2009 IEEE JTCMeeting Atlanta, GA IEEE St 1410 Revision Lightning Induced Voltages A. Borghetti C.A. Nucci M. Paolone

Lightning Performance of Distribution Lines To get the ___ we need: Statistical distribution of lightning current parameters (peak, rise time, …) Incidence model Induced-voltage model Statistical approach

1. Statistical Distribution of Lightning Current Amplitude For our purposes the two approaches are equivalent . 5 . 1 IEEE: Ip  20kA Ip = 61.1 kA ln Ip = 1.33 Ip > 20 kA Ip = 33.3 kA ln Ip = 0.605 Cigré: . 5 1 . 2 . 5 . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 9 5 . 9 8 . 9 9 . 9 9 . 5 9 9 . 9 9 9 . 9 5 9 9 . 9 9 [kA] 1 . 1 . 1 . 1 .

Lightning Performance of Distribution Lines To get the ___ we need: Statistical distribution of lightning current parameters (peak, rise time, …) Incidence model Induced-voltage model Statistical approach

Lightning Performance of Distribution Lines To get the ___ we need: Statistical distribution of lightning current parameters (peak, rise time, …) Incidence model Induced-voltage model Statistical approach

2. Incidence model IEEE WG lateral attractive distance Direct stroke Nearby stroke rs dl rg h It is just worth mentioning that other expressions exist: Eriksson Rizk Dellera and Garbagnati (LPM)

Lightning Performance of Distribution Lines To get the ___ we need: Statistical distribution of lightning current parameters (peak, rise time, …) Incidence model Induced-voltage model Statistical approach

3. Induced voltage calculation model (present) Rusck simplified formula v return stroke velocity Assumptions: single-conductor infinitely long lines above a perfectly cond. ground step current waveshape h=0,75 Too simple: not adequate in many cases!

3. Induced voltage calculation model (revised) Return stroke model: Modified Transmission Line Exponential Decay (MTLE) or any other type LEMP: Uman and McLain and Cooray-Rubinstein Coupling model: Agrawal extended to the case of lossy ground Note: the shield wire is simply one of the conductors of the n-conductor system 9

Lightning Performance of Distribution Lines To get the ___ we need: Statistical distribution of lightning current parameters (peak, rise time, …) Incidence model Induced-voltage model Statistical approach

4. Statistical approach (present) a) The assumed range of peak values of lightning current Ip at the channel base, from 1 kA to 200 kA, is divided in 200 intervals of 1 kA. b) For each interval i, the probability pi of current peak value Ii to be within interval i is found as the difference between the p for current to be  than the lower limit and the p for current to reach or exceed the higher limit. These ps are obtained by using the formula seen before c) For each interval i, also two distances form the line (in m) are calculated: 1) the minimum distance ymin,i (using the IEEE incidence model) for which lightning of peak current Ii (in kA) will not divert to the line, and 2) the maximum distance ymax,i at which lightning may produce an insulation flashover (using the Rusck formula), i.e. an induced voltage equal to the line critical flashover voltage CFO (in kV), multiplied by a factor equal to 1.5 (to take into account the turn-up in the insulation volt-time curve for short front-time surges). d)

4. Statistical approach (present) a) The assumed range of peak values of lightning current Ip at the channel base, from 1 kA to 200 kA, is divided in 200 intervals of 1 kA. b) For each interval i, the probability pi of current peak value Ii to be within interval i is found as the difference between the p for current to be  than the lower limit and the p for current to reach or exceed the higher limit. These ps are obtained by using the formula seen before c) For each interval i, also two distances form the line (in m) are calculated: 1) the minimum distance ymin,i (using the IEEE incidence model) for which lightning of peak current Ii (in kA) will not divert to the line, and 2) the maximum distance ymax,i at which lightning may produce an insulation flashover (using the Rusck formula), i.e. an induced voltage equal to the line critical flashover voltage CFO (in kV), multiplied by a factor equal to 1.5 (to take into account the turn-up in the insulation volt-time curve for short front-time surges). d)

4. Statistical approach (revised) Inputs: lightning current parameters, return stroke velocity, line and ground data Random generation of events ( Ip tf x y) (e.g. > 10 000) Selection of indirect lightning events by using a lightning incidence model Induced overvoltage calculation using advanced models (and relevant tools) Counting of the n events generating overvoltages greater than the insulation level (e.g. 1.5·CFO) Plot the graph: No. of flashovers/100 km/year vs CFO where No. of flashovers/100 km/year = (n/ntot)·ng·S·100/L (with ng = annual ground flash density, S = striking area, L=line length) correlated

4. Statistical approach (revised) Inputs: lightning current parameters, return stroke velocity, line and ground data Random generation of events ( Ip tf x y) (e.g. > 10 000) Selection of indirect lightning events by using a lightning incidence model Induced overvoltage calculation using advanced models (and relevant tools) Counting of the n events generating overvoltages greater than the insulation level (e.g. 1.5·CFO) Plot the graph: No. of flashovers/100 km/year vs CFO where No. of flashovers/100 km/year = (n/ntot)·ng·S·100/L (with ng = annual ground flash density, S = striking area, L=line length) correlated

4. Statistical approach (revised) The revised method and the new Statistical approach  equivalent as far as an ‘infinitely long line’ is concerned improved in the new version when distribution systems having realistic configurations are analyzed.

 Fig. 5 of rev. 1410 (Modelling details in Appendix B)

Validation – Scale Model, Univ Validation – Scale Model, Univ. of Tokyo and Real Lines, IIE, Cuernavaca From Ishii et al. CIGRE Colloquium SC33, Toronto, 1997 From De La Rosa et al, IEEE Trans. on PWDR, 1988

 Fig. B.3 in Appendix B of rev. 1410 – “Check”

 Fig. B.4 in Appendix B of rev. 1410 – Effect of shield wire

 Fig. B.5 a, b in Appendix B of rev. 1410 – Effect of SA Ideal ground σg = 1 mS/m

LIOV-EMTP computer code G LIOV-line n-port Concept at the basis of the interface The LIOV code calculates: LEMP Coupling The EMTP : calculates the boundary conditions makes available a large library of power components u (x,t) i(x,t) L'dx C'dx x x+dx + - i(x+dx,t) L u (x+dx,t) i (x,t) E (x,h,t)dx s G -u (L,t) (0,t) Link between LIOV and EMTP Data exchange between the LIOV code and the EMTP at the boundary conditions

The LIOV-EMTP code (http://www.liov.ing.unibo.it) i (0,t) LIOV V, I