0 + ) = V(0 - ) i(0 + ) =? X(0 + ) = 0 V( ) =? i( ) = 0 X( ) = Unit 5 Electro-Magnetic Transients 2005 PTI June

22 Step Response of 1st Order Circuits There are only 4 basic 1st order circuits: Series RL with a step voltage source Series RC with a step voltage source Parallel RL with a step current source Parallel RC with a step current source The solution to each are found on the following pages. Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

23 Series RL With a Step Voltage Source + V Industry, Inc., Power Technologies International R L i V = R = V ( 1 - V V R L = L R ( 1 - = V e e e t - t - t - ) ) Unit 5 Electro-Magnetic Transients 2005 PTI June

24 Parallel RL With a Step Current Source + I R Industry, Inc., Power Technologies International L i L i = I V R = = I ( 1 - = I L R e t - e R e t - t - ) Unit 5 Electro-Magnetic Transients 2005 PTI June

25 Series RC With a Step Voltage Source + V R C Industry, Inc., Power Technologies International V C i V = R = [ V - = V ( 1 - V - VC R e = RC V t - ) ( C 0 ) ( 0 ) + V C ] ( e t - e t - 0 ) e t - Unit 5 Electro-Magnetic Transients 2005 PTI June

26 Parallel RC With a Step Current Source + I R C Industry, Inc., Power Technologies International i V R = I i C = I = RC ( 1 - = I e R ( 1 - e t - t - e ) t - ) Unit 5 Electro-Magnetic Transients 2005 PTI June

27 V Circuit Reduction R S + R L or C VR R+R S Industry, Inc., Power Technologies International + RR S R+R S L or C Unit 5 Electro-Magnetic Transients 2005 PTI June

29 Sine and Cosine Functions V COSINE SINE degrees LL = 3 V LN V peak = 2 V Industry, Inc., Power Technologies International 2-2 rms V LN peak = 2 3 V LL rms Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

30 Waveform Digitization degrees between points degrees 30 degrees between points degrees Industry, Inc., Power Technologies International 2-3 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

31 Poor Waveform Digitization degrees between points degrees 200 degrees between points degrees Industry, Inc., Power Technologies International 2-4 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

32 Source Voltage & Load Voltage at Various Closing Angles 1.00 [V] V load V source [ms] 50 (file SINES60.pl4; x-var t) v:source v: 0 DEG v:45 DEG v:90 DEG t 0 1 V V load =1sin(ωt) u(t-t 0 ) Industry, Inc., Power Technologies International 2-5 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

33 Resistor Voltage, Current, Power & Energy V I P Energy 2 V V v(t) = Vcos t i(t) = cos t p(t) = (1 cos2 t) R 2R degrees Industry, Inc., Power Technologies International 2-6 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

34 Source Voltage & Resistor Current for Various Closing Angles V source I resistor [ms] 50 (file SINES60.pl4; x-var t) v:source c: 0 DEG- c:45 DEG- c:90 DEG- 1 V I= 1sin(ωt) u(t-t 0 )/R R = Industry, Inc., Power Technologies International 2-7 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

35 Inductor Voltage, Current, Power & Energy v(t) = Vcos t V I P Ene rgy V V i(t) = sin t = X X L L cos( t - 90) de gre e s 2 V p(t)= 2X sin2 t Industry, Inc., Power Technologies International 2-8 L Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

36 Source Voltage & Inductor Current for Various Closing Angles V source I inductor [ms] 50 (file SINES60.pl4; x-var t) v:source c: 0 DEG- c:45 DEG- c:90 DEG- I=1[sin(ωt-θ z )-sin(ωt 0 -θ z )] u(t-t 0 )/X L θ z = /2 X L = Industry, Inc., Power Technologies International V Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

37 Source Voltage & RL Current for Various Closing Angles V source I RL [s] 0.10 (file SINES60.pl4; x-var t) v:source c: 0 DEG- c:45 DEG- c:90 DEG- I=1[sin(ωt-θ z )-sin(ωt 0 -θ z )e (to-t)/ ) ] u(t-t 0 )/Z θ z = tan -1 (X L /R) = L/R = X L /ωr Z = ( X L 2 + R 2 ) Industry, Inc., Power Technologies International V 0.05 Ω 0.5 Ω Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

38 Capacitor Voltage, Current, Power & Energy V I P Ene rgy i(t) = I cos t v(t) = X de gre e s I sin t = X I cos( t - 90) Industry, Inc., Power Technologies International 2-11 C C p(t)= X C 2 I sin2 t 2 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

39 Source Voltage & RC Current for Various Closing Angles V source I [ms] 50 (file SINES60.pl4; x-var t) v:source c: 0 DEG- c:45 DEG- c:90 DEG- I=1{sin(ωt+θ z )+[Zsin(ωt 0 )/R-sin(ωt 0 +θ z )]e (to-t)/ ) } u(t-t 0 )/Z θ z = tan -1 (X c /R) = RC = R/ωX C Z = ( X C 2 + R 2 ) Industry, Inc., Power Technologies International V 0.5 Ω 0.5 Ω Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

40 Opening of a Capacitor Bank V source & V capacitor [ms] 50 (file SINES60.pl4; x-var t) c:source-cap v:source-cap v:source v:cap factors: offsets: 1 0 2E Open a capacitor at a current zero leaves a 1.0 pu trapped charge on the capacitor. A 2.0 pu peak voltage appears across the switch. I V switch = V source - V capacitor V capacitor Industry, Inc., Power Technologies International V V source Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

41 Capacitor Bank Opening Problem A capacitor bank rated 50 MVAR (3 phase) at 138 kv (rms LL) opens when the system is operated at 1.05 pu. The bank is solidly grounded. Find the voltage trapped on the capacitor Find the peak voltage across the switch Find the capacitance of one phase Industry, Inc., Power Technologies International 2-14 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

42 Second Order Circuits A second order circuit has 2 elements that store energy: LC or RLC circuits 1 inductor 1 capacitor The voltages and currents are (damped) sine/cosine waves at a natural frequency determined by the values of L & C Industry, Inc., Power Technologies International 2-15 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

43 Series LC Circuit Undamped response to a step change in voltage: + V Industry, Inc., Power Technologies International 2-16 L C V C (0) Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

44 Series LC Circuit (continued) i ( t ) = V V V C v L V-V C (0) Z S ( t) L( di / dt) L[( V VC(0)) / ZS] n cos( nt) ( t) [( V (0))]cos nt L VC sin ( n t ) 1 L = ( rad/sec ) Z = ( W ) n S LC C (t) V V L(t) c ( t ) = V [ 1 - cos ( n t ) ] + v ( 0 ) cos Industry, Inc., Power Technologies International 2-17 c ( n t ) Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

45 Energize Capacitor Bank - No Initial Charge V L V C (0 + )=0 I V C =V-V L ω N t [s] (file CAPTRAP.pl4; x-var t) v:l c: v: Industry, Inc., Power Technologies International V Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

46 Energize Capacitor Bank with Various Initial Charges 3.0 [V] ω [s] N t (file CAPTRAP.pl4; x-var t) v:stepup v: v: v: v: The peak of the overvoltage depends upon the initial charge V C (0) + V Industry, Inc., Power Technologies International 2-19 L C V C (0) Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

47 Damping The energy in the transient response never dissipates in an ideal LC circuit; it oscillates between the L & C. Resistance: dampens transients takes energy out of the transient response reduces the duration of the transient response reduces overshoots Industry, Inc., Power Technologies International 2-20 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

48 Damping in RLC Circuits The damping ratio ζ is: for series RLC circuits for parallel RLC circuits Calculate the resistance R at ω n High frequency power system transients are typically underdamped: 0.0 < ζ < 0.5 For critically damped circuits ζ = 1 Industry, Inc., Power Technologies International l = R 2 Z S = Z S 2R Unit 5 Electro-Magnetic Transients 2005 PTI June

49 Capacitor Voltages 2.0 [V] Damping ratio ω N t 6 8 [s] 10 (file RLC.pl4; x-var t) v:c v:c v:c v:c v:c v:c Industry, Inc., Power Technologies International 2-22 V peak + V Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

50 Inductor Voltages 1.00 [V] Damping ratio ω [s] N t (file RLC.pl4; x-var t) v:l 0.00-C 0.00 v:l 0.05-C 0.05 v:l 0.10-C 0.10 v:l 0.20-C 0.20 v:l 0.40-C 0.40 v:l 0.60-C 0.60 Industry, Inc., Power Technologies International V Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

51 Currents 1.00 [A] Damping ratio ω N t 6 8 [s] 10 (file RLC.pl4; Industry, Inc., x-var t) Power c:stepup-r Technologies 0.00 International c:stepup-r 0.05 c:stepup-r 0.10 c:stepup-r 0.20 c:stepup-r 0.40 c:stepup-r V Unit 5 Electro-Magnetic Transients 2005 PTI June

52 Energize Capacitor Bank - Voltages 200 [V] The first peak voltage is almost the same V cap [AC source] V cap [DC source] AC source voltage / [ms] 20 (file CAPCLOSE.pl4; x-var t) v:ac CAP- v:dc CAP- v:cosine Industry, Inc., Power Technologies International + V Unit 5 Electro-Magnetic Transients 2005 PTI June

53 Energize Capacitor Bank - Currents [A] The first peak voltage is practically the same DC source voltage / AC source voltage / [ms] 20 (file CAPCLOSE.pl4; x-var t) c:ac CAP- c:dc CAP- Industry, Inc., Power Technologies International + V Unit 5 Electro-Magnetic Transients 2005 PTI June

54 Capacitor Bank Outrush Currents Problem Your company has a 20 MVAR (3 phase) shunt capacitor bank (grounded wye) in a 115 kv substation. You have been assigned to determine the outrush currents from the capacitor bank from single line to ground faults in the substation. Assume a loop inductance of 0.1 mh. Analyze as a single phase problem without damping, and calculate: the magnitude of the peak fault current, the frequency of the current, the time to the first peak. Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

55 Solution to Capacitor Bank Outrush Currents Problem C From Q = ωcv 2 C = Q/ωV 2 = 20.E6/377(115000) 2 = 4 μf given inductance: L = 0.1 mh surge impedance: natural frequency: voltage: Z c = L/ C = 5 ohms ω 0 = 1 / LC = 50,000 radians/sec f 0 = ω 0 / 2 = 7,958 Hz V = 0 [no voltage source] V c (0) = 115 2/ 3 = 93.9 kv current: i(t) = [V c (0)/Z c ] sin(ω 0 t) for t > 0 i(t) = 18.8 sin(50000t) ka for t > 0 peak current: 18.8 ka time to peak current: ω 0 t p = / 2 t p = 31.4 μs Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

57 Sources of Traveling Waves Industry, Inc., Power Technologies International Industry, Inc., Power Technologies International Switching Lines or Cables Faults Lightning Unit 5 Electro-Magnetic Transients 2005 PTI June

58 Traveling Wave Wavetail Industry, Inc., Power Technologies International Industry, Inc., Power Technologies International Wavefront Wave velocity and direction Unit 5 Electro-Magnetic Transients 2005 PTI June

59 Traveling Waves: Functions of Time or Distance Time, t: or f(t ± x/v) Distance, x: f(vt ± x) Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

60 Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

61 Time Function Industry, Inc., Power Technologies International distortionless line x 1 x 2 x 3 Oscilloscope 1 Oscilloscope 2 Oscilloscope 3 t 1 t 2 >t 1 t 3 >t 2 Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June

62 Wave Velocity Waves travel at a constant velocity, v: dx/dt = +v Forward wave dx/dt = -v Backward wave Industry, Inc., Power Technologies International 3-7 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

63 Travel Time The travel time 12 for a wave to move from x 1 to x 2 is t2 - t1 = 12 Industry, Inc., Power Technologies International 3-8 = x 2 - v x 1 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

64 Travel Time Problem Industry, Inc., Power Technologies International 3-9 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

65 Waves travel forward & backward Forward & backward is relative to the choice for positive x Industry, Inc., Power Technologies International 3-10 x Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

66 Waves travel forward & backward At any point in time, or at any position, the total function is the sum of forward & backward waves: f = f F + f B f(t, x) = f F (t-x/v) u(t-x/v) + f B (t+x/v) u(t+x/v) Industry, Inc., Power Technologies International 3-11 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

67 Superposition of Waves t 1 t 2 t 3 Industry, Inc., Power Technologies International 3-12 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

68 TEM Transverse Electro-Magnetic Waves The electric (E) and magnetic (H) field vectors are orthogonal to each other and orthogonal to the direction of propagation. _ S _ E _ H Power (S) propagates in the direction of the Poyntig vector Industry, Inc., Power Technologies International 3-13 _ H _ E _ S S =E x H Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

69 Properties of Free Space permeability: µ = µ r x µ o permeability of free space: permittivity: µ o = 4 x 10-7 Henry/meter ε = ε r x ε o permittivity of free space: ε o = 10-9 / 36 Farad/meter = 8.85 x F/m Industry, Inc., Power Technologies International 3-14 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

70 TEM Velocity of Propagation TEM velocity of propagation: velocity of propagation in free space: v o = 3 x 10 8 m/s = 300 m/µs v o = 3 x 10 5 km/s v o = 186,450 miles/s v o = 984 feet/µs v = Industry, Inc., Power Technologies International Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

71 TEM Intrinsic Impedance TEM intrinsic impedance: intrinsic impedance of free space: o = 377 Industry, Inc., Power Technologies International 3-16 = E H = Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

72 Dielectric Properties = o r = 377 r intrinsic propagation ε r relative impedance velocity material permittivity (ohms) (m/µs) vacuum/gases oil/paper 3.3 to to to 165 XLPE 2.3 to to to 198 EPR 2.8 to to to 179 PVC» Polyethylene Industry, Inc., Power Technologies International 3-17 v= v o r = 300 r Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

73 Voltage & Current Traveling Waves Forward Traveling Wave V = +I Z s Backward Traveling Wave V = -I Z s Industry, Inc., Power Technologies International 3-18 x x Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

74 Current Direction The ammeter connection shows +I for positive forward current + I The ammeter connection shows -I for positive backward current V Industry, Inc., Power Technologies International 3-19 x Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

75 Surge Impedance Formulas General surge impedance formula: Zs Z = s Gf Zs = G η is the intrinsic impedance of the dielectric material G f is the geometric factor = L C C = G Industry, Inc., Power Technologies International 3-20 L = f G f {high frequencies only} f Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

76 Surge Impedance Problem Industry, Inc., Power Technologies International 3-21 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

77 Single Phase Geometric Factors Coaxial cable: One bundle over ground: {high frequencies only} 1 2 ln r r Industry, Inc., Power Technologies International 3-22 G f Gf = = 1 2 ln 2 1 2h r Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

78 Surge Impedance Matrix 11 = G Z s Z Z Z Z Z Z Traveling wave relationship: V = Z I f Industry, Inc., Power Technologies International 3-23 s Z Z Z f f Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

79 G f Matrix Construction self term: mutual term: where: G G f11 f12 = = = 2 h D ln r Industry, Inc., Power Technologies International D1 1 1 D D = ( ( h 1 = ( ( h 1 ln D D +h - h 2 2 ) ) ( + ( x x x x 2 2 ) 2 ) 2 ) 1/2 ) 1/2 2 average conductor height = conductor height at the tower - 3 sag Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

80 Coupling Factor Coupling Factor = V 2 /V 1 = Z 12 /Z 11 V 1 V 2 Coupling Factor Industry, Inc., Power Technologies International m Height of 2nd Conductor [m] Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

81 Equivalents Looking into Infinite Lines Single phase Two phase Single phase with an initial voltage Z S Industry, Inc., Power Technologies International 3-26 Z S Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

82 Traveling Waves Equivalents 2I Norton Z S Industry, Inc., Power Technologies International 3-27 Z S 2V Thevenin Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

83 Discontinuities in Surge Impedance Line & cable junction Junction of multiple lines Open end Short circuit Series reactor or capacitor Shunt reactor or capacitor Different line geometry Transformers and surge arresters Motors and generators Industry, Inc., Power Technologies International 3-28 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

84 Traveling Wave Equivalent at a Change in Surge Impedance 2V Z S V T Industry, Inc., Power Technologies International 3-29 Z T Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

85 Reflection Coefficients i Voltage reflection coefficient: v Z Z Current reflection coefficient: t t Z Z v Z Z s t s s Z Z t s Unit 5 Electro-Magnetic Transients 2005 PTI June 2008 Industry, Inc., Power Technologies International 3-30

86 Reflection Coefficient Problem Z t v i open 2Z s Z s 0.5Z s short Industry, Inc., Power Technologies International 3-31 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

87 Reflected and Refracted Waves Incident reflected Change in surge impedance Refracted Industry, Inc., Power Technologies International 3-32 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

88 Traveling Voltage Waves at Open End reflected (backward) Incident (forward) Industry, Inc., Power Technologies International 3-33 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

89 Traveling Wave at the Junction of 2 Lines The reflected wave has a magnitude of V/3 The initial wave from the left has a magnitude V Each line has the same surge impedance The refracted wave continuing to the right has a magnitude of 2V/3 Industry, Inc., Power Technologies International 3-34 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

91 EMTP Simulations The waveforms on the following pages are the result of EMTP (Electro-Magnetic Transients Program) simulations of travelling waves on distributed parameter lines. For some of the simulations, the line is lossless (no resistance) Series resistance is included in the simulations with line loss. Industry, Inc., Power Technologies International 4-2 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

92 Energize a Line With a DC Source [s] 7 (file OPENLINE.pl4; x-var t) v:dcopen c:dcvolt-dcline I I V Travel times of the line The line has no losses Industry, Inc., Power Technologies International 4-3 V Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

93 Fault at the End of a Line with a DC Source 6 [A] [A] [s] 50 (file SHORTEND.pl4; x-var t) c:dcfend- I e c:dcvolt-dcline I s [s] 5 (file SHORTEND.pl4; x-var t) c:dcfend- c:dcvolt-dcline I s Travel times of the line The line has no losses Industry, Inc., Power Technologies International 4-4 I e Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

94 Fault at the End of a Line with a DC Source (continued) 14 [A] (file SHORTEND.pl4; x-var t) c:dcrend- c:dcvolt-dcrine [s] 50 (file SHORTEND.pl4; x-var t) c:dcrend- c:dcvolt-dcrine I s 3.5 [A] I e [s] 5 Travel times of the line The line has losses Industry, Inc., Power Technologies International 4-5 I s I e Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

95 Fault at the End of a Line with an AC Source 6 [A] [s] 50 (file SHORTEND.pl4; x-var t) c:acfend- c:acvolt-acline I s 5 [A] I e [s] 6 (file SHORTEND.pl4; x-var t) c:acfend- Travel times of the line c:acvolt-acline The line has losses Industry, Inc., Power Technologies International 4-6 I s I e Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

96 Energize a Line with an AC Source V [s] 50 (file OPENLINE.pl4; x-var t) v:acopen c:acvolt-acline I I Travel times of the line The line has losses Industry, Inc., Power Technologies International 4-7 V Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

97 Energize a Reactor Terminated Line with a DC Source 2.0 [V] V m V e [s] 5 (file LCENDS.pl4; x-var t) v:llllll v:llhalf I Travel times of the line The line has no losses Industry, Inc., Power Technologies International 4-8 V m V e Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

98 Energize a Capacitor Terminated Line with a DC Source 3.0 [V] V m V e [s] 5 (file LCENDS.pl4; x-var t) v:cccccc v:cchalf I Travel times of the line The line has no losses Industry, Inc., Power Technologies International 4-9 V m V e Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

Tab 5A - Lightning Surges Power Technology Course Unit 9 Industry, Inc.

Effects of Lightning on Utility Systems Line Insulation Flashovers usually temporary faults Equipment failures Leads to: Transformers Underground cables Surge arresters Nuisance fuse operations

100 Effects of Lightning on Utility Systems Line Insulation Flashovers usually temporary faults Equipment failures Leads to: Transformers Underground cables Surge arresters Nuisance fuse operations Conductor burndown Insulator punctures Pole splintering Various other problems Outages Voltage dips Customer complaints O&M costs Niagara Mohawk Power Corp. Industry, Inc., Power Technologies International 5A-2 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

101 Electrification of the Thundercloud Cumulus clouds Formation of ice crystals above freezing level Charge separation 30,000-40,000' 10,000-25,000' Industry, Inc., Power Technologies International 5A Positive Charge Freezing Point Negative Charge Updraft of warm moist air Ground Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

102 Lightning Flash Development 1. Initial streamer breakdown 2. Stepped leader propagation 3. Upward connecting leader rising up to meet the downward leader 4. The high current return stroke propagates back up the channel the completely ionized channel creating a bright flash of light Ground Industry, Inc., Power Technologies International 5A-4 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

103 Types of Lightning Flashes Cloud to Ground Cloud to Cloud Ground Ground to Cloud Intracloud Industry, Inc., Power Technologies International 5A-5 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

104 Polarity of Lightning Stroke Currents Negative currents >90% cloud-to-ground flashes one or more strokes Positive currents Industry, Inc., Power Technologies International 5A-6 <10% of flashes typically just one stroke much higher peak current longer wavetails 10 to 100 times as much energy Ground Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

105 Rocket-Triggered Lightning Rocket Industry, Inc., Power Technologies International 5A-7 Wire Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

106 Rocket Triggered Lightning Pre-Launch Conditions Electric Field Active Storm Cloud Ground -7 kv per meter Industry, Inc., Power Technologies International 5A-8 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

107 Principle of Rocket Triggered Lightning Active Storm Cloud Enhanced Electric Field at Tip of Rocket Ground Industry, Inc., Power Technologies International 5A-9 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

108 Rocket Triggers Lightning Strike Direction of positive current flow Industry, Inc., Power Technologies International 5A-10 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

109 Rocket Launch Pad Stand Launcher Lightning Conductor Arrester Test Unit 5 Electro-Magnetic Transients 2005 PTI June 2008 Industry, Inc., Power Technologies International 5A-11

110 Triggered Lightning Flash to Test Stand Lightning attaches to wire Industry, Inc., Power Technologies International 5A-12 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

111 Lightning Flash Measurements Rocket Wire Shunt Transient Recorder Tall towers have also been used Industry, Inc., Power Technologies International 5A-13 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

112 Waveshape Parameters Peak Virtual Front Time= (t 90% - t 30% )/0.6 Rate of rise = Peak / Virtual Front Time Maximum rate of rise Time to half value % of crest Virtual Origin Virtual Front Time Maximum Slope units/ sec Time ( sec) Slope 30-90% units/ sec Slope 10-90% units/ sec Minimum Linear front Time Virtual Time to Half Value Industry, Inc., Power Technologies International 5A-14 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

113 Waveshape Parameters Example t (us) Industry, Inc., Power Technologies International 5A-15 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

114 Rocket Triggered Lightning Stroke Currents Industry, Inc., Power Technologies International 5A-16 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

115 Example of Lightning Surge Current (Data recorded in EPRI RP2542-1) Industry, Inc., Power Technologies International 5A-17 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

116 Percent Each Lightning Flash Can Have Multiple Strokes Percentage of flashes containing indicated number of strokes Percentage of flashes containing at least as many strokes as indicated >10 Number of Strokes in Flash Industry, Inc., Power Technologies International 5A-18 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

117 Lightning Waveshape Characteristics Note: Data shown is for negative downward strokes only First Stroke Subsequent Stroke % Exceeding the Value % Exceeding the Value Parameter 95% 50% 5% 95% 50% 5% Peak Current, ka Rate of Rise, ka/us Virtual Front Time, us Time to Half Value, us Industry, Inc., Power Technologies International 5A-19 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

118 Probability of exceeding current Peak Current Probability Distribution Peak Current (ka) Industry, Inc., Power Technologies International 5A-20 P 1 1 I Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

119 Current Wavetail Features 100% Region of Rapid Decay [initial decay] Typical durations microseconds. Note: time to half value measurements in this region Region of Slowed Decay [intermediate decay] (starts at 10-30% of crest magnitude and can last several milliseconds) 50% Continuing Current (typically amperes milliseconds) Time Industry, Inc., Power Technologies International 5A-21 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

120 Long Duration Currents Industry, Inc., Power Technologies International 5A-22 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

121 Summary of Main Lightning Parameters Negative downward flashes one or more strokes Peak current range: 2 ka to more than 200 ka. Majority of cloud-to-ground flashes Positive flashes can have typically just one stroke much higher peak current longer wavetails 10 to 100 times as much energy Industry, Inc., Power Technologies International 5A-23 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

122 Global Lightning Flash Density Industry, Inc., Power Technologies International 5A-24 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

123 US Lightning Flash Density Industry, Inc., Power Technologies International 5A-25 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

124 Problem: Number of Strikes to a Substation Data: Rectangular area E-W is 100 meters N-S is 50 meters Ground Flash Density is 2 Flashes/km²/year Find N S = strikes/year Find 1/N S = years between strikes Industry, Inc., Power Technologies International 5A-26 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

125 Number of Strikes to an Overhead Line Eriksson's Formula: N S N G = Ground Flash Density (Flashes/km²/year) H = Height (meters) b = Distance between outside conductors (meters) N S = Number of strikes/km/year b b 28H 0.6 G 1000 H N Industry, Inc., Power Technologies International 5A-27 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

126 Problem: Number of Strikes to an Overhead Line Data: Height (H) is 10 meters Width (b) is 5 meters Ground Flash Density (N G ) is 2 Flashes/km²/year Line is 40 km long Find N S = strikes/year Industry, Inc., Power Technologies International 5A-28 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

127 Lightning Strikes a Power Line When lightning hits a conductor at midspan, the current splits in half and initiates traveling waves of very high currents and voltages which moves away from the stricken point. 10 ka 4000 kv For example: 20 ka 10 ka 4000 kv lightning current = 20 ka Conductor surge impedance = 400 Ohm Voltage = 0.5 x 20 x 400 = 4000 kv Industry, Inc., Power Technologies International 5A-29 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

128 Problem: Lightning Surge Voltage Data: Lightning stroke is 50 ka peak Surge impedance is 400 ohms Find the peak current and voltage of the travelling wave Industry, Inc., Power Technologies International 5A-30 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

129 Cable Danger Zone Strike to tree Strike above cable Cable Danger Zone About 20 meters Cable 10 meters away from cable Industry, Inc., Power Technologies International 5A-31 Unit 5 Electro-Magnetic Transients 2005 PTI June 2008

131 Power Frequency Voltage Stresses Nominal voltage stresses Overvoltage stresses Industry, Inc., Power Technologies International Unit 6 - Insulation Coordination 2014 PTI October B-2

133 Peak vs. RMS Value of an Ideal Sine or Cosine Wave Amplitude Steady state analysis assumes continuous perfect sine/cosine waves. Ideal sine/cosine waves have just 1 frequency component Peak Value = 2 times the Root Mean Square (RMS) Value RMS y 0 x 0 Peak Industry, Inc., Power Technologies International 1/4f 1/2f 1/f t Unit 6 - Insulation Coordination 2014 PTI October B-4

134 Ideal Voltages of Three-phase Systems Ideal voltages are balanced with the same amplitude for each phase angles displaced 120 degrees ABC or Positive sequence rotation As phasors: V A = V 0 V B = V 240 V C = V 120 Three-phase voltages as cosine waves: Industry, Inc., Power Technologies International A [0] B [-120] C [120] degrees V C 120 V B V A Unit 6 - Insulation Coordination 2014 PTI October B-5

135 Voltage Relationships in Balanced Three-Phase Circuits The relationship between balanced line-to-neutral and phase-to-phase (lineto-line) voltages: V ab =V a -V b = V a (1-a 2 ) V LN V LL EXAMPLE: 3 V LL = 13,200 Volts VLL 13,200 VLN 7, 621Volts 3 3 Industry, Inc., Power Technologies International V c V b jy V ab V a x Unit 6 - Insulation Coordination 2014 PTI October B-6

136 Voltage relationships in a three-phase system A B C V LL V LL A V LN NEUTRAL CONDUCTOR V LL V LN V LN Industry, Inc., Power Technologies International B C Line-to-Line Voltage V LL measured between two phases Line-to-Neutral Voltage V LN measured between one phase and neutral (ground) Unit 6 - Insulation Coordination 2014 PTI October B-7

137 Per Unit System per unit (p.u.) instead of V or kv A per unit value is simply the actual value divided by a base, or reference value. Industry, Inc., Power Technologies International (pu) = (unit) base = 0.01 (%) (unit) = (pu) base (unit) Where is one of many variables such as V, I, S, Z, Y etc. Current, power, impedance, admittance and many other parameters can also be expressed in per unit. The nominal voltage is typically used as the line-to-line base voltage. Unit 6 - Insulation Coordination 2014 PTI October B-8

138 Base Voltage V LL (kv) = V (pu) x V LL-base (kv) V LN (kv) = V (pu) x V LN-base (kv) V LL = Industry, Inc., Power Technologies International V LN (kv pk ) = V (pu) x V LN-pk-base (kv pk ) V LL-base is usually the nominal line to line voltage in kv RMS 3 V LN Volts can also be used as the units V peak = 2 V rms V LN peak = 2 3 V LL rms Unit 6 - Insulation Coordination 2014 PTI October B-9

139 Voltage Base Example for a 138 kv system 138 kv is the nominal line-to-line voltage 138 kv is also the line-to-line voltage base. The phase-to-ground voltage base is VLN base 138 = 3 =79.67 The peak line-to-ground voltage at 1.00 pu is If the voltage is at 1.05 pu (105%), then V LL = 1.05 x 138 = kvrms V LN = 1.05 x = kvrms V LN-peak = 1.05 x = kv Industry, Inc., Power Technologies International kv 2 V LN peak = 138= rms kv 5B-10 Unit 6 - Insulation Coordination 2014 PTI October 2014

140 Nominal and Maximum RMS Voltages Nominal Voltage the steady state line-to-line rms voltage that names the system Maximum System Operating Voltage The highest voltage expected under normal operating conditions at any time and at any point of the system. Typically higher than the nominal voltage Equipment Maximum Voltage Rating The design level for equipment insulation Typically the maximum system operating voltage Industry, Inc., Power Technologies International 5B-11 Unit 6 - Insulation Coordination 2014 PTI October 2014

141 System Voltage Classes LV (Low Voltage) MV (Medium Voltage) HV (High Voltage) EHV (Extra High Voltage) UHV (Ultra High Voltage) Industry, Inc., Power Technologies International V LL < 1 kv 1 kv < V LL < 72.5 kv 72.5 kv < V LL < 242 kv 242 kv < V LL < 1000 kv 1000 kv < V LL 5B-12 Unit 6 - Insulation Coordination 2014 PTI October 2014

142 Class Problem System Voltages What are some of the system voltages used by your company? Class LV LV MV MV MV HV EHV Nominal Max operating V LLrms Equipment V LLrms 1.00 pu V LNrms 1.00 V LNpeak V LLrms Industry, Inc., Power Technologies International 5B-13 Unit 6 - Insulation Coordination 2014 PTI October 2014

144 Vrms (pu) Steady State Overvoltages Predominately power frequency Last indefinitely Causes: Line-to-ground faults Open conductors Backfeeding Ferranti rise Resonance Ferroresonance Industry, Inc., Power Technologies International time 5B-15 Unit 6 - Insulation Coordination 2014 PTI October 2014

145 Distributed Line Parameters... The parameters are distributed along its entire length. Each Δ has R series resistance L series inductance C shunt capacitance G shunt conductance very small R C L generally ignored for power flow analysis. Industry, Inc., Power Technologies International R L R L C C... 5B-16 Unit 6 - Insulation Coordination 2014 PTI October 2014

146 Equivalent Circuit: Short Line Model A simple pi equivalent can represent transmission lines less than 200 km where Z Z = (R1 + jx1) Ohms Y = jy1 is the length of the line R1, X1 & Y1 are the positive sequence parameters in per unit length Use a line parameters program (i.e LineProp) for the highest accuracy Industry, Inc., Power Technologies International Y 2 Y 2 5B-17 Unit 6 - Insulation Coordination 2014 PTI October 2014

147 Ferranti Rise Overvoltages V S Long lines or cables V E /V S = f ( X L, B C ) Industry, Inc., Power Technologies International V V E E V S V S jxc jxl jx L- 1 c 2 C 2 C V 1 ( ) E VS LC 2 2 V E > V S 5B-18 Unit 6 - Insulation Coordination 2014 PTI October 2014

148 Resonant Overvoltages V S V C /V S = f ( X L, B C, R) Usually a high impedance source & a large capacitance System restoration Backfeeding Industry, Inc., Power Technologies International V c c jxc V s R jxl jx / V s 1 1-(R jx V c > V S L c )/ jx V c 5B-19 Unit 6 - Insulation Coordination 2014 PTI October 2014

149 V (pu) Resonant Overvoltages V S Industry, Inc., Power Technologies International XL/XC V c > V S for R 0 1 V c / Vs 1- XL /X Resonant at the power frequency when X L = X C c 5B-20 Unit 6 - Insulation Coordination 2014 PTI October 2014

150 Backfeeding 345 kv MV bus Industry, Inc., Power Technologies International Backfeeding occurs when a circuit is fed from a lower voltage (non-generator) system This circuit could see an overvoltage when bus tie breaker opens Unit 6 - Insulation Coordination 2014 PTI October

151 Ferroresonant Overvoltages V S Often a transformer energized through a series capacitance Open Circuit Breaker Parallel Lines Open phase on a distribution feeder Industry, Inc., Power Technologies International V T = f ( X L, B C, R) 5B-22 Unit 6 - Insulation Coordination 2014 PTI October 2014

152 Overvoltages From Line-to-ground Faults Function of System Grounding Ungrounded source (generator or transformer) has delta winding Solidly Grounded source has wye winding with neutral connected to ground Impedance Grounded source has wye winding with neutral connected to ground through a reactor or resistor Industry, Inc., Power Technologies International 5B-23 Unit 6 - Insulation Coordination 2014 PTI October 2014

153 Voltages On Solidly Grounded Systems C V CN = V LN Source transformer winding Industry, Inc., Power Technologies International B A V BN = V LN V AN = 0 Fault to Ground Z 0 = Z 1 5B-24 Unit 6 - Insulation Coordination 2014 PTI October 2014

154 Overvoltages On Ungrounded Systems C B Source transformer winding Industry, Inc., Power Technologies International A Fault to ground V CN = V LL V BN = V LL V AN = 0 Z 0 = 5B-25 Unit 6 - Insulation Coordination 2014 PTI October 2014

155 Overvoltages On Impedance Grounded Systems Z N Source transformer winding Industry, Inc., Power Technologies International C B A Fault to Ground Air core reactor Z 0 > Z 1 V BN & V CN = f( Z 0, Z 1 ) V AN = 0 5B-26 Unit 6 - Insulation Coordination 2014 PTI October 2014

156 Vrms (pu) Temporary Overvoltages (TOV) Magnitudes above rated voltage Last more than 2 cycles A high power frequency component Plus the possibility of a higher frequency component TOV ratings or capability Curves for surge arresters Limited for most other power delivery equipment Industry, Inc., Power Technologies International time 5B-27 Unit 6 - Insulation Coordination 2014 PTI October 2014

157 Some Causes of Temporary Overvoltages Ferroresonance Load Rejection Single Line to Ground Faults Line Energizing Transformer Energizing Backfeeding EHV from MV MV from LV Industry, Inc., Power Technologies International 5B-28 Unit 6 - Insulation Coordination 2014 PTI October 2014

159 Transient Overvoltages Decay with time, usually within one or two cycles Often called surges The two most common types of transient overvoltages: Switching Surges Lightning Surges Industry, Inc., Power Technologies International 5C-2 Unit 6 - Insulation Coordination 2014 PTI October 2014

160 Time Functions & Transients Transient analysis considers many types of time varying functions: Sine & Cosine waves Power frequency Harmonic frequency Resonant frequncy Unit Step function Exponential functions Surge functions Industry, Inc., Power Technologies International 5C-3 Unit 6 - Insulation Coordination 2014 PTI October 2014

161 Switching Surges Generally contain frequencies from power frequency to tens of khz Caused by the closing or opening of switching equipment (circuit breakers, disconnectors, etc.): Energizing of lines cables transformers reactors buses Line re-energization or high speed reclosing Circuit breaker transient recovery voltages (TRV) Faults Industry, Inc., Power Technologies International 5C-4 Unit 6 - Insulation Coordination 2014 PTI October 2014

162 The Ideal Circuit Breaker or Switch Model When closed Z = 0 Y = 0 When open Z = Y = 0 Industry, Inc., Power Technologies International 5C-5 Unit 6 - Insulation Coordination 2014 PTI October 2014

163 Closing 120 V equipment will not conduct until metal-to-metal contact is made HV equipment will pre-strike when the dielectric strength of the gap between the contacts is less than the instantaneous applied voltage Industry, Inc., Power Technologies International 5C-6 Unit 6 - Insulation Coordination 2014 PTI October 2014

164 Slow Contact Movement Contacts will pre-strike only near the peak of a power frequency cycle cycle closing time t/closing time Industry, Inc., Power Technologies International 5C-7 Unit 6 - Insulation Coordination 2014 PTI October 2014

165 Fast Contact Movement Contacts may pre-strike at any point within the power frequency cycle cycle closing time t/closing time Industry, Inc., Power Technologies International 5C-8 Unit 6 - Insulation Coordination 2014 PTI October 2014

166 Energize Capacitor Bank at Various Angles: Voltages 200 [V] [ms] 20 (file capclose0.pl4; x-var t) v:cap 90- v:cap 45- v:cap 00- v:sine Industry, Inc., Power Technologies International 5C-9 + V Unit 6 - Insulation Coordination 2014 PTI October 2014

167 Energize Capacitor Bank at Various Angles: Inrush Currents [A] [ms] 20 (file capclose0.pl4; x-var t) c:cap 90- c:cap 45- c:cap 00- Industry, Inc., Power Technologies International 5C-10 + V Unit 6 - Insulation Coordination 2014 PTI October 2014

168 Three-phase voltages and currents captured by event recorder 5C-11 Unit 6 - Insulation Coordination 2014 PTI October 2014

Tab 2 Voltage Stresses Switching Transients

Tab 2 Voltage Stresses Switching Transients Distribution System Engineering Course Unit 10 2017 Industry, Inc. All rights reserved. Transient Overvoltages Decay with time, usually within one or two cycles